Original paper

Volume thermal expansion and related thermophysical parameters in the Mg, Fe olivine solid-solution series

Kroll, Herbert; Kirfel, Armin; Heinemann, Rolf; Barbier, Bruno


The thermal expansion of the Mg, Fe olivine solid-solution series was investigated from a total of 316 V(T) data, 141 of which were collected in this work by single-crystal X-ray diffraction over a wide range of temperatures. Functional forms currently in use for modelling thermal expansion are compared. The Kumar equation was found most useful for high-temperature extrapolation. With four parameters (θFoD, θFaD, kFo, kFa) fixed at values reported in the literature, it suffices to refine only two parameters (QFo0, QFa0) along with the composition-specific V(0 K) in order to describe the thermal expansion in the whole olivine series. The chosen data set is internally consistent as the thermal expansions of forsterite (Fo) and fayalite (Fa) are correctly predicted, even if only V(T) data of compositionally intermediate olivines are used. These results resolve the discrepancies between the thermal expansivities of Fo and Fa reported in the literature and are applied to a variety of thermophysical parameters with a significant dependence on the thermal expansion, as follows. (1) Experimental adiabatic bulk moduli KS of Fo are transformed into isothermal moduli KT so that both can be jointly fitted. (2) KS and KT values of Fa are deduced up to high temperatures assuming Fa to behave similarly to Fo with respect to the parameter αKT. (3) αKT of both Fo and Fa increases up to a temperature of 1.5 θD and then remains constant up to 4 θD. (4) The respective Anderson-Grüneisen parameters of both compounds follow parallel paths, with δS steadily decreasing and δT becoming constant above 1.5 θD. (5) The isobaric and isochoric thermodynamic Grüneisen parameters γth are deduced for Fo and Fa. (6) The Mie-Grüneisen-Debye parameter γrefMGD varies much less with temperature than the isochoric γth and may thus be approximated by a constant. (7) The thermal pressure ΔPth predicted by the Birch-Murnaghan equation-of-state (BM EoS) agrees with earlier experimental P-V-T results on Mg-rich olivines, according to which ΔPth depends on volume. (8) The thermodynamic (αKT) approach to ΔPth leads to small, however significant volume correction parameters. (9) The volume dependence of the isochoric heat capacity CV is deduced from a calculation of the entropy dependence on volume. Gillet-type polynomials yield CV as a function of temperature and compression. (10) The pressure dependence of α(T) between 0 and 15 GPa is determined from combining the BM EoS with the Kumar equation. The results were found to conform with a description using constant δT parameters.


olivinethermal expansionthermoelastic parametersforsteritefayalite