A lattice-dynamical treatment of the thermal-motion bond-length correction

The effect of the thermal motions of the atoms on interatomic distances is treated in terms of lattice dynamics. It is not only shown how the anisotropic vibration tensors of the atoms can be derived from the dynamical matrices of the crystal but also how mean binary-product coupling tensors are obtained. Each of these tensors expresses the coupling of the motions of two atoms in the unit cell as an average over time and lattice and thus is suitable for formulating the bond-length correction. Hence the discussion centres around the coupling tensors. The coupling tensors cannot be determined by experiment; but in order to calculate them and the bond-length correction, one is forced to conceive dynamical models of motion for the atoms in the unit cell. The corrections for the known models of uncorrelated motion, rigid-body motion and riding motion are rederived by using the coupling tensors.