Elastic X-ray scattering from solids containing non-rigid pseudoatoms

General methods for treating the elastic X-ray scattering from solids containing non-rigid pseudoatoms are developed. The methods are based on a model which involves the assumption of the adiabatic approximation and the representation of the total electron density as a sum of electron densities from dynamically deformable pseudoatoms. A basic result derived for this model is an expression for the X-ray structure factor in terms of generalized Born β parameters, the calculation being carried out to first order in the strength of the dynamic deformations. If the dynamic-deformation contribution is treated in the harmonic approximation, it is shown that considerable simplification of the expression for the structure factor can be achieved, especially at high temperature (i.e. T > θ_M, where θ_M is the Debye temperature). Another, fairly drastic, approximation discussed is that in which only the self-deformation contribution is retained. This latter approximation is used to estimate the effect of dynamic deformation for solid NaCI and NaF, utilizing some β's calculated from a shell model. Though the calculated effects are small, they are such as to be measurable in highly accurate experiments. Other cases are discussed where the effects of dynamic deformation may be expected to be somewhat larger.