The Physics of X-ray Scattering
Powder X-ray Diffraction (PXRD) is an analytical technique used to identify and characterize crystalline materials by studying how X-rays interact with their atomic structure. It allows researchers to determine the composition of unknown solids. PXRD is foundational in materials science, providing reliable information on the identity and purity of solid compounds that exhibit an ordered structure.
X-rays are used because they possess wavelengths typically in the range of 0.5 to 2.5 Angstroms (Å). This range is comparable to the spacing between atoms within a crystal lattice. When an X-ray beam strikes a crystalline material, the atoms act as scattering centers, causing the incident wave to be redirected.
A crystal is composed of many parallel planes of atoms, and X-rays scattered from different planes must travel different distances before they recombine. For a detectable signal, these scattered waves must be in phase, meaning their crests and troughs align perfectly to reinforce one another—a phenomenon known as constructive interference. This reinforcement occurs only when the difference in path length traveled is an exact integer multiple of the X-ray wavelength.
Bragg’s Law describes the condition for constructive interference. This principle mathematically links the X-ray wavelength, the spacing between the atomic planes, and the angle at which the beam strikes the sample. Since each crystalline material has a unique set of atomic plane spacings, interference is satisfied only at characteristic angles. By measuring the angles where these reinforced beams emerge, scientists can deduce the underlying structure of the material.
Generating the Diffraction Data
Data collection requires a specialized instrument called a powder diffractometer. The process begins with an X-ray source, typically a copper anode, which generates a monochromatic beam of a single, defined wavelength. This beam is directed onto the prepared sample, which has been ground into a fine powder.
The sample is ground into a fine powder containing millions of tiny microcrystals, each oriented randomly in space. This random orientation ensures that a small fraction of microcrystals will be positioned correctly to satisfy the Bragg condition at any specific angle. The resulting diffraction pattern represents an average of all possible crystal orientations.
A mechanical system called a goniometer changes the angle between the incident X-ray beam, the sample, and the detector. The detector systematically scans a wide range of diffraction angles, denoted as $2\theta$. It measures the intensity of the scattered X-rays at each point, precisely recording the angles where constructive interference occurs.
The output is a dataset of measured intensity values corresponding to specific $2\theta$ angles. This data maps the three-dimensional atomic structure onto a two-dimensional graph of intensity versus angle. The resulting data points are plotted to visualize the characteristic peaks that form the material’s structural fingerprint.
Reading the Powder Pattern
The powder pattern is the definitive structural signature of the crystalline material. It is an ordered display where the position and intensity of each peak carry specific structural information. Since no two crystalline compounds share the exact same pattern, it is a reliable tool for material identification.
The position of a peak along the $2\theta$ axis is directly related to the spacing between atomic planes within the crystal lattice. By analyzing all peak positions, researchers determine the size and shape of the unit cell. The unit cell is the smallest repeating block of atoms that defines the entire crystal structure.
The intensity of a peak provides information about the types of atoms and their arrangement within the unit cell. Heavier atoms scatter X-rays more strongly than lighter atoms. The intensity is also affected by how the atoms are positioned relative to one another, mapping the electron density distribution within the structure.
Material identification is accomplished by comparing the measured pattern to reference libraries, such as those provided by the International Centre for Diffraction Data (ICDD). Algorithms match the positions and relative intensities of the unknown pattern’s peaks to known compounds. A high-quality match confirms the identity and crystal structure of the material.
Real-World Uses of PXRD
The ability to obtain a unique structural fingerprint makes PXRD an indispensable technique across numerous scientific and industrial sectors.
Phase Identification
This involves identifying all the distinct crystalline components present in a mixture. For example, geologists use PXRD to determine the precise mineral composition of rock samples. This provides crucial insights into their formation history and origin.
Purity Determination
PXRD checks for the presence of unwanted crystalline contaminants. In the pharmaceutical industry, this is relevant for quality control. PXRD ensures drug substances are free of crystalline impurities that might affect their stability or efficacy. The detection of even small amounts of a second crystalline phase can be accurately quantified.
Crystallinity Analysis
PXRD is highly utilized for analyzing the ratio of ordered (crystalline) material to disordered (amorphous) material in a solid. Materials with higher crystallinity often exhibit different properties, such as increased rigidity or better thermal stability. This analysis is important in materials science for characterizing novel ceramics, polymers, and metallic compounds under development.
Polymorph Detection
The technique is also applied to detect different polymorphic forms of a compound. These are distinct crystal structures that share the same chemical formula. Pharmaceutical companies rely on PXRD to identify polymorphs because different crystal forms of a drug can have drastically different solubilities and dissolution rates. This directly impacts how the drug is absorbed by the body.