Powder diffraction
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.
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 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.
Both the positions (corresponding to lattice spacings) and the relative intensity of the lines in a diffraction pattern are indicative of a particular phase and material, providing a "fingerprint" for comparison.
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.
In contrast to a crystalline pattern consisting of a series of sharp peaks, amorphous materials (liquids, glasses etc.)
Many polymers show semicrystalline behavior, i.e. part of the material forms an ordered crystallite by folding of the molecule.
Powder XRD can be used to determine the crystallinity by comparing the integrated intensity of the background pattern to that of the sharp peaks.
Indexing programs exist to deal with the harder cases, but if the unit cell is very large and the symmetry low (triclinic) success is not always guaranteed.
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 example 0 °C for water at 1 atm, a new arrangement of atoms or molecules may become stable, leading to a phase transition.
If the material melts to an isotropic liquid, all sharp lines will disappear and be replaced by a broad amorphous pattern.
A crystal structure, together with instrumental and microstructural information, is used to generate a theoretical diffraction pattern that can be compared to the observed data.
Neutron diffraction techniques may therefore be used to detect light elements such as oxygen or hydrogen in combination with heavy atoms.
The neutron diffraction technique therefore has obvious applications to problems such as determining oxygen displacements in materials like high temperature superconductors and ferroelectrics, or to hydrogen bonding in biological systems.
The incoherent scattering length of deuterium is much smaller (2.05(3) barn) making structural investigations significantly easier.
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.
The use of each method depends on the knowledge on the analyzed system, given that, for instance, Rietveld refinement needs the solved crystal structure of each component of the mixture to be performed.
Vanadium has a negligible absorption and coherent scattering cross section for neutrons and is hence nearly invisible in a powder diffraction experiment.
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.
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.
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.
The advent of synchrotron sources has drastically changed this picture and caused powder diffraction methods to enter a whole new phase of development.
Many materials are readily available with sufficient microcrystallinity for powder diffraction, or samples may be easily ground from larger crystals.
In the field of solid-state chemistry that often aims at synthesizing new materials, single crystals thereof are typically not immediately available.
Particularly for neutron diffraction, which requires larger samples than X-ray diffraction due to a relatively weak scattering cross section, the ability to use large samples can be critical, although newer and more brilliant neutron sources are being built that may change this picture.
Since all possible crystal orientations are measured simultaneously, collection times can be quite short even for small and weakly scattering samples.
