Isotopic dependence of the heat capacity of c-C, Si, and Ge: an ab initio calculation

The vibrational spectra of crystalline diamond, silicon, and germanium are calculated with a first-principles local density functional scheme using 64 as well as 128 atoms supercells. The (harmonic) dynamical matrices are obtained from linear response theory. The phonon density of states, calculated for various isotopic masses M, are used to evaluate the vibrational heat capacities Cv and their dependence on M at low temperatures. Simple rules obeyed by the isotope effect of Cv are discussed. The results are compared with recent experimental data for Ge. It is hoped that this work will encourage and help to interpret analogous measurements in diamond and silicon with different isotopic compositions.