Reciprocal Space
Although the misleading common opinion reigns that Bragg's law measures atomic distances in real space, it does not. This first statement only seems to be true if it's further elaborated that distances measured during a Bragg experiment are inversely proportional to the distance d in the lattice diagram. Furthermore, the term demonstrates that it measures the number of wavelengths fitting between two rows of atoms, thus measuring reciprocal distances. Reciprocal lattice vectors describe the set of lattice planes as a normal vector to this set with length Max von Laue had interpreted this correctly in a vector form, the Laue equation
where is a reciprocal lattice vector and and are the wave vectors of the diffracted and the incident beams respectively.
Together with the condition for elastic scattering and the introduction of the scattering angle this leads equivalently to Bragg's equation. This is simply explained by the conservation of momentum transfer. In this system the scanning variable can be the length or the direction of the incident or exit wave vectors relating to energy- and angle-dispersive setups. The simple relationship between diffraction angle and Q-space is then:
The concept of reciprocal lattice is the Fourier space of a crystal lattice and necessary for a full mathematical description of wave mechanics.
Read more about this topic: Bragg's Law
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