Rare Fedorov groups in structural mineralogy
The crystal order in structure of a solid phase is provided by the symmetry of interatomic interactions. In its turn, the latter causes the symmetry of atomic spatial positions, i.e. the spatial symmetry of the structure. From this viewpoint, the phenomenon of mineral formation can formally be considered as a result of ordering the atoms by the operations of spatial symmetry. This ordering is selective. Most mineral structures are described by minor formally possible spatial symmetry groups. The peculiarities of «structural preferences» of mineral phases during crystallization and recrystallization are studied. The quantitative estimations for frequencies of Fedorov groups in crystal structures are given.
Figures 2. Tables 2. References 23.
Key words: mineral structure, spatial symmetry, Fedorov group.
Ya.О. Shablovsky, Gomel State Technical University, pr. Oktyabrya 48, Gomel, 246746 Belorussia; ya.shablowsky@yandex.ru
- Banaru А.М. (2018) [Informational entropy of Fedorov groups]. Ural’sky geologicheskiy zhurnal [Uralian Geological Journal], (3), 84–88. (in Russian)
- Belov N.V. (1959) [Hexagonal Fedorov groups]. Kristallographiya [Crystallography], 4(2), 268–276. (in Russian)
- Chesnokov B.V. (2005) [New symmetry laws in a kingdom of real crystals]. Ural’sky geologichesky zhurnal [Uralian Geological Journal], 1(43), 1–40. (in Russian)
- Voytekhovsky Yu.L. (1992) [Toward the analysis of aggregativity of rocks]. Zapiski Rossiiskogo mineralogicheskogo obshchestva [Proceedings of the Russian Mineralogical Society], 121(2), 34–40. (in Russian)
- Voytekhovsky Yu.L. (1995) [Complying the concepts of structure and texture]. Zapiski Rossiiskogo mineralogicheskogo obshchestva [Proceedings of the Russian Mineralogical Society], 124(2), 119–124. (in Russian)
- Voytekhovsky Yu.L. (2010) [Cubic-triclinic inversion in the system of mineral species and total asymmetry of mineral individuals]. In: Sovremennaya mineralogia: ot teorii k praktike. Materialy 11 s′ezda RMO [Modern mineralogy: from theory to practice], Proceedings of 11 th RMO Meeting. 24–26. Sankt-Peterburg. RMO SPGGI (TU) (in Russian)
- Voytekhovsky Yu.L., Stepanshchikov D.G (2004) [Combinatorial crystallomorphology. Real crystallographical simple forms]. Аpatity, K & M, 275 p. (in Russian)
- Ivanov О.К. (2016) [Factors of mineral crystallization] Ural’sky geologichesky zhurnal [Uralian Geological Journal], (4), 39–45. (in Russian)
- Kanzaki M. (1991) Ortho/clinoenstatite transition. Physics and Chemistry of Minerals, 17(8), 726–730.
- König A., Mermin N.D. (1999) Screw rotations and glide mirrors. Proceedings of the National Academy of Sciences of the USA, 96(7), 3502–3506.
- Litvin Yu.A., Spivak A.V. (2019) Genesis of diamonds and paragenetic inclusions under lower mantle conditions: the liquidus structure of the parental system at 26 GPa. Geochemistry International, 64(2), 128–144.
- Litvin Yu.A., Spivak A.V., Dubrovinsky L.S. (2016) Magmatic evolution of the material of the Earth’s lower mantle: Stishovite paradox and origin of superdeep diamonds (Experiments at 24–26 GPa). Geochemistry International 54(11), 936–947.
- Mehl M.J., Hicks D., Toher C., Levy O., Hanson R.M., Hart G., Curtarolo S. (2017) The AFLOW Library of Crystallographic Prototypes: Part 1. Computational Materials Science, 136, Supplement.
- Маkаgonov Е.P. (2002) [Аffine homology of crystals]. Мiass, IMin UrO RAN, 139 p. (in Russian) Pekov I.V. (1998) Minerals first discovered on the territory of the former Soviet Union. Moscow, Ocean Pictures Ltd, 369 p.
- Povarennykh А.S. (1966) [Laws of distribution of mineral species in syngonies, symmetry classes and space groups] Mineralogicheskiy sbornik L′vovskogo gosudarstvennogo universiteta [Mineralogical collection of Lvov State University], 20(4), 341–351. (in Russian)
- Popov V.А. (2018) [About current paradigm of mineralogy as a reflection of crystal anatomy laws]. Mineralogiya
[Mineralogy], 4(2), 62–69. (in Russian) - Shafranovsky I.I., Feklichev V.G. (1982) [Symmetry statistics of minerals]. Mineralogicheskiy zhurnal [Mineralogical Journal], 4(6), 31–36. (in Russian)
- Sunada T. (2013) Topological crystallography. Tokyo, Springer, 226 р.
- Urusov V.S. (1991) [Crystal chemical conditions for occupying regular point systems]. Vestnik Moskovskogo universiteta. Seriya 4. Geologiya [Moscow University Geology Bulletin], (4), 3–19. (in Russian)
- Urusov V.S., Таuson V.L., Аkimov V.V. (1997) [Solid state geochemistry]. Мoscow, GEOS, 500 p. (in Russian).
- Urusov V.S. (1998) [Natural selection of mineral species]. Sorosovsky obrazovatelny zhurnal [Soros Educational Journal], (4), 50–56. (in Russian)
- Urusov V.S., Nadezhinа Т.N. (2006) [«Empty» and rare spatial groups in structural mineralogy] Vestnik
- Moskovskogo universiteta. Seriya 4. Geologiya [Moscow University Geology Bulletin], (5), 52–60. (in Russian)
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