Vibrational Spectra of Solids

Abstract

The Bravais space cell is used by molecular spectroscopists to obtain the irreducible representation for the lattice vibrations. The crystallographic unit cell may be identical with the Bravais cell or it may be larger by a multiple of two, three or four. This information can be obtained from the capital letter in the x-ray symbol which is used to designate the crystal symmetry. For all crystal structures designated by a symbol P (primitive), the crystallographic unit cell and the Bravais unit cell are identical. Crystal structures designated with capital letters A, B, C, or I are doubly primitive and thus the crystallographic unit cells contain two Bravais cells. Crystal structures designated with capital letters R or F are triply and quadrupoly primitive, respectively, and the crystallographic unit cells contain three and four Bravais cells, respectively. Thus, to obtain the desired Bravais space cell from the crystallographic unit cell, one simply divides the number of molecules in the crystallographic unit cell by the number of lattice points. In summary, the number of molecules in the Bravais space cell Z^B is the number of molecules in the crystallographic unit cell (Z) divided by the number of lattice points (LP): Z^B = Z/LP and this reduction is summarized.