POWDER X-RAY DIFFRACTION
Dr. Muhammad Aslam
Lecture - 2.1
CHEM5134
X-Ray Diffraction Techniques
2
Course Contents
Powder X-Ray Diffraction
• Principles of powder X-ray diffraction, Generation of Xrays, Characteristic X-rays, Rietveld method, Significance
of peak shape in XRD, Preparing a powder specimen,
Powder diffractometer, Instrumentation of powder X-ray
diffractometer, working of powder X-ray diffractometer,
Spectral
contamination in diffraction patterns,
Goniometer, Identification of compounds, What
information obtained from powder X-ray diffraction, Data
collection, Results and presentation, Application of
powder X-ray diffraction, Strengths and limitations of Xray powder diffraction, X-ray diffraction at synchrotron
sources.
3
X-ray techniques
X-ray absorption methods
• Fraction of X-ray photons absorbed is considered.
• Used in elemental analysis and thickness measurements.
X-ray fluorescence methods
• Wavelength and intensity of generated X-rays are measured for
qualitative and quantitative analysis.
• Non-destructive and requires little sample preparation.
X-ray diffraction methods
• Scattering of X-rays by crystals.
• Determines crystalline structure.
4
Hard and soft x-rays
• X-ray diffraction in crystals was discovered by Max von Laue.
• The wavelength range of x-ray is 10-7 to about 10-15 m.
• The penetrating power of x-rays depends on energy also, there
are two types of x-rays:
• Hard x-rays: which have high frequency and have more
energy.
• Soft x-rays: which have less penetrating and have low energy
Max Von Laue
5
Powder X-ray Diffraction
The powder diffraction pattern as a “fingerprint
(‫”)اِنفرادی خصوصيت‬. The powder diffractogram of a
compound is its ‘fingerprint’ and can be used to
identify the compound.
8
Introduction
• Diffraction occurs when light is scattered by a periodic array
with long-range order, producing constructive interference at
specific angles.
• The atoms in a crystal are periodically arranged thus diffract
light.
• The wavelength of x-ray are similar to the distance between
atoms.
• Powder X-Ray Diffraction (PXRD) techniques uses this
principle to elucidate the crystalline nature of materials.
• The scattering of x-rays from atoms produce a diffraction
pattern that contains information about the atomic
arrangement in crystal.
• Amorphous materials like glass do not have periodic array
with long-range order so:
– They do not produce any significant peak in diffraction
9
pattern
Powder X-ray diffractometer
• A diffractometer is a measuring instrument for analyzing
the structure of a material from the scattering pattern
produced when a beam of radiation or particles (such as
x-rays or neutrons) interacts with it.
• Powder diffraction is a scientific technique using x-ray,
neutron, or electron diffraction on powder or
microcrystalline samples for structural characterization of
materials.
• An instrument dedicated to performing such powder
measurements is called a powder diffractometer.
• Powder diffraction stands in contrast to single crystal
diffraction techniques, which work best with a single,
well-ordered crystal.
10
Essential parts of the diffractometer
• X-ray Tube: The source of x-rays
• Incident-beam optics: Condition the x-ray beam before
it hits the sample
• The goniometer: The platform that holds and moves the
sample, optics, detector, and/or tube
• The sample and sample holder
• Receiving-side optics: Condition the x-ray beam after it
has encountered the sample
• Detector: Count the number of x-rays scattered by the
sample
11
12
Classical Powder Diffractometer
Goniometer
Detector
X-ray tube
Monochromator
Soller slit
Soller slit
Receiving
slit
Anti-scatter
slit
Divergence
slit
Mask
Sample stage
13
14
Use of  and 2
Receiving slit
2
X-ray tube
Goniometer axis

Sample
 : angle between incident beam and sample.
2 : angle between incident and diffracted beam.
16
17
Diffractogram
• An image produced by a diffractometer.
18
Explanation
• Powder XRD is a compact advanced instrument.
• Advancement: It has various salient features and new accessories
like:
– Variable temperature assembly
– Humidity chamber
that can further expand the horizon of its applications by providing
the information on effect of temperature and humidity on the nature of
material.
• When x-ray falls over a crystal, it diffracts in a pattern characteristic
to its structure.
• In powder x-ray diffraction, the diffraction pattern is obtained from
a powder of the material, rather than an individual crystal.
• Powder diffraction is often easier and more convenient than single
crystal diffraction as it does not require individual crystals.
• A diffraction pattern plots intensity against the angle of the detector,
2θ.
19
Each d-spacing in the polycrystalline material
forms “rings” centered around the incident
beam
20
• The result obtained is called diffractogram.
• In a diffraction pattern, the peak position depends upon the
wavelength.
• Absolute intensity (number of x-rays observed in a given peak) may
vary by instrumental and experimental parameters.
• Diffractometers can be operated both in transmission and in
reflection configurations.
• The reflection one is more common.
• Interactions between the incident x-ray beam and the sample produce
intense reflected x-rays by constructive interference when conditions
satisfy Bragg’s Law.
• This law describes the general relationship between the wavelength of the
incident x-rays, the incident angle of the beam and the spacing between
the crystal lattice planes of atoms.
• Constructive interference occurs when the differences in the travel path of
the incident x-rays is equal to an integer multiple of the wavelength. 21
Transmission
• Transmission of light is the moving of electromagnetic waves
through a material.
• This transmission can be reduced, or stopped, when light is
reflected off the surface or absorbed by the molecules in the
material.
22
Revision
of
"X-Ray Diffraction"
23
Link:
https://www.youtube.com/watch?v=xiKeQcBaeIo
24
Experimental setups
• Great diversity is employed in designing and carrying out powder
diffraction experiments, exploiting x-rays from a laboratory
generator or from a high energy storage ring optimized for the
generation of synchrotron radiation, or neutrons produced in a
reactor or spallation source.
• A typical wavelength used for a powder diffraction experiment lies
in the range 0.15A˚, comparable with the spacings between lattice
planes in crystals.
• The spectrum of the x-rays or neutrons employed can range from a
tightly defined monochromatic envelope to a wide polychromatic
distribution.
• The object of the experiment being undertaken dictates the radiation
to use.
• The sample can be a self-supporting polycrystalline slab or rod, or a
fine powder, mounted in a flat-plate sample holder or contained in a
thin-walled glass capillary tube, or are made of platinum for
measurements at very high temperatures.
26
• Data can be collected in transmission or reflection modes,
depending on how strongly the sample absorbs the radiation
employed.
• Sample environments play an important role in many powder
experiments, allowing measurements under a wide range of
conditions of temperature, pressure, applied stress, or chemical
environment.
• The detector system is a crucial part of any powder diffraction
experiment.
• A standard laboratory instrument may have a single point counter,
or may employ a multichannel, one-dimensional position-sensitive
detector (PSD), where the diffracted intensities at many diffraction
angles are recorded simultaneously.
• Diffractometers using monochromatic neutrons or synchrotron xrays often have several point detectors operating in parallel to
increase the efficiency of use of the valuable beam time.
27
• One-dimensional PSDs or two dimensional area detectors are also employed,
such as those based on charge coupled device (CCD) chips or image plates, as
these greatly improve the rate of data acquisition, registering complete (or large
fractions of) the individual Debye–Scherrer cones.
• Detectors for experiments using polychromatic X-rays need to be able to
distinguish the wavelength of each incoming photon, and therefore need good
energy resolution.
• Similarly, for neutrons from a pulsed source, the time of arrival of each neutron
needs to be recorded, so that its time of flight from the source to the detector is
known and its speed, and hence wavelength, can be calculated.
• With multichannel detector systems equipped with fast read-out electronics,
diffraction patterns can be measured repeatedly in just a few milliseconds,
allowing the investigation of systems that are evolving rapidly during the
measurements.
• In the following sections we describe in more detail the basic experimental
procedures that are used for powder diffraction measurements, and consider
important factors that control the performance of the instruments available for
laboratory-based experiments, or found at neutron and synchrotron radiation
facilities.
28
Fundamental principles of powder x-ray diffraction
(PXRD)
• Max von Laue, in 1912, discovered that crystalline
substances act as three-dimensional diffraction gratings
for x-ray wavelengths similar to the spacing of planes in a
crystal lattice.
• X-ray diffraction is now a common technique for the
study of crystal structures and atomic spacing.
• X-ray diffraction is based on constructive interference of
monochromatic x-rays and a crystalline sample.
31
• These x-rays are generated by a cathode ray tube, filtered
to produce monochromatic radiation, collimated to
concentrate, and directed toward the sample.
• The interaction of the incident rays with the sample
produces constructive interference (and a diffracted ray)
when conditions satisfy Bragg's Law (nλ = 2d sin θ).
• This law relates the
wavelength
of
electromagnetic radiation to
the diffraction angle and the
lattice
spacing
in
a
crystalline sample.
• These diffracted X-rays are
then detected, processed
and counted.
32
• Approximately 1% of the total energy of the electron beam is converted
into x-radiation.
• The remainder being dissipated as heat.
Evacuated glass bulb
Anode
Cathode
X-rays
33
34
(collimator)
35
• The x-ray is focused on the sample at some angle θ, while the
detector opposite the source reads the intensity of the x-ray it
receives at 2θ away from the source path.
• The incident angle is than increased over time while the detector
angle always remains 2θ above the source path.
• While other sources such as radioisotopes and secondary
fluorescence exist, the most common source of x-rays is an x-ray
tube.
• The tube is evacuated (‫ )خﺎﻟﯽ کرا ﻟيﺎ‬and contains a copper block with
a metal target anode, and a tungsten filament cathode with a high
voltage between them.
• The filament is heated by a separate circuit, and the large potential
difference between the cathode and anode fires electrons at the
metal target.
• The accelerated electrons knock core electrons out of the metal, and
electrons in the outer orbitals drop down to fill the vacancies,
emitting x-rays.
• The x-rays exit the tube through a beryllium window.
36
• Due to massive amounts of heat being produced in this process, the
copper block must usually be water cooled.
Figure: Cross section of sealed-off filament x-ray tube.
37
• By scanning the sample through a range of 2θ angles, all
possible diffraction directions of the lattice should be
attained due to the random orientation of the powdered
material.
• Conversion of the diffraction peaks to d-spacings allows
identification of the mineral because each mineral has a set
of unique d-spacings.
• Typically, this is achieved by comparison of d-spacings with
standard reference patterns.
• All diffraction methods are based on generation of x-rays in
an x-ray tube.
• These x-rays are directed at the sample, and the diffracted
rays are collected.
• A key component of all diffraction is the angle between the incident
and diffracted rays.
• Powder and single crystal diffraction vary in instrumentation
38
beyond this.
39
Explanation
• A powdered (polycrystalline) sample contains an
enormous number of very small crystallites, typically 0.1
to 10 μm in dimension and orientated at random.
• An X-ray beam striking a polycrystalline sample is
scattered in all directions; at some angles, those given by
Bragg’s equation, constructive interference occurs.
• As a result, each set of planes of atoms with lattice
spacing d gives rise to a cone of diffraction intensity.
• Each cone consists of a set of closely spaced diffracted
rays, each one of which represents diffraction from a
single crystallite within the powder sample (following
figure).
• With a very large number of crystallites these rays merge
(‫ )ضم‬together to form the diffraction cone.
40
Figure: (a) The cones of
diffraction that result from
X-ray scattering by a
powdered sample. The cone
consists of thousands of
individual diffraction spots
from individual crystallites,
that merge together. (b) A
photographic image of the
diffraction pattern from a
powdered sample. The
undiffracted straightthrough beam is at the
centre of the Image and the
various diffraction cones,
corresponding to different dspacings are observed as
concentric circles.
Debye-Scherrer rings
41
Debye-Scherrer rings
Figure: A cone of diffraction that results from X-ray scattering
by a powdered sample. The cone consists of thousands of
individual diffraction spots from individual crystallites that
42
merge together.
• These cones would intersect a flat photographic plate as
circles, known as Debye-Scherrer rings after the early
powder diffraction camera invented by Debye, Scherrer
43
and Hull.
• A powder diffractometer (following figure) uses an
electronic detector to measure the angles of the diffracted
beams.
Figure: Schematic diagram
of a powder diffractometer
operating in reflection mode
in which the X-ray
scattering occurs from a
sample mounted as a flat
plate. For weakly absorbing
compounds the
samples may be mounted in
a capillary and
the diffraction data
collected in transmission
mode.
44
• Scanning the detector
around the sample along
the circumference of a
circle cuts through the
diffraction cones at the
various
diffraction
maxima and the intensity
of the X-rays detected is
recorded as a function of
the
detector
angle
(following figure).
Figure: The form of a typical
powder
diffraction pattern showing a
series of
reflections as a function of angle.
45
• The number and positions of the reflections depend on the
cell parameters, crystal system, lattice type, and
wavelength used to collect the data; the peak intensities
depend on the types of atoms present and their positions.
• Nearly all crystalline solids have a unique powder X-ray
diffraction pattern in terms of the angles of the reflections
and their intensities.
• In mixtures of compounds, each crystalline phase present
contributes to the powder diffraction pattern its own
unique set of reflection angles and intensities.
• Typically, the method is sensitive enough to detect a small
level (5 to 10 per cent by mass) of a particular crystalline
component in a mixture.
• The effectiveness of powder X-ray diffraction has led to it
becoming the major technique for the characterization of
46
polycrystalline inorganic materials.
• Many of the powder diffraction data sets collected from
inorganic, organometallic, and organic compounds have
been compiled (‫ )ﺟﻣﻊ کرنﺎ‬into a database by the Joint
Committee on Powder Diffraction Standards (JCPDS).
• This database, which contains over 50,000 unique powder
X-ray diffraction patterns, can be used like a fingerprint
library to identify an unknown material from its powder
pattern alone.
• Powder X-ray diffraction is used routinely in the
investigation of phase formation and changes in structures
of solids.
• The synthesis of a metal oxide can be verified by collecting
a powder diffraction pattern and demonstrating that the data
are consistent with a single pure phase of that material.
• Indeed, the progress of a chemical reaction is often monitored by
observing the formation of the product phase at the expense of 47the
reactants.
• Basic crystallographic information, such as lattice
parameters, can normally be extracted easily from powder
X-ray diffraction data, usually with high precision.
• The presence or absence of certain reflections in the
diffraction pattern permits the determination of the lattice
type.
• In recent years the technique of fitting the intensities of the
peaks in the diffraction pattern has become a popular
method of extracting structural information such as atomic
positions.
• The analysis, which is known as the Rietveld method,
involves fitting a calculated diffraction pattern to the
experimental trace.
Limitation
• The technique is not as powerful as the single-crystal methods, for
it gives less accurate atomic positions, but has the advantage of not
48
requiring the growth of a single crystal.
Powder camera to powder diffractometer
• The early days of diffraction used photographic film to record the
diffracted X-rays; the diffraction device was appropriately called a
camera and the film is sometimes referred to as a two-dimensional
detector.
• An important technical advance was the moving X-ray electronic
detector, the early ones being based on the famous Geiger counter.
• To be effective however they had to be converted into proportional
counters, that is the output they generated had to be proportional
to the intensity of X-rays detected, unlike the original Geiger
counters which were radiation warning devices rather than
quantitative devices.
• As such these detectors could be said to be zero-dimensional (or
point) detectors, and to collect a diffraction pattern they had to be
mechanically moved around the crystal or powder in an appropriate
fashion.
• However the one really over-riding advantage of electronic detectors
was that the diffraction pattern could be fed directly into a computer.
49
• Crystallography and diffraction have always been heavy
computational subjects and therefore this link was of great initial
significance, even though the more modern electronic detectors
have increased dimensionality.
• As such one could here have added computers as a landmark in
powder diffraction history, though computers are ubiquitous in all
walks of life.
• The terms powder camera and powder diffractometer refer to any
diffraction device that uses photographic film or an electronic
detector (respectively) to record the diffraction pattern, though the
former are becoming obsolete.
• The figure below shows the diffraction pattern from quartz as
collected by a camera (a Debye-Scherrer camera) and by a modern
diffractometer.
• You might like to look at these and see if you can establish some
correspondence between the two.
50
Quartz: film output
Quartz: modern diffractometer output
51
X-rays are scattered in a sphere around the sample
• A cone along the sphere corresponds to a single Bragg
angle 2θ:
– The tens of thousands of randomly oriented crystallites in an
ideal sample produce a Debye diffraction cone.
• The linear diffraction
pattern is formed as
the detector scans
through an arc that
intersects
each
Debye cone at a
single point; thus
giving
the
appearance of a
discrete diffraction
peak.
52
X-Ray Production
53
Link:
https://www.youtube.com/watch?v=IsaTx5-KLT8
54
The X-Ray Tube and Components
56
Link:
https://www.youtube.com/watch?v=qcXLLxDZ1lA
57
Anode Heel Effect
X-Ray Tube
59
Link:
https://www.youtube.com/watch?v=M9S1ULdwav8
60
Powder X-ray diffraction (PXRD) is a somewhat
inefficient measurement technique
• Problem: Only a small fraction of crystallites in the sample
actually contribute to the observed diffraction pattern:
– Other crystallites are not oriented properly to produce
diffraction from any planes of atoms
• Solution: You can increase the number of crystallites
that contribute to the measured pattern by spinning the
sample
• Problem: Only a small fraction of the scattered X-rays are
observed by the detector:
– A point detector scanning in an arc around the sample
only observes one point on each Debye diffraction cone
• Solution: You can increase the amount of scattered Xrays observed by using a large area (2D) detector 63
Bragg's Law
• It is impossible to discuss powder diffraction much further without
Bragg's Law.
• While its derivation will be considered in more detail later we
need at least a basic understanding even at this stage.
• Although Laue is credited with the discovery of diffraction, it fell
to W. H. Bragg to devise an equation which predicted when
diffraction would actually take place.
• This equation became known as Bragg's Law and must surely be
one of the most well-known equations in science:
nλ = 2dsinθ
where λ is the wavelength of the radiation used, d is the
inter-planar spacing involved and θ is the angle between
the incident (or diffracted) ray and the relevant crystal
planes; n is an integer, referred to as the order of
diffraction, and is often unity.
• These ideas are far from obvious for a newcomer to diffraction. 4
• An idea of its application may be gleaned from the following diagram
depicting, schematically, X-ray diffraction from part of a single crystal:
• The basic idea behind Bragg's Law is that, when it is satisfied, X-ray
beams scattered from successive planes in the crystal (as shown) will
travel distances differing by exactly one wavelength (for the case of n =
1); this can be fairly easily proved from a geometrical consideration of
the above diagram.
• In this precise direction, i.e., at the angle θ calculated by Bragg's Law,
X-rays scattered from successive planes will interact constructively
when they eventually reach the X-ray detector thus registering the
passage of an intense beam which we call the diffracted beam.
• Of course it is not really the planes in the crystal that scatter the X-rays (since
planes are abstract mathematical items) but rather the atoms with their
5
electronic clouds.
• However this idea, developed by Bragg, of relating atoms to planes
proved to be a great simplification in the subject and for this reason we
still refer to individual diffracted beams as being "reflected" from certain
"planes" even though we know it is the atoms that actually perform the
scattering.
• At this point we do not need to understand the concept of planes in any
greater depth than this, but for those who feel they would like to know a
little more on next slides.
• One of the concluding ideas from Bragg's Law is that diffraction is, in
effect, an "arranged event"; three parameters need to be harmonized: the
wavelength of the X-rays, λ, the crystal orientation as defined by the
angle, θ (see diagram above), and the spacing, d, of the crystal planes
under consideration.
• For a given wavelength and set of planes one can conspire to arrange for
diffraction to occur by, for example, continuously changing the
orientation, i.e., changing theta, until a point arrives when Bragg's Law
is satisfied: this is precisely when diffraction occurs.
6
Derivation of Bragg’s equation
• When a beam of X-rays falls on a crystal plane composed
of regularly arranged atoms or ions, the X-rays are
diffracted.
• If the waves are in phase after reflection, the difference in
distance travelled by the two rays i.e., path difference must
be equal to an integral number of wavelength, nλ for
constructive.
• Thus, path difference = nλ = WY + YZ
As
WY = YZ
nλ = 2WY
sin θ = WY/d
WY = d sin θ
nλ = 2 d sin θ
• This equation is called Bragg’s equation.
• Where
– n = 1, 2, 3… (diffraction order)
– λ = wavelength of X-rays incident on crystal
– d = distance between atomic planes
– θ = angle at which interference occurs
A little more on crystal planes
• Crystal planes is an important concept used in powder diffraction
and crystallography in general.
• One can imagine a crystal being sub-divided into smaller
component units; crystallographers use, depending on context, two
alternative sub-divisions: one is the unit cell, the crystal building
block, which we will return to later, and the other components are
sets of planes invariably known as diffracting planes, reflecting
planes, Bragg planes, crystal planes or hkl planes.
• A set of such planes consists of parallel evenly spaced planes
which are extended to exactly fill the entire crystal; each plane is
an equal distance, d (the inter-planar spacing), from its
neighbouring plane.
• There are however an infinite number of such types of planes that
can be devised and, between them all, they cover every region of
space, and indeed every atom, within the crystal: this is one of the
properties that makes their concept useful.
9
• It is necessary to have some method of identifying and visualizing
the most useful planes.
• Crystallographers use an identification system referred to
as Miller, or hkl, indices (a sort of zip-code for the planes).
• Miller indices are simply a set of three numbers, hkl, which can
take on any combination of three integer values between +∞ and
−∞, e.g., (111), (-501) and (7-2-2).
• Each combination of hkl describes a unique set of planes filling
the crystal and so hkl is often presented as a subscript to a
property: e.g., dhkl which therefore means the d spacing between
the planes defined by hkl.
• The Miller indices, hkl, also provide a useful means for visualising
the planes.
• The convention is that if you have three axis, x,y,z, with three unit
spacings, a,b,c, on each then one of these hkl planes can be
visualized as the plane which intersects the x,y,z-axes at distances
of a/h, b/k, c/l respectively.
• The next such plane parallel to this would pass through the origin.
10
• The illustration below shows an example of such a set of planes
for the case of hkl = (222).
11
Basic X-ray
X-ray generation
12
Link:
https://www.youtube.com/watch?v=EzedRMAlGl0
13
Generation of X-rays
• Laboratory X-ray sources can be classified into two types:
• Sealed-tube
• Rotating anode
• Both may be used to generate monochromatic X-ray radiation and
they basically differ only in the intensity of the radiation produced.
White radiation
• X-rays are generated when matter is irradiated by a beam of highenergy charged particles such as electrons.
• In the laboratory, a filament is heated to produce electrons which
are then accelerated in vacuum by a high electric field in the range
20-60 kV towards a metal target, which being positive is called the
anode.
• The corresponding electric current is in the range 5-100 mA.
• The process is extremely inefficient with 99% of the energy of the
beam being dissipated as heat in the target.
• A typical X-ray spectrum from a copper target is shown below:
• The loss of energy of the electrons by collision with the atoms
17
usually takes place via multiple events.
18
• The result is the production of a continuous spectrum of X-rays known
as white radiation.
• The maximum energy lost, E(max), determines the shortest
wavelength, λ(min), that can be obtained according to the equation:
E=eV=hc/λ
where e is the charge on the electron, V is the accelerating
voltage, h is Planck's constant, and c is the speed of light.
• A more practical form of this equation is given by:
λ = 12.398 / V
where V is in kilovolts and λ is in Ångstroms (1 Å = 0.1 nm).
• Thus, the higher the accelerating voltage of the X-ray generator, the
shorter the minimum wavelength that can be obtained.
• The maximum in the intensity of the white radiation occurs at a
wavelength that is roughly 1.5× λ (min).
• Longer wavelengths are obtained by multiple-collision processes.
• The total intensity, I(w) of the white radiation is approximately
proportional to the filament current, i, the atomic number of the anode
target, Z, and the square of the accelerating voltage, V.
19
Characteristic radiation
• When the energy of the accelerated electrons is higher than a
certain threshold value (which depends on the metal anode), a
second type of spectrum is obtained superimposed on top of
the white radiation.
• It is called the characteristic radiation and is composed of
discrete peaks.
• The energy (and wavelength) of the peaks depends solely on
the metal used for the target and is due to the ejection of an
electron from one of the inner electron shells of the metal
atom.
• This results in an electron from a higher atomic level
dropping to the vacant level with the emission of an X-ray
photon characterized by the difference in energy between the
two levels.
• The diagram below show the electronic energy levels for a
20
copper atom:
21
• The characteristic lines in this type of spectrum are called K, L,
M,... and they correspond to transitions to orbitals with principal
quantum numbers 1, 2, 3,... When the two orbitals involved in the
transition are adjacent (e.g., 2 → 1), the line is called α.
• When the two orbitals are separated by another shell (e.g., 3 → 1),
the line is called β.
• Since the transition for β is bigger than for α, i.e., ΔEβ > ΔEα, then
λβ < λα .
• This is demonstrated by the values of the Kα and Kβ wavelengths in
the table below for two common anode materials:
Anode
Kα
Kβ
Cu
1.54184 Å 1.39222 Å
Mo
0.71073 Å 0.63229 Å
22
• In the copper X-ray spectrum, only 2 characteristic lines are seen at
low-energy resolution and a bar (-) is often used above the α to
indicate that it is a weighted mean value.
• This effect is difficult to achieve in the HTML language and so the
bar has been omitted.
• However, at higher resolution the Kα1 line is readily seen to be a
doublet, which is labelled as Kα1 and Kα2 where ΔEα1 > ΔEα2.
• The splitting of the 2p orbitals in copper, i.e., the splitting of the
energy levels LII and LIII, is very small (0.020 keV) and so the two
wavelengths Kα1 (= 1.54056 Å) and Kα2 (= 1.54439 Å) are very
similar.
• You may wonder why so few transitions are shown in the figure:
the allowed transitions are determined by a set of selection rules
that state that an outer s or d electron cannot fill the hole left by the
ejected 1s electron, but that p electrons can.
(HTML = Hypertext Mark-up Language)
23
Spectral line shape
• The above picture is actually a simplified version of reality since a
high-resolution analysis of the spectral lines of, say, Cu Kα shows
that both the α1 and α2 peaks are distinctly asymmetric.
• An explanation of the origin of this asymmetry is important in
understanding the so-called fundamental parameter approach to
the profile fitting of powder diffraction data peaks.
• The de-excitation process in which an outer 2p electron fills the
inner 1s electron shell is fast (≈ 10-12 s), but not fast enough to
stop double ionization events.
• In particular, the ejection of the initial 1s electron can be followed
by the loss of one of the 2s or 2p electrons from the energy levels
LI, LII, or LIII.
• The effect of the increased ionization on the atom is to change
slightly the energy gap between the K and L levels resulting in
slightly different wavelengths for the emitted X-ray photon.
• The resulting peak asymmetry in the spectral distribution of the
Kα lines of copper is shown in red in the diagram below:
24
• The dotted coloured lines represent individual spectral contributions
to the total.
25
26
Spectral intensity
• In the above figure, it is readily seen that the intensity of the Kα1 peak is almost
exactly double the intensity of the Kα2 peak.
• You might ask how this compares to the Kβ radiation or even the white radiation.
• The intensity of a K line is given approximately by the formula:
IK = c i (V - VK)n
where i is the electron beam current, (c is a constant,) and VK is the excitation
potential of the K line (as given earlier by VK = 12.398 [kV/Å] / λ ).
• The exponent n is approximately 1.5, but drops towards 1.0 when V > 2VK.
• The ratio IK : Iwhite is a maximum when the accelerating voltage V is
approximately 4× the excitation potential VK.
• For a Cu Kα anode, where VK is 8.0 kV, run with a typical operating voltage of
40 kV, the Kα line is approximately 90× more intense than the white radiation of a
similar wavelength.
• Thus the white radiation from a copper anode is too weak to be of any practical
use for powder diffraction in the laboratory.
What about the intensity of the Kβ radiation?
• Again considering a copper anode, the intensity of the Kα lines is approximately
5 times that of Kβ.
• Hence, all instrumental setups are optimized around the Kα radiation, and
preferably around Kα1 when high resolution monochromators are used as part
of
27
the X-ray optics.
K-shell knockout and emission of light
photon
• Visible light photons and X-ray photons are both
produced by the movement of electrons in atoms.
• Electrons occupy different energy levels, or orbitals,
around an atom's nucleus.
• When an electron drops to a lower orbital, it needs to
release some energy; it releases the extra energy in the
form of a photon.
• The energy level of the photon depends on how far the
electron dropped between orbitals.
28
29
• An electron in a higher orbital immediately falls to the
lower energy level, releasing its extra energy in the form
of a photon.
• It's a big drop, so the photon has a high energy level; it is
an X-ray photon.
• The free electron collides with the tungsten atom,
knocking an electron out of a lower orbital.
A higher orbital electron
fills the empty position,
releasing its excess energy
as a photon.
30
Figure: Kα1, Kα2, Kβ1.
31
X-Ray Spectra: Characteristic Lines
4
Link:
https://www.youtube.com/watch?v=1J8rkoPeiOw
5
Sealed glass x-ray tube
• Of the two experimental methods for creating x-rays in the
laboratory, only the sealed-glass x-ray tube is in common use for
powder diffraction studies.
• In recent years, the sealed glass tube has been improved by the use
of ceramics, but otherwise the two types are very similar.
• The latest developments have been the production of microfocus
tubes, but their use is still not established in the powder diffraction
community, probably because of cost and as yet unproven
reliability.
• Shown below is a picture of a typical sealed glass x-ray tube.
• The windows are made of beryllium metal which has a very low
absorption cross-section for x-rays.
• The tube shown here has a copper anode and electrons are
produced by heating a tungsten filament.
7
Figure: Sealed glass x-ray tube.
8
• The schematic diagram below emphasizes the key aspects behind
the operation of the x-ray tube.
• The exact operating voltage of the tube depends on the
characteristics of the filament, but generally the heat load on the
anode is of the order of kilowatts.
• Most of the energy of the electrons hitting the anode target is
dissipated as heat and so the tube is water cooled as indicated in
the diagrams.
• X-rays are generated in all directions, but the optimum angle for
viewing the source is typically at about 6° to the anode surface.
9
• X-ray tubes are described as short or long anode depending on the
distance between the middle of the beryllium window and the
upper surface of the tube housing.
• In addition, x-ray tubes are described as broad, normal, fine, and
long fine focus.
10
• The photograph below shows a close-up of the tungsten filament of a
long fine focus tube (with the scale in millimetres):
– The "fine" describes the coil width which is approximately 0.5 mm
and the "long" refers to the length (e.g., 12 mm).
• Fine focus tubes are similar, but have shorter filaments (e.g., 8 mm).
• Normal (1 mm width) and broad (2 mm width) focus tubes produce xrays of a lower brightness and are thus rarely used for powder diffraction
work.
• The final point to make is that you may have noticed that the X-ray tube
has four windows.
• Two of these are parallel to the filament and the other two are
perpendicular to it.
• If a spot source of x-rays is required, then the tube should be arranged so
that a window parallel to the filament axis is used, in contrast to when a
line source of x-rays is required when a window perpendicular to the
filament axis is used.
• Note that most modern powder diffractometers make use of a line source
in contrast to the older Debye-Scherrer cameras which made use of the
11
spot source.
X-radiation for diffraction measurements is produced by
a sealed tube or rotating anode
• Sealed x-ray tubes tend to operate at 1.8 to 3 kW.
• Rotating anode x-ray tubes produce much more flux
because they operate at 9 to 18 kW.
– A rotating anode spins the anode at 6000 rpm, helping
to distribute heat over a larger area and therefore
allowing the tube to be run at higher power without
melting the target.
• Both sources generate x-rays by striking the anode target
with an electron beam from a tungsten filament.
– The target must be water cooled.
– The target and filament must be contained in a vacuum.
12
13
The wavelength of X-rays is determined by the anode of the X-ray
source
• Electrons from the filament strike the target anode, producing
characteristic radiation via the photoelectric effect.
• The anode material determines the wavelengths of characteristic
radiation.
• While we would prefer a monochromatic source, the x-ray beam
actually consists of several characteristic wavelengths of x-rays.
14
X-ray filters
• The previous slides showed that the spectrum from a sealed X-ray
tube is composed of several X-ray lines.
• Laboratory powder diffraction requires an X-ray source that is
essentially monochromatic and so the Kβ line in the X-ray
spectrum needs to be removed.
• Metal foil filters are one way of achieving this.
• The following photograph shows the typical metals used to filter
X-rays produced by a sealed X-ray tube, i.e., Ni, Fe, Mn, V, or Zr.
• Shown below is a photograph of the X-ray filters available
on a standard Siemens X-ray tube housing.
• The beam passes through the top filter which in this case is a
nickel foil.
• Alternative metal foils can be set by rotation of the filter
housing to the appropriate position.
• One position on the filter housing is left open for the case
when a filter is not required.
• The top of the X-ray tube is visible above the tube housing.
• A cover plate with beam stop (not shown) is then fitted over
15
the filter housing during normal use.
• Filters preferentially reduce the intensity of the Kβ line in the X-ray
spectrum compared to Kα as explained below.
• Note that absorption filters cannot be used to remove the unwanted
Kα2 component from Kα radiation.
• Filters exploit the X-ray absorption edge of the particular element.
• At wavelengths longer than the absorption edge (i.e., just above the
edge), the absorption of the X-rays is considerably less than for
wavelengths shorter than the absorption edge (i.e., just below the
edge) as shown below for nickel metal:
16
• Note that the filter also removes much of the high energy
background radiation.
• The choice of filter material depends upon the choice of anode
material in the X-ray tube as shown in the following table:
Anode
Cu Co
Fe
Cr
Mo
Filter
Ni
Mn
V
Zr
Fe
• From the table it can be seen that the ideal choice of material for an
X-ray filter is a metal whose atomic number, Z, is one less than that
of the anode target metal for first row transition metals (or two less
for second row transition metals).
• The optimum thickness, x of the filter can be determined from the
mass-absorption law:
I(λ) / Io(λ) = exp{− (μ / ρ)λ ρx}
where (μ / ρ) is the mass absorption coefficient at the wavelength λ,
ρ is the density of the material, which for nickel metal is 8.92
g/cm3, and I(λ) and Io(λ) are the transmitted and incident X-ray
intensities, respectively.
17
• The mass absorption coefficients of nickel for Cu Kα and Cu Kβ are
49.2 and 286 cm2/g, respectively.
• The table below shows the percentage transmission for various
thicknesses of nickel foil:
Thickness (cm) I / Io (%) for Cu Kα I / Io (%) for Cu Kβ Reduction Ratio
0.0010
64.5
7.8
8
0.0015
51.8
2.2
24
0.0020
41.6
0.6
68
0.0025
33.4
0.2
197
• It can be seen from the table that the optimum thickness has to be a
compromise between reducing the intensity of the unwanted Cu Kβ
and reducing the intensity of the desired Cu Kα.
• Most commercial systems employing a nickel filter with a copper
anode target will choose the thickness of the foil so as to give a
reduction ratio in the range 25:1 to 50:1, i.e., foils between 15 and
20 µm thick.
• From the table, it can be seen that this range of foil thickness will
diminish the desired radiation by approximately a factor of 2.
18
β-filters can also be used to reduce the intensity of Kβ and Wwavelength radiation
• A material with an absorption edge between the Kα and Kβ
wavelengths can be used as a beta filter.
• This is often the element just below the target material on the
periodic table:
– For example, when using Cu radiation
• Cu Kα = 1.541 A
• Cu Kβ = 1.387 A
• The Ni absorption edge = 1.488 A
– The Ni absorption of Cu radiation is:
• 50% of Cu Kα
• 99% of Cu Kβ
19
• Some atoms absorb incident X-rays and fluoresce them as X-rays
of a different wavelength:
– The absorption of X-rays decreases the diffracted signal
– The fluoresced X-rays increase the background noise
• The increased background noise from fluoresced X-rays can be
removed by using:
– a diffracted-beam monochromator
– an energy sensitive detector
• The diffracted beam signal can only be increased by using a
different wavelength of radiation
• The most problematic materials are those two and three below the
target material:
– For Cu, the elements that fluoresce the most are Fe and Co
20
Monochromatic and broad spectrum of Xrays
Filter type
• A window that absorbs undesirable radiation and allows
required wavelength to pass.
• e.g. : Zr absorbs x-rays emitted by Mo.
Crystal type
• Positioned in the x-ray beam so that the angle of the
reflecting planes satisfied the Bragg’s equation for the
required wave length.
Characteristics of a crystal
• Mechanically strong and stable
• The mosaicity and resolution of the crystal, should be
small.
21
22
• X-rays can be created by bombarding a metal target with high
energy (> 104) electrons.
• Some of these electrons excite electrons from core states in the
metal, which then recombine, producing highly monochromatic Xrays.
• These are referred to as characteristic X-ray lines.
• Other electrons, which are decelerated by the periodic potential of
the metal, produce a broad spectrum of X-ray frequencies.
• Depending on the diffraction experiment, either or both of these Xray spectra can be used.
• Historically, X-ray filters were used to reduce the unwanted white
radiation from the X-ray source and to eliminate (as much as
possible) the Kβ radiation.
• The drawback of filters is that the background radiation is still high
and that the transmitted radiation is still not very monochromatic.
23
• An alternative and more selective way to produce a beam of
radiation with a narrower wavelength distribution is by using
single-crystal monochromators.
• In practice "single crystals" are made up of lots of little crystal
blocks all approximately aligned in the same orientation to form a
mosaic.
• The distribution of the alignment of the blocks determines the socalled mosaic spread of the crystal.
• Two types of monochromator may be distinguished based on the
difference being in the mosaic spread of the crystals.
• Two commonly used materials are pyrolytic graphite and silicon,
which can be used to make broad band and narrow band (Δλ / λ)
monochromators, respectively.
• For pyrolytic graphite, the mosaic spread is relatively broad in
contrast to silicon in which the alignment of the mosaic blocks is
near perfect.
24
Mosaicity (‫)ﭘﭼﯽ کاری‬
In
crystallography,
mosaicity is a measure
of the spread of crystal
plane orientations.
• The monochromator works by reflection of the wavelengths that
obey Bragg's Law for the particular d spacings of the
monochromator.
• For a silicon crystal (which is cubic with a unit cell size equal to
5.4309 Å), the largest d spacing [which is from the (111) planes] is
3.136 Å.
• Application of the Bragg equation (λ = 2d sin θ) shows that for Cu
Kα1, the diffraction condition will be satisfied for 2θ = 28.442°,
while for Cu Kα2, it will be satisfied for 2θ = 28.514°, giving a
difference in Bragg angle of only 0.072°.
• Hence only monochromator crystals with a narrow band pass, e.g.
silicon, will be able to separate the Kα1 and Kα2 wavelengths from
25
a laboratory copper X-ray source.
Figure: The Generating of X-rays.
26
• By contrast, pyrolytic graphite monochromators with their wide band
pass will pass both Kα wavelengths, but not Kβ for which the Bragg
angle is considerably different.
• Monochromator crystals partially polarize an unpolarised X-ray beam
because the operating principle is one of Bragg diffraction.
• In theory the effect of polarization on the intensity of the diffraction
pattern should be taken into account during data processing, but in
practice the correction effect is relatively small and often ignored.
What materials make good laboratory monochromators?
• The following properties are desirable for any material used as a
laboratory X-ray monochromator:
– The crystals must be mechanically strong and stable in the beam.
– The crystals should have suitable interplanar distances d so that the
desired wavelength λ can be obtained.
– The structure factor corresponding to the d spacing must be as large as
possible, i.e. the Bragg reflection should be very intense.
– The mosaicity of the crystal must be of suitable magnitude and the
distribution of crystal block orientations should preferably be gaussian.
– The absorption of the material should be low.
27
– The combination of d and λ should be chosen so that 2θ is
small. This is to minimize intensity loss due to polarisation and
geometric (Lorentz factor) effects.
– The crystals should be reasonably easy to cut.
– The crystals should have a small coefficient of thermal
expansion so that the wavelength is essentially unaffected by
any fluctations in ambient temperature that are likely to be
encountered.
• The most common materials for laboratory X-ray monochromators
are pyrolytic graphite for broad band use and either silicon,
germanium, or quartz for narrow band use.
Laboratory usage
• In the laboratory, the monochromator crystal can be positioned
before or after the sample.
• It is common practice to use graphite as a post sample
monochromator, but to use, say, silicon as a pre-sample
monochromator.
28
• The main reason for this is one of mechanical stability since
narrow-band pass monochromators require an extremely precise
alignment in order to effectively separate the two Kα wavelengths
and this cannot be maintained if the monochromator is made to
move with the detector arm.
• You might wonder what laboratory X-ray monochromators look
like in practice.
• The following pictures show two types that we have in our
laboratory:
29
• The left-hand picture shows a graphite monochromator that was used
as post-sample monochromator on a Bragg-Brentano diffractometer.
• The flat graphite crystal is stuck on to surface of the metal plate. The
right-hand picture shows a germanium monochromator crystal.
• It is cut exceedingly thin (< 0.5 mm) so that it can be gently bent by
clamping it between the two curved metal surfaces of the
monochromator housing.
Effect
• The choice of whether to use a broad-band or narrow-band
monochromator will depend on your experimental objectives.
• For some experiments where high intensities are required, the
graphite monochromator will be better.
• In addition, a post-sample graphite monochromator can reduce the
effect of fluorescence from the sample.
• For high-resolution work, pre-sample narrow-band monochromators
are often preferred.
• A comparison of good data obtained with both types of
monochromator is as shown below.
30
Graphite
versus
Quartz
Monochromators
• The powder diffraction patterns
below are of yttria, Y2O3, annealed
at 1200°C for several days, and
measured on two different BraggBrentano diffractometers, both
equipped with copper X-ray tubes.
• The first data set was measured on
a diffractometer equipped with a
post-sample
graphite
monochromator. The splitting of the
diffraction peaks due to the
presence of Kα1 and Kα2 radiation
is clearly illustrated.
• The second data set was measured
with
another
diffractometer
equipped this time with a presample quartz monochromator. The
peaks due to the Kα2 radiation have
vanished, but at a cost to the
diffracted intensity.
31
Monochromators remove unwanted wavelengths of
radiation from the incident or diffracted X-ray beam
• Diffraction from a crystal monochromator can be used to
select one wavelength of radiation and provide energy
discrimination.
• An incident-beam monochromator might be used to
select only Kα1 radiation for the tube source.
• A diffracted-beam monochromator, such as on the Rigaku
RU300, may be used to remove fluoresced photons, Kβ,
or W-contamination photons from reaching the detector.
– Without the RSM slit, the monochromator removes
~75% of unwanted wavelengths of radiation.
– When the RSM slit is used, over 99% of the unwanted
wavelengths of radiation can be removed from the
beam.
RSM = Receiving slits
32
Most of our powder diffractometers use the BraggBrentano parafocusing geometry
• A point detector and sample are
moved so that the detector is always
at 2θ and the sample surface is
always at q to the incident X-ray
beam.
• In the parafocusing arrangement, the
incident- and diffracted-beam slits
move on a circle that is centered on
the sample.
• Divergent x-rays from the source hit
the sample at different points on its
surface.
• During the diffraction process the xrays are refocused at the detector slit.
• This arrangement provides the best
combination of intensity, peak shape,
and angular resolution for the widest
number of samples.
•
•
•
•
•
•
•
F: the x-ray source
DS: the incident-beam divergence-limiting
slit
SS: the soller slit assembly
S: the sample
RS: the diffracted-beam receiving slit
C: the monochromator crystal
4
AS: the anti-scatter slit
Bragg-Brentano Parafocusing Geometry
5
Link:
https://www.youtube.com/watch?v=Dh_3szFxQJQ
6
Laboratory instrumental configurations
• There are two principal types of instrument geometry for
laboratory powder diffractometers:
– Reflection
– Transmission
• In reflection geometry, the sample is in the form of a flat
plate, while in transmission geometry a glass capillary or
thin foil is used.
8
Instrument x-ray optics
Reflection geometry
• The earliest flat-plate diffractometers had poor intensities and peak
widths due to lack of focussing.
• By contrast the modern flat-plate diffractometer has both good peak
intensities and excellent resolution due to focussing of the
diffracted beam.
• This reflection geometry, in which the divergent and diffracted
beams are focussed at a fixed radius from the sample position, is
commonly referred to as Bragg-Brentano geometry.
• With the simplest form of this setup, the anode can be fixed and the
sample and detector can be rotated by θ and 2θ, respectively.
• A common alternative is to fix the sample (usually in the horizontal
position) and to move both the source and the detector by -θ and θ,
respectively.
• The X-ray optics for this setup is illustrated schematically in the
9
diagram below:
10
Figure: Basic Bragg Brentano geometry. The dotted circle
centred on the sample position represents the goniometer circle
on which the image of the divergent source of X rays is focussed
by diffraction from the flat plate sample. Strictly speaking, true
focussing only occurs when the sample plate has a curved
surface. However, given that the footprint of the beam on the
sample plate is considerably smaller than the radius of the
focusing circle, the flat plate approximation works well in
practice. The source is usually fixed and to collect the diffraction
pattern the sample and detector are rotated by y and 2θ,
respectively. An alternative is to fix the sample (usually in the
horizontal position, e.g. useful for a liquid sample) and to move
both the source and the detector by θ and θ, respectively.
11
• The dotted-circle centred on the sample position in these figures
represents the goniometer circle on which the divergent source Xrays are "focussed" by diffraction from the flat-plate sample.
• Strictly speaking, true focussing only occurs when the sample plate
has a curved (or hemispherical if rotated) surface.
• However, given that the footprint of the beam on the sample plate
is considerably smaller than the radius of the focussing circle, then
the flat-plate approximation works extremely well.
• As can be seen in the later figures, monochromators also have a
monochromator circle associated with them, but in this case the
monochromators can be curved (as in Johansson geometry) to
ensure true focussing.
• The tube is aligned so that the beam divergent on the sample is at
angle ξ to the anode surface (which is typically about 6°), and the
divergence of the beam is controlled by one or more slits after the
source.
• In the absence of pre- or post-sample monochromator, an appropriate filter
should be inserted after the X-ray source as shown.
12
• The illumination of the sample by the X-ray beam is proportional
to cosθ and does not extend over the whole sample except at very
low scattering angles.
• In order to get a good powder average, the sample is usually spun
about an axis normal to the flat plate.
• The divergence of the beam can be controlled by one or more slits
positioned after the source.
• A typical X-ray slit is shown in the photograph below, the size of
the slit being quoted in degrees in this instance, though sometimes
they are given, for example, in millimetres.
13
Figure: A typical X-ray slit is shown in the photograph
on the left. The size of the slit is indicated in degrees here
(0.3o), though sometimes it is given in mm. Soller
collimators are shown on the right. These consist of a set
of fine parallel foils that prevent angular divergence of
the beam out of the θ/2θ plane.
14
• Sideways divergence of either the incident or scattered beam can be
controlled using Soller slits (shown in the right-hand photograph
above) inserted in the X-ray beam path.
• These consist of a set of fine parallel foils which prevent angular
divergence of the beam out of the θ/2θ plane.
• This gives a less asymmetric and narrower peak shape, especially at
low scattering angles.
• The next diagram shows the X-ray optics when a post-sample
graphite monochromator is employed.
• The X-ray filter is no longer used.
• Again several slits may be used to control the divergence of the
incident and diffracted beam.
• In addition, a beam catcher may be employed within the
monochromator housing (not shown) to prevent nonmonochromated X-rays from reaching the detector.
• With this setup, the source is normally fixed and the
monochromator moved in unison with the detector arm.
15
• The Bragg angle for the monochromator, 2θM, is a preset constant
determined by the interplanar distance, d, of the monochromator
crystal.
16
Figure: Bragg Brentano geometry with a
diffracted beam monochromator. The crystal is
usually graphite, which has a low degree of
crystalline perfection, and hence a large
acceptance angle (tenths of a degree). Thus a flat
crystal is adequate.
17
• An alternative experimental setup is the pre-sample monochromator shown in
the final diagram below and illustrated by the two photographs on the next
slide.
• In this setup, both the X-ray source and the monochromator are fixed, and only
the sample and detector rotate about the θ/2θ axis of the goniometer.
• In order to achieve separation of the Kα1 and Kα2 wavelengths together with a
reasonable X-ray intensity, the pre-sample monochromator is curved so that the
X-rays are focussed (or nearly focussed depending on the exact curvature used)
from all parts of the crystal.
18
Figure: Bragg Brentano geometry with a pre
sample monochromator. A near perfect crystal,
e.g. quartz or germanium, is required to separate
Kα1 and Kα2.
19
• The left hand photograph shows the position of the X-ray tube housing, primarybeam monochromator, and θ/2θ goniometer with a white powder mounted in
flat-plate holder.
• The motor for spinning the sample is clearly visible just above the sample
position.
• The right-hand picture shows the position of both incident and diffracted beam
slits plus the scintillation detector mounted on the 2θ circle of the goniometer.
• Post-sample soller slits are mounted in the housing between the post-sample
anti-scatter slit and the receiving slit of the detector.
20
Figure: Photograph of a Bragg Brentano diffractometer
equipped with a pre sample monochromator (on left) and
scintillation detector (on right). Sample stage and detector
move in the vertical plane about a horizontal axis in the
ratio 1 : 2. The sample is spun about an axis normal to the
flat plate. Although this instrument dates from the early
1990s, the latest generation of laboratory Bragg Brentano
diffractometers still function in a similar manner to the one
shown here.
21
Transmission geometry
• The Debye-Scherrer camera shown in the photograph used to be
one of the most common instruments for obtaining powder
diffraction data from a sample in transmission geometry.
• The camera is discussed here because much of the early data which formed the
JCPDS database were obtained with this type of instrument.
• The camera was built in a variety of sizes, the most popular having a radius of
180/π (= 57.295) mm.
• Powder diffraction patterns were collected on film which was wrapped around
the inside of the camera in such a way that both the incident beam collimator and
through beam collimator both passed through pre-punched holes in the film as
shown below.
22
• The Bragg scattering angle was readily obtained since the radius
was chosen so that 1 mm on the film corresponded to 1° 2θ.
• The sample was positioned at the centre of the camera; a shadow of
the sample in the X-ray beam could be seen on a small fluorescent
screen built into the end of the through beam collimator, and rotated
by an external motor attached to the rear of the camera.
• The cameras were normally used on the spot focus side of the X-ray
tube with a cylindrical incident beam collimator; slit collimators
were usually available for those occasions when the camera was
used with an X-ray line source.
• Although the collimators cut down on air scatter, they have little
focussing effect.
• The result is that Debye-Scherrer films measure relatively lowresolution powder diffraction data.
23
• However, the semi two-dimensional nature of the strip of film could
be used to test for texture in the sample.
• In addition, the film measured the full 360° of scattering thus
providing reasonably accurate lattice parameters from the very
high-angle reflections.
• The cameras were normally used on a filtered X-ray source and the
presence of the unresolved Kα wavelengths significantly broadened
the peaks at intermediate 2θ angles.
• At the highest angles, splitting of the peaks due to the two
wavelengths could be seen readily.
24
Focussing Debye-Scherrer Geometry
• The transmission geometry of the Debye-Scherrer camera
discussed above can be considerably improved with the
introduction of a focussing narrow-band pass monochromator as
shown in the diagram below:
25
Figure: Parafocussing Debye Scherrer diffractometer with
curvedmonochromator crystal and capillary sample. Given the
intrinsically worse peak to back ground ratios compared to Bragg
Brentano geometry, linear or curved position sensitive detectors
(PSDs) are employed to improve counting statistics. As with the
equivalent Bragg Brentano geometry, the angle ζ is optimised at about
6o.
26
• The divergent beam from the X-ray anode is focussed using a
curved silicon monochromator, not onto the cylindrical sample, but
beyond onto the 2θ measuring circle of the detector.
• As with the equivalent Bragg-Brentano geometry, the angle ξ is
optimised at about 6°; and the monochromator Bragg angle is
calculated according to the d spacing of, say, (111) silicon.
• With this geometry, diffraction peak widths of 0.1° or better are
easily obtained.
• An experimental setup for this geometry is illustrated in the
photograph below:
• The horizontal X-ray
tube is visible far right
and a small PSD
detector is seen on the
far left; the chrome
shielding
of
the
monochromator
housing dominates the
centre right of the
picture.
27
• An alternative transmission setup, in which the focussing effect of a
monochromator is also exploited, is the Guinier camera.
• This film-based camera employs thin flat samples in transmission
geometry and very high-resolution powder patterns may be
measured with it.
• A typical film from a Guinier camera is shown below for
comparison with the Debye-Scherrer film above. However, a
detailed usage of this camera will not be discussed further in this
course.
28
Brief summary of XRD
What the XRD mechines
can do???
29
Link:
https://www.youtube.com/watch?v=1J8rkoPeiOw
30
Characteristic interaction
4
Link:
https://www.youtube.com/watch?v=FjeF1xQHdwk
5
Bremsstrahlung interaction
7
Link:
https://www.youtube.com/watch?v=UkywJG9QPuE&t=2s
8
Bremsstrahlung radiation
• Bremsstrahlung (German pronunciation, from bremsen "to brake"
and Strahlung "radiation"; i.e., "braking radiation" or
"deceleration radiation", is electromagnetic radiation produced by
the deceleration of a charged particle when deflected by another
charged particle, typically an electron by an atomic nucleus.
10
Link:
https://www.youtube.com/watch?v=49IQTu5ocWo
11
The x-ray beam produced by the x-ray tube is divergent. Incident-beam
optics are used to limit this divergence
λ = 2dhklsinθ
• X-rays from an x-ray tube are:
– Divergent
– Contain multiple characteristic wavelengths as well as
Bremmsstrahlung radiation
• Neither of these conditions suit our ability to use x-rays for analysis
– The divergence means that instead of a single incident angle q, the
sample is actually illuminated by photons with a range of incident
angles.
– The spectral contamination means that the sample does not diffract a
single wavelength of radiation, but rather several wavelengths of
radiation.
• Consequently, a single set of crystallographic planes will produce
several diffraction peaks instead of one diffraction peak.
• Optics are used to:
– Limit divergence of the x-ray beam
– Refocus x-rays into parallel paths
13
– Remove unwanted wavelengths
Divergence slits are used to limit the divergence of the incident xray beam
• The slits block x-rays that have too great a divergence.
• The size of the divergence slit influences peak intensity and peak
shapes.
• Narrow divergence slits:
– Reduce the intensity of the x-ray beam
– Reduce the length of the x-ray beam hitting the sample
– Produce sharper peaks
• The instrumental resolution is improved so that closely
spaced peaks can be resolved.
14
Other optics
• Limit divergence of the x-ray
beam
– Divergence limiting slits
– Parallel plate collimators
– Soller slits
• Refocus x-rays into parallel
paths
– Parallel-beam optics
– Parabolic mirrors and
capillary lenses
– Focusing mirrors and
lenses
• Remove unwanted
wavelengths
– Monochromators
– Kβ filters
15
Detectors
• Point detectors
– Observe one point of space at a time
• Slow, but compatible with most/all optics
– Scintillation and gas proportional detectors count all photons,
within an energy window, that hit them
– Si(Li) detectors can electronically analyze or filter wavelengths
• Position sensitive detectors
– Linear PSDs (position-sensitive detector) observe all photons
scattered along a line from 2 to 10°long
– 2D area detectors observe all photons scattered along a conic
section
– Gas proportional (gas on wire; microgap anodes)
• Limited resolution, issues with deadtime and saturation
• CCD (charge coupled device)
• Limited in size, expensive
– Solid state real-time multiple semiconductor strips
16
• High speed with high resolution, robust
Spectral contamination in diffraction patterns
• The Kα1 and Kα2 doublet will almost always be present
– Very expensive optics can remove the Kα2 line
– Kα1 and Kα2 overlap heavily at low angles and are more
separated at high angles
• W-lines form as the tube ages: the W-filament contaminates the
target anode and becomes a new x-ray source
• W and Kβ lines can be removed with optics
17
The x-ray shutter is the most important safety device
on a diffractometer
• X-rays exit the tube through x-ray transparent Be
windows.
• X-ray safety shutters contain the beam so that you may
work in the diffractometer without being exposed to the
x-rays.
• Being aware of the status of the shutters is the most
important factor in working safely with x-rays.
18
19
Safety measures regarding in x-ray tube (X-ray shutters)
• No x-ray tube may be energized:
• while outside its protective tube housing, or
• with an unshielded aperture in the tube head or protective
barrier
• No sample, collimator or analyzing crystal shall be changed or
adjusted whilst a primary x-ray beam passes through that
collimator or is incident on that sample or crystal unless:
• the sample, collimator or crystal, during and after the change or
adjustment is within a shielded enclosure, and
• the change or adjustment is performed by remote means from
outside the enclosure
• Immediate measures must be taken to remove potentially
hazardous situations arising from x-ray beams that may be emitted
due to an equipment defect, misalignment or any other reason.
20
• XRD equipment must not be operated by inexperienced persons
unless under the direct supervision of an experienced operator.
• Visual alignments or adjustments must not be carried out while the
x-ray tube is energized, unless a viewing system is used which is
shielded or designed to prevent exposure of the eye or other parts
of the body to the primary beam.
• Controlled access (i.e., locks, interlock circuit, etc.) to rooms using
x-ray machines is required.
• Operators should know what the dose rates are at various stages in
the operation to ensure that maximum effort is directed at reducing
the time of exposure during higher dose rate procedures (i.e.,
consider the difficulties when handling large animals during
scintigraphy or other procedures that involve occupational
exposure).
21
Characteristic X-rays
• The atoms of each element in the sample consist of a
nucleus made up of neutrons and positively charged
protons, and a cloud of negatively charged electrons that
surrounds the nucleus.
• The number of protons in the nucleus of the atom defines
its atomic number, Z, while in a neutrally charged atom
the number of protons is matched by the number of
electrons.
• The electrons in the electron cloud have a stable set of
energy levels, also known as electron shells.
• The shell closest to the nucleus is known as the K shell,
followed outwards by the L, M, N, O, P and Q shells.
• Energy
dispersive
X-ray
spectroscopy
(EDS
microanalysis) is mostly concerned with electrons in the
24
inner shells, i.e., the K, L and M shells.
• The maximum number of electrons in each shell is
governed by quantum mechanics, with a maximum of two
electrons in the K shell; eight electrons in the L shell; 18
electrons in the M shell, and so on.
• Each shell, apart from the K shell, is split into subshells,
with the electrons in related subshells having slightly
different energies.
• The L shell has three subshells; the M shell has five
subshells, and so on.
• The K shell has the highest ionization energy or critical ionization
energy in the atom.
• That is, more energy is needed to remove an electron from this shell
than from subshells further from the nucleus.
• The further from the nucleus the electron is, the lower its ionization
energy.
• Characteristic x-rays are produced by electron transitions between
25
the inner electron shells.
Bohr atomic model
26
Orbitals
• Orbitals are regions in space that are occupied by electrons.
• To visualize this better, let us take a look at the following
illustration:
27
28
• The electrons in each shell and subshell have specific
ionization energies, and these are different for every
element, that is, the ionization energy for the K shell in Si
(1.84 keV) is different from the ionization energy of the K
shell in Pt (78.4 keV).
Figure: A schematic drawing of
an atom showing the nucleus
surrounded by the K, L and M
electron shells. The K shell can
have a maximum of two
electrons; the L shell has three
subshells and can have a
maximum of eight electrons;
the M shell has five subshells
and can have a maximum of 18
electrons.
29
• The production of characteristic x-rays is a two-stage process:
– Ionization followed by relaxation
Ionization
• Firstly, an electron is removed from one of the inner shells of
the atom by an electron from the primary beam so that the
atom is ionized and in an unstable state.
Relaxation
• Secondly, the atom regains stability when an electron from an
outer shell fills the inner shell vacancy and an x-ray photon is
emitted.
• The energy of the emitted x-ray is equal to the difference
between the ionization energies of the electrons involved in
the transition.
• Note that inner shell ionization and characteristic x-ray
emission can result from irradiation by a primary beam of
protons (PIXE) or x-rays (XRF) as well as electrons
30
(EDS/WDS).
Figure: An
electron from
the primary
beam dislodges
an electron from
the K shell of a
Si atom in the
sample. An
electron from
the L shell fills
the vacancy and
a Si Kα X-ray is
generated. The
energy of the Xray is equal to
the ionization
energy of the K
shell minus the
ionization
energy of the L
shell.
31
• As each element has specific ionization energies for each
subsell, so the difference between the energies is characteristic
of the element involved in producing the x-ray photon.
• For Si, the ionization energy of the K shell is 1.84 keV, the
ionization energy of the L shell is ~0.10 keV and the ionization
energy of the M shell is ~0.01 keV.
• The characteristic X-ray spectrum for Si shows three spectral
lines.
• The line at low energy (~0.09 keV) results from ionization of the
L shell with an electron from the M shell filling the vacancy: E =
0.10 – 0.01 keV (This line would be at or below the limit of
detection for most EDS detectors).
• The line at ~1.74 keV results from ionization of the K shell with
an electron from the L shell filling the vacancy (E = 1.84 – 0.10
keV), whereas the smaller peak at higher energy (~1.83 keV)
results from ionization of the K shell and an electron from the M
32
shell filling the vacancy (E = 1.84 – 0.01 keV).
~1.83 keV
~1.74 keV
~0.09 keV
Figure: The ideal Characteristic X-ray spectrum for Si. The
Characteristic X-ray lines, Kα, Kβ and Lα, have discrete energies. 33
Characteristic X-ray generation
34
An electron from the primary electron beam interacts with the electron
cloud around an atom in the sample.
Step-1
Interaction
35
The electron from the primary beam ionizes the target atom and an
electron is removed from the K-shell of the atom. Both the primarybeam electron and the ejected electron leave the atom.
Step-2
Ionization
36
An electron from an outer shell (in this case the M shell) fills the
vacancy in the K shell and a characteristic X-ray is produced.
Step-3
Fill vacancy
37
The energy of the X-ray photon is equal to the difference between the
energies of the two shells involved in the transition.
In this case E = EK - EM
Step-4
X-ray
38
Nomenclature of spectral lines
• In spectroscopy, the most commonly used naming
convention for characteristic X-ray lines is the Siegbahn
notation.
• The first component of the name is the element involved,
e.g., Si.
• The second component is the electron shell that was ionized to
produce the X-ray, e.g., K, L or M.
• The third component reflects the relative intensity of the line
within each shell, e.g., α is the most intense line, followed by β
and γ.
• The lines within each shell make up a family, or series, of lines
for that shell, e.g., the K family comprises the Kα and Kβ X-ray
lines.
• In the Si spectrum, the lowest energy X-ray line is the Si Lα line;
the line at 1.74 keV is the Si Kα line and the line at ~1.83 keV is
39
the Si Kβ line.
Figure: The electron transitions involved in generating the
40
Kα, Kβ and Lα X-ray photons.
• For each element, the electrons in the K shell have the
highest ionization energies while the ionization energies
of electrons in outer shells are lower.
• More energy is required to ionize the K shell, and it
follows that the energies of the K family X-ray lines for
each element are greater than those of the L family, which
are greater than those of the M family.
• That is, for every element: EK > EL > EM
41
Siegbahn notation
• The Siegbahn notation is used in X-ray spectroscopy to name
the spectral lines that are characteristic to elements.
• It was introduced by Manne Siegbahn.
• The characteristic lines in X-ray emission spectra correspond
to atomic electronic transitions where an electron jumps down to a
vacancy in one of the inner shells of an atom.
• Such a hole in an inner shell may have been produced by
bombardment with electrons in an X-ray tube, by other particles as
in Particle-induced X-ray emission or proton-induced X-ray
emission (PIXE), by other X-rays in X-ray fluorescence or
by radioactive decay of the atom's nucleus.
• Although still widely used in spectroscopy, this notation is
unsystematic and often confusing.
• For these reasons, International Union of Pure and Applied
Chemistry (IUPAC) recommends another newer nomenclature.
• The table below shows a few of the common electronic levels with
their names in Siegbahn and IUPAC notation.
42
43
X-ray optics
• Various optical elements can be placed in the beam path to tailor
the characteristics of the x-ray beam.
• These can work by diffraction (e.g., a monochromator crystal),
reflection (e.g., a mirror), or absorption (e.g., a filter or slits).
• A monochromator is used to select a particular wavelength, a
mirror can focus the beam or suppress higher harmonics, and
filters can be used to remove unwanted radiation.
Filters
• For powder diffraction experiments using a laboratory source
diffraction of the Cu Kβ radiation contaminates the powder pattern
from Cu Kα.
• Its intensity can be greatly attenuated by placing a Ni filter, a
uniform thin sheet of nickel, in the beam path.
• The energy of the Cu Kβ X-rays (λ = 1.392A˚) is slightly above the threshold
energy of the Ni K absorption edge (λ = 1.488A˚) which thus absorbs this
wavelength strongly, whereas Kα X-rays (λ = 1.542A˚) have insufficient energy
to excite this particular transition and are only modestly absorbed.
4
• The optimum thickness has to be a compromise between reducing
the intensity of the unwanted Cu Kβ and reducing the intensity of
the desired Cu Kα.
• Most laboratory setups employing a nickel filter for Cu radiation
choose 15–20 mm thick foils so as to attenuate Kβ by a factor of
25–50x more than Kα, and the overall Kα intensity by a factor of
about 2.
• At synchrotron sources, attenuators such as graphite, aluminium or
synthetic-diamond foils can be inserted into the primary beam path
to reduce the heat load on an optical element, to prevent saturation
of the x-ray detector, or to reduce the rate of radiation damage to
the sample.
Monochromators
• A monochromator is a large flat single crystal set to a particular
orientation, θm, in the beam that reflects by diffraction only those
wavelengths that satisfy the Bragg condition λ = 2d sinθm, where d
is the spacing between the chosen lattice planes.
5
• Typical crystals used include silicon, germanium, quartz, diamond
and graphite.
• For any material used as an x-ray monochromator the following
properties are desirable: forms large good quality crystal with an
appropriate interplanar distance; mechanically strong and
reasonably easy to cut; stable in the beam; large structure factor
for the chosen Bragg reflection; small coefficient of thermal
expansion; low absorption for x-rays.
• The actual choice of material also depends on the application, and
may take into account the thermal conductivity, degree of
crystalline perfection, intrinsic breadth of the Bragg reflection
(Darwin width), etc.
• In the laboratory, a monochromator may be placed in the incident
or the diffracted beam.
• Pre-sample monochromators such as quartz or Si 111 are highly
discriminating and can separate Cu Kα1 radiation from Kα2 (and
Kβ), though at the expense of overall intensity.
6
• Curving the crystal, which therefore must be thin, to focus the beam on
the sample or detector helps counteract this loss of intensity.
• Post sample monochromators, because of the motion of the detector
arm, are mechanically less stable, so a less-discriminating crystal such as
graphite is used.
• This can only remove Kβ, but has the additional advantage of reducing
any fluorescence from the sample.
• Monochromators for synchrotron-based diffractometers are used to
select the chosen wavelength from the polychromatic source.
• To preserve the direction of the incident beam, a double-crystal
(‘‘double-bounce’’) arrangement is used (following figure).
• This may be either a channel-cut crystal, or two independently-aligned
crystals.
• A common choice of crystal is Si because of its very high degree of
crystalline perfection, and its excellent thermal properties in the intense
synchrotron beam.
• The 111 reflection is a frequent choice, though 220 and 311 are also
used when higher energy resolution is desired.
• Cooling is essential to maintain a stable temperature for the crystal(s)
7
under the heat load from the source.
Figure: Schematic of a double bounce monochromator as
used at synchrotrons. The first crystal selects a wavelength
from the polychromatic source, which is reflected along the
initial direction by the second crystal. The lattice planes of the
latter must be perfectly aligned with the first crystal for
efficient transmission of the beam.
8
Mirrors
• Curved mirrors can be used to collimate or focus a divergent x-ray
beam.
• Still rather rare on laboratory instruments, graded-multilayer mirrors
may be used to produce a near-parallel incident beam, which may be
advantageous when working with non-flat or irregular samples or
with samples under non-ambient conditions.
• At synchrotrons, mirrors can be used to enhance further the
collimation of the already highly collimated beam.
• This can improve the angular and energy resolution of the instrument.
• Alternatively, the beam can be focused onto the sample if desired.
• A highly polished silicon substrate with a thin metal coating, such as
Pt or Rh, set at grazing incidence also provides a means to suppress
the high-energy X-rays in the beam.
• Thus a Rh-coated mirror set at an angle of 0.09o to the incident beam
will not transmit photons with a wavelength less than about 0.3A˚.
• Mirrors can sometimes have several stripes of different metal coatings
to allow adjustment of the upper-energy cut-off.
9
X-ray detectors
• X-ray detectors may be classified as point, linear or area, depending on
whether they record the diffraction pattern in zero, one or two spatial
dimensions.
• Point detectors must be scanned to measure the diffraction pattern,
whereas linear or area detectors can be fixed.
• Point detectors are easily compatible with post-sample optical elements.
• Linear and area detectors allow the data to be acquired much faster, but
as more open systems they are prone to detecting parasitic scatter from
the air or sample environment.
• Both linear and area detectors are types of position sensitive detector
(PSD).
Point detectors
• The most common type of detector in the laboratory is a scintillation
counter, which exploits a two-stage process.
• X-Ray photons collide with a phosphor screen (or scintillator) such as a
thallium-doped sodium iodide crystal.
• This emits photons in the blue region of the visible spectrum, which are
subsequently converted to voltage pulses by means of a photomultiplier
10
tube attached directly behind the scintillator.
• The number of electrons ejected by the photocathode is proportional to
the number of visible photons that strike it, which in turn is proportional
to the energy of the original X-ray photon.
• Owing to numerous losses, the energy resolution of the detector is poor,
and as such it cannot be used to resolve Kα and Kβ x-ray photons.
• However, it has high quantum efficiency and a low dead time, making it
the ideal detector for the point intensity measurements required for stepscanning diffractometers.
• For synchrotron applications, faster scintillators are often needed, and
materials such as doped YAP (yttrium aluminium perovskite) or LaCl3
are used as scintillators, though their light output per incident photon is
less.
• Solid-state detectors based on Si or Ge are used where better energy
discrimination is required, and avalanche-photodiodes can work at very
high count rates but have poor efficiency at high x-ray energies because
Si does not absorb such photons strongly.
11
Linear detectors
• Linear detectors may be straight or curved and record the 2θ
position of arrival of each x-ray photon.
• Linear PSDs may be broadly classified into single anode or multianode devices.
• Single anode devices have a wire or a blade in a gas-filled chamber
and work on the principle that x-ray photons can ionize inert gas
atoms such as argon or xenon into an electron (e-) and ion (e.g. Ar+)
pair.
• The ionization energy required to eject an outer electron is low (10–
20 eV) compared to the energy of the x-ray photon (8 keV for a Cu
x-ray tube) so that one x-ray photon can produce several hundred
ion pairs.
• The anode, which is a relatively poor conductor, is set to a potential of about
1000 V.
• The electrons of the ion pair accelerate towards the anode causing further
ionization and an enhanced signal by gas amplification.
• The burst of electrons on the wire is converted into a charge pulse which travels
to both ends of the anode.
12
• By comparing the relative arrival time of the pulse at both ends of
the wire or blade, the position of the detected x-ray photon is
obtained.
• Such ‘‘delay-line’’ detectors can measure only a single x-ray photon
at a time and so are relatively slow and lose their linearity at modest
count rates.
• To minimise the dead time of the system, a quenching gas such as
methane (CH4) is mixed with the inert gas (e.g. 90% Ar : 10%
CH4).
• For higher count rates, multi-wire or micro-strip anodes have been
developed in which each individual anode element is an
independent detector with a 2θ position fixed relative to the other
elements.
• Such a detector can process many events concurrently.
• PSDs record data over a whole range of scattering angles, which
can be useful where speed of acquisition is crucial, e.g. in timeresolved powder diffraction or thermodiffractometry.
13
• PSDs come in various shapes and sizes: small PSDs can only
collect data over a limited range, say, 5–10o 2θ; large PSDs are
usually curved and collect over a much wider range.
• Both types tend to have a similar number of channels of detection
(2n, n = 9–12) so that the 2θ channel width for the larger PSDs is
relatively coarse.
• PSDs can be used at a fixed scattering angle or may be scanned to
collect data over a wider angular range.
14
Area detectors
• Historically, area detectors in the form of photographic x-ray film were the
principle method for recording powder diffraction patterns, e.g. using Debye–
Scherrer and Guinier cameras.
• Modern area detectors for x-rays exploit image plate and charge-coupled device
(CCD) technology.
• These detectors accumulate an image of the diffraction pattern, which then has to
be read out and stored as a subsequent step.
• Typical read out times vary from 30s or more for image plates to 1s or less for
CCDs.
• Image plates are large area detectors and record the diffracted x-rays directly,
whereas CCD chips are small (e.g. 1ʺ x 1ʺ or 2ʺ x 2ʺ) and are coupled to a
phosphor screen with a bundle of optical fibres.
• Area detectors record part or even whole Debye–Scherrer powder diffraction
rings, enabling effects such as texture, granularity, and preferred orientation to be
observed directly in contrast to linear and point detectors.
• In addition, the large solid angle greatly increases the counting efficiency,
enabling data to be more easily recorded from weakly scattering samples.
• Data corrections to obtain quantitative intensities from 2D detectors requires
special handling.
15
Detector calibration
• In contrast to detectors used for point intensity measurements, position
sensitive detectors require careful calibration for both 2θ position and
efficiency so that scattering angles and intensities can be accurately
determined.
• For each channel an exact 2θ position is required together with an
efficiency coefficient.
• The efficiency can be determined using a sample such as an amorphous
foil that fluoresces in the x-ray beam (e.g. Fe in a beam of Cu Kα
radiation), producing a very high flat background and no Bragg peaks.
• The 2θ calibration is achieved by scanning the different parts of the
detector through the Bragg reflection of a strong peak (or peaks), e.g. the
Si 111 peak.
• For very large curved detectors, the 2θ calibration has to be made using
many diffraction peaks.
• The calibration can be checked by measuring the complete pattern of a
reference material.
• Sealed gas-filled PSDs should be recalibrated whenever the gas is
replenished, in contrast to detectors with a continuous flow of gas that
16
need checking regularly.
Measurements
Sample holders
• The choice of sample holder is governed by the choice of instrument geometry
used for the powder diffraction experiment, i.e. reflection or transmission.
• Following figure shows various sample holders for the flat-plate Bragg–
Brentano reflection geometry.
• Flat plate sample holders have one very big advantage over other sample
holders: they are easy to fill.
• Their biggest disadvantage is that the surface-flattening process induces a
preferred orientation in most samples.
• Other problems include: the sample can sometimes fall out especially if
spinning, with horizontal diffractometers when the sample is vertical, or for
vertical diffractometers at high θ angles; it is difficult to work with air-sensitive
samples; the holder is quite bulky and so less appropriate for work under nonambient conditions; peak positions from low-absorbing samples can suffer from
aberrations owing to significant penetration of the beam below the surface.
• For very tiny amounts of sample, e.g. for a forensic sample, flat-plate geometry
is in fact probably the method of choice, for the sample can be dusted over the
surface of a Si crystal, cut to avoid Bragg diffraction, and this gives near-zero
background.
• Block samples can also be mounted in a suitable, deep flat-plate holder.
4
Figure: Sample holders for flat plate Bragg Brentano geometry. All of the large (50mm Ø)
sample holders (A H) are for room temperature work, whilst the three smaller sample holders
(I K) are for high temperature furnace use. A and B are for stationary samples, A, F, and I are
for a light dusting of a powder on a low background silicon wafer, whereas H is for
smallquantities of sample in a shallow well silicon crystal. D is an example of a solid block
sample (e.g. solid quartz as used for diffractometer alignment work), while C is a deep well
sample holder, again for mounting solid objects. G is specially designed for back packing,
though even for front packing it is preferable to the plastic holders A and E. Sample holder J is
5
made of sapphire.
• For transmission geometry, either a cylindrical or thin flat foil sample holder is
required.
• The most common cylindrical sample holders are glass capillaries (following
figure).
• These come in various nominal sizes: 0.2, 0.3, 0.5, 0.7, 1.0, 1.5, and 2.0mm are
common internal diameter values, but other sizes are available.
• In the laboratory, the larger diameters are less useful for most powder diffraction
work because of sample absorption and decreased resolution, but are very
practical for use at synchrotrons given the parallel beam optics and the
availability of hard X-rays.
• Glass capillary sample holders should be flame, grease, or glue sealed to prevent
sample loss.
• They are ideal for low temperature powder diffraction studies as they are easy to
cool with liquid-N2 cold stream devices and are readily rotated in liquid-He
cryostats.
• Given their relatively low melting points, soda- or borosilicate-glass capillaries
are usually substituted by quartz-glass ones for high-temperature work.
• Capillaries are unpopular for several reasons: firstly, diffuse X-ray scattering
from the glass walls, which are approximately 10 mm thick, adds significantly to
the background count.
• Secondly, they take considerably longer to fill than the equivalent flat-plate
6
sample holder.
Figure: Photograph of a 1mmdiameter thin walled (10 mm thick)
borosilicate glass capillary, glued with melted wax into a brass holder
for clamping to a spinner. The sample is a white organic compound,
but exposure to an intense X ray beam turns it yellow. This sample was
translated between successive data collection scans to avoid radiation
damage, resulting in the striped appearance.
7
• Thirdly, capillaries may require careful alignment on the
diffractometer to ensure that the axis of the capillary is co-linear
with that of the diffractometer.
• Fourthly, for highly-absorbing samples either fine capillaries have
to be used or the sample has to be diluted, and, additionally, an
absorption correction should be employed when the data are used
for crystal structure refinement.
• After all these disadvantages, you might wonder why capillaries
are used at all.
• The huge advantage of capillary geometry is that preferred
orientation is much less of a problem, although it may still occur,
e.g. needle-shaped crystallites may align horizontally-rotated
capillaries.
• Capillaries are also a convenient way of mounting very air-sensitive
samples since they are easily sealed against exposure to the air.
• An alternative to the capillary is the use of a thin glass fibre, or even an
empty capillary, thinly coated in silicone grease and then covered by a
fine coating of powder.
8
• This latter may be better for highly absorbing samples.
• An alternative method for measuring powder samples in
transmission geometry is to use a very thin and flat sample.
• This can be achieved by sprinkling the powder onto an adhesive
tape, or by trapping the sample between two layers of a thin (say 3
μm or thinner) polymer film.
• Various polymers including Mylar and Kapton have been used,
some of which are better than others: the choice of material is a
compromise between obtaining a low background count and a
peak-free background count.
9
Standard samples
• It is essential to know that the diffractometer produces data that are reliable and
are not affected by systematic and or other, undiscovered errors.
• Data reliability can be considerably enhanced by pre-checking the diffractometer
with a known standard sample.
• It is good laboratory practice to do this regularly, and essential when the
instrument has been realigned or reconfigured.
• A standard sample can usually be measured relatively quickly and will provide
information on instrument calibration, alignment, resolution, background count,
source flux, spurious scattering from sample environment equipment (if any) and
so on.
• Even when assured by the person responsible for the instrument that everything
is well, a few minutes with a standard sample can avoid many months of wasted
effort later.
• A good calibrant for a powder diffractometer should be a material of high
symmetry because the intensity of the diffraction planes is concentrated into
relatively few diffraction peaks.
• The unit-cell volume, V, should be small since the intensity of the diffraction
peaks is inversely proportional to V.
• Ideally, the unit cell should contain only 1 or perhaps 2 crystallographic atoms
with large scattering factors.
10
• The thermal vibrations of the atom (or atoms) characterized by its
B value should be as small as possible so that the high-angle peaks
have maximum intensity.
• For capillary geometry the sample absorption should not be too
high since this can affect, in extreme cases, the position of the
powder lines in addition to reducing their intensity.
• It must also be possible to obtain large quantities of the material in
high purity and crystallinity together with reproducible crystallite
size.
• Obviously, the materials must be air stable and preferably nontoxic.
• Typical standards are powdered Si, LaB6, Ni, ZnO, TiO2, CeO2,
Al2O3, Cr2O3, and Y2O3.
• These samples can be used as calibrants for both X-ray and neutron
powder diffraction.
• All the materials listed above as standards have rigid-lattice
structures due to strong chemical bonding with highly charged
cations and anions.
11
• Note that a simple material such as NaCl does not make a good
standard because it is hygroscopic and the Na+ and Cl- ions have
large thermal parameters due to their single charge.
• The National Institute of Standards and Technology (NIST)
supplies standard calibrating materials for many applications.
• A standard may be excellent for one purpose (e.g. wavelength
calibration) and less useful for another (e.g. determination of
instrumental resolution) so choose a standard appropriate for the
task in-hand.
• The best samples to check the performance of the diffractometer at
low angles are layer-like: mica is one such material supplied by
NIST, or silver behenate, which has a layer spacing of 58.38A˚ .
Silver behenate is a silver salt of the long-chain fatty
acid behenic acid.
12
Data acquisition
• Before collecting a powder pattern, it is a good idea to know what
information you hope to get out of it, for this will influence the data
collection strategy.
• Parameters to be considered include angular range, step size,
counting time, statistical quality, wavelength, etc.
• For example, phase identification generally requires only a range of
2θ containing the strongest reflections from the sample, whereas
meaningful Rietveld refinement of a crystal structure requires high
quality data measured to small d.
• Variable count time strategies can improve enormously the
statistical quality of the high-angle data, to compensate for the
reduction in scattered intensity with geometric and X-ray form
factors, thermal motion, etc.
• Studies of a material’s microstructure need precise measurement of
the shape of the diffraction peaks, so a fine step size is desirable,
along with measurement of an appropriate standard, and possibly
higher-order reflections.
13
• Absorption or the presence of absorption edges will influence the
choice of wavelength.
• There are many factors to be considered for optimum data, and
some forethought and planning will make the difference between a
successful investigation, and a waste of effort, as it is not usually
worth struggling to analyse data that is not fit for the purpose.
• Despite one’s best efforts, carefully collected data may still suffer
from systematic sample errors, such as preferred orientation,
granularity, texture, inhomogeneity, impurity phases, radiation
damage (especially at the synchrotron) unexpected sensitivity to air
or moisture.
• Measuring the very-same sample again can detect sample evolution
during the measurement.
• Measuring with a different instrumental geometry can reveal some of the
other effects.
• A critical assessment of the data quality and the data-collection strategy
after the experiment is to be encouraged.
• In some cases, a new experiment with a revised strategy may be the
14
optimum course.
Many sources of error are associated with the focusing circle of
the Bragg-Brentano parafocusing geometry
• The Bragg-Brentano parafocusing geometry is used so that the
divergent X-ray beam reconverges at the focal point of the detector.
• This produces a sharp, welldefined diffraction peak in the data.
• If the source, detector, and sample are not all on the focusing
circle, errors will appear in the data.
• The use of parallel-beam optics eliminates all sources of error
associated with the focusing circle.
16
Sample displacement error
• When the sample is not on the focusing circle, the X-ray beam does not
converge at the correct position for the detector.
• The observed peak position is incorrect.
• This is the greatest source of error in most data
• This is a systematic error:
– s is the amount of displacement, R is the goniometer radius.
– at 28.4° 2theta, s = 0.006ʺ will result in a peak shift of 0.08°
• Ways to compensate for sample displacement:
– This is most commonly analyzed and compensated for using data
analysis algorithms
– For sample ID, simply remember that your peak positions may be
shifted a little bit
– Historically, the internal calibration standard was required for
publication quality data
• The computer algorithms for calculating the displacement error
are now much better
– Can be minimized by using a zero background sample holder
17
– Can be eliminated by using parallel-beam optics
18
Sample transparency error
• X Rays penetrate into your sample:
– Depth of penetration depends on:
• The mass absorption coefficient of your sample
• the incident angle of the X-ray beam
• This produces errors because not all X-rays are diffracting from the
same location in your sample:
– Produces peak position errors and peak asymmetry
– Greatest for organic and low absorbing (low atomic number)
samples
• Can be eliminated by using parallel-beam optics
• Can be reduced by using a thin sample
19
20
Other sources of error
• Flat specimen error:
– The entire surface of a flat specimen cannot lie on the focusing
circle
– Creates asymmetric broadening toward low 2theta angles
– Reduced by using small divergence slits, which produce a
shorter beam
• For this reason, if you need to increase intensity it is better
to make the beam wider rather than longer.
– Eliminated by parallel-beam optics
• Poor counting statistics
– The sample is not made up of thousands of randomly oriented
crystallites, as assumed by most analysis techniques
– The sample might have large grain sizes
• Produces ‘random’ peak intensities and/or spotty diffraction
peaks
21
22
Axial divergence
• Axial divergence
– Due to divergence of the X-ray beam in plane with the sample
– Creates asymmetric broadening of the peak toward low 2theta
angles
– Creates peak shift: negative below 90°2theta and positive
above 90°
– Reduced by Soller slits and/or capillary lenses
23
Rietveld method/analysis [Rietveld Structure Refinement]
(A Brief Introduction to Rietveld Analysis of XRD Patterns)
• Structure refinement is an essential part of practical crystallography
and must be distinguished from structure solution.
• Refinement as the name suggests implies taking an approximate
model of the structure and refining it so that diffraction data
calculated from the model structure has a closer resemblance to the
observed (i.e. measured) data.
• It cannot be emphasized strongly enough that it is the model
structure that is refined and not the data: it is not uncommon to hear
people (some senior academics included) who talk about refinement
of their powder diffraction data; worse still they even say it in
writing!!!
• The process of refinement does not solve structures.
• The majority of crystallographers treat the process of refinement as a
"black box" process as summarized in the flow diagram below
where measured data and model are used for input and refined
crystal structure (when things work smoothly) results as output.
6
Model Structure
+
Diffraction Data
→
"Black
Box"
→
Refined Crystal Structure
• Although several programs exist for the refinement of crystal structures
from diffraction data, the basic concepts behind all of them generally
remain the same.
• Thus the simple and highly-developed small-molecule single-crystal
refinement programs have much in common with the more complex
protein single-crystal and Rietveld powder refinement packages.
• The common theme throughout these programs is that they all use a
least-squares procedure to refine the initial structure model in order to
improve the agreement between the observed diffraction data and that
calculated from the model.
• An understanding of how the various programs work is valuable on
those occasions when the least-squares refinement program goes astray.
• This is particularly true today, since the improvements in
crystallographic software now enable the non-specialist crystallographer
to both solve and refine many crystal structures in a semi-automatic
7
fashion.
• In 1969 Rietveld wrote a revolutionary paper in which he discarded
the then conventional approach of analyzing a powder diffraction
pattern primarily in terms of diffraction events (or diffraction
peaks as they are termed), and instead analyzed the whole pattern
simultaneously in which many relevant factors were taken into
account regardless of whether they involved the atomic structure of
the specimen.
• In so doing this helped to overcome one of the principal problems
in powder diffraction (the congested diffraction peaks in the
pattern).
• Today the method is almost indispensable in structure analysis from
powder diffraction data, and see below example of a Rietveld
plot and the refined structure of a high-temperature super conductor
which it produced.
8
• The Rietveld method is used to refine the crystal structure model
of a material.
• It can be used for quantitative phase ID, lattice parameter and
crystallite size calculations, and determine atom positions and
9
occupancies.
• Whole Pattern Fitting Structure Refinement is now widely accepted
to be an exceptionally valuable method for structural analysis of
nearly all classes of crystalline materials not available as single
crystals.
• Rietveld refinement is a technique devised by Hugo Rietveld for
use in the characterization of crystalline materials.
• Rietveld refinement is a programmer to treat the data for the
removal of overlapped scatterings but as a result very low number
of intensities appear.
• Powdered sample is used.
• Many crystals (polycrystalline in nature), a large numbers of
lattices present.
• A large number of overlapped intensities of the rays observed.
• The information about the spatial distribution of reflections lost and
only the single dimension of the scattering angle remain and as a
result it become difficult to determine the unit cell.
10
• The neutron and x-ray diffraction of powder samples results in a
pattern characterized by reflections (peaks in intensity) at certain
positions.
• The height, width and position of these reflections can be used to
determine many aspects of the material's structure.
• This software approach refines various metrics (‫ )پيمائش ﮐﮯ معيار‬including lattice parameters, peak width and shape, and preferred
orientation - to derive a calculated diffraction pattern.
• Once the derived pattern is nearly identical to an unknown sample
data, various properties pertaining (‫ )سروﮐار رﮐهنا‬to that sample can
be obtained including:
– Accurate quantitative information
– Crystallite size
– Site occupancy factors
• The process of refining the pattern is computationally intensive,
requiring several minutes to calculate results for a multi-component
mixture.
11
• Rietveld Analysis has the advantage, over conventional quantitative
methods, that no standards are required to achieve accurate results
to within ±1%.
• Before this advance, an accurate and standardless quantitative phase
analysis of complex materials using powder diffraction was almost
impossible.
The Rietveld method refines user-selected parameters to
minimize the difference between an experimental pattern
(observed data) and a model based on the hypothesized crystal
structure and instrumental parameters (calculated pattern)
12
Difficulties with powder diffraction
• Systematic overlapping of diffraction peaks due to symmetry
conditions, for example in cubic space groups
• Accidental overlapping because of limited experimental resolution
• Considerable background difficult to define with accuracy
• Non-random distribution of the crystallites in the specimen,
generally known as preferred orientation.
What is Rietveld analysis?
• The Rietveld method refines user-selected parameters to minimize
the difference between an experimental pattern (observed data)
and a model based on the hypothesized crystal structure and
instrumental parameters (calculated pattern)
• Full profile fitting
• Using crystallographic constraints
– Lattice parameters and space group to constrain peak positions
– Crystal structure to constrain peak intensities
13
What Rietveld can do?
• Analysis of the whole diffraction pattern:
– Profile fitting is included
– Not only the integrated intensities
• Refinement of the structure parameters from diffraction data:
– Quantitative phase analysis (crystalline and amorphous)
– Lattice parameters
– Atomic positions and occupancies
– Temperature vibrations (isotropic and anisotropic)
• Other information:
– Grain size and micro micro-strain (isotropic and anisotropic)
– Stacking and twin faults
– Magnetic moments (neutrons)
• Not intended for the structure solution
– The structure model must be known before starting the Rietveld
refinement
14
Why the Rietveld refinement is widely used?
• It uses directly the measured intensities points
• It uses the entire spectrum (as wide as possible)
• Less sensible to model errors
• Less sensible to experimental errors
• It requires a model
• It needs a wide spectrum
• Rietveld programs are not easy to use
• Rietveld refinements require some experience (1-2 years?)
• Can be enhanced by:
– More automatic/expert mode of operation
– Better easy to use programs
15
Requirements of Rietveld method
• High quality experimental diffraction pattern
• A structure model that makes physical and chemical sense
• Suitable peak and background functions
16
Rietveld procedure
• Experiment:
– Choose the correct instrument/s
– Select the experiment conditions
– Prepare the sample and collect the pattern/s
• Analysis:
– Verify the data quality and perform the qualitative analysis
• Rietveld refinement:
– Choose appropriate program (GSAS, FullProf or MAUD)
– Load or input the phases in the sample
– Adjust manually some parameters (cell, intensities, background)
– Refine overall intensities and background
– Refine peaks positions
– Refine peaks shapes
Example
– Refine structures
• Defining the phases
– Assess the results
• Adjusting manually: cell parameters, intensities
•
•
•
•
Refining scale factors and background
Peaks positions
Peaks shapes
Crystal structure refinement
17
Rietveld method is used for refinement of crystal
structures, Justify.
What does this mean?
• Crystal structure considered known when atom positions known
very precisely.
• X-ray diffraction data used for structure determination:
– Reflection positions → cell size, space group symmetry
– Intensities → atom positions
• Thus precise lattice parameters and precise atom positions
determined in two separate steps:
– Initial values of atom positions obtained during structure
analysis rarely the most precise values and closest to truth
– Values must be refined:
• Use least squares procedure to make small adjustments in
atom positions
18
Previously
• Determine areas under all
observed Bragg peaks
• Use these intensities to
get model for structure
• Refine model on basis of
reflection intensities
• Mostly single crystal
intensities used, but same
procedure
used
for
“powder” patterns
19
• Problems with respect to powder patterns:
– Loss of information
• Peak shape, width, tails
20
Background removal
↓
?
21
Peak overlap problems
22
Rietveld refinement procedure
• First select the appropriate Rietveld program; depending on what
you need to analyze there could be a best solution.
• Several choices at ccp14.ac.uk (free programs):
– GSAS (General Structure Analysis System): Most used; very
good for crystal structure refinement and TOF neutron; not
easy to use but there is a lot of knowledge around. A friendly
graphical interface available with Expgui.
– FullProf: Best for magnetic materials; good for crystal
structure refinements; no graphical interface (in preparation).
– MAUD: For material scientists; good for quantitative phase
analysis, size-strain and texture. Best in the case of
texture/strain problems. Come with a graphical user interface.
– Rietan, Arit, Brass, DBWS, XRS-82, Topas-academic, XND
etc.
• Some commercial ones:
– BGMN, Topas etc.
23
Quality of the experiment
• A good diffraction fitting, a successful Rietveld analysis, they
depend strongly on the quality of the experiment:
• Instrument
– Instrument characteristics and assessment
– Choice of instrument options
• Collection strategies
– Range
– Step size
– Collection time etc.
• Sample
– Sample size
– Sample preparation
– Sample condition
24
Instrument
• Rietveld analyses do not require at all the most powerful
instrument but the one suitable for the analysis:
– Quantitative analyses of samples with big grain sizes (metal?,
high crystal symmetries) require a diffracting volume of
statistical significance → large sampling volume, large beam,
with not too low divergence → a medium to low resolution
diffractometer.
– Structural refinements of low symmetries compounds
(monoclinic, triclinic) require often a high resolution
diffractometer
• A low and linear background is the first requirement
• No additional lines (beta lines) are also in general preferred
• Large collectable ranges are important
• High diffraction intensities should be achieved
• Smaller peak broadening help the analysis reducing overlaps
• Simple geometries are better for subsequent Rietveld fitting
• There is not the perfect instrument to get everything
25
A good overall instrument
• For quantitative analysis:
– Medium resolution
– Monochromator on the diffracted beam
– Cu radiation ?
• Structural refinements or structure determination
– High resolution (and high intensities → very long collection
times)
– Monochromator
– No Kα2 (Structure determination)
• Microstructural analyses
– High resolution
• Texture and residual stress analyses
– Medium to low resolution
– Fast collection times
– Extremely good statistic
26
Instrument assessment
• In most cases (or always) the instrument alignment and setting is
more important than the instrument itself
• Be paranoid on alignment, the beam should pass through the
unique rotation center and hits the detector at zero 2θ
• The background should be linear, no strange bumps, no
additional lines and as low as possible
• Check the omega zero
• Collect regularly a standard for line positions and check if the
positions are good both at low and high diffraction angle (check
also the rest)
27
Data collection (Range)
• The range should always the widest possible compatible with
the instrument and collection time (no need to waste time if no
reliable informations are coming from a certain range)
28
Step size
• The step size should be compatible with the line broadening
characteristics and type of analysis.
• In general 5-7 points in the half upper part of a peak are sufficient
to define its shape.
• Slightly more points are preferred in case of severe overlapping.
• A little more for size-strain analysis.
• Too much points (too small step size) do not increase our
resolution, accuracy or precision, but just increase the noise at
equal total collection time.
• The best solution is to use the higher step size possible that do not
compromise the information we need.
• Normally highly broadened peaks → big step size → less noise as
we can increase the collection time per step (> 0.05)
• Very sharp peaks → small step size (from 0.02 to 0.05 for BraggBrentano)
29
Total collection time
• Ensure the noise is lower than the intensity of small peaks.
• If the total collection time is limited, better a lower noise than a
smaller step size.
• Better to collect a little bit more than to have to repeat an
experiment.
• If collection time is a problem go for line or 2D detectors:
– CPS 120: 2 to 5 minutes for a good spectrum of 120 degrees
(good for quantitative analyses or follow reactions,
transformations, analyses in temperature)
– Image plate or CCDs: very fast collection times when texture
is needed or is a problem
• Data quality (not related to intensity) of these detectors is a little
bit lower than the one from good point detectors. But sometimes
intensity rules!
30
Sample characteristics
• The sample should be sufficiently large that the beam will be
entirely inside its volume/surface (always)
• Sample position is critical for good cell parameters (along with
perfect alignment of the instrument)
• The number of diffracting grains at each position should be
significant (> 1000 grains). Remember that only a fraction is in
condition for the diffraction. Higher beam divergence or size
increases this number. So the sample should have millions grains in
the diffracting volume.
• Unless a texture analysis is the goal, no preferred orientations
should be present. Change sample preparation if necessary.
• The sample should be homogeneous.
• Be aware of absorption contrast problems
• In Bragg-Brentano geometry the thickness should be infinite respect
to the absorption.
• Quality of the surface matters.
31
Ambient conditions
• In some cases constant ambient condition are important:
– Temperature for cell parameter determination or phase
transitions
– Humidity for some organic compounds or pharmaceuticals
– Can your sample be damaged or modify by irradiation
(normally Copper or not too highly energetic radiations are not)
• There are special attachments to control the ambient for sensitive
compounds
32
Non-classical Rietveld applications
• Along with the refinement of crystal structures the concept of the
Rietveld method has been extended to other diffraction analyses.
• Most of them more useful for people working on material science.
• These are:
– Quantitative phase analyses
– Amorphous quantification
– Microstructural analyses
– Texture and Residual stresses
33
Possible cautions (Expert tricks/suggestion)
• First get a good experiment/spectrum
• Know your sample as much as possible
• Do not refine too many parameters
• Always try first to manually fit the spectrum as much as possible
• Never stop at the first result
• Look carefully and constantly to the visual fit/plot and residuals
during refinement process (no “blind” refinement)
• Zoom in the plot and look at the residuals. Try to understand what
is causing a bad fit.
• Do not plot absolute intensities; plot at iso-statistical errors. Small
peaks are important like big peaks.
• Use all the indices and check parameter errors.
34
Where to get crystal structures
• Publications
• Commercial Databases
– Inorganic Crystal Structure Database (ICSD)
– Linus Pauling File (LPF)
• This is included in ICDD PDF4 + Inorganic
– NIST Structural Database (metals, alloys, intermetallics)
– CCDC Cambridge Structure Database (CSD) (organic materials)
• Free Online Databases
– ICSD- 4% available as demo at:
• http://icsd.ill.eu/icsd/index.html
– Crystallography Open Database:
• http://www.crystallography.net/
– Mincryst:
• http://database.iem.ac.ru/mincryst/index.php
– American Mineralogist:
• http://www.minsocam.org/MSA/Crystal_Database.html
– WebMineral:
• http://www.webmineral.com/
– Protein Data Bank:
• http://www.rcsb.org/pdb/home/home.do
– Nucleic Acid Database:
• http://ndbserver.rutgers.edu/
– Database of Zeolite Structures:
• http://www.iza-structure.org/databases/
35
Best way to do Rietveld Refinement
using FullProf software
36
Links:
https://www.youtube.com/watch?v=mnxd5ACqR9E
https://www.youtube.com/watch?v=OOHB2lXU1J0
37
Rietveld refinement:
–The simplest way to refine
XRD results using MAUD
40
Link:
https://www.youtube.com/watch?v=8ErThaqgD-A
41
Finally: What is
Physically Meaningful?
Wel (1975)
43
An X-ray powder diffraction pattern is a plot of the intensity of X-rays scattered
at different angles by a sample
• The detector moves in a circle around the sample:
– The detector position is recorded as the angle 2theta (2θ)
– The detector records the number of X-rays observed at each angle 2θ
– The X-ray intensity is usually recorded as “counts” or as “counts per second”
• Many powder diffractometers use the Bragg-Brentano parafocusing geometry
• To keep the X-ray beam properly focused, the incident angle omega changes in
conjunction with 2theta
• This can be accomplished by rotating the sample or by rotating the X-ray tube.
4
Assignment
Question: The powder diffraction pattern as a “fingerprint”. The
powder diffractogram of a compound is its ‘fingerprint’ and
can be used to identify the compound, Justify
?????
Ans: See "Example Using powder X-ray diffraction".
Rutile
• Rutile is a mineral composed primarily of titanium dioxide, TiO2.
• Rutile is the most common natural form of TiO2.
Anatase
• Anatase is a polymorph with two other minerals, the other two being
brookite and rutile.
• The minerals rutile and brookite as well as anatase all have the same
chemistry, TiO2, but they have different structures.
Brookite
• Brookite is one of the three main forms of titanium dioxide.
• It forms distinct and unique crystals, and is often associated with the two
other minerals it is polymorphous with rutile and anatase.
• Brookite almost always forms together with quartz and is occasionally
6
entirely included within a quartz crystal.
Example
Using powder X-ray diffraction
• Titanium dioxide exists as several polymorphs, the most
common of which are anatase, rutile, and brookite.
• The experimental diffraction angles for the six strongest
reflections collected from each of these different
polymorphs are summarized in the table.
• The powder X-ray diffraction
pattern collected using 154 pm
X-radiation from a sample of
white paint, known to contain
TiO2 in one or more of these
polymorphic forms, showed
the diffraction pattern in
following figure.
• Identify the TiO2 polymorphs
present.
7
Answer
• We need to identify the polymorph that has a
diffraction pattern that matches the one observed.
• The lines closely match those of rutile (strongest
reflections) and anatase (a few weak reflections), so
the paint contains these phases with rutile as the
major TiO2 phase.
8
Figure: A powder diffraction pattern obtained from a
mixture of TiO2 polymorphs.
9
Other Examples:
Each “phase” produces a unique diffraction pattern
Quartz
Cristobalite
Glass
15
20
25
30
35
Position [°2Theta] (Cu K-alpha)
• A phase is a specific chemistry and
atomic arrangement.
• Quartz, cristobalite, and glass are all
different phases of SiO2
– They are chemically identical, but
the atoms are arranged differently.
– As shown, the X-ray diffraction
pattern is distinct for each
different phase.
– Amorphous materials, like glass,
do not produce sharp diffraction
40
peaks.
The X-ray diffraction pattern is a fingerprint that lets you figure out
10
sample.
Example (In case of mixture):
The diffraction pattern of a mixture is a simple sum of the
diffraction patterns of each individual phase
Quartz
Mixture
Cristobalite
Glass
0
15
20
25
30
35
Position [°2Theta] (Cu K-alpha)
40
15
20
25
30
35
Position [°2Theta] (Copper (Cu))
• From the XRD pattern you can determine:
– What crystalline phases are in a mixture
– How much of each crystalline phase is in the mixture
– If any amorphous material is present in the mixture
40
X-rays scatter from atoms in a material and therefore contain information
about the atomic arrangement
• The three X-ray scattering patterns below were produced by three chemically
identical forms SiO2
• Crystalline materials like Quartz and Cristobalite produce X-ray diffraction
patterns:
– Quartz and Cristobalite have two different crystal structures
– The Si and O atoms are arranged differently, but both have long-range
atomic order
– The difference in their crystal structure is reflected in their different
diffraction patterns
• The amorphous glass does not have long-range atomic order and therefore
produces only broad scattering features
12
Diffraction occurs when light is scattered by a periodic array with longrange order, producing constructive interference at specific angles
• The electrons in each atom coherently scatter light:
– We can regard each atom as a coherent point scatterer
– The strength with which an atom scatters light is proportional to the number of
electrons around the atom.
• The atoms in a crystal are arranged in a periodic array with long-range
order and thus can produce diffraction.
• The wavelength of X rays are similar to the distance between atoms in a
crystal.
• Therefore, we use X-ray scattering to study atomic structure.
The scattering of X-rays from atoms produces a diffraction pattern,
which contains information about the atomic arrangement within the
crystal
• Amorphous materials like glass do not have a periodic array with longrange order, so they do not produce a diffraction pattern. Their X-ray
scattering pattern features broad, poorly defined amorphous ‘humps’.
13
Crystalline materials are characterized by the long-range orderly periodic
arrangements of atoms
• The unit cell is the basic repeating unit that defines the crystal structure:
– The unit cell contains the symmetry elements required to uniquely define the
crystal structure.
– The unit cell might contain more than one molecule:
• For example, the quartz unit cell contains 3 complete molecules of SiO2.
– The crystal system describes the shape of the unit cell
– The lattice parameters describe the size of the unit cell
• The unit cell repeats in all dimensions to fill space and produce the macroscopic
grains or crystals of the material
14
The diffraction pattern is a product of the unique crystal
structure of a material
• The crystal structure describes the atomic arrangement of a material.
• The crystal structure determines the position and intensity of the diffraction
peaks in an X-ray scattering pattern.
– Interatomic distances determine the positions of the diffraction peaks.
– The atom types and positions determine the diffraction peak intensities.
• Diffraction peak widths and shapes are mostly a function of instrument and
microstructural parameters.
15
Diffraction pattern calculations treat a crystal as a collection of
planes of atoms
• Each diffraction peak is attributed to the scattering from a specific set
of parallel planes of atoms.
• Miller indices (hkl) are used to identify the different planes of atoms
• Observed diffraction peaks can be related to planes of atoms to assist
in analyzing the atomic structure and microstructure of a sample
16
Significance of peak shape in XRD
– Peak position
– Peak width
– Peak intensity
• Peak positions → determined by size and shape of unit
cell (d-spacings and systematic absences)
• Peak intensities → determined by the atomic number and
position of the various atoms within the unit cell
• Peak widths → determined by instrument parameters,
temperature, and crystal size, strain, and inhomogeneities
19
Sample collection and preparation
• Determination of an unknown requires: the material, an instrument
for grinding, and a sample holder.
– Obtain a few tenths of a gram (or more) of the material, as pure
as possible
– Grind the sample to a fine powder, typically in a fluid to
minimize inducing extra strain (surface energy) that can offset
peak positions, and to randomize orientation.
• Powder less than ~10 μm (or 200-mesh) in size is preferred
– Place into a sample holder or onto the sample surface:
• smear uniformly onto a glass slide, assuring a flat upper
surface
• pack into a sample container
• sprinkle on double sticky tape
• Typically the substrate is amorphous to avoid interference
– Care must be taken to create a flat upper surface and to achieve
a random distribution of lattice orientations unless creating an
oriented smear.
22
– For analysis of clays which require a single orientation,
specialized techniques for preparation of clay samples are given
by USGS.
• For unit cell determinations, a small amount of a standard with
known peak positions (that do not interfere with the sample) can be
added and used to correct peak positions.
23
Powder preparation
(Preparing a powder specimen)
• It needs to be a powder
• It needs to be a pure powder
• Its nice to have about 1/2 g of sample, but one can work
with less
• The powder needs to be packed tightly in the sample
holder.
24
• An ideal powder sample should have many crystallites in
random orientations
– The distribution of orientations should be smooth and
equally distributed amongst all orientations
• If the crystallites in a sample are very large, there will not
be a smooth distribution of crystal orientations.
• You will not get a powder average diffraction pattern.
– Crystallites should be <10mm in size to get good
powder statistics
• Large crystallite sizes and non-random crystallite
orientations both lead to peak intensity variation
– The measured diffraction pattern will not agree with
that expected from an ideal powder
– The measured diffraction pattern will not agree with
reference patterns in the Powder Diffraction File (PDF)
25
database
• Powders:
0.1 μm
<
Peak broadening
particle size
<
40 μm
less diffraction occurring
• Bulks:
– Smooth surface after polishing, specimens should be
thermal annealed to eliminate any surface deformation
induced during polishing.
Preventative measure
• Lose powders will give poor intensities
26
27
Fill the powder into the well
Ready for XRD measurement
Remove the excess powder
Align the samples surface plane
Figure: Powder sample preparation on a aluminium holder.
28
What is annealing
• Annealing, in metallurgy and materials science, is a heat
treatment that alters the physical and sometimes chemical
properties of a material to increase its ductility and reduce
its hardness, making it more workable.
• It involves heating a material to above its recrystallization
temperature, maintaining a suitable temperature, and then
cooling.
• In annealing, atoms migrate in the crystal lattice and the
number of dislocations decreases, leading to the change in
ductility and hardness.
29
Factors that Affect X-Ray Spectra
30
Link:
https://www.youtube.com/watch?v=QQ2IbjOmir8
31
Assignments
Q: On which the number and positions of the reflections
depend in PXRD?
Ans: The number and positions of the reflections depend on:
Cell parameters
Crystal system
Lattice type
Wavelength
used to collect the data.
Q: On which the peak intensities depend in PXRD?
Ans: The peak intensities depend on the types of atoms
present and their positions.
33
Assignment
Q: What will be the particle size of powder in PXRD for
broadening of peak?
Ans: The particle size of powder will be 0.1 μm.
Q: What are optical components in X-ray beam path?
Explain.
Ans: See in detail “optical components in X-ray beam path”
34
Demonstration
of
X-Ray Diffraction
4
Link:
https://www.youtube.com/watch?v=UPS5OK7lr0U
5
X-Ray Diffraction
7
Link:
https://www.youtube.com/watch?v=lwV5WCBh9a0
8
Instrumentation
• X-ray source:
• Crooke’s tube (cold cathode tube)
• Coolidge tube (hot cathode tube)
• Collimator
Note
• Monochromator
In phase → constructive interference
• Filter type
Out of phase → destructive interference
• Crystal type
• Detectors:
• Photographic methods
• Counter methods:
• Geiger-muller counter
Coolidge X-ray tube, from around 1917. The heated
• Proportional counter
cathode is on the left, and the anode is right. The Xrays are emitted downwards.
• Scintillation counter
• Solid-state semi-conductor detector
• Semi conductor detectors
12
X-ray source
X-ray tube
• An X-ray tube is a vacuum tube that converts electrical input power
into X-rays.
• X-ray tubes evolved from experimental Crookes tubes with which
X-rays were first discovered on November 8, 1895, by the German
physicist Wilhelm Conrad Röntgen.
• The availability of this controllable source of X-rays created the
field of radiography, the imaging of partly opaque objects with
penetrating radiation.
• In contrast to other sources of ionizing radiation, X-rays are only
produced as long as the X-ray tube is energized.
• X-ray tubes are also used in computerized tomography (CT)
scanners, airport luggage scanners, X-ray crystallography, material
and structure analysis, and for industrial inspection.
• Increasing
demand
for
high-performance
Computed
tomography (CT) scanning and angiography systems has driven
development of very high performance medical X-ray tubes.
13
Figure: The principle of an X-ray tube.
14
Crookes tube (cold cathode tube)
History
• A Crookes tube is an early experimental electrical discharge tube,
with vacuum, invented by English physicist William Crookes and
others around 1869-1875, in which cathode rays, streams of
electrons, were discovered.
• Wilhelm Röntgen discovered X-rays using the Crookes tube in
1895.
• The term Crookes tube is also used for the first generation, cold
cathode X-ray tubes, which evolved from the experimental Crookes
tubes and were used until about 1920.
• Until the late 1980s, X-ray generators were merely high-voltage,
AC to DC variable power supplies.
• In the late 1980s a different method of control was emerging, called
high speed switching.
• This followed the electronics technology of switching power
supplies, and allowed for more accurate control of the X-ray unit,
higher quality results, and reduced X-ray exposures.
15
Figure: Crookes X-ray tube from
around 1910.
Crookes X-ray tube from early 1900s. The
cathode is on the right, the anode is in the
center with attached heat sink at left. The
electrode at the 10 o'clock position is the
anticathode. The device at top is a 'softener'
used to regulate the gas pressure.
Sir William Crookes
Wilhelm Röntgen
16
• Wilhelm Conrad Röntgen
discovered 1895 the X-rays.
• 1901 he was honoured by the
Noble prize for physics.
• In 1995 the German Post
edited a stamp, dedicated to
W.C. Röntgen.
17
How a Crookes tube works
General
• Called as cold cathode tube.
• Electrons are generated by ionization of the residual air in the tube, instead of
heated filament so they were partially but not completely evacuated.
• They consisted of a glass bulb with around 10−6 to 5×10−8 atmospheric
pressure of air (0.1 to 0.005 Pa).
• An aluminum cathode plate at one end of the tube created a beam of electrons,
which struck a platinum anode target at the center generating X-rays.
• The anode surface was angled so that the X-rays would radiate through the side of
the tube.
• The cathode was concave so that the electrons were focused on a small (~1 mm)
spot on the anode, approximating a point source of X-rays, which resulted in
sharper images.
• The tube had a third electrode, an anticathode connected to the anode.
• It improved the X-ray output, but the method by which it achieved this is not
understood.
• A more common arrangement used a copper plate anticathode (similar in
construction to the cathode) in line with the anode such that the anode was
between the cathode and the anticathode.
18
Operation
• When the voltage applied to a Crookes tube is high enough, around 5,000 volts or
greater, it can accelerate the electrons to a fast enough velocity to create X-rays
when they hit the anode or the glass wall of the tube.
• The fast electrons emit X-rays when their path is bent sharply as they pass near
the high electric charge of an atom's nucleus, a process called bremsstrahlung, or
they knock an atom's inner electrons into a higher energy level, and these in turn
emit X-rays as they return to their former energy level, a process called X-ray
fluorescence.
• Crookes tubes were unreliable.
• As time passed, the residual air would be absorbed by the walls of the tube,
reducing the pressure.
• This increased the voltage across the tube, generating 'harder' X-rays, until
eventually the tube stopped working.
• To prevent this, 'softener' devices were used (see above diagram).
• A small tube attached to the side of the main tube contained a mica sleeve or
chemical that released a small amount of gas when heated, restoring the correct
pressure.
• The glass envelope of the tube would blacken in use due to the X-rays affecting its
structure.
19
Cold cathode and hot cathode
• A cold cathode is a cathode that is not electrically heated by a
filament.
• A cathode may be considered "cold" if it emits more electrons than
can be supplied by thermionic emission alone.
• It is used in gas-discharge lamps, such as neon lamps, discharge
tubes, and some types of vacuum tube.
• The other type of cathode is a hot cathode, which is heated by
electric current passing through a filament.
• A cold cathode does not necessarily operate at a low temperature:
– It is often heated to its operating temperature by other methods,
such as the current passing from the cathode into the gas.
20
Advantage
• Point source X-rays, which resulted in sharper images.
• Perhaps the first major advance in X-ray tube design was the
incorporation of a metal target, something that resulted in greater xray intensities than possible with a glass target.
• Nevertheless, the use of glass as a target had some advantages and
the method was not completely abandoned.
Disadvantage
• Unreliable (‫)ناقابل اعتماد‬
Work function
In solid-state physics, the work function is the minimum
thermodynamic work (i.e. energy) needed to remove an electron from
21
a solid to a point in the vacuum immediately outside the solid surface.
Coolidge tube (hot cathode tube)
General
• Called as hot cathode tube.
• Works with a very good quality vacuum (about 10-4 Pa, or 10−6
Torr).
• The electrons are produced by thermionic effect from a tungsten
filament heated by an electric current.
• There are two designs:
End-window tubes
• Have thin "transmission target" to allow X-rays to pass through the
target
Side-window tubes
• An Electrostatic Lens to focus the beam onto a very small spot on
the anode.
• A window designed for escape of the generated X-ray photons.
• Power 0.1 to 18 kW.
22
Figure: Coolidge X-ray tube, from around
1917. The heated cathode is on the left, and
the anode is right. The X-rays are emitted
downwards.
William David Coolidge
23
Operation
• The Crookes tube was improved by William Coolidge in 1913.
• The Coolidge tube, also called hot cathode tube, is the most widely
used.
• It works with a very good quality vacuum (about 10−4 Pa, or 10−6
Torr).
• In the Coolidge tube, the electrons are produced by thermionic effect
from a tungsten filament heated by an electric current.
• The filament is the cathode of the tube.
• The high voltage potential is between the cathode and the anode, the
electrons are thus accelerated, and then hit the anode.
• There are two designs:
– End-window tubes
– Side-window tubes
• End window tubes usually have "transmission target" which is thin
enough to allow X-rays to pass through the target (X-rays are
emitted in the same direction as the electrons are moving.)
24
Figure: Coolidge side-window tube (scheme). C: filament/cathode (-).
A: anode (+). Win and Wout: water inlet and outlet of the cooling
device.
25
• In one common type of end-window tube, the filament is around
the anode ("annular" or ring-shaped), the electrons have a curved
path (half of a toroid).
• What is special about side-window tubes is an electrostatic lens is
used to focus the beam onto a very small spot on the anode.
• The anode is specially designed to dissipate the heat and wear
resulting from this intense focused barrage of electrons.
• Some anodes are mechanically spun to increase the area heated by
the beam (e.g., edical "rotating anode") or cooled by circulating
coolant (indirectly on most rotating anodes).
• The anode is precisely angled at 1-20 degrees off perpendicular to
the electron current so as to allow the escape of some of the X-ray
photons which are emitted perpendicular to the direction of the
electron current.
• The anode is usually made out of tungsten or molybdenum.
• The tube has a window designed for escape of the generated X-ray
photons.
• The power of a Coolidge tube usually ranges from 0.1 to 18 kW. 26
Production of X-Rays
(Coolidge X-ray tube)
27
Link:
https://www.youtube.com/watch?v=T1WwHh4b__M
28
Rotating anode tube
• A considerable amount of heat is generated in the focal spot (the
area where the beam of electrons coming from the cathode strike to)
of a stationary anode.
• Rather, a rotating anode lets the electron beam sweep a larger area
of the anode, thus redeeming the advantage of a higher intensity of
emitted radiation, along with reduced damage to anode compared to
its stationary state.
• The focal spot temperature can reach 2,500 °C (4,530 °F) during an
exposure, and the anode assembly can reach 1,000 °C (1,830 °F)
following a series of large exposures. Typical anodes are a
tungsten-rhenium target on a molybdenum core, backed with
graphite.
• The rhenium makes the tungsten more ductile and resistant to wear
from the impact of the electron beams.
• The molybdenum conducts heat from the target.
• The graphite provides thermal storage for the anode, and minimizes
the rotating mass of the anode.
30
Figure: Simplified rotating anode tube schematic. A: Anode, C:
cathode, T: Anode target, W: X-ray window.
31
Figure: Typical rotating anode X-ray tube.
32
Rotating Anode X-Ray Tube
33
Link:
https://www.youtube.com/watch?v=Ene0GwgXXNc
34
Microfocus X-ray tube
• Some X-ray examinations (such as, e.g., non-destructive
testing and 3-D microtomography) need very high-resolution
images and therefore require X-ray tubes that can generate very
small focal spot sizes, typically below 50 μm in diameter.
• These tubes are called microfocus X-ray tubes.
• There are two basic types of microfocus X-ray tubes:
– Solid-anode tubes
– Metal-jet-anode tubes
Solid-anode microfocus X-ray tubes
• These are in principle very similar to the Coolidge tube, but with
the important distinction that care has been taken to be able to
focus the electron beam into a very small spot on the anode.
• Many microfocus X-ray sources operate with focus spots in the
range 5-20 μm, but in the extreme cases spots smaller than 1 μm
may be produced.
• The major drawback of solid-anode microfocus X-ray tubes is the
very low power they operate at.
4
• In order to avoid melting of the anode the electron-beam power density must
be below a maximum value.
• This value is somewhere in the range 0.4-0.8 W/μm depending on the anode
material.
• This means that a solid-anode microfocus source with a 10 μm electronbeam focus can operate at a power in the range 4-8 W.
Metal-jet-anode microfocus X-ray tubes
• In metal-jet-anode microfocus X-ray tubes the solid metal anode is replaced
with a jet of liquid metal, which acts as the electron-beam target.
• The advantage of the metal-jet anode is that the maximum electron-beam
power density is significantly increased.
• Values in the range 3-6 W/μm have been reported for different anode
materials (gallium and tin).
• In the case with a 10 μm electron-beam focus a metal-jet-anode microfocus
X-ray source may operate at 30-60 W.
• The major benefit of the increased power density level for the metal-jet Xray tube is the possibility to operate with a smaller focal spot, say 5 μm, to
increase image resolution and at the same time acquire the image faster,
since the power is higher (15-30 W) than for solid-anode tubes with 10 μm
focal spots.
5
Thermionic emission
• Thermionic emission is the thermally induced flow of charge
carriers (electrons or ions) from a surface or over a potentialenergy barrier.
• This occurs because the thermal energy given to the carrier
overcomes the work function (i.e., energy) of the material.
• The charge carriers can be electrons or ions.
• The classical example of thermionic emission is the emission
of electrons from a hot cathode into a vacuum (also known as
thermal electron emission or the Edison effect) in a vacuum
tube.
• The hot cathode can be a metal filament, a coated metal
filament, or a separate structure of metal or carbides or borides
of transition metals.
• Vacuum emission from metals tends to become significant only
for temperatures over 1,000 K (730 °C; 1,340 °F).
6
• The term "thermionic emission" is now also used to refer to
any thermally-excited charge emission process, even when the
charge is emitted from one solid-state region into another.
• This process is crucially important in the operation of a variety
of electronic devices and can be used for electricity generation
(such as thermionic converters and electrodynamic tethers) or
cooling.
• The magnitude of the charge flow increases dramatically with
increasing temperature.
7
Edison effect
• The "Edison effect" was the name given to a phenomenon that Edison
observed in 1875 and refined later, in 1883, while he was trying to
improve his new incandescent lamp.
• The effect was that, in a vacuum, electrons flow from a heated
element - like an incandescent lamp filament - to a cooler metal plate.
• Edison saw no special value in the effect, but he patented it anyway.
• Edison patented everything in sight.
• Today we call the effect by the more descriptive term, "thermionic
emission."
• Now the Edison effect has an interesting feature.
• The electrons can flow only one way - from the hot element to the
cool plate, but never the other way - just like the water flow through a
check valve.
• Today we call devices that let electricity flow only one way, diodes.
8
The Edison effect in a diode
tube.
A diode tube is connected in
two configurations, one has
a flow of electrons and the
other does not.
Note that the arrows
represent electron current,
not conventional current.
Conventional current
• An electric current is the rate of flow of electric charge past a point or region.
• An electric current is said to exist when there is a net flow of electric charge
through a region.
• In electric circuits this charge is often carried by electrons moving through
a wire. It can also be carried by ions in an electrolyte, or by both ions and
electrons such as in an ionized gas (plasma).
9
Thermionic Emission
10
Link:
https://www.youtube.com/watch?v=_2u2XaGoqKE
11
Factors Affecting the Rate
of Thermionic Emission
13
Link:
https://www.youtube.com/watch?v=OYAacIEWpGc
14
Edison Effect
16
Link:
https://www.youtube.com/watch?v=U0oz_ZbQuGM
17
X-ray fluorescence (XRF)
• X-ray fluorescence (XRF) is the emission of characteristic
"secondary" (or fluorescent) X-rays from a material that has been
excited by bombarding with high-energy X-rays or gamma rays.
• The phenomenon is widely used for elemental analysis and chemical
analysis, particularly in the investigation of metals, glass, ceramics
and building materials, and for research in geochemistry, forensic
science, archaeology and art objects such as paintings and murals.
19
Bremsstrahlung X-ray generation
• Bremsstrahlung, (from bremsen "to brake" and Strahlung
"radiation"; i.e., "braking radiation" or "deceleration radiation") is
electromagnetic radiation produced by the deceleration of a charged
particle when deflected by another charged particle, typically an
electron by an atomic nucleus.
• Electromagnetic radiation produced by the acceleration or
especially the deceleration of a charged particle after passing
through the electric and magnetic fields of a nucleus.
20
Figure: The principle of generation Bremsstrahlung.
21
• The moving particle loses kinetic energy, which is converted into a
photon, thus satisfying the law of conservation of energy.
• The term is also used to refer to the process of producing the
radiation.
• Bremsstrahlung has a continuous spectrum, which becomes more
intense and whose peak intensity shifts toward higher frequencies
as the change of the energy of the decelerated particles increases.
Figure: Bremsstrahlung produced
by a high-energy electron deflected
in the electric field of an atomic
nucleus
22
• Broadly speaking, bremsstrahlung or braking radiation is any
radiation produced due to the deceleration (negative acceleration)
of a charged particle, which includes synchrotron radiation (i.e.
photon emission by a relativistic particle), cyclotron radiation (i.e.
photon emission by a non-relativistic particle), and the emission of
electrons and positrons during beta decay.
• However, the term is frequently used in the more narrow sense of
radiation from electrons (from whatever source) slowing in matter.
• Bremsstrahlung emitted from plasma is sometimes referred to
as free-free radiation.
• This refers to the fact that the radiation in this case is created by
charged particles that are free; i.e., not part of an ion, atom or
molecule, both before and after the deflection (acceleration) that
caused the emission.
23
• Two types of X-rays are produced by interaction of the electron beam
with the sample:
– Bremsstrahlung (which means ‘braking radiation’)
– Characteristic X-rays
• Bremsstrahlung X-rays are produced by slowing down of the primary
beam electrons by the electric field surrounding the nuclei of the
atoms in the sample.
• Bremsstrahlung
X-rays
are
also
referred
to
as continuum or background X-rays.
• The primary-beam electrons lose energy and change direction due to
inelastic scattering in the sample.
• Some of the lost energy is converted to X-rays which have a range of
energies, from ~0 up to Eo – the energy of the electrons in the primary
beam.
• Bremsstrahlung X-rays cannot have energies greater than the energy
of the electrons in the primary beam so this energy forms the upper
energy limit of the X-ray spectrum and is known as the Duane-Hunt
limit.
24
Figure: The primary beam electrons are slowed down or deflected by the
electric field around the atoms in the specimen. Part of the energy that they
lose is converted to Bremsstrahlung X-rays with energies between ~0 and the
Duane-Hunt limit.
25
• A primary beam electron may lose all of its energy in a single
interaction event in which case it will produce one X-ray with
energy Eo, but it is much more likely that the energy will be lost in
a number of interactions in which small proportions of the initial
energy are lost and an equivalent number of low-energy X-rays is
produced.
• The X-ray intensity, or number of X-rays produced, is zero where
E = Eo (the Duane-Hunt limit) but increases rapidly at very low
energies.
• This means that the X-rays produced by the primary beam
electrons comprise mostly a large (almost infinite) number of lowenergy X-rays.
• Although a large number of low-energy Bremsstrahlung X-rays
is generated, most are absorbed within the sample or the detector
and the X-ray intensity observed in the spectrum decreases at low
energy so that the Bremsstrahlung X-ray spectrum resembles a
‘whale’.
26
Figure: The difference between generated and observed Bremsstrahlung X-ray
spectra. Although many low-energy X-rays are generated most of them are
absorbed so the observed spectrum records a decrease in X-ray intensity at low
energy.
27
Kramers’ Law
• The intensity, I, of the Bremsstrahlung X-rays at any energy E in
the spectrum is given by Kramers’ Law:
I ≈ ip.Z(Eo-E)/E
where ip is the electron probe current and Z is the mean atomic
number.
• The intensity is zero where E = Eo (the Duane-Hunt limit) but
approaches infinity (∞) as E approaches zero.
• Note that according to Kramers’ Law, the intensity of the
Bremsstrahlung X-rays is proportional to Z, the mean atomic
number of the specimen.
• This means that heavier materials like Pb or Au will produce more
Bremsstrahlung X-rays than samples made from lighter elements
such as C or Al.
28
Oak Ridge Associated Universities Museum
Collection for X-Ray and Gas Discharge Tubes
• Students can see different X-ray and gas discharge
tubes at following web address:
– https://www.orau.org/ptp/collection/xraytubes/xraytubes.htm
4
Oak Ridge Associated Universities Museum Collection for X-Ray
and Gas Discharge Tubes
5
6
7
Introduction to Gas Discharge Tubes and Cold Cathode
X-ray Tubes
Gas Discharge Tubes - The Basics
• Prior to Roentgen’s discovery of x-rays in 1895, many different
types of gas discharge tubes were already in use (e.g., Geissler,
Crookes, Hittorf, Lenard tubes).
• After the discovery, new types were developed that were specially
designed to produce x-rays.
• Today, gas discharge x-ray tubes are commonly referred to as “cold
cathode” tubes in order to distinguish them from “hot cathode”
Coolidge x-ray tubes that employ a heated filament.
• But at the time they were being manufactured, they were simply
known as x-ray tubes.
• What these different tubes had in common was the fact that they
were made of glass and were partially evacuated.
• Depending on the type of tube, the residual gas might or might not be air.
• Tubes designed for x-ray work usually contained air, although some (e.g., Snook
tube) employed helium or hydrogen.
8
• The configuration of these tubes varied, but there were always at
least two electrodes (an anode and a cathode) that might, or might
not, be located at opposite ends of tube.
• It was not unusual for x-ray tubes to have three electrodes: a
negatively charged cathode, a positively charged anode, and what
was known as an "anticathode."
• The latter (aka auxiliary anode) was usually given a positive
charge, but it sometimes had no electrical charge at all.
• Tubes with both an anode and anticathode were often referred to as
bi-anode tubes.
• When a sufficient electric potential (high voltage) is applied across
the tube's electrodes, a stream of electrons (aka cathode rays)
travels through the gas from the cathode to the target.
• If the tube had an anticathode, it was the target.
• If the tube had no anticathode, the anode almost always served as the target.
• When the electrons struck the target, x-rays were emitted.
• The greater the current (on the order of a milliamp) supplied by the operator to
the tube, the greater the intensity of the emitted x-rays.
9
• The higher the applied voltage, the higher the energy of the x-rays,
and the more penetrating they became.
• For diagnostic imaging, more penetrating x-rays were preferred.
• For therapy, less penetrating x-rays were desired.
• Several problems had to be overcome when designing the tubes.
• Perhaps the most important were an overheating of the target when
the tube was under heavy use, short and long-term variability in the
gas pressure, reversals in the direction of the current through the
tube(inverse discharges), and electrical discharges that might
puncture the glass wall of the tube.
• Making the target more massive was the primary method used to
prevent it from overheating.
• Adding one or two special appendages to the tube (regulators or
regenerative devices) helped control the gas pressure inside the
tube.
• The primary ways that x-ray tubes differ involve the construction
of the target and the design of the regulator.
10
Gas Discharge Tubes - Some Details
• The application of even a relatively low potential between the
anode and cathode will cause any free ions in the gas (electrons and
positively charged gas molecules) to migrate to the electrodes.
• Free ions are always present due to interactions with of the gas
cosmic rays and background gamma rays.
• If the potential is sufficiently high, many of the electrons that
accelerate towards the anode will pick up sufficient kinetic energy
to cause a further ionization of the residual gas.
• The resulting positively charged gas ions (known as anode, canal or
channel rays) accelerate towards the cathode, and the freed
electrons (cathode rays) accelerate towards the target.
• Upon striking the cathode, some of the positively charged gas ions
dislodge electrons which join the other electrons accelerating
towards the anode.
• The fundamentals of this process are illustrated in the next series of drawings.
• Of course, in reality many more electrons and gas ions would be involved than
are pictured.
11
• First we see a partially evacuated tube containing residual nitrogen
(air) gas molecules:
• The next drawing shows that one of these molecules has been
ionized by background radiation.
12
• The next figure shows the electron travelling towards the anode
and the positively charged nitrogen ion travelling to the cathode.
• In the following figure we see that the electron travelling to the
anode has ionized two more gas molecules.
• As a result, we now have three electrons (cathode rays) travelling
to the anode and three positively charged gas ions (canal rays)
travelling to the cathode.
13
• In the final figure, we see an electron being knocked off the
cathode where the latter was struck by one of the gas ions.
• For every electron striking the target, a positive gas ion strikes the
cathode.
• As long as a high enough potential is maintained between the two
electrodes, the cathode ray beam (and canal ray beam) is selfsustaining and the region between the electrodes contains a mix of
free electrons, positively charged gas ions, and neutral gas
molecules (both excited and unexcited).
• The positive gas ions travelling to the cathode are less likely than the electrons
travelling to the anode to ionize the gas.
• However, over time these ions might damage the cathode when they strike it if
14
the tube was operated at high enough currents and voltages.
• This damage involves "sputtering," a process whereby some of the
atoms of a material are knocked free when struck by ions.
• Electrons striking the target don't have sufficient mass to cause
significant sputtering.
• As the electrons travel to the anode, they excite, as well as ionize,
some of the residual gas molecules.
• This causes the gas to glow.
• Ionization and excitation will not occur in the gas close to the
cathode because the electrons have not had enough time to gain the
required kinetic energy.
15
Working of Discharge Tube
16
Link:
https://www.youtube.com/watch?v=Wl6xln2vyl4
17
Typical Cold Cathode X-ray Tubes
• The following diagram illustrates the key components of a typical
heavy anode cold cathode x-ray tube.
19
Cathode
• The original cathodes were flat plates that emitted a broad beam of
cathode rays (electrons).
• The resulting x-rays issued from the extended region of the target
upon which the cathode rays impinged.
• Such x-rays produced relatively poor radiographic images.
• It was soon recognized that better results would be obtained by
focusing the cathode rays on a small region of the target.
• If the resulting x-rays issued from a small point on the target, the
images produced by such x-rays would be much sharper.
• To achieve this, the cathode was curved so that the focal point for
the cathode rays was located on the target.
• For this reason, these tubes were often referred to as "focus
tubes" and their cathodes described as "cups."
• The earliest type of x-ray tube with a focussed cathode was
the Jackson tube.
• Professor H. Jackson of Kings College, London is usually credited
to being the first to use a cupped cathode in an x-ray tube.
20
• Nevertheless, William Crookes had employed focussed cathodes in
his "Crookes tubes" in the days before x-rays were discovered.
• The cathode was almost always made of aluminum because
aluminum is less prone to "sputtering" than other metals.
• Sputtering is a volatilization of the metal that occurs when it is
struck by gas ions.
• The volatilized metal, which deposits on the glass walls of the
tube, has a tendency to absorb some of the gas in the tube.
• This increases the tube's resistance to the flow of current and
ultimately shortens its life.
• If sufficient metal deposits on the tube's glass walls, the latter
might darken.
• In general, a visibly darkened tube is likely to have too high a
vacuum (too low a gas pressure) to be usable.
• In almost all cold cathode x-ray tubes, the cathode cup (aka mirror) is positioned
near the circumference of the spherical bulb portion of the tube.
• Unfortunately, I have never seen the reason for this clearly explained.
21
• The position of the cup along the glass arm that leads to the bulb
certainly affects the voltage required to generate a given intensity
of x-rays: the farther along the glass arm (i.e., the closer to the
bulb) the lower the required operating voltage and the lower the
energy of the x-rays produced.
• The reason, as Hittorf noted, is that a static charge will accumulate
on glass (e.g., the glass arm) located near an electrode.
• The greater this charge, and proximity of the glass to the electrode,
the more resistant the electrode becomes to the emission of
electrons.
• Perhaps positioning it on the bulb's circumference results in the
optimal combination of high voltage, x-ray intensity and x-ray
energy.
22
Anode
• In many of the earliest tubes employed for x-ray production (e.g.,
Crookes and Hittorf tubes), the anode was located off to the side at
one end of the tube.
• The cathode rays streamed past the anode and struck the glass end
of the tube which served as the source of the x-rays.
• Unfortunately, the glass could not hold up under prolonged use.
• Furthermore, the x-rays were of low intensity.
• One early solution was to position the anode (a flat metal plate) at
the far end of the tube opposite the cathode.
• In this configuration, the anode served as the target of the cathode
rays and the source of the x-rays.
Anticathode
• Most of the early x-ray tubes were what was known as bi-anode
tubes, i.e., they had two anodes: the anode proper and an auxiliary
anode known as the "anticathode."
• The term "anticathode" was coined by Silvanus Thompson to refer
to the target upon which the cathode rays (electrons) impinged. 23
• Sometimes the anode and anticathode were one and the same, but in
most of the early tubes they were distinct entities.
• In most cases the anticathode was electrically connected to the
anode so that both possessed a positive charge.
• In some cases, the operator might disconnect the anticathode in an
attempt to improve tube performance.
• In many tubes, the supporting arm for the anticathode came in from
the side of the tube at a 45 degree angle and the anode was located
along the tube axis.
• In other cases, the anticathode was positioned along the tube axis
and the anode entered the tube at a 45 degree angle- from above and
behind the target as seen in the above figure.
• The earliest anticathodes were thin and flat metal (e.g., platinum)
plates oriented at a 45 degree angle to the tube axis, but these were
prone to overheating under prolonged or intense use.
• Where this was an issue, more massive "heavy" targets were used to facilitate
heat dissipation.
• For some reason, they were referred to as "heavy anodes" rather than "heavy
24
anticathodes" or "heavy targets."
• Anyway, these "heavy anodes" or targets generally consisted of two
different types of metals bonded together.
• A metal with a high atomic number (e.g., platinum, osmium,
molybdenum, tungsten) served as the actual target for the cathode rays
and the source of x-rays, while the surrounding metal (always copper)
helped dissipate the heat.
• There was no clear understanding as to why it was useful to have an
anticathode (target) in addition to the separate anode.
• The general assumption was that having both prolonged the life of the
tube and/or reduced undesirable variations in the gas pressure.
• Even though some manufactures believed that eliminating the anticathode
was just fine, they still produced tubes with separate anodes and
anticathodes because their customers expected it.
• Eventually (ca. 1920), almost everyone recognized that employing both
an anode and anticathode served no useful purpose.
• As a result, late model tubes eliminated the anticathode and positioned the
anode on the long axis of the tube opposite the cathode.
• But by this time, cold cathode tubes had been made obsolete by General
Electric’s hot cathode high vacuum Coolidge tube.
• That tube signaled the end of an era, and the beginning of a new one. 25
The importance of the gas pressure
• For proper operation of the tube, the pressure of the residual gas
inside the tube needed to be on the order of 0.2 to 0.5 mm Hg.
• A tube with higher pressures (a low vacuum) was too "soft," while
a tube with a lower pressure (high vacuum) was too "hard."
• The x-rays emitted by softer tubes were more intense but of lower
energy than those emitted by harder tubes.
• As a rule, the more intense and lower energy x-rays emitted by soft
tubes were desired for therapy - these lower energy x-rays were
more likely to be absorbed by the malignant tissue being treated.
• For diagnostic imaging (radiography), the higher energy x-rays
emitted by harder tubes were preferred for their penetrating power.
• The greater the thickness of the tissue being imaged, the higher the
x-ray energy desired.
• Most physicians would maintain a variety of x-ray tubes, the softer
tubes for therapy and the harder tubes for imaging.
• Unfortunately, a tube's internal gas pressure was not constant.
4
• Over time, the long-term trend was for the gas pressure to decrease
(an increasing vacuum) as some of the gas was adsorbed by the
tube’s walls and other components.
• This inevitable long-term hardening of the tube reduced the
intensity of the x-rays.
• At the same time, the x-rays became more penetrating (higher
energy).
• If the tube became too hard, arcing might occur when power was
supplied and the resulting sparks might puncture the tube's glass
wall.
• Short-term variability could also occur.
• For example, as a tube warmed up during use, the heating might
cause an outgassing from some of the tubes metal components
(especially the aluminum) and soften the tube - at least temporarily.
• A problem: there was no simple way to measure the gas pressure in
the tube.
• A comparison of "hard" and "soft" tubes is provided in the
following table (after Satterlee, 1913).
5
Hard Tube
Characteristics of Hard and Soft X-Ray Tubes
Soft Tube
Low gas pressure/high vacuum
High gas pressure/low vacuum
Lower intensity x-rays due to lower
current
Higher energy (more penetrating) xrays
Higher intensity x-rays due to higher
current
Less danger of skin overexposure
Greater danger of overexposure to skin
Less contrast in radiograph
More contrast in radiographic image
Electrical charge (static) on outside of
tube
Glass wall of tube more likely to
puncture
Surface of target less likely to be
damaged
Yellowish color.
Lower energy (less penetrating) x-rays
No static charge on outside of tube
Glass wall of tube less likely to
puncture
Target more likely to be damaged
Blue-green colors. Red if extremely
high pressure (tube puncture?)
6
• One method that was used to help maintain a more constant
pressure in the tube was to make it larger.
• The physically bigger the tube, the slower the decrease or increase
in the gas pressure.
• As a result, there was also a relationship between the tube size and
its maximum load.
• The larger the diameter of the tube, the greater the current and
high voltage that it could tolerate.
• The downside of making the tube larger was that it was also
necessary to make the glass thicker and this reduced the emission
of low energy x-rays.
• If the latter were needed (e.g., superficial therapy), the tube was
small.
7
Jackson X-ray Tube (ca. 1896)
• Following Rontgen's discovery of x-rays in late 1895, the first
significant development in the design of x-ray tubes was the use of
a concave cathode that focused the electrons (cathode rays) on the
target.
• William Crookes had constructed such a tube many years earlier,
but not, of course, to increase the production of x-rays. Various
workers (e.g., Sidney Rowland and Herbert Schallenberger) made
x-ray tubes with concave cathodes in early 1896, but rightly or
wrongly, professor Herbert Jackson of Kings College in London is
usually credited as being the first to do so.
• As seen in this example, the Jackson tube was usually oriented so
that the cupped cathode faced down while the upwardly facing
target (typically platinum) was mounted at 45 degrees to the tube
axis.
• It is not visible in the photo, but the glass stem supporting the
anode is cracked, probably because of a drop during shipping.
• As a result, the cathode and anode don't line up correctly.
8
Size: ca. 11" high (including
stand) and 3" diameter
What is ca.: a written abbreviation
of circa (=about).
9
How Does X-Ray Tube Works
10
Link:
https://www.youtube.com/watch?v=3_bZCA7tlFQ
11
Collimator
• Inserted in the diffracted-beam
to get a narrow x-ray beam.
• It consists two sets of closely
packed metal plates separated by a
gap.
• The left end of the collimator
shown is mounted on the X-ray
tube.
• The yellow-colored region at
the left end determines the size of
the beam.
• The green region at the right
end removes parasitic radiation.
← Mounted on the X-ray tube
→ Yellow
Green ←
13
Explanation
• A collimator is a device that narrows a beam of particles or
waves.
• To narrow can mean either to cause the directions of motion to
become more aligned in a specific direction (i.e., make
collimated light or parallel rays), or to cause the spatial cross
section of the beam to become smaller (beam limiting device).
• The use of collimators for generating narrow x-ray beams is
straightforward, but can suffer from loss of intensity as the beam
diameter decreases.
• Passing a relatively large x-ray beam through a small aperture
results in most of the primary x-rays being blocked by the
material around the aperture.
• X-rays only pass through the aperture itself, yielding a beam
with a diameter approaching that of the aperture.
• However, as the aperture is narrowed, the proportion of x-rays
14
which are blocked increases dramatically.
• Thus, beams generated in this manner with diameters below 500
µm become low in intensity, and diameters below 100 µm
become unworkable because of this problem.
• Today collimators are successfully used for high spatial
resolution analysis (beam diameters < 20 µm) on synchrotron
sources, where the extremely high beamline intensities mean that
intensity losses are not an issue.
• For benchtop instruments with less bright x-ray sources,
collimators are not used for ultra-high spatial resolutions.
Example of a particle collimator.
15
In short……
• In order to get a narrow beam of x-rays, the x-rays generated by
the target material are allowed to pass through a collimator which
consists of two sets of closely packed metal plates separated by a
small gap.
• The collimator absorbs all the x-rays except the narrow beam that
passes between the gap.
16
Types of monochromators
• In order to do monochromatization, two methods are
available:
• Filter
– Flat crystal monochromator
• Crystal monochromator
– Curved crystal monochromator
• Materials used: NaCl, quartz etc.
Filter
• X-ray beam may be partly monochromatized by insertion of a
suitable filter
• A filter is a window of material that absorbs undesirable
radiation but allows the radiation of required wavelength to
pass.
17
Crystal monochromator
• Crystal monochromators is made up of suitable crystalline material
positioned in the x-ray beam so that the angle of reflecting planes
satisfied the Bragg’s equation for the required wavelength the beam
is split up into component wavelengths crystals used in
monochromators are made up of materials like NaCl, lithium
fluoride, quartz etc.
18
Detectors
• The x-ray intensities can be measured and recorded either by:
– Photographic methods
– Counter methods
• Geiger - Muller tube counter
• Proportional counter
• Solid state semi-conductor detector
• Semi conductor detectors
• X-ray detectors
– Scintillation detector
– Gas-filled detectors
• Both these types of methods depends upon ability of x-rays to
ionize matter and differ only in the subsequent rate of electrons
produced by the ionizing process.
19
Photographic methods
• To record the position and intensity of x-ray beam a plane or
cylindrical film is used
• The film after exposing to x-ray is developed
• Contains photographic plate
• Blackening of developed film is expressed in terms of density units,
D:
D = Log Io / I
I₀ - Incident intensities
I - Transmitted intensities
D - Total energy that causes blackening of the film
• D is measured by densitometer
• The photographic method is mainly used in diffraction studies since
it reveals the entire diffraction pattern on a single film.
20
Photostimulable phosphors
• An increasingly common method is the use of:
– Photostimulated luminescence
• Photostimulable phosphor plate (PSP plate) is used in place of the
photographic plate.
• After the plate is X-rayed, excited electrons in the phosphor material
remain ‘trapped' in 'colour centres' in the crystal lattice until stimulated
by a laser beam passed over the plate surface.
• The light given off during laser stimulation is collected by a
photomultiplier tube.
Advantage
• The PSP plate can be reused.
Disadvantage
• Time consuming and uses exposure of several hours.
21
Photostimulated luminescence
• Photostimulated luminescence (PSL) is the release of stored energy
within a phosphor by stimulation with visible light, to produce a
luminescent signal.
• X-rays may induce such an energy storage.
• A plate based on this mechanism is called a photostimulable phosphor
(PSP) plate and is one type of X-ray detector used in projectional
radiography.
• Creating an image requires illuminating the plate twice: the first exposure,
to the radiation of interest, "writes" the image, and a later, second
illumination (typically by a visible-wavelength laser) "reads" the image.
• The
device
to
read
such
a
plate
is
known
as
a phosphorimager (occasionally spelled phosphoimager, perhaps
reflecting its common application in molecular biology for
detecting radiolabeled phosphorylated proteins and nucleic acids).
• Projectional radiography using a photostimulable phosphor plate as an Xray detector can be called "phosphor plate radiography" or "computed
radiography" (not to be confused with computed tomography which uses
computer processing to convert multiple projectional radiographies to
22
a 3D image).
Counter methods
1. Geiger-muller counter
• Filled with an inert gas like
argon.
• Central wire anode is maintained
at a positive potential of 800 to
2500V .
• Measures ionizing radiation.
• Detect the emission of nuclear
radiation: alpha particles, beta
particles or gamma rays.
• The electron is accelerated by
the potential gradient and causes
the ionization of large number of
argon atoms, resulting in the
production of avalanche of
electrons that are travelling
towards central anode.
23
Advantages
• Trouble free
• Inexpensive
Disadvantages
• Cannot be used to measure energy of ionizing radiation.
• Used for low counting rates
• Efficiency falls off below 1A
24
Links:
Geiger-Muller Tube
• https://www.youtube.com/watch?v=U7KV-TPrN2M
Working of Geiger Muller Counter
• https://www.youtube.com/watch?v=PIsWy2q0hVc
Detecting Nuclear Radiation
• https://www.youtube.com/watch?v=KmOYdVk73S8
25
2. Proportional counter
• Construction is similar to Geiger tube
counter
• Filled with heavier gas like xenon or
krypton as it is easily ionized.
• Operated at a voltage below the geiger
plateau
• The dead time is very short (~0.2μs), it
can be used to count high high rates
without significant error.
• Output pulse is dependent on intensity of
X-rays falling on counter.
• Count the particles of ionizing radiation
and measures their energy.
Advantages
• Count high rates with out significant
error.
Disadvantages
• Associated electronic circuit is complex.
• Expensive.
4
Links:
Ionosation Chamber
• https://www.youtube.com/watch?v=M--8-XFA_M0
Proportional Counter
• https://www.youtube.com/watch?v=Utep0WG-tYk
5
3. Solid state semi-conductor detector
• The electrons produced by X-ray beam are promoted into
conduction bands and the current which flows is directly
proportional to the incident X-ray energy.
Disadvantage
• Should be maintained at very low temperature to minimize the
noise and prevent deterioration of the detector.
4. Semi-conductor detectors
• The principle is similar to gas ionization detector.
• When x-ray falls on silicon lithium drifted detector an electron (-e)
and a hole (+e)
• Pure silicon made up with thin film of lithium metal plated onto
one end
• Under the influence of voltage electrons moves towards +ve
charge and holes towards –ve
• Voltage generated is measure of the x-ray intensity falling on
crystal.
8
• Upon arriving at lithium
pulse is generated
• Voltage of pulse = q/c
– q - total charge collected
on electrode
– c - detector capacity
Application
• In
neutron
analysis
Semi-conductor detector
activation
9
5. X-ray detectors
• The two most common types of X-ray detector used in the laboratory for
powder diffraction (excluding the case of X-ray film) are the:
– Scintillation detectors
– Gas-filled detectors
both of which are described below:
Scintillation detectors
• In a scintillation detector there is large sodium iodide crystal activated
with a small amount of thallium.
• When x-ray is incident upon crystal, the pulses of visible light are
emitted which can be detected by a photo multiplier tube
• Useful for measuring x-ray of short wavelength
• Crystals used in scintillation detectors include sodium iodide,
anthracene, napthalene and p-terphenol
• In the scintillation counter, the conversion of X-ray photons into an
electrical signal is a two-stage process:
• The X-ray photon collides with a phosphor screen, or scintillator, which
forms the coating of a thallium-doped sodium iodide crystal.
• The latter produces photons in the blue region of the visible spectrum.
10
• These are subsequently converted to voltage pulses by means of a
photomultiplier tube attached directly behind the scintillator.
• The number of electrons ejected by the photocathode is
proportional to the number of visible photons which strike it,
which in turn is proportional to the energy of the original X-ray
photon.
• Due to a large number of losses, the energy resolution of the
detector is poor, and as such it cannot be used to resolve X-ray
photons due to Kα and Kβ radiation.
• However, it has a very high quantum efficiency and a very low
dead time making it the ideal detector for the point intensity
measurements required for step-scanning diffractometers.
11
In short…..
• Measures X-rays of shorter wavelengths.
• The sensor, called a scintillator, consists of a transparent crystal,
usually phosphor, plastic (usually containing anthracene), or
organic liquid that fluoresces when struck by ionizing radiation.
• The PMT is attached to an electronic amplifier to count and
possibly quantify the amplitude of the signals.
Advantages
• Count high rates.
12
Links:
Scintillation Counter (Working)
• https://www.youtube.com/watch?v=7jQ12uUqK6E
Scintillation Mechanism (NaI)
• https://www.youtube.com/watch?v=f_VioPizSy4
Scintillation Counter
• https://www.youtube.com/watch?v=Cb6OBVrkuRo
Photo Multiplier Tube
• https://www.youtube.com/watch?v=7KSgt8vEbro
13
Gas-filled detectors
• The second type of detector commonly used in the laboratory is the
gas-filled detector.
• This detector works on the principle that X-ray photons can ionize
inert gas atoms such as argon or xenon into an electron (e-) and ion
(e.g., Ar+) pair.
• The ionization energy required to eject an outer electron is low (1020 eV) compared to the energy of the X-ray photon (8 keV) so that
one X-ray photon can produce several hundred ion pairs.
• A wire placed inside the detector is set to a potential of about
1,000 V.
• This accelerates the electrons of the ion pair towards the wire
causing further ionization and an enhanced signal by gas
amplification.
• The burst of electrons on the wire is converted into a voltage pulse which
is then shaped and counted by the electronics.
• In order to minimize the dead time of the system, a quenching gas such
as methane (CH4) is mixed with the inert gas (e.g., 90% Ar : 10% CH4).
18
19
• A disadvantage of gas-filled detectors is their loss of linearity at
high count rates, but they have a better energy resolution than
scintillation detectors.
• The simple gas-filled detector is much less-commonly used than a
more sophisticated form known as a:
• Position sensitive detector (PSD)
• PSDs are gas-filled detectors with a long poorly-conducting anode
wire to which a high tension voltage is applied at both ends.
• In consequence, the pulse moves towards both ends of the wire
simultaneously and by measuring the rate at which it arrives at
both ends of the wire, it is possible to determine from whereabouts
on the wire the pulse originated.
• The pulses are stored in a multi-channel analyser (MCA) device
according to the pulse position on the wire.
• This enables PSDs to record data over a whole range of scattering
angles, which can be useful where speed of acquisition is crucial,
e.g., in time-resolved powder diffraction or thermodiffractometry.
20
• PSDs come in a variety of shapes and sizes:
– Small PSDs usually have a straight wire and can only collect
data over, say, 5-10° 2θ.
– Large PSDs require curved wires, but collect over a much wider
range of scattering angle.
• In addition, some gas-filled PSDs are sealed, while others require a
continuous flow of gas for their operation.
• Linear and curved PSDs are illustrated in the photographs below:
Linear PSDs
Curved PSDs 21
Link:
Gas Filled Detector (Principle, construction and
working)
• https://www.youtube.com/watch?v=8kQT1zaosp0
22
Calibration
• In contrast to the scintillation and simple gas-filled detectors used
for point intensity measurements, position sensitive detectors
require careful calibration for both wire position and efficiency so
that both scattering angles and intensities can be reliably
determined.
• For each channel of the MCA an exact 2θ position is required
together with an efficiency coefficient.
• The wire efficiency can be determined using a sample such as an
amorphous iron foil that produces a very high flat background and
no Bragg peaks.
• The 2θ calibration is achieved by scanning the different parts of the
detector through the Bragg reflection of a strong peak (or peaks).
• For example the Si 111 peak.
• For very large curved detectors, the 2θ calibration has to be made
using many diffraction peaks.
24
X-ray diffraction methods
• These are generally used for investigating the internal structures and
crystal structures of various solid compounds.
1. Laue photographic method
• The Laue method is mainly used to determine the orientation of large
single crystals.
• White radiation is reflected from, or transmitted through, a fixed
crystal.
• The diffracted beams form arrays of spots, that lie on curves on the
film.
• The Bragg angle is fixed for every set of planes in the crystal.
• Each set of planes picks out and diffracts the particular wavelength
from the white radiation that satisfies the Bragg law for the values
of d and q involved.
• Each curve therefore corresponds to a different wavelength.
• The spots lying on any one curve are reflections from planes
belonging to one zone.
• Laue reflections from planes of the same zone all lie on the surface of
25
an imaginary cone whose axis is the zone axis.
Experimental
• There are two practical variants of the Laue method, the backreflection and the transmission Laue method.
• You can study these below:
Back-reflection Laue
• In the back-reflection method, the film is placed between X-ray
source and crystal.
• The beams which are diffracted in a backward direction are recorded.
• One side of the cone of Laue reflections is defined by the
transmitted beam.
• The film intersects the cone, with the diffraction spots generally
lying on an hyperbola.
Advantages
• This method is similar to transmission method however, backreflection is the only method for the investigation of large and thick
specimen.
Disadvantages
• A large crystal is required
26
Transmission Laue
• In the transmission Laue method, the film is placed behind the crystal
to record beams which are transmitted through the crystal.
• One side of the cone of Laue reflections is defined by the
transmitted beam.
• The film intersects the cone, with the diffraction spots generally
lying on an ellipse.
• Can be used to orient crystals for solid state experiments.
• Most suitable for the investigation of preferred orientation sheet
particularly confined to lower diffraction angles.
• Also used in determination of symmetry of single crystals.
Disadvantage
• Big crystals are required
27
28
Back-reflection Laue
Transmission Laue
• Crystal orientation and perfection is determined from the
position of spots.
29
• Each spot can be indexed, i.e., attributed to a particular plane,
using special charts.
• The Greninger chart is used for back-reflection patterns and
the Leonhardt chart for transmission patterns.
• The Laue technique can also be used to assess crystal
perfection from the size and shape of the spots.
• If the crystal has been bent or twisted in anyway, the spots
become distorted and smeared out.
30
Greninger chart
• In crystallography, a Greninger chart is a chart that allows angular
relations between zones and planes in a crystal to be directly read
from an x-ray diffraction photograph.
How to use the chart?
• The use of the chart is described in the Ch. S. Barrett, Structure of
Metals, McGraw-Hill, New York, 1952, pages 185-190, as well as
in the book of Amoros, Buerger and Amoros, The Laue method,
Academic Press, New York, 1975, page 212.
31
Greninger chart for interpretation of back-reflection Laue photographs
32
2. Bragg x-ray spectrometer method
• Bragg analyzed the structures of NaCl, KCl and ZnS.
• Method is based on Bragg’s law.
• The strength of ionization current is directly proportional to
intensity of entering reflected X-rays.
• SO2 or CH3I increases ionization in the chamber.
A-anti cathode, B-B'– Adjustable slits, C-crystal, E-ionization
chamber
33
• One plate of ionization chamber is connected to the positive
terminal of a H.T Battery, while negative terminal is connected to
quadrant electrometer (measures the strength of ionization
current).
Working
• Crystal is mounted such that θ = 0° and ionization chamber is
adjusted to receive x-rays.
• Crystal and ionization chamber are allowed to move in small
steps.
• The angle through which the chamber is moved is twice the angle
through which the crystal is rotated.
• X-ray spectrum is obtained by plotting a graph between ionization
current and the glancing angle θ.
• Peaks are obtained peaks corresponds to Bragg’s reflection.
• Different order glancing angles are obtained with known values of
d and n and from the observed value of θ, λ can be measured.
34
Determination of crystal structure by Bragg’s Law
• X-Rays falls on crystal surface.
• The crystal is rotated and x-rays are made to reflect from various
lattice planes.
• The intense reflections are measured by Bragg’s spectrometer and
the glancing angles for each reflection is recorded.
• Then on applying Bragg’s equation ratio of lattice spacing for
various groups of planes can be obtained.
• Ratio’s will be different for different crystals.
• Experimentally observed ratio’s are compared with the calculated
ratio’s, particular structure may be identified.
35
3. Rotating crystal method
• Shaft is moved to put the
crystal into slow rotation.
• This cause sets of planes
coming successively into their
reflecting position.
• Each plane will produce a spot
on the photographic plate.
• Can take a photograph of the
diffraction pattern in two ways:
– Complete rotation method
– Oscillation method
36
• Photographs can be taken by:
• 1. Complete rotation method: in this method series of complete
revolutions occur.
• Each set of a plane in a crystal diffracts four times during rotation.
• Four diffracted beams are distributed into a rectangular pattern in the
central point of photograph.
• 2. Oscillation method: the crystal is oscillated at an angle of 15° or
20°.
• The photographic plate is also moved back and forth with the crystal.
• The position of the spot on the plate indicates the orientation of the
crystal at which the spot was formed.
37
4. Powder crystal method
• 1mg material is sufficient for study.
• X-ray powder diffraction (XRD) is a rapid analytical technique
primarily used for phase identification of a crystalline material
and can provide information on unit cell dimensions.
• The analyzed material is finely ground, homogenized, and
average bulk composition is determined.
38
• Fine powder is struck on a hair with a gum, it is suspended
vertically in the axis of a cylindrical camera
• When monochromatic beam is allowed to pass different
possibilities may happen:
– There will be some particles out of random orientation of
small crystals in the fine powder
– Another fraction of grains will have another set of planes in
the correct positions for the reflections to occur
– Reflections are possible in different orders for each set
39
• If the angle of incidence is θ then the angle of reflection will be
2θ
• If the radius is r the circumference 2πr corresponds to a scattering
angle of 360°
θ = 360*1 / πr
• From the above equation the value of θ can be calculated and
substituted in Bragg’s equation to get the value of d.
Applications
• Useful for:
– Cubic crystals
– Determining complex structures of metals and alloys
– Making distinction between allotropic modification of the
same substance
• Characterization of crystalline materials
• Identification of fine-grained minerals such as clays and mixed
layer clays that are difficult to determine optically
• Determination of unit cell dimensions
• Measurement of sample purity
40
Classical Powder Diffractometer
Goniometer
Detector
X-ray tube
Monochromator
Soller slit
Soller slit
Receiving
slit
Anti-scatter
slit
Divergence
slit
Mask
Sample stage
6
Optical components in
X-ray beam path
Figure: Geometry of a x-ray diffractometer with
monochromator.
7
X-ray beam path
Incident beam path:
• X-ray tube focus
• Soller slit
• Divergence slit
• Beam mask (Width mask)
• Beta-filter
• Monochromator
Diffracted beam path:
• Receiving slit
• Soller slit
• Anti-scatter slit
• Width mask
• Beta-filter
• Monochromator
8
Incident beam path
(Width mask)
9
X-ray tube
• The tube is evacuated (‫ )ﺧﺎﻟﯽ کرا ﻟيﺎ‬and contains a copper
block with a metal target anode, and a tungsten filament
cathode with a high voltage between them.
• The filament is heated by a separate circuit, and the large
potential difference between the cathode and anode fires
electrons at the metal target.
• The accelerated electrons knock core electrons out of the
metal, and electrons in the outer orbitals drop down to
fill the vacancies, emitting x-rays.
• The x-rays exit the tube through a beryllium window.
• Due to massive amounts of heat being produced in this
process, the copper block must usually be water cooled.
10
Cross section of sealed-off filament x-ray tube
11
Line focus
• Was incorporated into x-ray tube targets to allow a large
area for heating while maintaining a small focal spot.
• Used to reduce the effective area of the focal spot.
• More signal due:
– To larger irradiated volume
• Soller slits are necessary.
12
Receiving slit
Soller slits
Figure: Use of the line focus – traditionally.
13
Soller slits
• Sideways divergence (‫ )منتشر ہونﺎ‬of either the incident or scattered
beam can be controlled using soller slits inserted in the x-ray beam
path.
(2)
(1)
(2)
(1)
14
• Soller slits consist of large numbers of parallel plates in
plane of diffraction.
• Soller slits limit the spread of the incident and
diffracted X-ray beam out of the plane of diffraction:
• 0.01, 0.02, 0.04 and 0.08 rad
• It is good practice to place similar soller slits in the
incident and diffracted beam.
15
Divergence slits
• The slits block x-rays that have too great a divergence.
• The size of the divergence slit influences peak intensity
and peak shapes.
• Narrow divergence slits:
– Reduce the intensity of the x-ray beam
– Reduce the length of the x-ray beam hitting the sample
– Produce sharper peaks:
• The instrumental resolution is improved so that
closely spaced peaks can be resolved.
• The length of the incident beam
is determined by the divergence
slit, goniometer radius, and
incident angle.
16
Divergence slits
17
(1)
(2)
(3)
(3)
(2)
(1)
Divergence slits
18
Beam mask (width mask)
• Limits (‫ )حدود‬the beam width.
(3)
(1)
(2)
(3)
(2)
(1)
19
-filter and monochromator
• These are used for removing unwanted radiation.
• -filter and diffracted beam monochromator remove unwanted
wavelengths like K-line and continuous radiation
• -filters selectively absorb radiation
• Monochromators select radiation by means of diffraction and take
out sample fluorescence
• Incident-beam optics (monochromators) → condition the x-ray
beam before it hits the sample
Possible places -filter
diffracted
beam
monochromator
20
• Monochromators remove unwanted wavelengths of
radiation from the incident or diffracted X-ray beam.
• Diffraction from a crystal monochromator can be used to
select one wavelength of radiation and provide energy
discrimination.
• An incident-beam monochromator might be used to select
only Kα1 radiation for the tube source.
• A diffracted-beam monochromator may be used to
remove fluoresced photons, Kβ, or W-contamination
photons from reaching the detector.
– Without the RSM slit, the monochromator removes
~75% of unwanted wavelengths of radiation.
– When the RSM slit is used, over 99% of the unwanted
wavelengths of radiation can be removed from the
beam.
Repeated
21
β-filters can also be used to reduce the intensity of Kβ
and W-wavelength radiation
• A material with an absorption edge between the Kα and
Kβ wavelengths can be used as a beta filter.
• This is often the element just below the target material
on the periodic table:
– For example, when using Cu radiation
• Cu Kα = 1.541 A
• Cu Kβ = 1.387 A
• The Ni absorption edge = 1.488 A
– The Ni absorption of Cu radiation is:
• 50% of Cu Kα
• 99% of Cu Kβ
Repeated
22
Repeated
23
Filters (old way)
• A foil of the next lightest
element (Ni in the case of Cu
anode) can often be used to
absorb the unwanted higherenergy radiation to give a clean
Kα beam.
Monochromators
• Monochromators use diffraction
from a curved crystal (or
multilayer) to select x-rays of a
specific wavelength.
24
25
Removal of K-line
The spectrum from
an x-ray tube is NOT
monochromatic!
Cu K
As diffractionists,
we only want to see K!
Cu K
In other words:
Use tricks to limit
the spectrum:
0
kV/mA settings,
filters, monochromators,…
Continuous or white
radiation
(influenced by kV
setting)
10
20
30
40
kV
26
Diffracted beam path
27
Receiving slit
• Increasing the width of the receiving slit generally increases the
peak height and width and decreases the ability to resolve peaks.
(1)
(2)
(3)
(2)
(3)
(1)
28
Anti-scatter slit
• Anti-scatter slit determines observed length on the
sample
– Major effect on the intensity
– Used to reduce background
– Ideally the illuminated area equals the observed
area
29
Receiving-side optics (Monochromators)
• Condition the X-ray beam after it has encountered the
sample
Detector
• Count the number of X-rays scattered by the sample
– The area detector
• The area detector catches a part of several
diffraction rings at once
• The detector records the angles at which the families of
lattice planes scatter (diffract) the x-ray beams and the
intensities of the diffracted x-ray beams.
• The detector is scanned around the sample along a circle,
in order to collect all the diffracted X-ray beams.
• The angular positions (2θ) and intensities of the diffracted peaks of
radiation (reflections or peaks) produce a two dimensional pattern.
30
• This pattern is characteristic of the material analysed
(fingerprint).
• Each reflection represents the x-ray beam diffracted by a
family of lattice.
• http://prism.mit.edu/xray/oldsite/Basics%20of%20XRay%20Powder%20Diffraction.pdf
31
Summary
Optical Element
Effect
Divergence Slit Adjusts beam length
on the sample
Soller Slit
Reduces peak
asymmetry
Anti-Scatter Slit Reduces background
signal
Beam Mask
Adjusts beam width
on the sample
Receiving Slit Adjusts peak width /
resolution
Kβ Filter
Reduces Kβ peaks
Graphite
Eliminates Kβ peaks
Monochromator
Too Small
Loss of intensity
Loss of intensity
Better resolution
Loss of intensity
Loss of intensity
Loss of intensity
Better resolution
Too Large
Beam spills over
sample
More asymmetry
Less resolution
High background
Beam spills over
sample
Loss of resolution
Higher intensity
32
Summary
33
Working of powder x-ray diffraction
• X-ray diffractometers consist of three basic elements:
– An x-ray tube
– A sample holder
– An x-ray detector
• X-rays are generated in a cathode ray tube by heating a
filament to produce electrons, accelerating the electrons toward
a target by applying a voltage, and bombarding the target
material with electrons.
• When electrons have sufficient energy to dislodge (‫ )نکال دينا‬inner
shell electrons of the target material, characteristic x-ray spectra are
produced.
• These spectra consist of several components, the most common
being Kα and Kβ.
• Kα consists, in part, of Kα1 and Kα2.
• Kα1 has a slightly shorter wavelength
and twice the intensity as Kα2.
6
Most diffraction data contain Kα1 and Kα2 peak
doublets rather than just single peaks
K- α1
K- α2
K- α1
K- α2
K- α1
K- α2
• The Kα1 and Kα2 peak doublets are further apart at higher
angles 2theta
• The Kα1 peaks always as twice the intensity of the Kα2
• At low angles 2theta, you might not observe a distinct
second peak
7
Generating of X-rays
8
9
10
11
Bohr`s model
• The specific wavelengths are characteristic of the target
material (Cu, Fe, Mo, Cr).
• Filtering, by foils or crystal monochrometers, is required to
produce monochromatic x-rays needed for diffraction.
• Kα1 and Kα2 are sufficiently close in wavelength such that a
weighted average of the two is used.
• Copper is the most common target material for single-crystal
diffraction, with CuKα radiation = 1.5418Å.
• These x-rays are collimated and directed onto the sample.
• As the sample and detector are rotated, the intensity of the
reflected x-rays is recorded.
• When the geometry of the incident x-rays impinging (‫)ٹکرانا‬
the sample satisfies the Bragg equation, constructive
interference occurs and a peak in intensity occurs.
• A detector records and processes this x-ray signal and converts
the signal to a count rate (intensity) which is then output to a
12
device such as a printer or computer monitor.
13
14
Powder diffraction diffractogram
15
• The geometry of an x-ray diffractometer is such that the sample
rotates in the path of the collimated x-ray beam at an angle θ while
the x-ray detector is mounted on an arm to collect the diffracted xrays and rotates at an angle of 2θ.
• The instrument used to maintain the angle and rotate the sample is
termed a goniometer.
• For typical powder patterns, data is collected at 2θ from ~5° to 70°,
angles that are preset in the x-ray scan.
16
An x-ray diffraction pattern is a plot of the
intensity of x-rays scattered at different angles by a
sample
17
• The detector moves in a circle around the sample
– The detector position is recorded as the angle 2theta
(2θ)
– The detector records the number of x-rays observed at
each angle 2θ
– The x-ray intensity is usually recorded as “counts” or as
“counts per second” (x-rays of a specific wavelength)
• To keep the x-ray beam properly focused, the sample will
also rotate.
– On some instruments, the x-ray tube may rotate instead
of the sample.
18
19
• One can use a x-ray source where x-rays with a known
wavelength are emitted.
• These are sent through a crystal (or crystals) with an
unknown structure.
• The crystal and a detector are both rotated in the x-ray
"beam."
• The x-rays diffract at specific angles as predicted by the
Bragg equation.
20
• This diagram illustrates how crystalline structure may be
determined through x-ray diffraction.
• As the crystal and detector rotate, x-rays diffract at
specific angles.
• The detector reports the intensity (I) of x-ray photons as
it moves.
• Angles of diffraction (where the Bragg equation is
satisfied) are marked by peaks.
• The peak height is a function of the interaction of the xrays with the crystal and the intensity of the source.
• With respect to the Bragg equation, we are looking for d
as we change theta (lambda is constant).
21
22
23
24
Diffraction patterns are collected as 2θ vs absolute
intensity, but are best reported as dhkl vs relative
intensity
• The peak position as 2θ depends on instrumental
characteristics such as wavelength.
– The peak position as dhkl is an intrinsic ( ‫درتی ۔‬
َ ُ‫َپيدائشی ۔ ق‬
‫) َحقيقی ۔ ان َدر‬, instrument-independent, material property.
• Bragg’s Law is used to convert observed 2θ
positions to dhkl.
• The absolute intensity, i.e. the number of x-rays observed
in a given peak, can vary due to instrumental and
experimental parameters.
– The relative intensities of the diffraction peaks should
be instrument independent.
25
• To calculate relative intensity, divide the absolute
intensity of every peak by the absolute intensity of
the most intense peak, and then convert to a
percentage. The most intense peak of a phase is
therefore always called the “100% peak”.
– Peak areas are much more reliable than peak heights as
a measure of intensity.
26
The wavelength of x-rays is determined by the anode of
the x-ray source
• Electrons from the filament strike the target anode,
producing characteristic radiation via the photoelectric
effect.
• The anode material determines the wavelengths of
characteristic radiation.
• While we would prefer a monochromatic source, the xray beam actually consists of several characteristic
wavelengths of x-rays.
Repeated
29
Repeated
30
Spectral contamination in diffraction patterns
Repeated
• The Kα1 and Kα2 doublet will almost always be present
– Very expensive optics can remove the Kα2 line
– Kα1 and Kα2 overlap heavily at low angles and are more separated
at high angles
• W lines form as the tube ages: the W-filament contaminates the target
anode and becomes a new x-ray source
31
• W and Kβ lines can be removed with optics
Goniometer (‫)زاويہ پيما‬
"An important part of the study of crystallography consists
in the measuring and classifying of the interfacial ( ‫جو دو‬
‫شامل ہو‬
ِ ‫سطحوں ميں‬
َ ) angles on the crystals of all minerals.
These measurements are accomplished (‫ )حاصل کيا‬by means
of instruments known as goniometers." — Ford, 1912
• A goniometer is an instrument that either measures an angle
or allows an object to be rotated to a precise angular
position.
• The term goniometry is derived from two Greek words,
gōnia, meaning angle, and metron, meaning measure.
• The first description of a goniometer, derived from the
Astrolabe, was apparently in 1538, by Gemma Frisius.
• The platform that holds and moves the sample, optics,
detector, and/or tube.
34
35
Astrolabe
• The astrolabe is a very ancient astronomical computer for
solving problems relating to time and the position of the
Sun and stars in the sky.
• An astrolabe ("star-taker") is an elaborate inclinometer,
historically used by astronomers, navigators, and
astrologers.
36
Identification of compounds
• Powder diffraction data from known compounds have
been compiled into a database (PDF) by the Joint
Committee on Powder Diffraction Standard, (JCPDS)
• ‘Search-match’ programs are used to compare
experimental diffractograms with patterns of known
compounds included in the database
• This technique can be used in a variety of ways
7
Strontium copper oxide: SrCuO2
8
Amorphous materials compare to the
crystalline materials
• Amorphous materials do not possess long periodicity (no long
range order) compare to the crystalline materials (poses very
long range order) and atoms are randomly distributed in 3D
space.
• Amorphous materials have order only few atomic or
molecular dimensions (very short range).
• While diffracting amorphous materials with x-rays will be
scattered in many directions leading to a large bump
distributed in a wide angle or range (2 Theta) instead of high
intensity narrower peaks.
9
10
Powder X-ray diffraction of amorphous materials
• Amorphous materials have a disordered structure, i.e. no repeating
segments as is the case with crystalline materials.
• As such they do not produce distinct peaks in a diffraction pattern.
• This can be seen in the comparison below that shows the diffraction
pattern of a crystalline silica sample and an amorphous glass
sample, that has a predominantly silica composition.
• Glass is commonly made from silicon dioxide or quartz sand,
which has a crystalline structure.
• When the sand is melted and the liquid is cooled rapidly enough to
avoid crystallization, an amorphous solid called a glass is formed.
• Amorphous solids do not show a sharp phase change from solid to
liquid at a definite melting point, but rather soften gradually when
they are heated.
• The physical properties of amorphous solids are identical in all
directions along any axis so they are said to have isotropic
properties.
11
Figure: Comparison of crystalline SiO2 and amorphous SiO2. Quartz
is crystalline due to orderedness in bonding and repeating pattern
whereas glass is amorphous lacking a well ordered structure and
12
repetition of bonds.
Figure: X-Ray diffraction pattern for silica (quartz), a crystalline
13
material showing characteristic peaks.
Figure: X-Ray diffraction pattern for glass, an amorphous
material showing no distinct peaks.
14
Assignment
Find out the atomic structure of crystal like
TABLE SALT, ZINC SULPHIDE and
DIAMOND.
Link:
• https://www.youtube.com/watch?v=wtvs1t3YZPw
• https://www.youtube.com/watch?v=C1cYJthlBZY
15
What information do we get or can we get from
powder X-ray diffraction
• Following informations can we get from powder X-ray
diffraction:
– Lattice parameters (lattice constant)
– Phase identity (composition identification)
– Phase purity
– Crystallinity
– Crystal structure
– Percent phase composition
19
Illustration………
Lattice parameters (lattice constant)
• The lattice constant, or lattice parameter, refers to the
physical dimension of unit cells in a crystal lattice.
• Lattices in three dimensions generally have three lattice
constants, referred to as a, b, and c.
• A group of lattice constants could be referred to as lattice
parameters.
• However, the full set of lattice parameters consist of the
three lattice constants and the three angles between them.
• For example, the lattice constant for diamond is a =
3.57 Å at 300 K.
20
Lattice constants for various materials at 300 K
List of
lattice constants
Material
C (diamond)
C (graphite)
Si
Ge
AlAs
AlP
AlSb
GaP
GaAs
GaSb
InP
InAs
InSb
MgO
SiC
CdS
Lattice constant (Å)
Crystal structure
3.567
a = 2.461
c = 6.708
5.431
5.658
5.6605
5.4510
6.1355
5.4505
5.653
6.0959
5.869
6.0583
6.479
4.212
a = 3.086
c = 10.053
5.8320
Diamond (FCC)
Hexagonal
Diamond (FCC)
Diamond (FCC)
Zinc blende (FCC)
Zinc blende (FCC)
Zinc blende (FCC)
Zinc blende (FCC)
Zinc blende (FCC)
Zinc blende (FCC)
Zinc blende (FCC)
Zinc blende (FCC)
Zinc blende (FCC)
Halite (FCC)
Wurtzite
21
Zinc blende (FCC)
How to find lattice constant
• Identify the space lattice
– Identify the space lattice of the cubic crystal system based
on the arrangement of the atoms in the unit cell
• Find the atomic radii
– Find the atomic radius (r) of the atoms in the unit cell
• Calculate the lattice constant
– Calculate the lattice constant, a, of the cubic unit cell
22
• The length of the unit cell along the x, y, and z direction
are defined as a, b, and c.
• Alternatively, we can think of the sides of the unit cell in
terms of vectors a, b, and c.
• The angles between the crystallographic axes are defined
by:
– α = The angle between b and c
– β = The angle between a and c
– γ = The angle between a and b
• a, b, c, α, β, γ are collectively known as the lattice
parameters (often also called ‘unit cell parameters’, or just
‘cell parameters’).
23
Unit cell
24
Phase identity (composition identification)
• Powder diffraction data are commonly used to identify or
‘finger print’ crystalline materials.
• X-ray powder diffraction (XRD) is a rapid analytical
technique primarily used for phase identification of a
crystalline material and can provide information on unit
cell dimensions.
• General
X-ray
diffraction
phase/composition
identification will distinguish the major, minor, and trace
compounds present in a sample.
• The data usually includes mineral (common) name of the
substance, chemical formula, crystalline system, and reference
pattern number from the ICDD International database.
• A summary table of analysis results and diffraction plot with
reference pattern markers for visual comparison is shown
25
below:
26
Major phases
Minor phases
Trace phases
Anhydrite, CaSO4 Calcite, syn CaCO3 Portlandite, syn,
orthorhombic ICDD #
rhombohedral ICDD Ca(OH)2 -hexagonal
72-0916
# 05-0586
ICDD# 44-1181
Gypsum, syn
Brucite, Mg(OH)2 Quartz, SiO2 CaSO4.2H2O hexagonal ICDD# 74- hexagonal ICDD# 64monoclinic ICDD#
2220
0312
33-031
• General X-ray diffraction phase identification and bulk
elemental X-ray fluorescence are complimentary
analyses, which provide elemental composition and
chemical phase and crystal structures actually present in a
sample.
27
Each “phase” produces a unique diffraction pattern
Quartz
Cristobalite
Glass
15
20
25
30
35
Position [°2Theta] (Cu K-alpha)
• A phase is a specific chemistry and
atomic arrangement.
• Quartz, cristobalite, and glass are
all different phases of SiO2
– They are chemically identical,
but the atoms are arranged
differently.
– As shown, the X-ray diffraction
pattern is distinct for each
different phase.
– Amorphous materials, like
40
glass, do not produce sharp
diffraction peaks.
The X-ray diffraction pattern is a fingerprint that lets you figure out
28
what is in your sample.
The diffraction pattern of a mixture is a simple sum of the
diffraction patterns of each individual phase.
Quartz
Mixture
Cristobalite
Glass
0
15
20
25
30
35
Position [°2Theta] (Cu K-alpha)
40
15
20
25
30
35
Position [°2Theta] (Copper (Cu))
• From the XRD pattern you can determine:
– What crystalline phases are in a mixture
– How much of each crystalline phase is in the mixture
– If any amorphous material is present in the mixture
40
Some uses of phase identification
• A phase is a crystalline solid with a regular 3-dimensional
arrangement of the atoms.
• The measured diffraction peak positions and intensities are like a
fingerprint of a particular crystalline phase.
• Identification is accomplished by comparison of the measured
pattern with the entries.
• Typical examples where phase identification is being applied are:
• Identification of minerals in geological samples:
– Phase identification aids understanding of the formation
mechanisms of samples, which can provide valuable
information regarding the presence of ores or fuels.
– Grade control of ores and rocks: for exploration of mineral
deposits.
– Detection of polymorphs to distinguish substances with the
same chemical composition in different phases of a certain
material, an important task for the pharmaceutical industry.
30
• Quality control:
– Determination of the presence of impurities in a pure phase.
– With modern X-ray optics and detectors, impurities down to
0.1 weight-% can be detected
• Nanomaterials:
– For example, the rutile phase of nano-titania is required for UV
blocking applications (e.g., in sunscreens) whereas
photocatalytic activity requires the anatase phase.
• Polymers and plastics:
– Identification of crystalline phases and polymorphs, as well as
of filler materials by WAXS (wide-angle X-ray scattering).
– Detection of phase transitions under non-ambient conditions,
such as variable temperature or humidity
• Forensics:
– Phase identification can be a deciding factor in determining the
origin of traces found at crime scenes.
31
• Corrosion in boilers and power plants:
– The phases found give valuable information about the
conditions and reactions leading to problems.
– Indirectly they give hints on how to prevent or minimize
corrosion processes.
32
Phase purity
• When an X-ray is shined on a crystal, it diffracts in a
pattern characteristic of the structure.
• In powder x-ray diffraction, the diffraction pattern is
obtained from a powder of the material, rather than an
individual crystal.
• Powder diffraction is often easier and more convenient
than single crystal diffraction since it does not require
individual crystals be made.
• Powder x-ray diffraction (XRD) also obtains a diffraction
pattern for the bulk material of a crystalline solid, rather
than of a single crystal, which doesn't necessarily
represent the overall material.
• A diffraction pattern plots intensity against the angle of
the detector, 2θ.
5
• Since most materials have unique diffraction patterns,
compounds can be identified by using a database of
diffraction patterns.
• The purity of a sample can also be determined from its
diffraction pattern, as well as the composition of any
impurities present.
• A diffraction pattern can also be used to determine and
refine the lattice parameters of a crystal structure.
• A theoretical structure can also be refined using a method
known as Rietveld refinement.
• The particle size of the powder can also be determined by
using the Scherrer formula, which relates the particle size
to the peak width.
6
• The Scherrer fomula is:
with
• λ is the x-ray wavelength
• BM is the observed peak width
• BS is the peak width of a crystalline standard
• θ is the angle of diffraction
7
• The Scherrer equation is a widely used tool to determine the
crystallite size of polycrystalline samples.
• However, it is not clear if one can apply it to large crystallite
sizes because its derivation is based on the kinematical
theory of x-ray diffraction.
• For large and perfect crystals, it is more appropriate to use
the dynamical theory of x-ray diffraction.
• Because of the appearance of polycrystalline materials with
a high degree of crystalline perfection and large sizes, it is
the authors' belief that it is important to establish the
crystallite size limit for which the Scherrer equation can be
applied.
Kinematical x-ray scattering theory
• The essence of the kinematical x-ray scattering theory lies in the assumption
that an x-ray photon, after being scattered by an electron, cannot be scattered
by another electron again. Thus, only one scattering act can take place on a
8
single ray.
intensity
Figure: XRD pattern for Ba24Ge100. The x-axis is 2θ and the y-axis is the
9
intensity.
Crystallinity
Crystallinity refers to the degree of structural order in a solid. In a
crystal, the atoms or molecules are arranged in a regular, periodic
manner. The degree of crystallinity has a big influence on hardness,
density, transparency and diffusion.
• Properties of textile fibers are determined by their chemical
structure, degree of polymerization, orientation of chain molecules,
crystallinity, package density and cross linking between individual
molecules.
• Polymer crystallinity is one of the important properties of all
polymers.
• Polymer exists both in crystalline and amorphous form.
• Crystallinity is indication of amount of crystalline region in polymer with
respect to amorphous content.
• Crystallinity influences many of the polymer properties some of there are:
– Hardness
– Modulus
– Tensile
– Stiffness
10
Figure: Shows the arrangement of polymer chain forming
crystalline and amorphous regions. It can be seen that part of
molecules are arranged in regular order, these regions are
called crystalline regions. In between these ordered regions
molecules are arranged in random disorganized state and these
11
are called amorphous regions.
– Crease
– Melting Point
• So while selecting polymer for required application its
crystallinity plays foremost role.
• X-Ray diffraction is also used to measure the nature of
polymer and extent of crystallinity present in the polymer
sample.
• Following figure shows the schematic diagram of x-ray
diffraction pattern.
• Crystalline regions in the polymer seated in well-defined manner
acts as diffraction grating.
• So the emerging diffracted pattern shows alternate dark and light
bands on the screen.
• X-ray diffraction pattern of polymer contain both sharp as well as
defused bands.
• Sharp bands correspond to crystalline orderly regions and defused
12
bands correspond to amorphous regions.
Figure: Schematic diagram of x-ray diffraction pattern.
• Crystalline structure is regular arrangement of atoms.
• Polymer contains both crystalline and amorphous phase
within arranged randomly.
• When beam of x-ray passed through the polymer sample,
some of the regularly arranged atoms reflect the x-ray
beam constructively and produce enhanced intense
13
pattern.
• Following figure shows schematic pattern of x-ray
diffraction.
• Amorphous samples gives sharp arcs since the intensity of
emerging rays are more, where as for crystalline samples,
the incident rays get scattered.
• Arc length of diffraction pattern depends on orientation.
• If the sample is highly crystalline, smaller will be the arc
length.
(a)
(b)
Figure: X-ray diffraction pattern of (a) amorphous sample and
14
(b) Semi-crystalline polymer sample.
Crystal structure
A crystal structure is a unique arrangement of atoms in a crystal. A crystal
structure is composed of a unit cell, a set of atoms arranged in a particular
way; which is periodically repeated in three dimensions on a lattice
• Crystal structure can be determined by measuring inter-planar
spacing.
• We use X-ray Diffraction to measure this spacing.
• Inter-planar spacing can be calculated using:
• Bragg’s Law:
• Depending on crystal types, certain {hkl} planes will diffraction
and can be used to identify the crystal structure.
Note:
• We have a set of selection rules to help us identify them.
• You do not need to memorize these rules – they would be given to
you on an exam, if a question was asked.
15
16
Interplanar spacing
• The interplanar distance (or interplanar spacing) is the
perpendicular distance between adjacent planes in this family.
Order reflection
• If the path difference is simply one wavelength the Bragg
condition can be stated as:
• This is a first order reflection.
• If the path difference is two wave lengths the Bragg condition
becomes:
and the reflection is a second order reflection.
17
18
19
20
Body-Centered Cubic = BBC
A polycrystalline sample should contain thousands of
crystallites. Therefore, all possible diffraction peaks should be
observed.
21
• For every set of planes, there will be a small percentage
of crystallites that are properly oriented to diffract (the
plane perpendicular bisects the incident and diffracted
beams).
• Basic assumptions of powder diffraction are that for
every set of planes there is an equal number of
crystallites that will diffract and that there is a statistically
relevant number of crystallites, not just one or two.
22
Percent phase composition
• General x-ray diffraction phase/composition identification will
distinguish the major, minor, and trace compounds present in a
sample.
• The data usually includes mineral (common) name of the substance,
chemical formula, crystalline system, and reference pattern number
from the ICDD International database.
hkl Parameters
• In particular, a family of lattice planes is determined by three
integers h, k, and ℓ, the Miller indices.
• They are written (hkℓ), and denote the family of planes orthogonal
to , where are the basis of the reciprocal lattice vectors.
• Powder XRD is used to obtained spacing between lattice planes
(hkl Miller indices) → this interplanar spacing (d. hkl. ) is the
distance between parallel planes of atoms or ions
23
What information do we NOT get from powder x-ray
diffraction
• Elemental analysis
– How much lithium is in this sample?
– Is there iron in this sample
– What elements are in this sample
• Tell me what this sample is ????
– Unless you know something about this sample,
powder XRD won’t have answers !!!
24
Applications of Powder X-Ray Diffraction in Science and Technology
Polymorph study
In materials science, polymorphism is the ability of a solid material to
exist in more than one form or crystal structure. Polymorphism can
potentially be found in any crystalline material
including polymers, minerals, and metals, and is related to allotropy,
which refers to chemical elements.
• PXRD is helpful in identification and characterization of polymorph,
monitoring the stability, method development and validation for
identification and quantification of drugs in Pharmaceutical Industries.
• X-rays are partially scattered by atoms when they strike the surface of
a crystal.
• The part of the x-ray that is not scattered simply passes through the
next layer of atoms, where again part of the x-ray is scattered and part
of it passes through to the next layer.
• This causes an overall diffraction pattern, similar to how a grating
diffracts a beam of light.
• In order for an x-ray to diffract, the sample must be crystalline and the
6
spacing between atom layers must be close to the radiation wavelength.
• If beams diffracted by two different layers are in phase, constructive
interference occurs and the diffraction pattern shows a peak.
• However, if they are out of phase, destructive interference occurs
appear and no peak is observed.
• Diffraction peaks only occur if it follows Bragg’s Law.
• Since, a highly regular structure is needed for diffraction to occur,
only crystalline solids diffract, the PXRD of amorphous materials do
not depict any significant peak in diffraction pattern.
Variable temperature and relative humidity study by PXRD
• Solid phase transitions such as polymorph inter-conversions are
routinely examined by x-ray diffractometer using variable
temperature sample stages (VT-XRD).
• Both subambient and elevated temperature stages are available that
can help to study the sample behavior at variable temperature
conditions.
• VT-XRD helps to directly identify the crystalline phase as a function
of temperature.
7
• XRPD is also commonly used to investigate the structure of variable
hydrates that are crystalline and contain nonstoichiometric water
within channels in the crystal lattice.
• The amount of water present in a variable hydrate occurs as a
function of the change in relative humidity (RH) in the environment
of the sample.
• The peak positions in the diffractogram refers to dimensions of the
unit cell so a change in the size of the unit cell due to the presence of
water can be screened by comparison of XRPD patterns under
different RH environments.
Screening the crystal structure and lattice parameters using PXRD
• While it will always be advantageous to solve the crystal structure
using single-crystal diffraction, it is not always possible as some
crystalline substances do not possess the necessary size and quality.
• Traditionally, structural analyses using powder diffraction data are
conducted using patterns obtained from synchrotron sources.
8
• When a complete structural solution is not possible from PXRD, it may
still be possible to use a high quality PXRD pattern to obtain useful
informations such as unit cell parameters and the crystalline space
group.
• Crystal structure determination from powder diffraction data is
sometimes tedious due to the overlap of reflections in a powder
experiment.
• A number of methods are used for structural determination like
simulated annealing and charge flipping.
• The crystal structures of known materials can be evaluated as a
function of temperature or pressure, using the Rietveld method.
• It is full pattern analysis technique.
• It is used to determine unknown structures from powder data.
• A number of programs can be used for structure determination such as
TOPAS.
• X-ray diffraction provides ample information about the lattice
parameters.
• The position of a diffraction peak is determined by the size and shape
9
of unit cell of the crystalline phase.
• Peak represents a lattice plane and therefore can be characterized by
Miller index.
• If the symmetry is high as in case of cubic or hexagonal, it is not
difficult to identify the peak index for an unknown phase.
• This is very useful in solid state chemistry to identify new materials.
• Once a pattern gets indexed, it serves as reference for new entities.
Use of PXRD in pharmaceutical industry
• XRD is the key technique for drug analysis.
• It serves a major role in all stages of drug development, testing and
production.
• It is an essential part of analytical research and development, quality
control of the active ingredients, excipients and final products
• Minor changes may cause major batch-to-batch inconsistency that
may cause critical problems and lead to problems in the
manufacturing of the pharmaceutical dosage form, the quality of the
formulation, the bioavailability and drug stability.
• Many new drug moiety exhibit different forms (polymorphs or
solvates) that vary in their physical properties.
10
• Differences in these forms can affect the quality or efficacy of the new
drug.
• It helps in elucidation of the relevant polymorphic and pseudopolymorphic forms in pharmaceutical development.
• The materials ranging from Active Pharmaceutical Ingredients to
finished dosage forms have to be properly screened by XRD as it
ultimately cause changes in diffraction patter and affects the bioavailability.
Use of PXRD in nano and material science
• The term particle size and crystallite size refer to two distinct
properties in a material.
• Particles comprise of several small crystallite.
• Crystallite size is the fundamental property of materials.
• Properties of nanomaterials depend on crystals size and not particle
size.
• PXRD can measure millions of crystals and accurately determine the
size distribution of nanomaterials.
• It can be widely used for studying the nature of polymers and
11
composites in Material Science.
PXRD use in forensic studies
• PXRD is useful in trace analysis.
• It can be used to contact traces of paint flakes, hair, glass
fragments, stains of any description and loose powdered materials.
• Identification and comparison of trace quantities of material can
help in the conviction of a suspect of his involvement in a crime.
Paint Flakes
Flaking refers to a paint failure, where the paint lifts up and peels
away from the substrate due to the loss of adhesion. When paint is
applied over a moist, greasy, chalky or any other improper
surface, flaking is the most likely result.
Geological applications of PXRD
• PXRD is the key tool in mineral exploration.
• The advent of PXRD has revolutionized the geological sciences to
a great extent.
• It is not easy to precede the characterization and identification of
the samples without powder XRD.
12
• Every mineral is defined by a characteristic crystal structure that
gives a unique x-ray diffraction pattern, allowing rapid identification
of minerals present within a rock and soil sample.
• The PXRD data can be fruitful to determine the proportion of the
different minerals present in a given sample.
Microelectronics industry using PXRD
• Microelectronics industry uses silicon and gallium arsenide
substrates in integrated circuit production; there is a need to fully
characterize these materials by incorporating the information’s
obtained by PXRD.
• XRD topography detects and forms the image of the defects within a
crystal.
Use of PXRD in glass industry
• Glasses are amorphous in nature.
• The x-ray pattern of amorphous compounds does not contain any significant
peak.
• However, there are many uses of PXRD in the glass industry.
• It includes identification of crystalline particles that creates faults in bulk
quantity of glass, measurements of crystalline coatings for texture, crystalline
13
size and crystallinity.
Crystallinity study by PXRD
• The XRD analysis of crystalline compounds gives a diffraction
pattern consisting of a well-defined, narrow, sharp and significant
peak while amorphous materials do not give clear peaks rather the
pattern has noise signals, smeared peak or it can have some short
order bumps.
• Many polymers depict semi-crystalline behavior and produce halo
pattern.
• Powder XRD can be used to determine the crystallinity by
comparing the integrated intensity of the background pattern to
that of the sharp peaks.
• Different scientists have reported variable methods to find out the
percentage crystallinity and crystallinity index.
• Ashish Chauhan and Balbir Kaith have widely used it for polymer
characterization.
14
Studying phase transitions by PXRD
• Under certain conditions, such as 0°C for water at 1 atm, a new
arrangement of atoms or molecules may become stable, leading to a
phase transition.
• At this point new diffraction peaks will appear or old ones
disappear according to the symmetry of the new phase.
• If the material melts to an isotropic liquid, all sharp lines will
disappear and be replaced by a broad amorphous pattern.
• If the transition produces another crystalline phase, one set of lines
will suddenly be replaced by another set.
• In some cases however lines will split or collapse, e.g., if the
material undergoes a continuous, second order phase transition.
• In such cases the symmetry may change because the existing
structure is distorted rather than replaced by a completely different
one.
• For example, the diffraction peaks for the lattice planes (100) and
(001) can be found at two different values of q for a tetragonal phase,
but if the symmetry becomes cubic the two peaks may coincide. 15
Isotropy
Isotropy is the property of molecules and materials of having
identical physical properties in all directions.
Size and strain broadening
• Peak size broadening in PXRD pattern gives many informations.
• There are many factors that cause peak broadening such as
instrumental factors, the presence of defects, differences in strain,
size of the crystallites.
• It is easy to calculate the effects of size and strain.
• Where size broadening is independent of q (K=1/d), strain
broadening increases with increasing q-values. In most cases there
will be both size and strain broadening.
16
In short……
• X-ray powder diffraction is most widely used for the
identification of unknown crystalline materials (e.g.,
minerals, inorganic compounds).
• Determination of unknown solids is critical to studies in
geology, environmental science, material science,
engineering and biology.
Other applications include:
• Characterization of crystalline materials
• Identification of fine-grained minerals such as clays and
mixed layer clays that are difficult to determine optically
• Determination of unit cell dimensions
• Measurement of sample purity
17
With specialized techniques, XRD can be used to:
• Determine crystal structures using Rietveld refinement
• Determine of modal amounts of minerals (quantitative
analysis)
• Characterize thin films samples by:
– Determining lattice mismatch between film and substrate
and to inferring stress and strain
– Determining dislocation density and quality of the film by
rocking curve measurements
– Measuring superlattices in multilayered epitaxial structures
– Determining the thickness, roughness and density of the
film using glancing incidence x-ray reflectivity
measurements
• Make textural measurements, such as the orientation of grains,
in a polycrystalline sample
18
Summary
19
Conclusions
• Advances in PXRD instrumentation and software have improved
the efficacy of pharmaceutical drugs, efficiency of solid state
characterization and rapid analysis of composites and materials.
• Variable temperature and humidity techniques are especially
powerful in understanding structural changes of pharmaceutical
drugs to enhance the stability and screen the drug substances under
variable conditions.
• Ongoing developments involving structure determination directly
from PXRD are encouraging to determine the crystal structures of
new synthesized compounds and in pharmaceuticals.
• XRD in association with DSC, TGA, DTA, FTIR techniques can
solve numerous problems encountered in industries for
pharmaceutical formulation and pharmaceutic developments.
• The excellence of this technique is catering to academic research
and commercial use in industries.
• Powder X-Ray Diffraction technique is a key analytical technique
to serve the growth and development of Science and Technology.
20
Strengths and Limitations of Powder X-ray Diffraction (PXRD)
Strengths of X-ray Powder Diffraction
• Powerful and rapid (< 20 min) technique for identification of an
unknown mineral
• In most cases, it provides an unambiguous mineral determination
• Minimal sample preparation is required
• XRD units are widely available
• Data interpretation is relatively straight forward
Limitations of X-ray Powder Diffraction
• Homogeneous and single phase material is best for identification
of an unknown
• Must have access to a standard reference file of inorganic
compounds (d-spacings, hkls)
6
• Requires tenths of a gram of material which must be ground into a
powder
• For mixed materials, detection limit is ~2% of sample
• For unit cell determinations, indexing of patterns for non-isometric
crystal systems is complicated
• Peak overlay may occur and worsens for high angle 'reflections'
• The technique is not as powerful as the single-crystal methods, for
it gives less accurate atomic positions, but has the advantage of
not requiring the growth of a single crystal.
• If beams diffracted by two different layers are in phase,
constructive interference occurs and the diffraction pattern shows
a peak.
• However, if they are out of phase, destructive interference occurs
appear and no peak is observed.
• Diffraction peaks only occur if it follows Bragg’s Law.
• Since, a highly regular structure is needed for diffraction to occur,
only crystalline solids diffract, the PXRD of amorphous materials
7
do not depict any significant peak in diffraction pattern.
Advantages and disadvantages of Powder XRD
• PXRD has numerous advantages like non-destructive nature, high
sensitivity, reliability, depth profiling (glancing incident angle),
easy sample preparation, system is user friendly, operational
procedure is convenient, fast speed, effective resolution, low
maintenance cost, proper automation, easy data interpretation that
could be used for both qualitative and quantitative analysis, in
wide range of applications.
• However, it has a few disadvantages due to use of harmful
radiations moreover there is requirement of standard reference to
match for an inference and an expensive instrument.
• It is used to study the crystalline content, identify the crystalline
phases, spacing between lattice planes, scales of existence,
preferential order and epitaxial growth of crystallites.
• Since every material has its unique diffraction patterns so
materials and compounds can be identified by using a database of
diffraction patterns.
10
• The percentage purity of a sample can be accessed by diffraction pattern
by considering the proportion and composition of impurities present.
• PXRD is the basic requisite for differentiating the crystalline sample
from semi crystalline like in a polymer e.g., cotton and amorphous
material e.g., phenol formaldehyde complex resins.
• It is the primary tool for solid state characterization.
11
12
• The samples subjected for analysis are generally in the form of
finely divided powders and diffraction can be obtained from flat
surfaces made coplanar to the holder.
• The sample for analysis could be of vast array, including inorganic
complexes, organic compounds, fiber, polymers, metals,
composites, metallurgical samples, pharmaceuticals, earth
sciences, microelectronics and nanotechnology.
• PXRD can also be wisely used to study and explore the pseudo
crystalline structure of mesoporous materials and colloidal
materials provided that the length scales are in the correct regime
and proportion.
• It is frequently used for the analysis of asbestos, catalyst,
ceramics, chemicals, clays and minerals, cement, composite,
corrosion
products,
fly-ash,
environmental
studies,
semiconductors, textiles, plastics, nanomaterials, pharmaceuticals,
metals, alloys etc.
13
In short…….
Advantages of powder x-ray diffraction
• X-ray is the cheapest, the most convenient and widely used
method
• There is no need of an evacuated chamber for specimen as x-rays
are not absorbed by air
Disadvantages of powder x-ray diffraction
• X-rays do not interact strongly with lighter elements
• Pure crystal of higher regularity must needed for analysis
• Large crystals can not be studied
Thin film
• A thin film is a layer of material ranging from fractions of a
nanometer (monolayer) to several micrometers in thickness.
• The controlled synthesis of materials as thin films (a process
referred to as deposition) is a fundamental step in many
14
applications.
Powder X-Ray Diffraction (PXRD) v/s Single Crystal X-Ray
Diffraction (SCXRD)
• The original discovery of diffraction was made using a single
crystal rather than a powder specimen.
• Single crystal diffraction has dominated crystallography ever since
though powder diffraction has had its moments and has seen a
sustained revival over the last 25 years.
• In short, a single crystal provides an unambiguous way in which
a dhkl can be chosen (fixed) and rotated (theta scanned) to yield a
diffraction event.
• However powder specimens provide for an alternative strategy in
which crystal rotation is not necessary: the millions of crystallites
present in a powder specimen are randomly oriented; there is no
requirement for rotation since, statistically, all possible orientations
are represented in the powder i.e., those crystallites at the
appropriate orientation satisfying Bragg's Law will diffract the xrays, whereas those at the wrong orientation do not diffract.
17
• The simplicity arising from not having to grow a sufficiently large
crystal nor having to provide an arranged sample rotation can be
considerable in certain cases though this gain is achieved at some
cost.
• We need to consider what are the ideal characteristics of a powder
specimen.
• First the individual crystallites composing the specimen must be:
– Highly crystalline
– The crystallites must be randomly oriented to represent all
possible crystal orientations
– The size of the crystallites must be small enough such that a
sufficiently large statistical number can be present within a
powder specimen to represent all possible orientations
• However, the size of the crystallites must also be large enough such
that poor diffraction does not result from certain adverse effects of
too small a crystallite size.
18
• If the crystallites have highly asymmetric shapes (e.g. plates or
needles) they will tend to become aligned when packed
together as a powder specimen; the best shapes are termed
equi-axed, the closest realistic approximation to the ideal
shape which would be a sphere.
• It is found empirically that, for most materials, a crystallite
size of between 1 and 10 µm (1 µm = 10-3 mm = 10-6 m) is
ideal.
• For example, an ideal crystallite with approximately cubic
shape might have a volume of 1 µm3 (i.e. 10-9 mm3 or 10-36
m3).
19
Summary………
• PXRD is not as powerful as single crystal XRD
• PXRD gives less accurate atomic positions as compared to
SCXRD
• SCXRD requires the growth of single crystals while there is no
need for PXRD
• In PXRD sample must be in powder form while in SCXRD only
single crystal is required
• In PXRD large crystallite sizes and non-random crystallite
orientations both lead to peak intensity variation
• PXRD obtains diffraction pattern for bulk material of crystalline
solid while SCXRD does not necessarily represent the overall
material
• In PXRD diffraction pattern is obtained from a powder of material,
rather in SCXRD individual crystal gives the diffraction pattern
• PXRD is easier and more convenient than SCXRD as it does not
require individual crystal be made
20
• X-rays (single crystals) will be scattered only in certain directions
when they hit the formed lattice planes (formed by atoms).
• This will cause high intensity peaks
• For polycrystalline materials x-rays will be scattered in many
directions leading to a large bump distributed in a wide range (2
Theta)
instead
of
high
intensity
narrower
peaks.
21
Data collection, results and presentation
Data collection
• The intensity of diffracted x-rays is continuously recorded as the
sample and detector rotate through their respective angles.
• A peak in intensity occurs when the mineral contains lattice planes
with d-spacings appropriate to diffract x-rays at that value of θ.
• Although each peak consists of two separate reflections (Kα1 and
Kα2), at small values of 2θ the peak locations overlap with
Kα2 appearing as a hump on the side of Kα1.
• Greater separation occurs at higher values of θ.
• Typically these combined peaks are treated as one.
• The 2λ position of the diffraction peak is typically measured as the
center of the peak at 80% peak height.
Data reduction
• Results are commonly presented as peak positions at 2θ and x-ray counts
(intensity) in the form of a table or an x-y plot.
• Intensity (I) is either reported as peak height intensity, that intensity
above background, or as integrated intensity, the area under the peak.
24
• The relative intensity is recorded as the ratio of the peak intensity to that of the
most intense peak (relative intensity = I/I1 x 100 ).
Determination of an Unknown
• The d-spacing of each peak is then obtained by solution of the Bragg equation
for the appropriate value of λ.
• Once all d-spacings have been determined, automated search/match routines
compare the ds of the unknown to those of known materials.
• Because each mineral has a unique set of d-spacings, matching these d-spacings
provides an identification of the unknown sample.
• A systematic procedure is used by ordering the d-spacings in terms of their
intensity beginning with the most intense peak.
• Files of d-spacings for hundreds of thousands of inorganic compounds are
available
from
the
International
Centre
for
Diffraction
Data (https://www.icdd.com/) as the Powder Diffraction File (PDF).
• Many other sites contain d-spacings of minerals such as the American
Mineralogist
Crystal
Structure
Database
(http://rruff.geo.arizona.edu/AMS/amcsd.php).
• Commonly this information is an integral portion of the software that comes
with the instrumentation.
Determination of Unit Cell Dimensions
• For determination of unit cell parameters, each reflection must be indexed to a
25
specific hkl.
X-ray diffraction: Crystal structure determination
Link:
• https://www.youtube.com/watch?v=pRwv3kiAkOQ&t=120s
26
Factors that affect x-ray spectra
Link:
• https://www.youtube.com/watch?v=QQ2IbjOmir8
28
How
to
plot
x-ray
diffraction
(diffractogram) in Origin Pro?
pattern
Link:
• https://www.youtube.com/watch?v=Amccrzc_nq0
30
Tricky X-ray Question (Tricky XRD)
Link:
• https://www.youtube.com/watch?v=c4RouhWOUcw
32
X-ray diffraction worked example problem
Link:
• https://www.youtube.com/watch?v=6IzrOWIw3zQ
34
Miller Bravais for hexagonal crystals
Link:
• https://www.youtube.com/watch?v=toRd5L7S--A&t=4s
36
Miller Indicies Practice Examples
Link:
• https://www.youtube.com/watch?v=n84gzYlB0BQ&t=29s
38
41