Bragg's Law Calculator

Bragg's Law describes the condition for constructive interference when X-rays are diffracted by crystal lattice planes. It is expressed as nλ = 2d·sin(θ), where n is the diffraction order, λ is the X-ray wavelength, d is the interplanar spacing, and θ is the angle of incidence. When this condition is satisfied, reflected beams from successive planes reinforce each other, producing an intense diffracted beam.

Bragg's law tells us the specific angles at which an X-ray beam will be diffracted by a crystalline material to produce maximum constructive interference. By measuring these diffraction angles, scientists can determine the interplanar spacing and ultimately the atomic structure of a crystal. It forms the basis of X-ray crystallography.

Bragg's Law is used extensively in X-ray crystallography to determine crystal structures of minerals, proteins, and pharmaceuticals. It is also applied in neutron diffraction, electron diffraction, and the analysis of thin films and nanostructures. Industries like materials science, chemistry, and biology rely on it for structural characterisation.

Interplanar spacing, or d-spacing, is the perpendicular distance between adjacent parallel planes of atoms in a crystal lattice. It is a fundamental property of a crystal and varies depending on the Miller indices of the planes. In Bragg's equation, d-spacing directly determines which wavelengths and angles satisfy the diffraction condition.

The diffraction order n is a positive integer (1, 2, 3, …) that represents the number of wavelengths in the path length difference between beams scattered from successive planes. First-order diffraction (n = 1) is the most commonly observed and typically the strongest. Higher orders occur at larger angles for the same d-spacing and wavelength.

Yes. Bragg's Law applies to any wave — X-rays, neutrons, or electrons — as long as the wavelength is comparable to the interplanar spacing of the crystal. Neutron diffraction is particularly useful for locating hydrogen atoms and studying magnetic structures, since neutrons interact differently with matter than X-rays do.

Bragg's Law requires sin(θ) ≤ 1, which means the angle θ must be between 0° and 90°. If the combination of n, λ, and d would require sin(θ) > 1, diffraction cannot physically occur for that order. This sets a practical limit on the diffraction orders observable for a given wavelength and d-spacing.

Select 'Incidence Angle (θ)' from the 'Solve For' dropdown, then enter the wavelength (λ), interplanar spacing (d), and diffraction order (n). The calculator applies θ = arcsin(nλ / 2d) and returns the angle in degrees along with the scattering angle 2θ and a breakdown table for multiple diffraction orders.