CONSTRAINTS ON THE MOVEMENT OF ATOMS IN THE TOTALLY SYMMETRICAL VIBRATIONS OF CRYSTAL LATTICES - LATTICE FORCE-CONSTANT CALCULATIONS FOR SODALITES

Atoms in crystal structures at certain special positions are forbidden by symmetry to move in the zero wavevector totally symmetric lattice vibrations. A rule for identifying these special positions is given, and use is made of the constraint on atom movement to derive equations that give the valence force constants for the aluminosilicate framework of sodalite from Raman spectroscopic data. The Si-O-Al bending force constant is found to be relatively small, and the equations define a relationship between the totally symmetric frequencies and the Si-O-Al angle, thus providing the basis of a method for determining this angle from experimental Raman data.