High‐temperature thermodynamic properties of forsterite

The high‐temperature thermodynamic properties of forsterite were reviewed in the light of a new determination of the isobaric heat capacity ( C p ), up to 1850K, and Raman spectroscopic measurements, up to 1150K and 10 GPa. The C p measurements and available data on thermal expansion (α) and bulk modulus ( K ) show that the isochoric specific heat ( C v ) exceeds the harmonic limit of Dulong and Petit above 1300 K. This intrinsic anharmonic behavior of C v can be modeled by introducing anharmonic parameters a i = (∂lnv i /∂T) V which are calculated from the measured pressure and temperature shifts of the vibrational frequencies. These parameters are all negative, with absolute values lower for the stretching modes of the SiO 4 tetrahedra (a i ≈ − 1×10 −5 K −1 ) than for the lattice modes (a i ≈ − 2×10 −5 K −1 ). Through the relation C p = C v +α 2 K T VT the calculated anharmonic C v and the measured C p are then used to determine the temperature dependences of the thermal expansion and bulk modulus of forsterite, up to 2000 K, in agreement with recent experimental results. Finally, all these data point to an inconsistency for the Grüneisen parameter of forsterite, whereby the macroscopic parameter γ= α VK T / C v cannot be evaluated simply at high temperature by summation of the individual isothermal mode Grüneisen parameters γ iT = K T (∂lnv i /∂ P ).