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

Herbert Kroll, Armin Kirfel, Rolf Heinemann and Bruno Barbier
Volume thermal expansion and related thermophysical parameters in the Mg,Fe olivine solid-solution series
European Journal of Mineralogy (October 2012) 24 (6): 935-956


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 (theta (super Fo) (sub D) , theta (super Fa) (sub D) , k (sub Fo) , k (sub Fa) ) fixed at values reported in the literature, it suffices to refine only two parameters (Q (super Fo) (sub 0) , Q (super Fa) (sub 0) ) 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 K (sub S) of Fo are transformed into isothermal moduli K (sub T) so that both can be jointly fitted. 2. K (sub S) and K (sub T) values of Fa are deduced up to high temperatures assuming Fa to behave similarly to Fo with respect to the parameter alpha K (sub T) . 3. alpha K (sub T) of both Fo and Fa increases up to a temperature of 1.5 theta (sub D) and then remains constant up to 4 theta (sub D) . 4. The respective Anderson-Gruneisen parameters of both compounds follow parallel paths, with delta (sub S) steadily decreasing and delta (sub T) becoming constant above 1.5 theta (sub D) . 5. The isobaric and isochoric thermodynamic Gruneisen parameters gamma (sub th) are deduced for Fo and Fa. 6. The Mie-Gruneisen-Debye parameter gamma (super ref) (sub MGD) varies much less with temperature than the isochoric gamma (sub th) and may thus be approximated by a constant. 7. The thermal pressure Delta P (sub th) 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 Delta P (sub th) depends on volume. 8. The thermodynamic (alpha K (sub T) ) approach to Delta P (sub th) leads to small, however significant volume correction parameters. 9. The volume dependence of the isochoric heat capacity C (sub V) is deduced from a calculation of the entropy dependence on volume. Gillet-type polynomials yield C (sub V) as a function of temperature and compression. 10. The pressure dependence of alpha (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 delta (sub T) parameters.

ISSN: 0935-1221
EISSN: 1617-4011
Serial Title: European Journal of Mineralogy
Serial Volume: 24
Serial Issue: 6
Title: Volume thermal expansion and related thermophysical parameters in the Mg,Fe olivine solid-solution series
Affiliation: Westfaelische Wilhelms-Universitaet, Institut fuer Mineralogie, Muenster, Germany
Pages: 935-956
Published: 201210
Text Language: English
Publisher: Schweizerbart'sche Verlagsbuchhandlung (Naegele u. Obermiller), Stuttgart, Germany
References: 83
Accession Number: 2013-002482
Categories: Mineralogy of silicates
Document Type: Serial
Bibliographic Level: Analytic
Illustration Description: illus. incl. 4 tables
Secondary Affiliation: Steinmann Institut, DEU, Germany
Country of Publication: Germany
Secondary Affiliation: GeoRef, Copyright 2017, American Geosciences Institute. Abstract, copyright, Schweizerbart'sche Verlagsbuchhandlung. Reference includes data from GeoScienceWorld, Alexandria, VA, United States
Update Code: 201302
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