Jc. Noya et al., ISOTOPE DEPENDENCE OF THE LATTICE-PARAMETER OF GERMANIUM FROM PATH-INTEGRAL MONTE-CARLO SIMULATIONS, Physical review. B, Condensed matter, 56(1), 1997, pp. 237-243
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.