User:Nittany XRD/Sandbox/PXRD

Figure 2. Electron powder pattern (red) of an Al film with a face centered cubic (fcc) spiral overlay (green) and a line of intersections (blue) that determines lattice parameters.

Powder Diffraction is a scientific technique that uses X-rays (commonly abbreviated as PXRD), neutrons (NPD), or electrons to study and characterize solid materials. It is one of the first and the most used experimental techniques of X-ray crystallography. A common instrument dedicated to performing such measurements is called a powder diffractometer. Powder diffraction measurements can also be performed with cameras equipped with film or by use of a goniometer with a variety of detectors. The specimen in a powder diffraction experiment is typically a finely ground powder, the use of which eliminates many specimen-related and instrumental aberrations; however, the powder diffraction method doesn’t require a powder, it can be performed on any polycrystalline sample and is commonly applied to parts, such as electronic components, artistic pieces, polymer films or other solids.

Powder diffraction is used in a wide variety of diverse applications to measure fundamental material and structural properties, many of which are described in this article. However, the most common application of powder diffraction is to identify and often quantify the components that make up multiphase mixtures.  While we will discuss the crystallography and physics of a diffraction pattern, it should be noted that the pattern itself is characteristic of a crystalline solid and can be used to identify materials by comparison to a database of materials. This is much like how fingerprints can be used to identify a person, and therefore, the phase identification portion of the data analysis process is frequently referred to as a “fingerprint” technique for this reason.

A few examples of where the technique is being used are listed below.

1.   Powder diffraction is being performed on operating batteries to evaluate the components of the battery (i.e., cathode, anode, and electrolyte), and how they interact with each other and change structure during operation of the battery.

2.   The composition of soil and rock specimens can be determined and utilized to understand ground stability (Figure 1). A miniaturized diffractometer is on the Mars Rover Opportunity studying the geochemistry of Mars.

3.   On-site and laboratory diffractometers are used to study the composition of cultural heritage objects to restore and preserve historical artifacts.

4.   In law enforcement, powder diffraction is used to analyze evidence, determine the authenticity of formulated drugs, and authenticate explosives and explosive residues in forensic analyses.

Figure 1. Note this is a stock image of an XRD pattern, not the correct pattern we would like to use! X-ray powder diffraction from a drill core specimen taken near the San Andreas fault. The experimental data are shown in red at the top. The subsequent data are reference data sets of the minerals identified in the drill core specimen; quartz, albite, laumontite, clinochlore, richterite, microcline, and montmorillonite. Geologists use such data and information about the mantle's composition below the fault as one means to indirectly study ground stability around the fault line.

One of the hallmarks of the powder diffraction method is its versatility. Powder diffraction is useful in nearly every field of human endeavor which requires the characterization and design of materials which is why the method is widely used by industry, academia, and governments worldwide. The technique is typically performed in the laboratory using X-rays as a radiation source, but it can also be performed with electrons and variable energy X-rays, and neutrons at some of the world’s largest accelerators, synchrotrons, and reactors. The instrumentation can be miniaturized to perform micro-diffraction with specialized focusing optics and/or adopted as microscope attachments using electron diffraction (Figure 2). The interpretation of powder diffraction data is facilitated by coherent diffraction from highly crystalline materials, but it can also apply to characteristic incoherent diffraction from semi-crystalline, nano-crystalline, amorphous, and disordered layered materials (i.e., clays).

Explanation

See also: Diffraction grating

A diffractometer produces electromagnetic radiation (waves) with a known wavelength determined by the selected source. The source is often X-rays, because X-ray sources are relatively economical, easy to produce, and readily available and the wavelength of X-ray is optimal for interatomic-scale diffraction. Both the wavelength and interplanar distances are measured in Ångstroms (1Å = 10 nm = 10^-10 m). However, electrons and neutrons are also common sources, with their frequency determined by their de Broglie wavelength. When these waves reach the sample, the incoming beam is either reflected off the surface or transmitted through the material.  In both cases, a portion of the beam can be diffracted by the atoms that compose the structure of the material. If the atoms show long-range order, i.e., if the material is crystalline, the ordered atoms show characteristic interplanar spacings (d), also known as d-values. These waves will interfere constructively only when the path-length difference (2dsinθ) is equal to an integer multiple of the wavelength, producing a diffraction maximum in accordance with Bragg's law (Figure 3). At points between the intersections where the waves are out of phase, destructive interference occurs.

nλ = 2dsinθ

Figure 3. A schematic diagram of an incident X-ray beam interacting with atoms in a crystalline sample.  When the path length difference 2dsinθ equals an integer multiple of the wavelength, constructive interference occurs, and a peak maximum is noted in the diffraction pattern.

Powder diffraction is a complementary technique to single-crystal diffraction. Figure 4 illustrates the differences between the data collected on single crystals (4a), poorly prepared powder (4b), and ideally prepared powder samples (4c). Single crystal diffraction works best with a single, macroscopic, well-ordered crystal; whereas powder diffraction works best with randomly oriented crystals.[le1] [WM2]  A distinction between powder and single crystal diffraction is the degree of texturing in the sample. Single crystals have maximal texturing and are said to be anisotropic. In contrast, in powder diffraction, every possible crystalline orientation is represented equally in an ideal powdered sample, the isotropic case.  In other words, powder X-ray diffraction operates under the assumption that the sample is randomly arranged. Therefore, a statistically significant number of each orientation of the crystal structure will be in the proper orientation to diffract the X-rays. Therefore, all crystallographic relevant orientations (d-spacings) will be represented in the signal as shown in Figure 4c.  To achieve a statistically significant number of each family of planes, samples are usually ground to a fine particle size, optimally 1-10 microns. In practice, for a number of reasons, this is often difficult to achieve, and samples are often rotated or precessed (wobbled) to improve randomness and reduce the effects of texturing, also called orientation. 

Insert Figure 4 here

Figure 4. Debye-Scherrer cones obtained from single crystal (a), polycrystalline – non-ideal specimen (b), and polycrystalline – ideal specimen (c).

Mathematically, crystals can be described by a 3D ordered arrangement of atoms with some regularity in the interatomic distances. Because of this regularity, we can describe this structure in a different way using the reciprocal lattice, which is related to the original structure by a Fourier transform. This three-dimensional space can be described with reciprocal axes x*, y*, and z* or alternatively in spherical coordinates q, φ*, and χ*. In powder diffraction, intensity is homogeneous over φ* and χ*, and only q remains as an important measurable quantity. This is because orientational averaging causes the three-dimensional reciprocal space that is studied in single crystal diffraction to be averaged to the same distribution in all directions of reciprocal space (therefore it behaves as if it is projected onto a single dimension).

Insert Figure 5 here

Figure 5. Two-dimensional powder diffraction setup with flat plate detector

When the scattered radiation is collected on a flat plate detector, as shown in Figure 5, the rotational averaging leads to smooth diffraction rings around the beam axis (Debye-Scherrer rings), rather than the discrete Laue spots observed in single crystal diffraction. The angle between the beam axis and the ring is called the scattering angle and in X-ray crystallography always denoted as 2θ (in scattering of visible light the convention is usually to call it θ). In accordance with Bragg's law, each ring corresponds to a particular reciprocal lattice vector G in the sample crystal. This leads to the definition of the scattering vector as:$|G|=q=2k\sin(\theta )={\frac {4\pi }{\lambda }}\sin(\theta ).$

In this equation, G is the reciprocal lattice vector, q is the length of the reciprocal lattice vector, k is the momentum transfer vector, θ is half of the scattering angle, and λ is the wavelength of the source. Powder diffraction data are usually presented as a diffractogram in which the diffracted intensity, I, is shown as a function either of the scattering angle 2θ, d-spacing as determined from θ by Braggs Law, or as a function of the scattering vector length q. Both q and d-spacings have the advantage that the diffractogram no longer depends on the value of the wavelength λ. However, the most common expression is the scattering angle 2θ because it is the angle that is recorded by the instrument. Most modern software enables diffraction patterns to be expressed as 2θ, d, or q (x-axis) vs. intensity (y-axis) either as direct counts, square root, log, or log-normal counts depending on user preference. Each type of display has advantages depending on the type of diffraction analysis being conducted.

In practice, a diffraction pattern can be easily explained. The peak locations, as determined by Bragg’s Law, are related to directions where constructive interference occurs among waves diffracted by all the atoms in each crystal; geometrically simplified to spacings between planes of atoms within the material. The peak intensity, as shown by Debye and others, is related to the electrons around each atom and is characteristic of the number, type, and relative position of atoms within the crystal structure. Therefore, each material having a unique chemical formula and arrangement of atoms produces a characteristic pattern. A multiphase powder sample will produce a powder diffraction pattern containing diffraction maxima coming from all crystalline phases that combine in an additive fashion such that the intensity of each phase is directly related to concentration. Many other applications of powder diffraction, such as the determination of crystallinity, crystallite size, stress, and strain relate to fundamental changes in the peak profiles.

Uses

Relative to other methods of analysis, powder diffraction allows for rapid, non-destructive analysis of single or multi-component samples without the need for extensive sample preparation. This gives laboratories around the world the ability to quickly analyze unknown materials and perform materials characterization in such fields as[le1] [WM2]  archaeology, biology, chemistry, condensed matter physics, crystallography, forensic science, materials science, metallurgy, mineralogy and pharmaceutical sciences among others. Identification is performed by comparison of the diffraction pattern to a known standard or to a database such as the Powder Diffraction File (PDF). Advances in hardware and software, particularly improved optics and fast detectors, have dramatically improved the analytical capability of the technique, especially relative to the speed of the analysis. The fundamental physics upon which the technique is based provides high precision and accuracy in the measurement of interplanar spacings, typically to a few picometres (fractions of Å), resulting in authoritative identification frequently used in patents, criminal cases, and other areas of law enforcement. The ability to analyze multiphase materials also allows analysis of how materials interact in a particular matrix such as a pharmaceutical tablet, a circuit board, a mechanical weld, a geologic core sampling, cement and concrete, or a pigment found in a historic painting. The method has been historically used for the identification and classification of minerals, but it can be used for nearly any material, even amorphous ones, if a suitable reference pattern is known, or can be calculated or simulated. The calculation of powder patterns from experimental single crystal structures and their scattering factors enables databases to be calculated from single crystal databases such as the  Inorganic Crystal Structure Database (ICSD), the Linus Pauling File (LPF), etc. There are also several single-crystal crystal databases that deal with specific fields of science. Experimental reference patterns can contain both coherent and incoherent diffraction contributions enabling the user to identify amorphous and semi-crystalline materials frequently found in polymers, clays and pharmaceuticals. the user to identify amorphous and partially crystalline materials frequently found in polymers, clays and pharmaceuticals.

Phase identification

The most widespread use of powder diffraction is in the identification and characterization of crystalline solids, each of which produces a distinctive diffraction pattern. Both the positions (corresponding to lattice spacings) and the relative intensity of the lines (corresponding to atomic composition and ordering) in a diffraction pattern are indicative of a particular phase and material, providing a "fingerprint" for comparison. A multi-phase mixture, e.g. a soil sample, will show more than one pattern superposed, allowing for determination of the relative concentrations of phases in the mixture.

J.D. Hanawalt, an analytical chemist who worked for Dow Chemical in the 1930s, realized the analytical potential of creating a database and combining it with a method for unknown identification. Today it is represented by the Powder Diffraction File (PDF) of the International Centre for Diffraction Data (formerly Joint Committee for Powder Diffraction Standards). This has been made searchable by computers through the work of global software developers and equipment manufacturers. There are now over 1,046,331 reference materials in the 2024 Powder Diffraction File Databases, and these databases are interfaced to a wide variety of diffraction analysis software and distributed globally. The Powder Diffraction File contains many subfiles, such as minerals, metals and alloys, pharmaceuticals, forensics, excipients, superconductors, semiconductors, etc., with large collections of organic, organometallic, and inorganic reference materials.

Crystallinity

In contrast to a crystalline pattern consisting of a series of sharp peaks, amorphous materials (glasses, waxes etc.) produce a broad background signal. Many polymers show semi-crystalline behavior, i.e. part of the material forms intermediate-range ordered regions (crystallites) by ordering identical parts of the long polymer molecules. A single polymer molecule may well be folded into two different, adjacent crystallites and thus form a tie between the two. The tie part is prevented from crystallizing (achieving long-range order). The result is that the crystallinity will never reach 100% and the polymer may show a combination of sharp and broad peaks that may vary from sample to sample. Powder XRD can be used to determine the crystallinity by comparing the integrated intensity of the background pattern to that of the sharp peaks. Values obtained from powder XRD are typically comparable but not quite identical to those obtained from other methods such as DSC and FTIR. Many, if not most polymers, can be made into an amorphous form by rapid heating and quenching. In fact, there are many techniques used to produce amorphous pharmaceuticals, which are often desirable to obtain high surface areas and increased drug solubility. Powder XRD is frequently used to distinguish crystalline, semi-crystalline, nanocrystalline and amorphous solids.

Unit cell parameters

The position of a diffraction peak is determined by (1) the atomic positions of the atoms in the unit cell (which relates to the size and shape of the unit cell of a crystalline phase) and (2) the wavelength of the radiation used to collect the data if the x-axis is plotted in degrees 2θ. If the data is plotted with q on the x-axis, the wavelength used is irrelevant.  Each peak represents a certain set of lattice planes and can therefore be characterized by a Miller index. If the symmetry is high, e.g.: cubic or hexagonal, it is usually not too hard to identify the index of each peak, even for an unknown phase. This is particularly important in solid-state chemistry, where one is interested in finding and identifying new materials. Once a pattern has been indexed, this characterizes the reaction product and identifies it as a new solid phase. Indexing programs exist to deal with the harder cases, but if the unit cell is very large and the symmetry low (triclinic, monoclinic), success is not always guaranteed.

Expansion tensors, bulk modulus

Figure 6. Thermal expansion of a sulfur powder

Unit Cell parameters are temperature and pressure dependent. Powder diffraction can be combined with in situ temperature and pressure control. As these thermodynamic variables are changed, the observed diffraction peaks will migrate continuously to indicate higher or lower lattice spacings as the unit cell distorts. This allows for measurement of such quantities as the thermal expansion tensor and the isothermal bulk modulus, as well as determination of the full equation of state of the material.

The study of materials as a function of temperature and pressure enables scientists to explore the chemistry of the earth’s core and develop materials useful for the aerospace industry, energy conversion devices, oceanic, and space exploration. It has also led to the development of improved products like better construction materials and cookware

Phase transitions

At some critical set of conditions, for example at 0 °C for water at 1 atm, a new arrangement of atoms or molecules may become stable when liquid water converts to ice in a physical process known as a phase transition. As commonly taught in most science courses, and defined in the Wikipedia page for phase transitions, “Commonly the term is used to refer to changes among the basic states of matter: solid, liquid, and gas, and in rare cases, plasma.”  Often, however, phase transitions from the perspective of powder diffraction are solid-solid phase transitions; meaning that a transition occurs between different crystalline forms (polymorphs) of the same compound.  When a solid-solid phase transition occurs, new diffraction peaks will appear, or old ones disappear according to the symmetry of the new phase in what is called a first order phase transition. If the transition produces another crystalline phase, one set of lines will suddenly be replaced by another set. In other cases, lines will split or coalesce, 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 d for a tetragonal phase, but if the symmetry becomes cubic the two peaks will coincide or merge to form one peak.

Famous cases of phase transitions are the six crystalline forms of chocolate. Ref. or the allotropic transformation of metallic tin (Sn) popularly known as tin pest. The transition and crystallization process at different temperatures is often accompanied by changes in texture, aspect and taste, of obvious interest to chocolate lovers.

Crystal structure refinement and determination

Crystal structure determination from powder diffraction data is extremely challenging due to the overlap of reflections and loss of 3D spatial information when analyzing an isotropic (perfectly randomly oriented crystals) solid. Several different methods exist for structural determination, derived from the well-developed single-crystal X-ray diffraction technique and specialized for the additional challenges of powder diffraction. The most successful programs, implementing variations of simulated annealing {https://en.wikipedia.org/wiki/Simulated_annealing} and/or direct methods {https://en.wikipedia.org/wiki/Direct_methods_(crystallography)} and related approaches are Fox, DASH, PSSP, EXPO2014, TOPAS and GSAS-II.

The crystal structures of known materials can be refined (improved in precision and detail from an approximate starting model), i.e. as a function of temperature or pressure, using the Rietveld method. The Rietveld method is a full pattern analysis technique. A model or preliminary crystal structure, together with instrumental and microstructural information, is used to generate a theoretical diffraction pattern that can be compared to the observed data. A least squares procedure is then used to minimize the difference between the calculated pattern and each point of the observed pattern by adjusting model parameters. Specialized software for Rietveld refinement can be standalone FULLPROF, BMGN, Maud, Rietan (originally in Japanese).[le3] [WM4] etc) {https://en.wikipedia.org/wiki/Rietveld_refinement} or could be found associated with structure determination programs (EXPO2014, TOPAS and GSAS-II.).

Size and strain broadening

There are many factors that determine the width B of a diffraction peak. These include:

1.    instrumental factors

2.    the presence of defects to the perfect lattice

3.    differences in strain in different grains

4.    the size of the crystallites

It is often possible to separate the effects of size and strain. When 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. It is possible to separate these by combining the two equations in what is known as the Hall–Williamson method:

$B\cdot \cos(\theta )={\frac {k\lambda }{D}}+\eta \cdot \sin(\theta ),$

Thus, when we plot $\displaystyle B\cdot \cos(\theta )$ vs. $\displaystyle \sin(\theta )$ we get a straight line with slope $\displaystyle \eta$ and intercept $\displaystyle {\frac {k\lambda }{D}}$.

The expression is a combination of the Scherrer equation for size broadening and the Stokes and Wilson expression for strain broadening. The value of η is the strain in the crystallites, the value of D represents the size of the crystallites. The constant k is typically close to unity and ranges from 0.8 to 1.39.

Frequently, strain and size effects on crystallites are anisotropic, producing peak widths that depend on hkl and on q. This is particularly important in very anisotropic materials such as fibrous or lamellar crystal structures. A generalization of the previous equations to include crystal direction dependent broadening parameters has been derived.

Modern Rietveld software allows one to compute automatically from the refined profile parameters the size and strain parameters both isotropic and anisotropic, provided that a calibration for the instrumental broadening is given.

Comparison of X-ray and neutron scattering

X-ray photons scatter by interaction with the electron density cloud of the material, neutrons are scattered by the nuclei producing neutron diffraction. This means that, in the presence of heavy atoms with many electrons, it may be difficult to detect light atoms by X-ray diffraction. In contrast, the neutron scattering lengths of nuclei are independent on the atomic number and are approximately equal in magnitude. Neutron diffraction techniques may therefore be used to detect light elements such as oxygen or hydrogen in combination with heavy atoms or distinguish among nearby elements with very similar number of electrons. The neutron diffraction technique therefore has obvious applications to problems such as determining oxygen displacements in materials like high temperature superconductors and ferroelectrics, Li ions in batteries or to hydrogen bonding in biological systems.

As neutrons also have a magnetic moment, they are additionally scattered by any atomic magnetic moments in a sample. In the case of long-range magnetic order, this leads to the appearance of new Bragg reflections or additional intensity in the peaks present. In most cases, neutron powder diffraction may be used to determine the size of the moments and their spatial orientation (so called magnetic structure).

Aperiodically arranged clusters

Predicting the scattered intensity in powder diffraction patterns from gases, liquids, and randomly distributed nano-clusters in the solid state is (to first order) done rather elegantly with the Debye scattering equation:

$I(q)=\sum _{i=1}^{N}\sum _{j=1}^{N}f_{i}(q)f_{j}(q){\frac {\sin(qr_{ij})}{qr_{ij}}},$

where the magnitude of the scattering vector q is in reciprocal space units (typically Å^-1 or nm^-1), N is the number of atoms, f_i(q) is the atomic scattering factor for atom i and scattering vector q, while r_ij is the distance between atom i and atom j. One can also use this to predict the effect of nano-crystallite shape on detected diffraction peaks, even if in some directions the cluster is only one atom thick. Even though this is a powerful equation, computing the scattered intensity even for a small nanoparticle would require the calculation of hundreds of thousands of terms for each value of q, therefore, translating this computation to a sample of hundreds of thousands of particles with different sizes and strains requires significant time or the realization of approximations that could only be applied case by case to each system.

Semi-quantitative analysis

Semi-quantitative analysis of polycrystalline mixtures can be performed by using traditional methods such as the Relative Intensity Ratio (RIR) or whole-pattern methods using Rietveld Refinement or PONCKS (Partial Or No Known Crystal Structures) method. The use of each method depends on the knowledge of the analyzed system, given that, for instance, Rietveld refinement needs the solved crystal structure of each component of the mixture to be performed.

The ability to perform complex multiphase quantitation in the timeframe of single analysis has large implications on industrial throughput and productivity. Rietveld analyses are routinely used by some of the world’s largest materials industries (cement, mining) and are included in most commercial software packages sold with diffraction equipment. In many of these cases the scale factors and unit cell parameters are being refined.

Quantitative methods are continuously being developed with modifications and improvements to all the above methods including many hybrid techniques used to address non-crystalline containing samples or combining complimentary analytical data. In the last decades, multivariate analysis began spreading as a complimentary method for phase quantification. 

Traditional analytical methods such as standard calibration and standard addition are also useful with powder XRD. While more intensive, usually requiring multiple samples for each analyte, the results are often more accurate and precise.

Devices

Cameras

The simplest cameras for X-ray powder diffraction consist of a small capillary and either a flat plate detector (originally a piece of X-ray film, now more and more a flat-plate detector or a CCD-camera) or a cylindrical one (originally a piece of film in a cookie-jar, but increasingly bent position sensitive detectors are used). The two most frequently used types of cameras are the Laue and the Debye–Scherrer camera.

In order to ensure complete powder averaging, the specimens are finely ground and the capillary is usually spun around its axis.

The Guinier camera is built around a focusing bent crystal monochromator. The sample is usually placed in the focusing beam, e.g. as a dusting on a piece of sticky tape. A cylindrical piece of film (or electronic multichannel detector) is put on the focusing circle, but the incident beam is prevented from reaching the detector to prevent damage from its high intensity. The main advantage of a Guinier camera is the high resolution provided by the focusing optics and crystal monochromator. Cameras based on hybrid photon counting technology, such as the are widely used in applications where high data acquisition speeds and increased data quality are required. A review of the history of hybrid pixel detectors was published in 2014 from the 15^th International Workshop on Radiation Imaging Detectors (June 23-27, 2013 in Paris, France). Cite P Delpierre 2014 JINST 9 C05059

For neutron diffraction, vanadium cylinders are used as sample holders. Vanadium has a negligible absorption and coherent scattering cross section for neutrons and is hence nearly invisible in a powder diffraction experiment.

Diffractometers

Figure 7. Hemisphere of diffraction showing the incoming and diffracted beams K₀ and K that are inclined by an angle θ with respect to the sample surface.  This image represents a θ-θ  configuration.

Diffractometers can be operated both in transmission and reflection geometry, but reflection is more common. The powder sample is loaded in a small disc-like container and its surface carefully flattened. The disc is put on one axis of the diffractometer and tilted by an angle θ while a detector (scintillation counter is one type) rotates around it on an arm at twice this angle. This configuration is known under the name Bragg–Brentano θ-2θ.

Another configuration is the Bragg–Brentano θ-θ configuration in which the sample is stationary while the X-ray tube and the detector are rotated around it. The angle formed between the x-ray source and the detector is 2θ. This configuration is most convenient for loose powders and simplifies the use of multiple sample stages on a single diffractometer.

Diffractometer settings for different experiments can schematically be illustrated by a hemisphere, in which the powder sample resides in the origin. The case of recording a pattern in the Bragg-Brentano θ-θ mode is shown in the figure, where K₀ and K stand for the wave vectors of the incoming and diffracted beam that both make up the scattering plane. Various other settings for texture or stress/strain measurements can also be visualized with this graphical approach.

Position-sensitive detectors (PSD) and area detectors, which allow collection from multiple angles at once, are becoming more popular on currently supplied instrumentation.

Neutron diffraction

Main article: Neutron diffraction

Sources that produce a neutron beam of suitable intensity and wavelength for diffraction are only available at a small number of dedicated research reactors and spallation sources in the world. Angle dispersive (fixed wavelength) instruments typically have a battery of individual detectors arranged in a cylindrical fashion around the sample holder, and can therefore collect scattered intensity simultaneously on a large 2θ range. Time of flight instruments normally have a small range of banks at different scattering angles which collect data at varying resolutions, however modern instruments are equipped with hundreds of detectors at all angles to obtain data at faster rates POWGEN. Huq A., Hodges J.P., Gourdon O.A., Heroux L., "POWGEN: a third-generation high resolution high-throughput powder diffraction instrument at the Spallation Neutron Source", Zeitschrift fur Kristallographie, 1, 127-135 (2011).

Neutron diffraction has never been an in-house technique because it requires the availability of an intense neutron beam only available at a nuclear reactor or spallation source. Typically, the available neutron flux, and the weak interaction between neutrons and matter require relatively large samples.

X-ray tubes

Main article: X-ray crystallography

Figure 8. X-ray powder diffractometer Bruker D8 Advance at FZU – Institute of Physics of the Czech Academy of Sciences. The X-ray tube is located inside the tube housing which is the vertical rectangular-shaped object on the left side of this image.

Laboratory X-ray diffraction equipment relies on the use of an X-ray tube, which is used to produce the X-rays. Copper anode X-ray tubes are most common, but cobalt and molybdenum are also popular. The wavelength varies for each source. The table below shows these wavelengths, determined by Bearden and quoted in the International Tables for X-ray Crystallography (all values in nm):

According to the last re-examination of Hölzer et al. (1997), these values are respectively:

Element	Kα2	Kα1	Kβ
Cr	0.2293663	0.2289760	0.2084920
Co	0.1792900	0.1789010	0.1620830
Cu	0.1544426	0.1540598	0.1392250
Mo	0.0713609	0.0709319	0.0632305

Note that most commercial diffractometer systems and XRD powder diffraction application software will cite these values in angstroms (Å). (x10 in the above Table).

Other sources

In-house applications of X-ray diffraction have always been limited to the relatively few wavelengths shown in the table above. The available choice was much needed because the combination of certain wavelengths and certain elements present in a sample can lead to strong fluorescence which increases the background in the diffraction pattern. A notorious example is the presence of iron in a sample when using copper radiation. In general, elements showing absorption edges at energies just below the anode element emission energy in the period system need to be avoided.

Another limitation is that the intensity of traditional generators is relatively low, requiring lengthy exposure times and precluding any time dependent measurement. The advent of synchrotron sources has drastically changed this picture and caused powder diffraction methods to enter a whole new phase of development. Not only is there a much wider choice of wavelengths available, but the high brilliance of the synchrotron radiation makes it possible to observe time-sensitive changes in the pattern during chemical reactions, temperature ramps, pressure changes etc. Tremendous advances in detector technology, both in energy resolution and photon efficiency, now enable time-dependent measurements with all types of diffraction equipment. Data collection time scales are typically several minutes to hours for laboratory sources and as little as fractions of a second to minutes with a synchrotron.

The tunability of the wavelength also makes it possible to observe anomalous scattering effects when the wavelength is chosen close to the absorption edge of one of the elements of the sample.

Advantages and disadvantages

Powder X-ray diffraction is a powerful and useful technique. It is mostly used to characterize, identify, and quantify phases, frequently in mixtures, but as described above there are many other applications. Like any analytical technique, the method has both advantages and disadvantages.

Advantages of the technique are:

1. the non-destructive nature of the method
2. can differentiate between crystalline and amorphous materials
3. can differentiate between different crystalline polymorphs of the same substance
4. simplicity of sample preparation (in most cases)
5. rapidity of measurement
6. the ability to analyze mixed phases, e.g. soil samples
7. well suited for "in situ" analyses, which can include structure determination, thermal behavior, on-site forensic analysis, mineralogy, and analysis of objects with cultural heritage
8. provides bulk information representative of a statistically significant volume of material
9. provides information on how materials interact in mixtures

Disadvantages of the technique are:

1. detection limits are relatively high (weight percent)
2. sensitive to sample preparation techniques
3. relatively high instrumentation cost
4. considerable knowledge may be needed to correctly interpret the data

Many materials are readily available with sufficient microcrystallinity for powder diffraction, or samples may be easily ground from larger crystals. In the fields of solid-state chemistry, catalysis, or pharmaceutical chemistry that often aim at synthesizing new materials, single crystals thereof are typically not immediately available.

Since all possible crystal orientations are measured simultaneously, collection times can be quite short even for small and weakly scattering samples. This is not merely convenient but can be essential for samples which are unstable either inherently or under X-ray or neutron bombardment, or for time-resolved studies.

In recent years advances in sources, optics and detectors have improved time-resolved powder diffraction in accuracy, power, and speed, independent of whether the source is a synchrotron, lab, benchtop instrument, or portable instrument such as a Mars rover.

See also

• Bragg diffraction
• Condensed matter physics
• Crystallographic database
• Crystallography
• Diffractometer
• Electron crystallography
• Electron diffraction
• Materials science
• Metallurgy
• Neutron diffraction
• Pair distribution function
• Solid state chemistry
• Texture (crystalline)
• Ultrafast x-ray
• X-ray crystallography
• X-ray scattering techniques

Further reading

• Gilmore, C.J.; Kaduk, J.A.; Schenk, H., eds. (2019). International Tables for Crystallography - Volume H: Powder Diffraction. Wiley. ISBN 978-1-118-41628-0.

External links

• International Centre for Diffraction Data
• Powder Diffraction on the Web

Category:Diffraction Category:Neutron-related techniques Category:Synchrotron-related techniques Diffraction