Part 1.
General Information
XRD Basics
X-ray Generation and Properties of X-rays
X-rays are electromagnetic radiation with photon energies in the range of 100 eV
- 100 keV. For diffraction applications, only short wavelength x-rays (hard x-rays) in the
range of a few angstroms (Å) to 0.1 angstrom (1 keV - 120 keV) are used. X-rays are
ideally suited for probing the atomic structure of solids because their wavelengths (0.1-2
Å) are of comparable length to the radii of atoms and they are sufficiently energetic to
penetrate most solid materials to provide information about the bulk structure.
Most XRD instruments produce x-rays with an x-ray generating tube. For
example the Bruker D8 ADVANCE uses an x-ray tube with a Cu anode as the primary xray beam source. In this component x-rays are generated when a focused electron beam
accelerated across a high voltage field bombards a stationary solid Cu target. As electrons
collide with atoms in the target and slow down, a continuous spectrum of x-rays is
emitted, which is termed Bremsstrahlung radiation. The high energy electrons also eject
inner shell electrons in atoms through the ionization process. When a free electron fills
the shell, an x-ray photon with energy characteristic of the target material is emitted.
Common targets used in x-ray tubes include Cu and Mo, that emit 8 keV and 14 keV xrays with corresponding wavelengths of 1.54 Å and 0.8 Å, respectively. (The energy E of
an x-ray photon and it's wavelength () is related by the equation E = hc/, where h is
Planck's constant and c the speed of light).
In recent years synchrotron facilities have become widely used as preferred
sources for x-ray diffraction measurements. Synchrotron radiation is emitted by electrons
or positrons traveling at near light speed in a circular storage ring. These powerful
sources, which are thousands to millions of times more intense than laboratory x-ray
tubes, have become indispensable tools for a wide range of structural investigations and
brought advances in numerous fields of science and technology. Learn more about these
facilities by exploring the following national synchrotron facility web pages:
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Stanford Synchrotron Radiation Laboratory (SSRL)
http://www-ssrl.slac.stanford.edu/
Argonne National Laboratory Advanced Photon Source (APS)
http://www.aps.anl.gov/
Lawrence Berkeley National Laboratory Advanced Light Source (ALS)
http://www-als.lbl.gov/
Brookhaven National Laboratory National Synchrotron Light Source
(NSLS)
http://www.nsls.bnl.gov/
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Lattice Planes and Bragg's Law
X-rays primarily interact with electrons in atoms. When x-ray photons collide
with electrons, some photons from the incident beam will be deflected away from the
direction where they original travel, much like billiard balls bouncing off one anther. If
the wavelength of these scattered x-rays did not change (meaning that x-ray photons did
not lose any energy), the process is called elastic scattering (Thompson Scattering) in that
only momentum has been transferred in the scattering process. These are the x-rays that
we measure in diffraction experiments, as the scattered x-rays carry information about
the electron distribution in materials. On the other hand, In the inelastic scattering
process (Compton Scattering), x-rays transfer some of their energy to the electrons and
the scattered x-rays will have different wavelength than the incident x-rays.
Diffracted waves from different atoms can interfere with each other and the
resultant intensity distribution is strongly modulated by this interaction. If the atoms are
arranged in a periodic fashion, as in crystals, the diffracted waves will consist of sharp
interference maxima (peaks) with the same symmetry as in the distribution of atoms.
Measuring the diffraction pattern therefore allows us to deduce the distribution of atoms
in a material.
The peaks in an x-ray diffraction pattern are directly related to the atomic
distances. Consider an incident x-ray beam interacting with the atoms arranged in a
periodic manner as shown in 2 dimensions in the following illustrations. The atoms,
represented as green spheres in the graph, can be viewed as forming different sets of
planes in the crystal (colored lines in graph on left). For a given set of lattice plane with
an inter-plane distance of d, the condition for a diffraction (peak) to occur can be simply
written as
2dsin = n 
which is known as the Bragg's law, after W.L. Bragg, who first proposed it. In the
equation, is the wavelength of the x-ray,  the scattering angle, and n an integer
representing the order of the diffraction peak. The Bragg's Law is one of most important
laws used for interpreting x-ray diffraction data. It is important to point out that
although we have used atoms as scattering points in this example, Bragg's Law applies to
scattering centers consisting of any periodic distribution of electron density. In other
words, the law holds true if the atoms are replaced by molecules or collections of
molecules, such as colloids, polymers, proteins and virus particles.
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Powder X-ray Diffraction
Powder XRD is perhaps the most widely used x-ray diffraction technique for
characterizing materials. As the name suggests, the sample is usually in a powder form,
consisting of fine grains of single crystalline material to be studied. The technique is also
used widely for studying particles in liquid suspensions or polycrystalline solids (bulk or
thin film materials).
The term 'powder' really means that the crytalline domains are randomly oriented
in 3-D space in the sample. Therefore when the 2-D diffraction pattern is recorded, it
shows concentric rings of scattering peaks corresponding to the various d spacings in the
crystal lattice. The positions and the intensities of the peaks are used for identifying the
underlying structure (or phase) of the material. For example, the diffraction lines of
graphite would be different from diamond even though they both are made of carbon
atoms. This phase identification is important because the material properties are highly
dependent on structure.
Powder diffraction data can be collected using either transmission or reflection
geometry, as shown below. Because the particles in the powder sample are randomly
oriented, these two methods will yield the same data. At SFSU, powder diffraction data
are measured using the Bruker D8 ADVANCE x-ray diffractometer, which measures data
in reflection mode as opposed to transmission mode which is more suitable for liquid
phase samples.
A powder XRD scan of corundum (Al2O3) standard reference material provided with the
D8 instrument is shown below as a plot of scattering intensity vs. the scattering angle 2
or the corresponding d-spacing. The peak positions, intensities, widths and shapes all
provide important information about the structure of the material.
XRD pattern of corrundum (Al2O3) generated
by the Bruker D8 ADVANCE
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Signal intensity (CPS)
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Scattering angle (degrees 2)
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About the Bruker D8 ADVANCE
The Bruker D8 ADVANCE XRD is located in room 615 Thornton Hall at San
Francisco State University. An image of the instrument is linked here.
Photo of the Bruker D8 ADVANCE in Thornton 615. On the left is the Haskris water chiller for the
X-ray tube. The D8 includes the power supply and electronics compartment in the base. The glass
shielded cabinet (center) houses the x-ray tube, primary beam optics, sample stage, goniometer,
secondary beam optics and the x-ray detector. The unit is computer operated (left).
The Bruker D8 ADVANCE instrument is a standard XRD platform allowing several
configurations of primary X-ray beam optics, sample holders and compartments,
secondary beam optics, and detector types. The D8 has a modular design using “push
plug” technology allowing for relatively quick changes between primary and secondary
beam optic components without realignment of the system. General information about
Bruker x-ray equipment can be found at the Bruker AXS web site: http://www.brukeraxs.de/
General user information about X-ray Safety and Training as well as Access to the D8
ADVANCE XRD can be found in later sections of this manual.
Photo of the components in the main compartment of the Bruker D8 ADVANCE. On the left is the
X-ray tube and Bragg-Brentano primary beam optic unit. The sample stage (center) is mounted on
the goniometer for precision angle measurement. Diffracted x-rays are collected by the detector
(right). The sodium iodide (NaI) scintillation detector is shown here. In the foreground is a sample
holder and a fluorescent plate used for beam-to-sample alignment.
As noted earlier, the D8 ADVANCE is a powder XRD instrument. Appropriate
sample types include all crystalline inorganic solids such as metals, oxides, clay minerals,
soil and sediment, rocks, cement, and synthetic inorganic materials. The XRD technique
is generally a nondestructive technique; therefore, samples are not consumed or destroyed
during the measurement. Samples must be homogenized (pulverized and well mixed)
prior to the XRD measurement. It is critical that samples are composed of completely
randomly oriented crystallite grains in the x-ray beam path otherwise spurious, inaccurate
peaks will be generated. Samples can be mounted on the sample stage using a variety of
sample holders including standard steel cups (provided by the manufacturer), shallow
small sample-size compartments, and plexi-glass domes for air-sensitive samples.
Generally, ~0.5 g of dried, homogenized sample powder is sufficient to make the
measurement.
Two detectors are available with the D8 ADVANCE. For routine work, the
NaI scintillation detector is easiest to operate and provides excellent signal-to-noise
for well prepared, crystalline inorganic solids. The D8 may also be run using an
energy dispersive Sol-X detector which selectively measures a user-defined diffracted
beam energy window. More specific information regarding operation of the D8
detectors can be found in the D8 ADVANCE SOP.