Analytical expressions to determine the isothermal compressibility tensor and the isobaric thermal expansion tensor for monoclinic crystals: application to determine the direction of maximum compressibility in jadeite
Expressions are presented to allow the simple determination of the magnitudes and directions of the principal axes for the isothermal compressibility tensor and the isobaric thermal expansion tensor for monoclinic crystals. The method is applied to re-evaluate the apparently contradictory results that have recently been obtained for the direction of maximum compressibility in jadeite. The term ‘unit strain’ to describe these second rank tensors is discouraged and the use of the representation quadric for visualisation of second rank tensors is recommended.
KeywordsCompressibility Thermal expansion Second rank tensors Jadeite
I am grateful to Dr A. D. Fortes (University College, London) for commenting on an early draft of this manuscript, and to Prof. R. J. Angel (Virginia Polytechnic Institute) for his robust views on the desirability of the term ‘unit strain’ for describing pressure-dependent and temperature-dependent changes in the unit cell metric. Prof. I Jackson (Australian National University) is thanked for providing the expressions for infinitesimal calculations and for his reviewer’s comments which have improved the manuscript.
- Neumann FE (1885) Vorlesungen über die Theorie der Elastizität der fester Körper und die Lichtäthers (ed: Meyer OE). Teubner, LeipzigGoogle Scholar
- Nye JF (1985) Physical properties of crystals. Oxford University Press, OxfordGoogle Scholar
- Ohashi Y (1982) A program to calculate the strain tensor from two sets of unit-cell parameters (STRAIN). In: Hazen RM, Finger LW (eds) Comparative crystal chemistry. Wiley, New York, pp 92–102Google Scholar
- Origlieri MJ, Downs RT, Thompson RM, Pommier CJS, Denton MB, Harlow GE (2003) High-pressure crystal structure of kosmochlor, NaCrSi2O6, and systematics of anisotropic compression in pyroxenes. Am Mineral 88:1025–1032Google Scholar
- Pippard AB (1961) Elements of classical thermodynamics. Cambridge University Press, CambridgeGoogle Scholar
- Schofield PF, Knight KS, Stretton I (1996) Thermal expansion of gypsum investigated by neutron powder diffraction. Am Mineral 81:847–851Google Scholar
- Wallace DC (1972) Thermodynamics of crystals. Wiley, New YorkGoogle Scholar
- Zemansky MW, Dittman RH (1981) Heat and thermodynamics. McGraw-Hill, New YorkGoogle Scholar