Bulk modulus—volume relationship for cation‐anion polyhedra

American Geophysical Union (AGU) - Tập 84 Số B12 - Trang 6723-6728 - 1979
Robert M. Hazen, L. W. Finger

Tóm tắt

A bulk modulus—volume relationship is demonstrated for cation coordination polyhedra in a variety of structure types including oxides, silicates, halides, sulfides, phosphides, and carbides: Kp 〈d〉3/S2zcza = 7.5 (Mbar Å3), where KP is the polyhedral bulk modulus (in megabars), 〈d〉 is the mean cation‐anion separation (in angstroms), zc and za are the cation and anion formal charge, and S2 is an empirical ionicity term, defined as 0.50 for oxides and silicates and calculated to be 0.75 for halides; 0.40 for sulfides, selenides, and tellurides; 0.25 for phosphides, arsenides, and antimonides; and 0.20 for carbides. The bulk modulus of a substance depends on the bulk moduli of component polyhedra and the manner in which these polyhedra are linked. In corner‐linked structures, such as quartz and framework silicates, mineral bulk moduli are significantly less than those of constituent corner‐linked polyhedra, because of accommodations resulting from changes of the metal‐oxygen‐metal angles. In layer structures such as micas, with extensive edge sharing within the layers but weak bonds between the layers, compression is highly anisotropic. Structures such as periclase, spinel, and garnet, with extensive edge sharing between polyhedra in three dimensions, have large bulk moduli similar to those of constituent polyhedra. Bulk moduli of mantle mineral phases approximate the moduli of component polyhedra because most mantle mineral structure types have edge sharing in three dimensions. Compression for a given polyhedron does not appear to depend upon the linkage topology of the structure.

Từ khóa


Tài liệu tham khảo

10.1029/JB075i017p03494

Anderson O. L., 1972, Nature of the Solid Earth, 575

10.1029/JZ070i016p03951

Bassett W. A., 1974, X ray diffraction studies up to 300 kbar, Advan. High Pressure Res., 4, 165

10.1130/MEM97-p97

10.2307/20025987

10.1063/1.1726610

Finger L. W., 1979, Bulk moduli and high‐pressure crystal structures of Fe2O3 and V2O3: A comparison with Al2O3 and Cr2O3 (abstract), Eos Trans. AGU, 60, 386

Finger L. W., 1979, Crystal structure and electron densities of nickel and iron silicate spinels at elevated temperature or pressure, Amer. Mineral., 62

Hazen R. M., 1976, Effects of temperature and pressure on the crystal structure of forsterite, Amer. Mineral., 61, 1280

Hazen R. M., 1977, Compressibility and crystal structure of Angra dos Reis fassaite to 52 kbar, Carnegie Inst. Wash. Yearb., 76, 512

Hazen R. M., 1978, Crystal structures and compressibilities of layer minerals at high pressure, II, Phlogopite and chlorite, Amer. Mineral., 63, 293

Hazen R. M., 1978, Crystal structures and compressibilities of pyrope and grossular to 60 kbar, Amer. Mineral., 63, 297

Hazen R. M., 1978, The crystal structures and compressibilities of layer minerals at high pressure, Amer. Mineral., 63, 289

10.1063/1.325880

Hazen R. M., 1979, Studies in high‐pressure crystallography, Carnegie Inst. Wash. Yearb., 78

Hazen R. M., 1979, Crystal structure and compressibility of zircon at high pressure, Amer. Mineral., 64, 196

Hazen R. M., 1977, Effects of temperature and pressure on interatomic distances in oxygen‐based minerals, Amer. Mineral., 62, 309

Hazen R. M., 1977, Linear compressibilities of low albite: High‐pressure structural implications, Amer. Mineral., 62, 554

Hazen R. M., 1978, Crystal structure and compressibility of MnF2 to 15 kbar, Carnegie Inst. Wash. Yearb., 77, 841

10.1063/1.324517

10.1029/JB077i026p04934

10.1029/JB078i035p08470

10.1063/1.1726442

10.1063/1.326625

10.1111/j.1151-2916.1966.tb13230.x

Simmons G., 1971, Single Crystal Elastic Constants

10.1016/0022-3697(78)90037-9

Thông tin
Thông tin xuất bản

American Geophysical Union (AGU)

Tập 84 Số B12

6723-6728

Thông tin tác giả