Bragg’s law

Loi de Bragg (Fr). Bragg-Gesetz (Ge). Legge di Bragg (It). Ley de Bragg (Sp). Условие Брэгга-Вульфа (Ru).

Bragg’s Law is an equation formulated by Sir W. H. Bragg and his son, which predicts whether diffraction can take place or not[1]. The equation provides the condition for a plane wave to be diffracted by a family of lattice planes:

2 d sin θ = n λ

where d is the interplanar spacing, θ the angle between the incident ray and crystal planes, λ its wavelength of the used radiation and n is an integer, the order of the reflection. It is equivalent to the diffraction condition in reciprocal space and to the Laue equations.[2]

Fig. 1 Bragg’s law [3]

The basic idea behind Bragg’s Law is that, when it is satisfied, X-ray beams (for example) scattered from successive planes in the crystal will travel distances differing by exactly one wavelength (for the case of n=1); this can be fairly easily proven from a geometrical consideration of the above diagram. In this precise direction, i.e. at the angle θ calculated by Bragg’s Law, X-rays scattered from successive planes will interact constructively when they eventually reach the X-ray detector, thus registering the passage of an intense beam which we call the diffracted beam.[4]

Bragg’s Law does not apply only to X-rays, but also neutrons and electrons can be used instead. Because the diffraction pattern is independent of the wavelength used, such principle is very valuable for Electron Diffraction (ED) experiments. This is the underlying issue behind ED for nano-crystallography.

References:

1 W. L. Bragg, “The Crystalline State: Volume I”, The Macmillan Company, New York 1934.

2 “Bragg’s law”, accessed on September 21, 2020, https://dictionary.iucr.org/Bragg%27s_law

3 S. Baskaran, “Structure and Regulation of YeastGlycogen Synthase”, PhD thesis, Indiana University, IN, 2010.

4 “Bragg’s law”, accessed on September 21, 2020, http://pd.chem.ucl.ac.uk/pdnn/powintro/braggs.html