Anharmonicity and high-temperature heat capacity of crystals: the examples of Ca₂GeO₄, Mg₂GeO₄ and CaMgGeO₄ olivines

Abstract

Drop-calorimetry determinations of the isobaric heat capacity (C_P) of Mg₂GeO₄, Ca₂GeO₄ and CaMgGeO₄ have been made up to 1700 K. The thermal expansion coefficient (α) of these olivine germanates has been determined from high-temperature X-ray measurements up to 1500 K. From these measurements and available compressibility data, one calculates that the isochoric heat capacity (C_V) exceeds the harmonic limit of Dulong and Petit above 1000–1200 K. Such an intrinsic anharmonic behaviour can be accounted for by introducing anharmonic parameters a_i=(∂ ln v _i/∂T)_V in vibrational modelling of C_V. These parameters are calculated from pressure and temperature shifts of the vibrational frequencies as measured by Raman spectroscopy up to 10 GPa at room temperature and up to 1300 K at 1 bar. A comparison of the Raman spectra of the three germanates with those of natural olivines justifies once again the use of germanates as silicate analogues. Extensive Ca,Mg disordering likely takes place in CaMgGeO₄, beginning at about 1100 K and leading to unusually high increases of the heat capacity and thermal expansion coefficient.