Bragg's Law Calculator

The perpendicular distance between parallel crystal planes with the same Miller indices (hkl). For a cubic crystal with lattice parameter a: d_hkl = a/sqrt(h^2+k^2+l^2). Measuring d-spacings from XRD gives the lattice parameters.

In X-ray diffractometry, the detector moves to twice the Bragg angle (2*theta) from the incident beam direction to collect the diffracted beam. XRD patterns are plotted as intensity vs 2-theta, typically from 5 to 80 degrees for powder diffraction.

Crystal plane spacings are 0.1-1 nm, comparable to X-ray wavelengths (0.05-0.25 nm). Visible light wavelengths (400-700 nm) are far too large to be diffracted by atomic planes.

Phase identification (mineral/drug analysis), crystal structure refinement (Rietveld method), crystallite size from peak broadening (Scherrer equation), residual stress analysis, and thin film characterization in materials science and pharmaceuticals.

John Kendrew and Max Perutz solved the first protein structures (myoglobin and hemoglobin, respectively) in 1958-1960, earning the 1962 Nobel Prize in Chemistry. Watson and Crick used X-ray data from Rosalind Franklin to propose the DNA double helix structure in 1953.

Tau = K*lambda/(beta*cos(theta)), where tau is the crystallite size, K is a shape factor (~0.9), lambda is the X-ray wavelength, and beta is the full width at half maximum of the diffraction peak. Broad peaks indicate small crystallites.

Neutrons (with wavelengths of 50-300 pm, similar to X-rays) are diffracted by crystals following Bragg's law. Neutrons interact with atomic nuclei (not electrons), making them sensitive to light atoms (H, Li) invisible to X-rays and to magnetic ordering in materials.

Yes. Electrons accelerated through kilovolt potentials have de Broglie wavelengths of 1-100 pm and are diffracted by crystal planes. Electron diffraction patterns (LEED, RHEED, TEM) also follow Bragg's law and are used to study surface structures and thin films.

The structure factor F_hkl is a complex number whose magnitude determines the intensity of the Bragg reflection (hkl). It depends on atom positions within the unit cell and atomic scattering factors. Some reflections may have F=0 (systematic absences) due to crystal symmetry.