Determination of the one-particle potential for an atom with highly anharmonic thermal motion

Abstract

Analytical expressions are derived relating the coefficients (α, β, γ, and δ) of the anharmonic one-particle-potential (OPP) model at a cubic site to the parameters of the higher cumulant expansion of the Debye-Waller factor. These expressions are used to derive the shape of the potential for the Al(4) site in the structure of VAl10.42 from refinements of X-ray data measured at 100 K and room temperature, including third and fourth cumulant thermal parameters. Reasonable potentials are obtained at both temperatures. A negative value of β indicates a softening of the potential in the (111) directions in contradiction to the results of previous pseudopotential calculations. A siingle set of potential parameters is obtained by least-squares fit to the cumulants at both temperatures. Deviations from the fit indicate a lower temperature dependence for the anharmonic terms than predicted by the OPP model. Corrections for quantum statistical effects are small at both temperatures.