Powder diffraction
Powder diffraction is a scientific technique using X-ray, neutron, or electron diffraction on powder or microcrystalline samples for structural characterization of materials. An instrument dedicated to performing such powder measurements is called a powder diffractometer.
Powder diffraction stands in contrast to single crystal diffraction techniques, which work best with a single, well-ordered crystal.
Explanation
The most common type of powder diffraction is with X-rays, the focus of this article, although some aspects of neutron powder diffraction are mentioned. Typical diffractometers use electromagnetic radiation with known wavelength and frequency, which is determined by their source. The source is often X-rays, 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 can enter the lattice and be diffracted by the atoms present in the sample. If the atoms are arranged symmetrically with a separation distance d, these waves will interfere constructively only where the path-length difference 2d sin θ is equal to an integer multiple of the wavelength, producing a diffraction maximum in accordance with Bragg's law. These waves interfere destructively at points between the intersections where the waves are out of phase, and do not lead to bright spots in the diffraction pattern. Because the sample itself is acting as the diffraction grating, this spacing is the atomic spacing.The 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 a powdered sample, the isotropic case. Powder X-ray diffraction operates under the assumption that the sample is randomly arranged. Therefore, a statistically significant number of each plane of the crystal structure will be in the proper orientation to diffract the X-rays. Therefore, each plane will be represented in the signal. In practice, it is sometimes necessary to rotate the sample orientation to eliminate the effects of texturing and achieve true randomness.
Mathematically, crystals can be described by a Bravais lattice with some regularity in the spacing between atoms. 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 projected onto a single dimension.
When the scattered radiation is collected on a flat plate detector, the rotational averaging leads to smooth diffraction rings around the beam axis, 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 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:
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 or as a function of the scattering vector length q. The latter variable has the advantage that the diffractogram no longer depends on the value of the wavelength λ. The advent of synchrotron sources has widened the choice of wavelength considerably. To facilitate comparability of data obtained with different wavelengths the use of q is therefore recommended and gaining acceptability.
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 the ability to quickly analyze unknown materials and perform materials characterization in such fields as metallurgy, mineralogy, chemistry, forensic science, archeology, condensed matter physics, 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 or the Cambridge Structural Database. 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, 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 nearly any material, even amorphous ones, so long as a suitable reference pattern is known or can be constructed.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 and the relative intensity of the lines 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 the determination of the relative concentrations of phases in the mixture.J.D. Hanawalt, an analytical chemist who worked for Dow Chemical in the 1930s, was the first to realize the analytical potential of creating a database. Today it is represented by the Powder Diffraction File of the International Centre for Diffraction Data. This has been made searchable by computer through the work of global software developers and equipment manufacturers. There are now over 1,047,661 reference materials in the 2021 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.