Quantification of the deviations from closest sphere packings

European Journal of Mineralogy

Volumn 16, Issue 2, 2004, Pages 255-260

  Sowa, Heidrun ^a   Koch, Elke ^a  

^a PHILIPPS UNIVERSITY MARBURG   (Germany)

Author keywords

Closest sphere packings; Distortion parameter; Standard deviation

Indexed keywords

CHANNEL CODING; CRYSTAL ATOMIC STRUCTURE; PACKING; SILICATE MINERALS; STATISTICS;

DISTORTION PARAMETERS; SPHERE PACKINGS; SPINEL-TYPE STRUCTURES; STANDARD DEVIATION; THOMPSON; TWO PARAMETER;

SPHERES;

CRYSTAL STRUCTURE; PACKING; SPHERE;

EID: 2142661718     PISSN: 09351221     EISSN: None     Source Type: Journal    
DOI: 10.1127/0935-1221/2004/0016-0255     Document Type: Article

References (41)

1. 3. Phys. Chem. Minerals, 27, 719-731.
2. Baur, W. H. (1974): The geometry of polyhedral distortions. Predictive relationships for the phosphate group. Acta Cryst., B30, 1195-1215.
3. 20,) at T = -130°, 250°, 400° and 700°C. Z. Kristallogr., 192, 183-199.
4. Brown, G. E. (1982): Olivines and silicate spinels. in "Orthosilicates, Reviews in Mineralogy 5", P. H. Ribbe, ed. Mineralogical Society of America, Washington, D.C., 275-382.
5. Cameron, M., Sueno, S., Prewitt, C.T., Papike, J.J. (1973): High-temperature crystal chemistry of acmite, diopside, hedenbergite, jadeite, spodumen, and ureyite. Am. Mineral., 58, 594-618.
6. Comodi, P., Montagnoli, M., Zanazzi, P.F., Ballaran, T.B. (2002): Isothermal compression of staurolite: A single crystal study. Am. Mineral., 87, 1164-1171.
7. Dollase, W.A. (1974): A method of determining the distortion of coordination polyhedra. Acta Cryst., A30, 513-517.
8. Finger, L.W., Hazen, R.M., Yagi, T. (1979): Crystal structures and electron densities of nickel and iron silicate spinels at elevated temperature or pressure. Am. Mineral., 64, 1002-1009.
9. Hazen, R.M. (1976): Effects of temperature and pressure on the crystal structure of forsterite. Am. Mineral., 61, 1280-1293.
10. Hazen, R.M. (1977): Effects of temperature and pressure on the crystal structure of ferromagnesian olivine. Am. Mineral., 62, 286-295.
11. 4: Insights on the origin of olivine elastic anisotropy, Phys. Chem. Minerals, 14, 13-20.
12. Hazen, R.M. & Finger, L.W. (1982): Comparative crystal chemistry. John Wiley & Sons, New York, 231 p.
13. Hazen, R.M. & Finger, L.W. (1985): Crystals at high pressure. Sci. Am., 252, 110-117.
14. 4: An olivine with nearly isotropic compression. Am. Mineral., 81, 327-334.
15. Hazen, R.M., Finger, L.W., Hemley. R.J., Mao, H.K. (1989): High-pressure crystal chemistry and amorphization of α-quartz. Solid Stat Comm., 72, 507-511.
16. 4, with x = 0 and 0.25. Am. Mineral., 85, 770-777.
17. Hugh-Jones, D.A., Woodland, A.B., Angel, R.J. (1994): The structure of high-pressure C2/c ferrosilite and crystal chemistry of high-pressure C2/c pyroxenes. Am. Mineral., 79, 1032-1041.
18. 2 under high pressure. Physica, B 139/140, 333-336.
19. 4 under high pressure up to 149 kb. Z. Kristallogr., 171, 291-302.
20. Lager, G.A. & Meagher, E.P. (1978): High-temperature structural study of six olivines. Am. Mineral., 63, 365-377.
21. Levien, L. & Prewitt, C.T. (1981): High-pressure structural study of diopside. Am. Mineral., 66, 315-323.
22. 4. Acta Cryst., B33, 713-716.
23. 6, and systematics of anisotropic compression in pyroxenes. Am. Mineral., 88, 1025-1032.
24. Pannhorst, W. (1984): High temperature crystal structure refinements of low-clinoenstatite up to 700°C. N. Jb. Miner. Abh., 150, 219-228.
25. Robinson, K., Gibbs, G.V., Ribbe, P.H. (1971): Quadratic elongation: A quanititative measure of distortion in coordination polyhedra. Science, 172, 567-570.
26. 4. Am. Mineral., 72, 748-755.
27. Smyth, J.R. (1975): High temperature crystal chemistry of fayalite. Am. Mineral., 60, 1092-1097.
28. 3 under high pressure. Z. Kristallogr., 184, 257-268.
29. 6. Acta Cryst., B53, 25-31.
30. 3-type compounds. Acta Cryst., B54, 578-584.
31. 6 and the crystal structure of the high-pressure phase. Z. Kristallogr., 214, 751-757.
32. Sowa, H., Koch, E., Fischer, W. (2003): Hexagonal and trigonal sphere packings. I. Invariant and univariant lattice complexes. Acta Cryst., A59, 317-326.
33. Thompson, R.M. & Downs, R.T. (2001): Quantifying distortion from ideal closest-packing in a crystal structure with analysis and application. Acta Cryst., B57, 119-127.
34. Thompson, R.M. & Downs, R.T. (2003): Model pyroxenes I: Ideal pyroxene topologies. Am. Mineral., 88, 653-666.
35. 5 by time-of-flight neutron powder diffraction. Acta Cryst., B45, 542-549.
36. 5 polymorphs. Am. Mineral., 64, 573-586.
37. Wittlinger, J., Werner, S., Schulz, H. (1998): Pressure-induced order-disorder phase transition of spinel single crystals. Acta Cryst., B54, 714-721.
38. 4. Am. Mineral., 59, 486-490.
39. 5, at high pressure. Am. Mineral., 82, 467-474.
40. 1 cn phase transition in protopyroxene. Am. Mineral., 84, 245-256.
41. Zhang, L., Ahsbahs, H., Hafner, S., Kutoglu, A., (1997): Single-crystal compression and crystal structure of clinopyroxene up to 10 GPa. Am. Mineral., 82, 245-258.