dSpacings

dSpacings are the distances between parallel crystallographic planes in a crystal lattice. Each spacing is labeled d_hkl, associated with a set of planes defined by Miller indices h, k, and l. D-spacings are fundamental for describing crystal structure and are commonly reported in angstroms (Å).

In X-ray diffraction, the relation between d-spacings and diffraction geometry is given by Bragg's law: n times wavelength equals two times d times sine of the scattering angle. For a measured diffraction peak, the spacing is d = nλ / (2 sin θ), where θ is the Bragg angle and λ is the X-ray wavelength. In powder diffraction, a spectrum consists of peaks corresponding to different d-spacings, and indexing these peaks with hkl allows identification of phases and estimation of lattice parameters.

The connection between d-spacings and lattice parameters depends on crystal symmetry. In a cubic system, d_hkl = a / sqrt(h^2 + k^2 + l^2). For tetragonal systems, 1/d^2 = (h^2 + k^2)/a^2 + l^2 / c^2. Orthorhombic systems satisfy 1/d^2 = h^2/a^2 + k^2/b^2 + l^2/c^2. Hexagonal systems use 1/d^2 = (4/3)(h^2 + hk + k^2)/a^2 + l^2 / c^2. These relations enable calculation of lattice parameters from measured d-spacings.

Applications of d-spacings include phase identification, determination of lattice parameters, and assessment of microstructural features such as strain and crystallite size through peak positions and widths. Limitations arise from disorder, defects, and preferred orientation, which can complicate indexing and interpretation; accurate analysis requires appropriate calibration and consideration of instrumental effects.