Powder diffraction
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Powder diffraction is a scientific technique using X-Ray or neutron diffraction of powder or polycrystalline samples for structural characterization of materials. The dedicated machine to perform such measurements is called a powder diffractometer.
Diffraction from a microcrystalline powdered sample differs from that from a single crystal because -ideally- the crystallites are randomly oriented, and it is thus not possible to see individual diffraction spots as in single crystal X-ray crystallography. Instead one observes rings of diffracted intensity as a function of reciprocal lattice units or momentum transfer. In practice the randomness is often incomplete and spotty rings will be observed. To promote randomization the sample is often rotated during the exposure time.
Advantages and disadvantages
The great advantage of the technique is that it does not require the growing and mounting of a single crystal. For neutron diffraction, a technique that requires larger samples than X-Ray Diffraction this is a more important consideration than for its X-ray equivalent, and indeed powders are very much the standard for neutron diffraction, and single crystal work the exception.
Powder diffraction also allows the sampling of larger objects. In single crystal work one strongly depends on that one tiny crystal that is selected to do all analysis on. For powder work a larger object can be ground up and a sample taken.
The great disadvantage is that the three dimensional information of the reciprocal space of a crystal is collapsed into a one dimensional diffractogram. Nevertheless powder diffraction is a widely used technique.
Powder diffraction allows various in situ experiments to be carried out, and also the characterization of mixed phase samples, which is clearly impossible with single crystals.
Use of the technique
- With Powder Diffraction one can do:
- Crystal Structure Determination
- Precise Lattice Parameter Measurements
- Identification of Unknown Specimen
- Quantitative Analysis of Powder Mixtures
- Determination of Crystal Size and Lattice Strain
- Phase Diagram Determination
- Detection of Long-Range Ordering
- Evaluation of Textures in polycrystalline solids
Phase identification
The most widespread use of the technique is in the identification of crystalline solids. Each crystalline solid produces its own line spectrum. Both the positions (values of the scattering angle θ) and the intensity of the lines are characteristic of that particular phase and the pattern thus provides a fingerprint of the material. A multi phase mixture, e.g. a soil sample, will show more than one pattern superposed. A rule of thumb is that a phase present in quantities lower than 5% by weight is usually not detected.
Hanawalt, an Analytical Chemist that worked for Dow Chemical in the 1930 was the first to realize the Analytical potential of creating a data base. Today it is represented by the JCPDS (Joint Committee of Powder Diffraction Standards) and has been made searcheable by computer.
The method is used most extensively for the identification of minerals, but it can even be used for organic solids as long as they are crystalline and a reference pattern is known.
Reference patterns can also be calculated from the crystal structure if this had been determined e.g. by means of single crystal methods.
Crystallinity
In contrast to a crystalline pattern that consists of a series of sharp peaks, amorphous materials (liquids, glasses etc.) produce a broad background signal. Many polymers show semicrystalline behavior, i.e. part of the material forms an ordered crystallite by folding of the molecule. One and the same molecule may well be folded into two different crystallites and thus form a tie between the two. The tie part is prevented from crystallizing. The result is that the crystallinity will never reach 100%. Powder XRD can be used to determine the crystallinity by comparing the integrated intensity of the background pattern to that of the sharp peaks.
Crystallite size
If the crystallites of the powder are very small the peaks of the pattern will broaden. From the broadening it is possible to determine an average crystallite size, in Å, by Debye-Scherrer formula: Dhkl = k λ/β cosθ;
here k = 0.8 -- 1.39 (usually close to unity e.g. 0.9), λ-wavelength of the radiation λCu = 1.54056 Å, β - FWHM (full width at half maximum, or half-width) in radians, β = half-width (degree) Pi/180, θ - the position of the maximum of diffraction.
Note: on the diffractogram you usually plot 2θ on the x axis, not θ.
An error for the crystallite size by this formula can be up to 50%, so caution is needed when making assertions based solely on this technique.
Broadening due to Small Crystallite Size Bcrystallite = kλ/D cosθ
Broadening due to Strain Bstrain = η tanθ, where η is the strain in the material
The width of the diffraction peak Bresult = Bcrystallite + Bstrain =
kλ/D cosθ + η tanθ, multiplying this by cosθ we get: Bresult cosθ = kλ/D + η sinθ
Thus, when we plot Bresult cosθ vs sinθ we get a straight line with slope η and intercept kλ/D.
Crystal structure
Although it is certainly easier to determine a complete crystal structure from the pattern of a single crystal it is also possible to do it from a powder pattern, at least in certain cases. A common method is to fit the entire profile of the diffractogram. This method is known as the Rietveld refinement method.
Lattice expansion, phase transitions
The method can be combined with temperature control. It is possible to monitor the changes in the pattern as a function of temperature. Especially now that sources of synchrotron radiation have become more readily available this has become a more common technique to study phase transitions of changes in the lattice. Thermal expansion will cause the peaks to shift and from the shift the elements of the expansion tensor can be obtained.
Magnetic structures and the detection of hydrogen
X-ray photons scatter by interaction with the electron cloud of the material, neutrons are scattered by the nuclei. This means that the scattering power for XRD is roughly linear with atomic number, but fluctuates from isotope to isotope for neutrons. Both protons and deuterons (the stable nuclei of the element hydrogen) are strong scatterers for neutrons. The one electron of the atom makes it difficult to detect by X-rays. This makes neutron powder diffraction an attractive way to gain better insight of the precise location of hydrogen in a structure.
Neutrons can also undergo scattering if the material has an ordered magnetic structure. Neutrons have a spin and thus a small magnetic moment which interacts with the magnetic moments of electrons in an incomplete shell. The powder pattern can be used to determine the magnetic structure.
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, now more and more a bent position sensitive detector). The two types of cameras are known as the Laue and the Debye-Scherrer camera.To promote randomization the capillary is usually spinning around its axis.
For neutron diffraction vanadium cylinders are used as sample holders. Vanadium is all but transparant for neutrons. The element hardly scatters at all.
A later development in X-ray cameras is the Guinier camera. It is built around a focussing bent crystal monochromator. The sample is usually placed in the focussing 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 focussing circle, but the incident beam prevented from reaching the detector to prevent damage from its high intensity.
Diffractometers
Diffractometers can be operated both in transmission and in reflection configurations. The reflection one is more common. The powder sample is filled 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 -Geiger counter- rotates around it on an arm at twice this angle. This configuration is known under the name Bragg-Brentano.
The availability of position sensitive detectors and CCD-cameras is making this type of equipment more and more obsolete.
Neutron diffraction
Neutron sources suitable for diffraction are only available at a small number of research reactors and spallation sources in the world. To compensate for the low flux of neutron, they usually 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.
X-ray tubes
Laboratory X-ray diffraction equipment relies on the use of an X-ray tube, which is used to produce the X-rays.
For more on how X-ray tubes work, see for example [here] or X-ray.
The most commonly used laboratory X-ray tube uses a Copper anode, but Cobalt, Molybdenum are also popular. The wavelength in nm varies for each source:
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large user facilities
- Bragg Institute, OPAL
- *ECHIDNA - High Resolution Powder Diffractometer
- *WOMBAT - High Intensity Powder Diffractometer
- *KOWARI - Residual-Stress Diffractometer
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