Hostname: page-component-cd9895bd7-dk4vv Total loading time: 0 Render date: 2024-12-24T15:59:50.579Z Has data issue: false hasContentIssue false

Structural complexity of minerals: information storage and processing in the mineral world

Published online by Cambridge University Press:  05 July 2018

S. V. Krivovichev*
Affiliation:
Department of Crystallography, St Petersburg State University, University Emb. 7/9, 199034 St Petersburg, Russia Nanomaterials Research Centre, Kola Science Centre of Russian Academy of Sciences, Apatity, Russia
*

Abstract

Structural complexity of minerals is characterized using information contents of their crystal structures calculated according to the modified Shannon formula. The crystal structure is considered as a message consisting of atoms classified into equivalence classes according to their distribution over crystallographic orbits (Wyckoff sites). The proposed complexity measures combine both size- and symmetry-sensitive aspects of crystal structures. Information-based complexity parameters have been calculated for 3949 structure reports on minerals extracted from the Inorganic Crystal Structure Database. According to the total structural information content, IG, total, mineral structures can be classified into very simple (0–20 bits), simple (20–100 bits), intermediate (100–500 bits), complex (500–1000 bits), and very complex (> 1000 bits). The average information content for mineral structures is calculated as 228(6) bits per structure and 3.23(2) bits per atom. Twenty most complex mineral structures are (IG, total in bits): paulingite (6766.998), fantappieite (5948.330), sacrofanite (5317.353), mendeleevite-(Ce) (3398.878), bouazzerite (3035.201), megacyclite (2950.928), vandendriesscheite (2835.307), giuseppetite (2723.097), stilpnomelane (2483.819), stavelotite-(La) (2411.498), rogermitchellite (2320.653), parsettensite (2309.820), apjohnite (2305.361), antigorite (m = 17 polysome) (2250.397), tounkite (2187.799), tschoertnerite (2132.228), farneseite (2094.012), kircherite (2052.539), bannisterite (2031.017), and mutinaite (2025.067). The following complexity-generating mechanisms have been recognized: modularity, misfit relationships between structure elements, and presence of nanoscale units (clusters or tubules). Structural complexity should be distiguished from topological complexity. Structural complexity increases with decreasing temperature and increasing pressure, though at ultra-high pressures, the situation may be different. Quantitative complexity measures can be used to investigate evolution of information in the course of global and local geological processes involving formation and transformation of crystalline phases. The information-based complexity measures can also be used to estimate the 'ease of crystallization' from the viewpoint of simplexity principle proposed by J.R. Goldsmith (1953) for understanding of formation of simple and complex mineral phases under both natural and laboratory conditions. According to the proposed quantitative approach, the crystal structure can be viewed as a reservoir of information encoded in its complexity. Complex structures store more information than simple ones. As erasure of information is always associated with dissipation of energy, information stored in crystal structures of minerals must have an important influence upon natural processes. As every process can be viewed as a communication channel, the mineralogical history of our planet on any scale is a story of accumulation, storage, transmission and processing of structural information.

Type
Research Article
Copyright
Copyright © The Mineralogical Society of Great Britain and Ireland 2013

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

Brantley, S.L., White, T.S., White, A.F., Sparks, D., Richter, D., Pregitzer, K., Derry, L., Chorover, J., Chadwick, O., April, R., Anderson, S. and Amundson, R. (2006) Frontiers in Exploration of the Critical Zone. An NSF-sponsored Workshop. National Science Foundation.Google Scholar
Feklichev, V.G. (1979) Density of atomic arrangement in the crystal structures of minerals. Novye Dannye o Mineralakh SSSR (New Data on the U.S.S.R. Minerals), 28, 145152. [in Russian].Google Scholar
Hazen, R.M., Papineau, D., Bleeker, W., Downs, R.T., Ferry, J.M., McCoy, T.J., Sverjensky, D.A. and Yang, H. (2008) Mineral evolution. American Mineralogist, 93, 16931720.CrossRefGoogle Scholar
Hazen, R.M., Ewing, R.C. and Sverjensky, D.A. (2009) Evolution of uranium and thorium minerals. American Mineralogist, 94, 12931311.CrossRefGoogle Scholar
Hazen, R.M., Bekker, A., Bish, D.L., Bleeker, W., Downs, R.T., Farquhar, J., Ferry, J.M., Grew, E.S., Knoll, A.H., Papineau, D.F., Ralph, J.P., Sverjensky, D.A. and Valley, J.W. (2011) Needs and opportunities in mineral evolution research. American Mineralogist, 96, 953963.CrossRefGoogle Scholar
Hazen, R.M., Golden, J., Downs, R.T., Hystad, G., Grew, E.S., Azzolini, D. and Sverjensky, D.A. (2012) Mercury (Hg) mineral evolution: a mineralogical record of supercontinental assembly, changing ocean geochemistry, and the emerging terrestrial biosphere. American Mineralogist, 97, 10131042.CrossRefGoogle Scholar
Khomyakov, A.P. and Yushkin, N.P. (1981) The principle of inheritance in crystallogenesis. Doklady Akademii Nauk SSSR, 256, 12291233. [in Russian].Google Scholar
Khomyakov, A.P. Kulikova, I.E., Sokolova, E., Hawthorne, F.C. and Kartashov, P.M. (2003) Paravinogradovite, (Na,□)2[(Ti4+,Fe3+)4{Si2O6}2 {Si3AlO10}(OH)4]·H2O, a new mineral species from the Khibina alkaline massif, Kola peninsula, Russia: description and crystal structure. The Canadian Mineralogist, 41, 9891002.CrossRefGoogle Scholar
Khomyakov, A.P., Cámara, F., Sokolova, E., Abdu, Y. and Hawthorne, F.C. (2010) Paraershovite, Na3K3Fe3+ 2 (Si4O10OH)2(OH)2(H2O)4, a new mineral species from the Khibina alkaline massif, Kola peninsula, Russia: description and crystal structure. The Canadian Mineralogist, 48, 279290.CrossRefGoogle Scholar
Khomyakov, A.P., Cámara, F., Sokolova, E., Abdu, Y. and Hawthorne, F.C. (2011) Sveinbergeite, Ca(Fe3+)Ti2(Si4O12)2O2(OH)5(H2O)4, a new astrophyllite- group mineral from the Larvik Plutonic Complex, Oslo Region, Norway: description and crystal structure. Mineralogical Magazine, 75, 26872702.CrossRefGoogle Scholar
Popkova, T.N. (1982) The VIth Meeting of the All- Union Mineralogical Society. Zapiski Vsesoyuznogo Mineralogicheskogo Obshchestva, 116, 392395. [in Russian].Google Scholar
Smirnova, N.L. and Belov, N.V. (1979) Evolution in the system of structure types. Pp. 94102. in: History and Methodology of Natural Sciences. Moscow.Google Scholar
Sorensen, H. and Larsen, N.M. (2001) The hyperagpaitic stage in the evolution of the Ilímaussaq alkaline complex, South Greenland. Geology of Greenland Survey Bulletin, 190, 8394.CrossRefGoogle Scholar
Yakovenchuk, V.N., Ivanyuk, G.Yu., Pakhomovsky, Y.A., Selivanova, E.A., Men’shikov, Y.P., Korchak, J.A., Krivovichev, S.V., Spiridonova, D.V., and Zalkind,O, A. (2010) Punkaruaivite , LiTi2[Si4O11(OH)](OH)2·H2O, a new mineral species from hydrothermal assemblages, Khibiny and Lovozero Alkaline Massifs, Kola Peninsula, Russia. The Canadian Mineralogist, 48, 4150.CrossRefGoogle Scholar
Yushkin, N.P. (1982) Evolutionary ideas in modern mineralogy. Zapiski Vsesoyuznogo Mineralogicheskogo Obshchestva, 116, 432442. [in Russian].Google Scholar
yushkin, N.P. (1990) evolutional regularities of the mineral world. pp. 127129. in: the xv general meeting of the international mineralogical association. beijing. Vol. 1.Google Scholar
Yushkin, N.P. (2008) Evolution of the mineral world, origin of the biosphere and biomineral co-evolution. Pp. 455459. in: Minerals, Mineral Formation, Structure, Diversity and Evolution of the Mineral World, the Role of Minerals in the Origin of Life, BioMineral Interactions (N.P. Yushkin, editor). Syktyvkar [in Russian].Google Scholar
Yushkin, N.P., Khomyakov, A.P. and Evzikova, N.Z. (1984) The principle of inheritance in crystallogenesis. Syktyvkar, Scientific Reports of the Komi section of the SSSR Academy of Sciences [in Russian].Google Scholar
Zhabin, A.G. (1979) Is there evolution of mineral species on Earth? Doklady Akademii Nauk SSSR, 247, 199–202. English translation: Doklady Earth Sciences Sections, 247, 142144.Google Scholar
Zhabin, A.G. (1983) Problems of the mineral phylogeny. Pp. 712. in: New Ideas in Genetic Mineralogy. Leningrad, Nauka [in Russian].Google Scholar
Supplementary material: PDF

Krivovichev supplementary material

Supplementary file

Download Krivovichev supplementary material(PDF)
PDF 2.9 MB