Ab initio determination of crystal lattice constants and thermal expansion for germanium isotopes

The temperature dependence of the equilibrium lattice constants for five isotopically pure Ge crystals (70Ge, 72Ge, 73Ge, 74Ge and 76Ge) and naturally occurring Ge were calculated from ab initio electronic theory within the quasiharmonic approximation. It is shown that at very low temperature, calculations including zero point motions contribution to the free energy correctly reproduced the experimental unit cell parameters for the five isotopes. For 70Ge, 74Ge, 76Ge and naturally occurring Ge, the predicted thermal expansion coefficients agree very well with experiments. The calculated thermal expansitivity for 73Ge does not agree well with experiment. It is speculated that this anomaly may due to the non-zero nuclear spin of the 73Ge isotope.