ISOTOPE DEPENDENCE OF THE LATTICE-PARAMETER OF GERMANIUM FROM PATH-INTEGRAL MONTE-CARLO SIMULATIONS

The dependence of the lattice parameter upon the isotope mass for five isotopically pure Ge crystals was studied by quantum path-integral Mo nte Carlo simulations. The interatomic interactions in the solid were described by an empirical potential of the Stillinger-Weber type. At 5 0 K the isotopic effect leads to an increase of 2.3 x 10(-4) Angstrom in the lattice parameter of Ge-70 with respect to Ge-76. Comparison of the simulation results with available experimental data for Ge-74 sho ws that the employed model provides a realistic description of this an harmonic effect. The path-integral results were compared to those deri ved from a quasiharmonic approximation of the crystal. Within this app roximation, the calculated fractional change of the lattice parameter of Ge-74 with respect to a crystal whose atoms have the average mass o f natural Ge amounts to Delta a/a = -9.2 x 10(-6) at T = 0 K. Some lim itations of the quasiharmonic approximation are shown at temperatures above 200 K.