Powder diffraction
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Powder diffraction is a scientific technique using X-Ray or neutron diffraction on powder or microcrystalline samples for structural characterization of materials. Ideally, every possible crystalline orientation is represented equally in the sample, leading to smooth diffraction rings around the beam axis rather than the discrete Laue spots observed for single crystal diffraction. In accordance with Bragg's law, each ring corresponds to a particular reciprocal lattice vector in the sample crystal, with intensity proportional to the number of such planes. In practice, it is sometimes necessary to rotate the sample orientation to eliminate the effects of texturing and achieve true randomness. The dedicated machine to perform such measurements is called a powder diffractometer.
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[edit] Advantages and disadvantages
The great advantages of the technique are simplicity of sample preparation, rapidity of measurement, a better representation of some real materials, and the ability to analyze mixed phases. Growth and mounting of large single crystals is notoriously difficult, whereas many materials are readily available with sufficient microcrystallinity for powder diffraction, or samples may be easily ground from larger crystals. Particularly for neutron diffraction, which requires larger samples than X-Ray Diffraction due to a relatively weak scattering cross section, the ability to prepare large samples can be critical. 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. As with any technique, sample preparation must be taken into account before analysis. For instance, the crystalline grains in industrial rolled steel strongly orient with the more compressible hexagonal c-axis perpendicular to the plane of rolling. This texturing distorts the observed peak intensity ratios despite a grain size which would otherwise be sufficiently small for the powder condition to obtain. In this case, sample rotation is required for accurate crystal phase determination. Once the phase is known, the degree of preferential orientation may be determined for various preparations by directly measuring the degree of texturing, which information is never available through single crystal diffraction. Mixed phases occur when multiple crystalline arrangements of scatterers are thermodynamically stable or metastable. For instance, tin exhibits two allotropes at ambient temperature and pressure. At low temperatures, the α-Sn, or grey tin, phase is favored, and the degree to which a sample has converted may be measured with powder diffraction.
Powder diffraction data is measured in terms of reciprocal space, analysis of which is less straightforward than single crystal data. Further, the three dimensional information of the reciprocal lattice of a crystal is collapsed into a one dimensional diffractogram, yielding somewhat less information than a corresponding single crystal diffraction experiment.
[edit] Uses
Relative to other methods of analysis, powder diffraction allows for rapid, non-destructive analysis of multi-component mixtures without the need for extensive sample preparation. This gives laboratories around the world the ability quickly to analyse unknown materials and perform materials characterization in such fields as metallurgy, mineralogy, forensic science, archeology and the biological and pharmaceutical sciences. Identification is performed by comparison of the diffraction pattern to a known standard or to a database such as the International Centre for Diffraction Data's Powder Diffraction File (PDF) or the Cambridge Structural Database (CSD). Advances in hardware and software, particularly improved optics and fast detectors, have dramatically improved the anaytical 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, sometimes to fractions of an Ångström, 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 an historic painting. The method has been historically used for the identification and classification of minerals, but it can be used for any materials, even amorphous ones, so long as a suitable reference pattern is known or can be constructed.
[edit] Crystal Structure Determination
The most widespread use of powder diffraction is in the identification and characterisation 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 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 relative concentration.
J.D. Hanawalt, an Analytical Chemist who worked for Dow Chemical in the 1930's, was the first to realize the analytical potential of creating a database. Today it is represented by the Powder Diffraction File (PDF) of the International Centre for Diffraction Data (formerly Joint Committee for Powder Diffraction Studies). This has been made searchable by computer through the work of global software developers and equipment manufacturers. There are now over 550,000 reference materials in the 2006 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.
For further information on matching an observed powder diffraction pattern to a quantitative model fully describing the phase, crystallinity, grain size, strain broadening, texturing, and other characteristics, see Rietveld refinement.
[edit] Crystallinity
In contrast to a crystalline pattern consisting 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.
[edit] 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.
[edit] Phase transitions
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 determination of the full equation of state of the material. At some critical set of conditions, for instance 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.
[edit] 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.
[edit] Devices
[edit] 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 transparent 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.
[edit] 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 (scintillation 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.
[edit] 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 neutrons, 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.
[edit] 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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[edit] See also
- Bragg Institute, OPAL
