Covariances of thermal parameters and their effect on rigid-body calculations

An isotropic approximation is developed for the covariance matrix of atomic vibration components in an arbitrary coordinate system. The effect of alternative treatments of these covariances on derived rigid-body vibration parameters is illustrated by a numerical comparison. Serious errors may result from neglect of the correlations between different components of the vibration tensors U if these are referred to non-orthogonal axes.