When a crystal with an interplanar spacing d (crystal lattice constant) is irradiated by X-ray beam with a comparable wavelength λ, the X-ray diffraction, or the constructive interference between elastically scattered X-ray beams can be observed at specific angles 2θ when the the Bragg’s Law is satisfied
nλ = 2dsinθ
where n is any integer. In most diffractometers the X-ray wavelength λ is fixed and the diffraction angle θ is measured by goniometer, therefore the crystal lattice constants can be decided by above equation.
Bragg-Brentano (BB) Geometry
Most of powder diffractometers use Bragg-Brentano parafocusing geometry, offering high-resolution and high beam-intensity analysis at the cost of very precise alignment requirements and carefully prepared samples.
- The incident angle ω between X-ray source and the sample is always 1/2 of the detector angle 2θ: 1) ω:2θ or θ:2θ scan: with the X-ray tube fixed, the sample rotates at θ/min and the detector always at 2θ/min; and 2) θ:θ scan: the sample is fixed and the tube rotates at the same rate as the detector at θ/min.
- Sample surface is kept on the tangent plane of the focusing circle defined by three spots at sample, X-ray source and receiving slit.
- The incident- and diffracted-beam slits move on a circle that is centered on the sample. Divergent X rays from the source hit the sample at different points on its surface. During the diffraction process the X rays are refocused at the detector slit.
Parallel-Beam (PB) Geometry
The PB optics provides accurate measurement of diffracted X-ray positions unaffected by sample shape. It is generally used to analyze powder sample profiles, the degree of preferred orientation and thin films.
- A polycapillary collimating optic (Göbel Mirror) is used to form an intense parallel X-ray excitation beam resulting in very high X-ray intensities at the sample surface.
- No restrictions on XRD configuration from BB geometry which allows broader range of sample shapes and sizes.