Phase Identification by X-ray diffraction
Group 3
Amir Keyvan Edalat Nobarzad
Mahdi Masoumi Khalilabad
Keivan Heirdari
SYS862/Autumn 2014
Prof. Mohammad Jahazi
Table of Contents
1
Introduction ...................................................................................................................... 3
2
Generation of X-ray ......................................................................................................... 3
3
Bragg`s Law ..................................................................................................................... 6
4
Diffraction Intensity ......................................................................................................... 7
5
Structure factor ................................................................................................................. 8
6
X-ray Diffractometry........................................................................................................ 9
6.1
Instrumentation ....................................................................................................... 10
6.2
System Aberrations ................................................................................................. 12
7
Samples and Data Acquisition ....................................................................................... 13
7.1
Sample Preparation ................................................................................................. 13
7.2
Acquisition and Treatment of Diffraction Data ...................................................... 14
8
Distortions of Diffraction Spectra .................................................................................. 14
8.1
Preferential Orientation ........................................................................................... 14
8.2
Crystallite Size ........................................................................................................ 15
8.3
Residual Stress ........................................................................................................ 15
9
Application ..................................................................................................................... 16
9.1
Phase Identiication .................................................................................................. 16
9.2
Quantitative Measurement ...................................................................................... 17
10
Wide-Angle X-Ray Diffraction and Scattering .......................................................... 17
11
Refrences .................................................................................................................... 18
1 Introduction
X-ray diffraction (XRD analysis or XRPD analysis) is very useful to identify the phases in
powder specimens, poly crystalline aggregate solids and thin-film samples. The key for
identifying of materials by this method is their unique crystalline structure. XRD has wide
variety applications such as:








Detecting crystalline minority phases (at concentrations greater than ~1%)
Determining crystallite size for polycrystalline films and materials
Determining percentage of material in crystalline form versus amorphous
Measuring sub-milligram loose powder or dried solution samples for phase identification
Analyzing films as thin as 50 angstroms for texture and phase behaviors
Determining strain and composition in epitaxial thin films
Determining surface offcut in single crystal materials
Measuring residual stress in bulk metals and ceramics
2 Generation of X-ray
X-rays are short wavelength and high energy waves of electromagnetic radiation which are
characterized either by wavelength or photon energy. Most X-rays have a wavelength in the
range of 0.01 to 10 nanometers; X-ray wavelengths are shorter than those of UV rays and
typically longer than those of gamma rays.
Figure 2-1. The electromagnetic spectrum, presented as a function of wavelength, frequency,
and energy. X-rays and γ-rays comprise the high-energy portion of the electromagnetic spectrum[1]
X-rays are produced by high speed electrons accelerated by a high voltage filled colliding
with a metal target. rapid deceleration of electrons on target enables the kinetic energy of
electrons to be converted to energy of X-ray radiation, the wavelength of x-ray radiation, λ, is
related to the acceleration voltage of electrons(V)as shown in the following equation [2]:
𝜆=
1.2398 ∗ 103
(𝑛𝑚)
𝑉
Eq. 2-1
Figure 2-2. X-ray tube schematic[2].
Figure 2-2 indicates an X-ray tube containing a source of electrons and two metal electrodes
in a vacuum tube, the high voltage maintained across these electrodes rapidly draws the electrons
to the anode (target) there are windows to guide X-rays out of the tube. Extensive cooling is
necessary for the X-ray tube because most of the kinetic energy of electrons is converted into
heat; less than one percent is transformed into X-rays.
As we can see in equation more voltage we have we will produce an X-ray with shorter
wavelength which has maximum radiation energy. For XRD we need we need a single wave Xray radiation which is generated by filtering out other radiations from the spectrum. Figure 2-3
indicates the phenomenon of X-ray generation.
Figure 2-3. electronic transition in an atom (schematic), emission
processes indicated by arrows [3].
In this phenomenon an incident electron with enough energy excites an electron in inner
shell of an atom (our target) to a higher state; another electron from outer shell will be replaced
instead of excited electron. The energy released by this action is in form of X-ray. The
wavelengths can be different depending that the electron in replace to which layers, these lines
are called characteristics lines, for example if we have molybdenum as target metal, the K lines
have a wavelength of 0.7A, L lines about 5A, and M lines still higher, usually only K lines are
used for X-ray diffraction because the longer wavelengths are being too easily absorbed.
As shown in Figure 2-3 K layer can be filled by an electron from L or M layer, the waves
produced are named Kα and Kβ respectively. Intensity of Kα is higher than Kβ because the
probability of filling an electron from L to K is more than M to K. Table 2-1 shows the X-ray
characteristics of usual target materials. If the heavier metal that we always use is Mo, because
the metals with high density are not appropriate for target.
Table 2-1. X-ray characteristics of usual target materials[2].
Many X-ray diffraction experiments need radiation which is as closely monochromatic as
possible to We need to also filter the rays in order to keep only Kα, to do this filters made of
some materials which can absorb all other rays except Kα.Table 2-2 indicates the appropriate
filters for each target.
Table 2-2. Filters for suppression of Kβ radiations[3].
Before explaining the Braggs law, let’s make a quick review on phenomenon of wave
interferences, as indicated in Figure 2-4 Constructive interference occurs when combining two
same-wavelength waves that do not have a phase difference between them. However, completely
destructive interference occurs when combining two waves with phase difference of a half
wavelength (λ/2). In fact When they have a phase difference of nλ (n is an integer), called ‘in
phase’, constructive interference occurs. When they have a phase difference of nλ/2, called
‘completely out of phase’, completely destructive interference occurs.
Figure 2-4. Constructive(upper figure) and destructive interface[2].
3 Bragg`s Law
The interpretation of XRD is based on Brag law which determines the scattering angles at
which peaks of strong scattered intensity may occur, composition is measured through
identification of positions and intensities of diffraction peaks which are unique to a given
chemical compound.
When an X-Ray beam with a known wavelength is incident to a crystalline solid, the
crystalline planes will make the diffraction, according to Bragg`s Law the deflected waves will
not be in phase except when the following relationship is satisfied:
𝑛𝜆 = 2𝑑 sin 𝜃
Eq. 3-1
The Eq. 3-1 is the Bragg`s law, with this equation when we have constructive interface we
can determine the distance between atomic planes and therefore we can determine the crystalline
structure of material.
Figure 3-1.Brags law [2].
Bragg's law, as stated above, can be used to obtain the lattice spacing of a particular cubic
system through the following relation:
𝑑=
𝑎
√ℎ2
𝑘2
Eq. 3-2
𝑙2
+ +
Where a is the lattice spacing of the cubic crystal, and h, k, and l are the Miller indices of the
Bragg plane. Combining this relation with Bragg's law:
(sin 𝜃)2
𝜆 2
( ) = 2
2𝑎
ℎ + 𝑘 2 + 𝑙2
Eq. 3-3
One can derive selection rules for the Miller indices for different cubic Bravais lattices; here,
selection rules for several will be given as is.
4 Diffraction Intensity
Even if we satisfy the Bragg`s law we cannot make sure that we can detect diffraction from
crystallographic planes. We need also appropriate diffraction intensity. Diffraction intensity may
vary among planes even though the Bragg conditions are satisfied. X-ray diffraction by a crystal
arises from X-ray scattering by individual atoms in the crystal. The diffraction intensity relies on
collective scattering by all the atoms in the crystal. In an atom, the X-ray is scattered by
electrons, not nuclei of atom. An electron scatters the incident X-ray beam to all directions in
space. The scattering intensity is a function of the angle between the incident beam and
scattering direction (2θ). The X-ray intensity of electron scattering can be calculated by the
following equation.
𝐼0 1 + (cos 2𝜃)2
𝐼(2𝜃) = 2 𝐾
𝑟
2
Eq. 4-1
Io is the intensity of the incident beam, r is the distance from the electron to the detector and
K is a constant related to atom properties. The last term in the equation shows the angular effect
on intensity, called the polarization factor. The incident X-ray is unpolarised, but the scattering
process polarizes it.
The total scattering intensity of an atom at a certain scattering angle, however, is less than
the simple sum of intensities of all electrons in the atom. There is destructive interference
between electrons due to their location differences around a nucleus, as illustrated in Figure 4-1.
Destructive interference that results from the path difference between X-ray beams scattered
by electrons in different locations is illustrated in Figure 3-1. Figure 3-1-b shows an example of a
copper atom, which has 29 electrons. The intensity from a Cu atom does not equal 29 times that
of a single electron in Equation 2.9 when the scattering angle is not zero. The atomic scattering
factor (f) is used to quantify the scattering intensity of an atom.
𝑎𝑚𝑝𝑙𝑖𝑡𝑢𝑑𝑒 𝑜𝑓 𝑡ℎ𝑒 𝑤𝑎𝑣𝑒 𝑠𝑐𝑎𝑡𝑡𝑒𝑟𝑒𝑑 𝑏𝑦 𝑜𝑛𝑒 𝑎𝑡𝑜𝑚
Eq. 4-2
𝑚𝑝𝑙𝑖𝑡𝑢𝑑𝑒 𝑜𝑓 𝑡ℎ𝑒 𝑤𝑎𝑣𝑒 𝑠𝑐𝑎𝑡𝑡𝑒𝑟𝑒𝑑 𝑏𝑦 𝑜𝑛𝑒 𝑒𝑙𝑒𝑐𝑡𝑟𝑜𝑛
The atomic scattering factor is a function of scattering direction and X-ray wavelength as
shown in Figure 3-1-b for copper atom. The scattering intensity of an atom is significantly
reduced with increasing 2θ when the X-ray wavelength is fixed.
𝑓=
Figure 4-1. (a) Scattering of an X-ray by electrons in an atom and (b) the intensity of a
scattered beam represented by the atomic scattering factor (f), which is a function of scattering angle
(θ) with the maximum value at 0◦. The maximum is equal to the number of electrons in the atom[2].
5 Structure factor
Structure Extinction refers to interference between scattering atoms in a unit cell of a crystal
if there is more than one atom in a unit cell. The resultant of the waves scattered by all the atoms
in the unit cell, in the direction of the h, k and l reflection, is called the structure factor (Fhkl).
The structure factor depends on both the position of each atom and its scattering factor. For j
atoms in a unit cell,
𝐹ℎ𝑘𝑙 = ∑ 𝑓𝑗 𝑒 2𝜋𝑖(ℎ𝑥𝑗+𝑘𝑦𝑗+𝑙𝑧𝑗)
𝑗
Eq.
5-1
Where fj is the scattering factor of the jth atom and xj, yj, and zj are its fractional coordinates.
This series can be expressed in terms of sines and cosines (periodic nature of a wave) and is
called a Fourier series. In a crystal with a center of symmetry and n unique atoms in the unit cell
(the unique set of atoms is known as the asymmetric unit):
For example, a body-centered cubic (BCC) united cell has two atoms located at [0,0,0] and
[0.5, 0.5, 0.5].We can calculate the diffraction intensity of (001) and (002) using Equation 2.11.
𝐹001 = 𝑓𝑒𝑥𝑝[2𝜋𝑖(0 + 0 + 1) + 𝑓𝑒 2𝜋𝑖(0∗0.5+0∗0.5+1+0.5) ] = 𝑓 + 𝑓𝑒 𝜋𝑖 = 0
𝐹002 = 𝑓𝑒𝑥𝑝[2𝜋𝑖(0 + 0 + 2 ∗ 0) + 𝑓𝑒 2𝜋𝑖(0∗0.5+0∗0.5+2∗0.5) ] = 𝑓 + 𝑓𝑒 2𝜋𝑖 = 2𝑓
This structure factor calculation confirms the geometric argument of (001) extinction in a
Body-centered crystal. Practically, we do not have to calculate the structure extinction using Eq.
5-1 for simple crystal structures such as BCC and face-centered cubic (FCC). Their structure
extinction rules are given in Table 2.2, which tells us the detectable crystallographic planes for
BCC and FCC crystals. From the lowest Miller indices, the planes are given as following.
BCC (1 1 0), (2 0 0), (2 1 1), (2 2 0), (3 1 0), (2 2 2), (3 2 1), ….
FCC (1 1 1), (2 0 0), (2 2 0), (3 1 1), (2 2 2), (3 3 1), ....
A unit cell with more than one type of atom, the calculation based on Eq. 5-1 will be more
complicated because the atomic scattering factor varies with atom type. We need to know the
exact values of f for each type of atom in order to calculate F. Often, reduction of diffraction
intensity for certain planes, but not total extinction, is seen in crystals containing different types
of atoms.
𝐹ℎ𝑘𝑙 = 2 ∑ 𝑓𝑗 cos 2𝜋(ℎ𝑥𝑛 + 𝑘𝑦𝑛 + 𝑙𝑧𝑛 )
Eq. 5-2
𝑗
6 X-ray Diffractometry
The XRD instrument is called an X-ray diffractometer. Single wave length incidents to the
specimen surface and detector measure the intensity of the diffracted beam. The beam incident
angle changes continuously thus a spectrum of diffraction intensity versus the angle between
incident and diffraction beam is produced. This spectrum is compared with database containing
over 60,000 diffraction spectra of known crystalline substances
6.1 Instrumentation
Diffractometer functions are the x-ray diffraction detecting from material and the measuring
of diffraction intensity. Figure 6-1 shows a real picture of a powder X-ray diffractometer. Figure
6-2 demonstrates the geometrical arrangement of X-ray source, specimen and detector. The Xray radiation generated by an X-ray tube passes through special slits which collimate the X-ray
beam. These Soller slits are commonly used in the diffractometer. They are made from a set of
closely spaced thin metal plates parallel to plane of Figure 6-2 to prevent beam divergence in the
director perpendicular to the figure plane. A divergent X-ray beam passing through the slits
strikes the specimen (Figure 6-3). X-rays are diffracted by the specimen and form a convergent
beam at receiving slits before they enter a detector. The diffracted X-ray beam needs to pass
through a monochromatic filter (or a monochromator) before being received by a detector.
Relative movements among the X-ray tube, specimen and the detector ensure the recording of
diffraction intensity in a range of 2θ. Note that the θ angle is not the angle between the incident
beam and specimen surface; rather it is the angle between the incident beam and the
crystallographic plane that generates diffraction. Diffractometers can have various types of
geometric arrangements to enable collection of X-ray data. The majority of commercially
available diffractometers use the Bragg–Brentano arrangement, in which the X-ray incident
beam is fixed, but a sample stage rotates around the axis perpendicular to the figure plane of
Figure 6-2 in order to change the incident angle. The detector also rotates around the axis
perpendicular to the plane of the figure but its angular speed is twice that of the sample stage in
order to maintain the angular correlation of θ–2θ between the sample and detector rotation. The
Bragg–Brentano arrangement, however, is not suitable for thin samples such as thin films and
coating layers. The technique of thin film X-ray diffractometry uses a special optical
arrangement for detecting the crystal structure of thin films and coatings on a substrate. The
incident beam is directed to the specimen at a small glancing angle (usually <1◦) and the
glancing angle is fixed during operation and only the detector rotates to obtain the diffraction
signals as illustrated in Figure 6-4. Thin film X-ray diffractometry requires a parallel incident
beam, not a divergent beam as in regular diffractometry. Also, a monochromator is placed in the
optical path between the X-ray tube and the specimen, not between the specimen and the
detector. The small glancing angle of the incident beam ensures that sufficient diffraction signals
come from a thin film or a coating layer instead of the substrate[2].
Figure 6-1. Image of a powder X-ray diffractometer. The incident beam enters from
the tube on the left, and the detector is housed in the black box on the right side of the
machine. This particular XRD machine is capable of handling six samples at once, and is
fully automated from sample to sample[4].
Figure 6-2.
diffractometer[2].
Geometric
arrangement
of
X-ray
Figure 6-3. Soller slit position [5]
Figure 6-4. Optical arrangement for thin film diffractometry[2].
6.2 System Aberrations
The ideal and experiment situations are not completely same in other words there are errors
in experiments. XRD data are sensitive to as many as 35 different factors. These factors can be
grouped in to three general sources of "error".



Instrument sensitive
Sample sensitive
Specimen sensitive
The experimental d value is not exactly same with d theoretical value[6]:



Theoretical d-value (nλ = 2d sinθ)
Practical d-value (theoretical + inherent aberrations)
Experimental d-value (practical + inherent sample aberrations + errors)
Errors due to parafocusing always exists. The errors of parafocusing are referred:



Axial divergence error;
Flat-specimen error; and
Specimen transparency error.
Focusing circles for various geometries is shown in Figure 6-5.The incident X-ray beam has
a certain degree of divergence; part of the specimen surface is not located on the focusing circle
and the atomic planes inside the specimen are not located on the focusing circle. These
aforementioned conditions generate system errors which affect the peak positions and widths in
the diffraction spectrum[2].
Figure 6-5. Focusing circles for
various geometries in Bragg–Brentano
arrangement[6]
7 Samples and Data Acquisition
7.1 Sample Preparation
The X-ray diffractometer was originally designed for examining powder samples. However,
the diffractometer is often used for examining samples of crystalline aggregates other than
powder. Polycrystalline solid samples and even liquids can be examined. Importantly, a sample
should contain a large number of tiny crystals (or grains) which randomly orient in threedimensional space because standard X-ray diffraction data are obtained from powder samples of
perfectly random orientation. Relative intensities among diffraction peaks of a non-powder
sample can be different from the standard because perfect randomness of grain orientation in
solid samples is rare. The best sample preparation methods are those that allow analysts to obtain
the desired information with the least amount of treatment because chemical contamination may
occur during the sample treatments[2]. The most commonly used approach to reduce particle size
is to grind the substance using a mortar and pestle, but mechanical mills also do a fine job
(Figure 7-1). Both the former and the latter are available in a variety of sizes and materials.
Mortars and pestles are usually made from agate or ceramics. Agate is typically used to grind
hard materials (e.g., minerals or metallic alloys), while ceramic equipment is suitable to grind
soft inorganic and molecular compounds. Mechanical mills require vials and balls, which are
usually made from hardened steel, tungsten carbide, or agate[7].
Figure 7-1. The tools most commonly used in sample preparation for powder diffraction
experiments: agate mortar and pestle (left), and ball-mill vials made from hardened steel (middle) and
agate (right).
7.2 Acquisition and Treatment of Diffraction Data
A diffractometer records diffraction intensity versus 2θ angle. A number of intensity peaks
located at different 2θ provide a ‘fingerprint’ for a crystalline solid such as Fe2O3. Each peak
represents diffraction from a certain crystallographic plane. Matching an obtained peak spectrum
with a standard spectrum enables us to identify the crystalline substances in a specimen.
Spectrum matching is determined by the positions of the diffraction peak maxima and the
relative peak intensities among diffraction peaks. For example Figure 7-2 shows comparing
between a standard reference pattern [8] for Fe2O3 and result of an experiment [9]. To obtain
adequate and data of sufficient quality for identifying a material, the following factors are
important:



Choice of 2θ range
Choice of X-ray radiation
Choice of step width for scanning
To obtain a satisfactory diffraction spectrum, the following treatments of diffraction data
treatment should be done:



Smooth the spectrum curve and subtracting the spectrum background;
Locate peak positions; and
Strip Kα2 from the spectrum, particularly for peaks in the mid-value range of 2θ[2].
a
b
Figure 7-2. comparing between a standard reference pattern and result of an experiment a)
standard refrence pattern[8], b) result of an experiment[9].
8 Distortions of Diffraction Spectra
8.1 Preferential Orientation
It is supposed to match both peak locations and relative peak intensities between the
acquired spectrum and the standard if the sample is the same substance as the standard.
However, it is not always possible to match relative intensities even when the examined
specimen has the same crystalline structure as the standard. One reason for this discrepancy
might be the existence of preferential crystal orientation in the sample. This often happens when
we examine coarse powder or non-powder samples. Preferential orientation of crystals (grains in
solid) may even make certain peaks invisible.
Figure 8-1. Change of peak line width with crystal
size[10].
Figure 8-2. X-ray diffraction of nano-SiC synthesized for TMS
at 1573K andBragg reflex positions according to the β-SiC
Phase[11].
8.2 Crystallite Size
Ideally, a Bragg diffraction peak is a line without width, as shown in Figure 7-2-a. In reality,
diffraction from a crystal specimen produces a peak with a certain width, as shown in Figure 7-2b. The peak width can result from instrumental factors and the size effect of the crystals. Small
crystals cause the peak to be widened due to incompletely destructive interference. The
crystalline phases of the silicon carbide powders were identified by X-ray powder diffraction
with a Siemens D5000 diffractometer using a CuKα source (Figure 8-2). The crystallite or grain
size, dXRD, can be calculated from the XRD line broadening using Scherrer's formula:
𝑑 𝑋𝑅𝐷 =
𝐾. 𝜆
𝛽. 𝑐𝑜𝑠𝜃
Where K is a shape constant (here assumed as 1), A. is the wavelength of the X-rays (0.154
nm for Cu-Ka), β is the difference of the width (full width at half maxi-mum. b) of the (220) peak
at 2θ= 59.9 of the ultrafine powders and of a standard microcrystalline β-SiC powder (bs Aldrich,
99.9%):
β=b-bs
8.3 Residual Stress
Any factor that changes the lattice parameters of crystalline specimens can also distort their
X-ray diffraction spectra. For example, residual stress in solid specimens may shift the
diffraction peak position in a spectrum. Residual stress generates strain in crystalline materials
by stretching or compressing bonds between atoms. Thus, the spacing of crystallographic planes
changes due to residual stress[2]. Figure 8-3 shows Peak Shift in an alloy 625 C-Ring Due to
residual stress[12]. The strain 𝜀𝑧 can be measured experimental by measuring the peak position
2θ, and Bragg equation for a value of dn. If we know the unstrained inter-planar spacing d0
then[13];
𝜀𝑧 =
𝑑𝑛 − 𝑑0
𝑑0
Figure 8-3. Peak Shift in an alloy 625 C-Ring Due to residual
stress[12].
9 Application
9.1 Phase Identiication
Identification of crystalline substance and crystalline phases in a specimen is achieved by
comparing the specimen diffraction spectrum with spectra of known crystalline substances. Xray diffraction data from a known substance are recorded as a powder diffraction file (PDF).
Most PDFs are obtained with CuKα radiation (example Figure 9-1). Standard diffraction data
have been published by the ICDD, and they are updated and expanded from time to time. When
we need to identify the crystal structure of a specimen that cannot be prepared as powder,
matches of peak positions and relative intensities might be less than perfect. In this case, other
information about the specimen such as chemical composition should be used to make a
judgment [2].
Figure 9-1. The Indexed PDF card NiMnO3 [7].
9.2 Quantitative Measurement
The intensity of the diffraction peaks of a particular crystalline phase in a phase mixture
depends on the weight fraction of the particular phase in the mixture. Thus, we may obtain
weight fraction information by measuring the intensities of peaks assigned to a particular
phase.Generally, we may express the relationship as the following
𝐼𝑖 =
𝐾𝐶𝑖
𝜇𝑚
Where the peak intensity of phase i in a mixture is proportional to the phase weight fraction
(Ci), and inversely proportional to the linear absorption coefficient of the mixture (μm). K is a
constant related to the experimental conditions including wavelength, incident angle, and the
incident intensity of the X-ray beam.
10 Wide-Angle X-Ray Diffraction and Scattering
Wide-angle X-ray diffraction (WAXD) or wide-angle X-ray scattering (WAXS) is the
technique that is commonly used to characterize crystalline structures of polymers and fibers.
The technique uses monochromatic X-ray radiation to generate a transmission diffraction pattern
of a specimen that does strongly absorb X-rays, such as an organic or inorganic specimen
containing light elements. WAXD or scattering refers to X-ray diffraction with a diffraction
angle 2θ >5◦, distinguishing it from the technique of small-angle X-ray scattering (SAXS) with
2θ <5◦[2].Nanoparticles are essential building blocks to make many new materials with tailored
optical, magnetic, mechanical, and electrical properties. Examples include new magnetic
recording media, sensors, and catalyst supports. Such particles are often anisotropic in shape and
resemble disks, rods, or ellipsoids. Scientific interest in nanometre-sized particles focuses on
their size-dependent physical properties that include specific surface area, quantum confinement,
and super paramagnetism. Characterization of both shape and size of such particles is important
in the development of these materials and as a means to control the quality of the synthesis.
Wide-angle X-ray diffraction with conventional laboratory equipment can be used as a tool for
this characterization[14].
11 Refrences
1.
2.
3.
4.
5.
6.
7.
8.
9.
10.
11.
12.
13.
14.
Seibert, J.A., X-Ray Imaging Physics for Nuclear Medicine Technologists. Part 1: Basic Principles
of X-Ray Production. Journal of Nuclear Medicine Technology, 2004. 32(3): p. 139-147.
Leng, Y., Materials Characterization: Introduction to Microscopic and Spectroscopic Methods.
2013: Wiley.
Cullity, B.D., Elements of X Ray Diffraction. 2011: BiblioBazaar.
Barron, A., Physical Methods in Chemistry and Nano Science August 7, 2012: Connexions, Rice
University.
Bargar, J. Guide to XAFS Measurements at SSRL 07 DEC 2004; Available from: http://wwwssrl.slac.stanford.edu/mes/xafs/index.html.
Schroeder, P.
Factors that
affect
d's
and I's. 2014; Available from:
http://clay.uga.edu/courses/8550/XRD.html.
Pecharsky, V.K. and P.Y. Zavalij, Fundamentals of Powder Diffraction and Structural
Characterization of Materials. 2009: Springer US.
Bernal, D., D.R. Dasgupta, and A.L. Mackay, The Oxides and Hydroxides of Iron and Their
Structural Inter-Relationships. Clay Minerals, 1959. 4: p. 15.
Augustyn, C.L., et al., One-Vessel synthesis of iron oxide nanoparticles prepared in non-polar
solvent. RSC Advances, 2014. 4(10): p. 5228-5235.
Committee, A.S.M.I.H., ASM Handbook, Volume 06 - Welding, Brazing, and Soldering. ASM
International.
Winterer, M., Nanocrystalline Ceramics: Synthesis and Structure. 2002: Springer.
Berman, R.M. and I. Cohen, Method for improve x-ray diffraction determinations of residual
stress in nickel-base alloys. 1990, Google Patents.
Fitzpatrick, E. and N.P. Laboratory, Determination of Residual Stresses by X-ray Diffraction. 2005:
National Physical Laboratory.
Qazi, S.J.S., et al., Use of wide-angle X-ray diffraction to measure shape and size of dispersed
colloidal particles. Journal of Colloid and Interface Science, 2009. 338(1): p. 105-110.