Quantum-thermodynamic treatment of intrinsic anharmonicity; Wallace's theorem revisited

Physics and Chemistry of Minerals

Volumn 32, Issue 8-9, 2005, Pages 614-626

  Jacobs, Michel H G ^a   de Jong, Bernard H W S ^a  

^a UTRECHT UNIVERSITY   (Netherlands)

Author keywords

Anharmonicity; Equation of state; Forsterite; Sound velocity; Thermal expansivity

Indexed keywords

ACOUSTIC WAVE VELOCITY; CRYSTAL LATTICES; EQUATIONS OF STATE; LATTICE VIBRATIONS; MAGNESIUM COMPOUNDS; THERMAL EXPANSION; THERMODYNAMIC PROPERTIES;

ANHARMONICITY; FORSTERITE; WALLACE THEOREM;

SILICATES;

ACOUSTIC WAVE; EQUATION OF STATE; FORSTERITE; THERMAL EXPANSION;

EID: 29544442554     PISSN: 03421791     EISSN: 14322021     Source Type: Journal    
DOI: 10.1007/s00269-005-0038-x     Document Type: Article

References (44)

1. 4 olivines: An X-ray diffraction study up to 70 GPa. Phys Chem Minerals 22:99-107 10.1007/ BF00202469
2. Ashida T, Kume S, Ito E (1987) Thermodynamic aspects of phase boundary among α-, β-, and γ-Mg2SiO4. In: Manghnani MH, Syono Y (eds) High pressure research in mineral physics. Terra Scientific Publishing Company (TERRAPUB), Tokyo/American Geophysical Union, Washington, pp 269-274
3. Barin I (1989) Thermochemical data of pure substances, part II. VCH Verlags-gesellschaft mbH, pp 873
4. Birch F (1952) Elasticity and constitution of the Earth's interior. J Geophys Res 57:227-286
5. Boehler R and Chopelas A (1991) A new approach to laser heating in high pressure mineral physics. Geophys Res Lett 18:1147-1150
6. Bouhifd MA, Andrault D, Fiquet G, Richet P (1996) Thermal expansion of forsterite up to the melting point. Geophys Res Lett 23:1143-1146 10.1029/96GL01118
7. Chopelas A (1990) Thermal properties of forsterite at mantle pressures derived from vibrational spectroscopy. Phys Chem Minerals 17:149-156
8. Chopelas A (2000) Thermal expansivity of mantle relevant magnesium silicates derived from vibrational spectroscopy at high pressure. Am Miner 85:270-278
9. Downs RT, Zha CS, Duffy TS, Finger LW (1996) The equation of state of forsterite to 17.2 GPa and effects of pressure media. Am Mineral 81:51-55
10. Fei Y, Bertka CM (1999) Phase transformations in the Earth's mantle and mantle mineralogy. In: Fei Y, Bertka CM, Myssen BO (eds) Mantle petrology: Field observations and high pressure experimentation, vol 6. The Geological Society, Washington, pp 189-207
11. Gillet P, Richet P, Guyot F, Fiquet G (1991) High-temperature thermodynamic properties of Forsterite. J Geophys Res 96:11805-11816
12. 4-forsterite measured from the volume dependence of the Raman spectrum. Eur J Mineral 9:255-262
13. 3 perovskite derived from pressure and volume dependence of the Raman mode frequences. Phys Earth Plan Inter 117:361-384 10.1016/S0031-9201(99)00107-7
14. Grüneisen E (1926) Zustand de festen Körpers. Handbuch der Physik 10:1-59
15. Hazen RM (1976) Effects of temperature and pressure on the crystal structure of forsterite. Am Mineral 61:1280-1293
16. Isaak DG, Anderson OL, Goto T (1989) Elasticity of single-crystal forsterite measured to 1700 K. J Geophys Res 94:5895-5906
17. 4 using Grover, Getting and Kennedy's empirical relation between volume and bulk modulus. Phys Chem Minerals 28:572-585 10.1007/s002690100180
18. Jacobs MHG, de Jong BHWS (2003) The high-temperature and high-pressure behavior of MgO derived from lattice vibration calculations Kieffer's model revisited. Phys Chem Chem Phys 5:2056-2065 10.1039/b301550e
19. 4. Geochim Cosmochim Acta 69:4361-4375
20. Kajiyoshi K (1986) High temperature equation of state for mantle minerals and their anharmonic properties. MS Thesis, Okayama University
21. 4 at high pressures and temperatures: precise determination of stabilities of olivine, modified spinel, and spinel. J Geophys Res 94:15663-15670
22. Kiefer B, Stixrude L, Hafner J, Kresse G (2001) Structure and elasticity of wadsleyite at high pressure. Am Mineral 86:1387-1395
23. Kieffer SW (1979) Thermodynamics and lattice vibrations of minerals: 3 Lattice dynamics and an approximation for minerals with application to simple substances and framework silicates. Rev Geophys Space Phys 17:35-59
24. 4 under high pressure up to 149 kb. Z für Kristallographie 171:291-302
25. 4 at earth's transition zone pressures. Geophys Res Lett 23:2259-2262 10.1029/96GL02084
26. Manghnani MH, Matsui T (1981) Temperature dependence of pressure derivatives of single-crystal elastic constants of pure forsterite. ISPEI Symposium on properties of materials at high pressures and high temperatures. Toronto, Canada
27. Matsui T, Manghnani MH (1985) Thermal expansion of single-crystal forsterite to 1023 K by fizeau interferometry. Phys Chem Minerals 12:201-210 10.1007/BF00311289
28. 4. J Geophys Res 98:22199-22207
29. Oganov AR, Dorogukupets PI (2004), Intrinsic anharmonicity in equations of state and thermodynamics of solids. J Phys Condens Matter 16:1351-1360 10.1088/0953-8984/16/8/018
30. Orr RL (1953) High temperature heat contents of magnesium orthosilicate and ferrous orthosilicate. J Am Chem Soc 75:528-529 10.1021/ja01099a005
31. Piriou P, McMillan P (1983) The high-frequency vibrational spectra of vitreous and crystalline orthosilicates. Am Mineral 68:426-443
32. 4 between 5 and 380 K. Am Mineral 67:470-482
33. Sumino Y, Nishizawa O, Goto T, Ohno I, Ozima M (1977) Temperature variation of elastic constants of single-crystal forsterite between -190 and 400°C. J Phys Earth 23:377-392
34. Suzuki I (1975) Thermal expansion of periclase and olivine, and their anharmonic properties. J Phys Earth 23:145-159
35. 4 up to 1200 K. Phys Chem Minerals 10:38-46 10.1007/BF01204324
36. Suzuki I, Takei H, Anderson OL (1984) Thermal expansion of single-crystal forsterite, Mg2SiO4. In: The proceedings of the eighth international thermal expansion symposium, sponsored by the national bureau of standards. Plenum Pub Co, New York, pp 79-88
37. Vinet P, Ferrante J, Smith JR, Rose JH (1986) A universal equation of state for solids. J Phys C 19:L467-L473 10.1088/0022-3719/19/20/001
38. DC Wallace 1972 Thermodynamics of crystals Wiley New York
39. Wang SY, Sharma SK, Cooney TF (1993) Micro-Raman and infrared spectral study of forsterite under high pressure. Am Mineral 78:469-476
40. H Watanabe 1982 Thermochemical properties of synthetic high-pressure compounds relevant to the earth's mantle In: MH Manghnani S Akimoto (eds) High-pressure research in geophysics Center for Academic Publications Japan 441-464
41. Will G, Hoffbauer W, Hinze E, Lauterjung J (1986) The compressibility of forsterite up to 300 kbar measured with synchrotron radiation. Physica 139-140B:193-197
42. 3 perovskite derived from large scale molecular dynamics. Phys Chem Miner 18:407-415 10.1007/BF00200963
43. Zha CS, Duffy TS, Downs RT, Mao HK, Hemley RJ (1996) Sound velocity and elasticity of single-crystal forsterite to 16 GPa. J Geophys Res 101:17535-17545 10.1029/96JB01266
44. 4 olivines. Phys Chem Minerals 25:308-312 10.1007/s002690050119