Anharmonic contributions to the Debye-Waller factor of aluminium

Abstract

We have proposed theoretical results for the quasiharmonic (QH) and anharmonic contributions to the Debye-Waller factor (DWF) of Al in the temperature (T) range 300 K ⩽ T ⩽ 850 K. The calculations have been carried out from two different pseudopotentials (Harrison modified point ion and Ashcroft) and three different screening functions (Hubbard-Sham, Hubbard and Vashishta-Singwi) as well as a nearest neighbour central force (n.n.c.f.) three parameter Morse potential. The anharmonic contributions are evaluated in the lowest order (λ 2) perturbation theory (PT) (viz. cubic and quartic contributions) as well as to all orders of anharmonicity from a recently proposed Green's function method. The latter method sums certain anharmonic contributions from cubic and quartic terms in the Hamiltonian to all orders of PT. Excellent agreement in the entire temperature range is obtained with the experimental results from the Green's function method with Harrison modified point ion pseudopotential and Hubbard-Sham screening function by including the volume dependence of the pseudopotentials. The results from the Green's function method and Ashcroft pseudopotential with Vashishta-Singwi and Hubbard screening functions agree well with experiments up to 600 K. The Morse potentials has limited applicability. The results agree for T ⩽ 500 K but differ from experiments by as much as 22% at higher temperatures where the calculated values of DWF are lower. Since in the entire temperature range the λ 2 PT results, which include the QH results, are lower than the Green's function results, higher order anharmonic terms included in the Green's function method seem to make important contributions to the DWF in Al for all the potential functions.