Bragg's law: a standalone construct

William Lawrence Bragg's 1913 paper The diffraction of short electromagnetic waves by a crystal derived the condition under which X-rays scattered by the regularly spaced sheets of atoms in a crystal reinforce one another into a strong beam: nλ = 2d sin θ, where λ is the X-ray wavelength, d is the spacing between neighbouring atomic planes, θ is the angle between the incoming ray and those planes, and n is a whole number that counts the order of the reflection. Reinforcement happens when the extra distance travelled by rays bouncing off successive planes equals a whole number of wavelengths, so the waves stay in step and add together (constructive interference); at other angles the waves fall out of step and cancel, and no beam appears. In the same year W. L. Bragg worked with his father W. H. Bragg to confirm the relation experimentally and to build the X-ray spectrometer, reported in The reflection of X-rays by crystals, which turned the equation into a working instrument for measuring wavelengths and atomic spacings. The same geometry holds for neutron and electron diffraction, because any wave scattered by a periodic lattice obeys it, and the relation remains the founding equation of X-ray crystallography, the method through which the atomic and molecular structures of minerals, metals, proteins, and DNA have been determined.[1][2][3]

Unit

A diffraction condition expressed as an equation, not a measured quantity; it links the wavelength, the interplanar spacing d, and the glancing angle θ

Recovery means

Not applicable

Measured by

Applied by recording the angles at which a crystal yields sharp diffracted beams and solving nλ = 2d sin θ for the interplanar spacing d, using X-ray, neutron, or electron diffractometers