Reciprocal Space

Miller indices steriographic projection.

Reciprocal space. Although the misleading common opinion reigns that bragg s law measures atomic distances in real space it does not. For those of you who know reciprocal space is the four year transform of real space. The points will be at k vectors which are perpendicular to the blue lines planes in three dimensions and with lengths which are multiples of 1 the distance between the planes.

Note that the areas of the first and second brillouin zones are the same. Reciprocal space will now consist of only a series of points. They are related by a fourier transform and the reciprocal space is also called fourier spaceor phase space.

The distribution of intensity in reciprocal space can be arbitrarily complex. It may also be called inverse space q space or fourier space. Reciprocal space is a non physical space.

Reciprocal space also called k space is the space in which the fourier transform of a spatial function is represented similarly the frequency domain is the space in which the fourier transform of a time dependent function is represented. If you are new to reciprocal space then this is the point where most people s brains reach overload. The miller indices can be determined from the steriographic projection by measuring the angles relative to known crystallographic directions and applying the law of cosines.

A fourier transform takes us from real space to reciprocal space or vice versa. Reciprocal space is a conceptual three dimensional space which contains the full 3d scattering pattern of a given sample. In material science it is mainly used to portray diffraction phenomena.

Reciprocal space in which a point has one bragg plane between it and the origin. It is the 3d fourier transform of the sample s realspace electron density distribution. This area is shaded yellow in the picture below.