Anharmonic effects in the thermodynamic properties of solids VI. Germanium: heat capacity between 30 and 500 $deg$C and analysis of data

The heat capacity of germanium has been measured between 30 and 500 °C with an accuracy of ± 0·3% for T less, similar 400 °C and ± 0·5% at the highest temperatures. The average deviation of the experimental points from a smoothed curve is less than 0·1%. The entropy, the constant volume heat capacity and the Grüneisen function have been analysed to yield quasi-harmonic and explicit anharmonic contributions. The explicit anharmonic contributions to the entropy and heat capacity are consistent with the predictions of anharmonic perturbation theory, and give A ( V 0 ) = 3·1 ± 1·0 × 10 -5 degk -1 and B ( V 0 ) = 1·4 ± 1 × 10 -8 degk -2 for the first- and second-order anharmonic coefficients respectively. The analysis of γ( T, V ) gives γinfinity qh ( V 0 ) = 0·70 ± 0·04 and γ anh = 4·5 ± 1·5. The explicit anharmonic contributions are much larger than those arising through thermal expansion of the crystal, in contrast to the crystals previously studied. The temperature dependence of the geometric mean frequency calculated from the results of the anharmonic analysis is somewhat lower than that derived from measurements on nine normal modes by inelastic neutron scattering. The value of the first-order anharmonic coefficient calculated using a phenomenological elastic continuum model is in good agreement with experiment.