Glass Physics and Chemistry

, Volume 36, Issue 1, pp 1–9 | Cite as

Cellular automata and local order in the structural chemistry of the lovozerite group minerals

  • V. Ya. Shevchenko
  • S. V. Krivovichev
  • A. L. Mackay
Article

Abstract

The structural chemistry of the lovozerite group of minerals is considered using concepts of coordination polyhedra, finite automata and local order. A formal language for these lovozerite-type structures is constructed and the concept of a genetic code for this structure family is suggested. Information and structure are seen to be dialectically interlinked.

Key words

structural chemistry lovozerite cellular automata 

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References

  1. 1.
    Fedonkin, M.A., The Role of Hydrogen and Methane in the Origin and Evolution of Metabolic Systems in the Problem of the Origin and Evolution of the Biosphere, in Problemy zarozhdeniya i evolyutsii biosfery (Problems of the Origin and Evolution of the Biosphere), Galimov, E.M., Ed., Moscow: Librokom, 2008, p. 419 [in Russian].Google Scholar
  2. 2.
    Von Neumann, J., On a Logical and General Theory of Automata, in Cerebral Mechanisms in Behaviour: The Hixon Symposium, Jeffries, L., Ed., New York: Wiley, 1951, pp. 1–32.Google Scholar
  3. 3.
    Wolfram, S., A New Kind of Science, Urbana, IL, United States: Wolfram Media, 2002.MATHGoogle Scholar
  4. 4.
    Mackay, A., Crystal Symmetry, Phys. Bull., 1976, vol. 27, p. 495.Google Scholar
  5. 5.
    Krivovichev, S., Crystal Structures and Cellular Automata, Acta Crystallogr., Sect. A: Found. Crystallogr., 2004, vol. 60, pp. 257–262.CrossRefMathSciNetGoogle Scholar
  6. 6.
    Shevchenko, V. and Krivovichev, S., Where Are Genes in Paulingite? Mathematical Principles of Formation of Inorganic Matter on the Atomic Level, Struct. Chem., 2008, vol. 19, pp. 571–577.CrossRefGoogle Scholar
  7. 7.
    Malinovski, Yu., Burzlaff, H., and Rothammed, W., Structures of the Lovozerite Type-A Quantitative Investigation, Acta Crystallogr., Sect. B: Struct. Sci., 1993, vol. 49, pp. 158–164.CrossRefGoogle Scholar
  8. 8.
    Kuo, K., Mackay, Anti-Mackay, Double-Mackay, Pseudo-Mackay, and Related Icosahedral Shell Clusters, Struct. Chem., 2002, vol. 13, pp. 221–230.CrossRefGoogle Scholar
  9. 9.
    Shevchenko, V., Samoilovich, M., Talis, A., and Madison, A., Nanostructures with Coherent Boundaries and the Local Approach, Fiz. Khim. Stekla, 2004, vol. 30, no. 6, 731–748 [Glass Phys. Chem. (Engl. transl.), 2004, vol. 30, no. 6, pp. 537–550].Google Scholar
  10. 10.
    Ilyushin, G.D. and Dem’yanets, L.N., Ionic Conductors in the Class of Na,Zr Silicates: A New Family of Three-Dimensional Conductors—Crystals of the Lovozerite Type Na8 − xHxZrSi6O18, Kristallografiya, 1986, vol. 31, no. 1, pp. 76–81 [Sov. Phys. Crystallogr. (Engl. transl.), 1986, vol. 31, no. 1, pp. 41–44].Google Scholar
  11. 11.
    Chernitsova, N.M., Pudovkina, Z.V., Voronkov, A.A., Kapustin, Yu.L., and Pyatenko, Yu.A., New Crystal Chemical Family of Lovozerite, Zap. Vses. Mineral. O-va, 1975, vol. 104, pp. 18–27.Google Scholar
  12. 12.
    Otroshchenko, L.P., Simonov, V.I., and Belov, N.V., Crystal Structure of the Sodium-Manganese Synthetic Metasilicate Na5(Mn,Na)3Mn[Si6O18], Dokl. Akad. Nauk SSSR, 1973, vol. 208, pp. 845–848.Google Scholar
  13. 13.
    Engel, P., Geometric Crystallography: An Axiomatic Introduction to Crystallography, Dordrecht: Kluwer, 1986.MATHGoogle Scholar
  14. 14.
    Grunbaum, B. and Shepard, G., Tiling with Congruent Tiles, Bull. Am. Math. Soc., 1980, vol. 3, pp. 951–973.CrossRefGoogle Scholar
  15. 15.
    Hopcroft, J.E., Motwani, R., and Ullma, J.D., Introduction to Automata Theory, Languages, and Computation, Boston: Addisson-Wesley, 2001.MATHGoogle Scholar
  16. 16.
    Morey, J., Sedig, K., Mercer, R.E., and Wilson, W., Crystal Lattice Automata, in Proceedings of the Fourth International Conference on Implementations and Applications of Automata, Pretoria, South Africa, July, 2001 (Lecture Notes Computer Science, Watson, B.W. and Wood, D., Eds., Berlin: Springer, 2002, vol. 2494, pp. 214–220.Google Scholar
  17. 17.
    Shevchenko, V. and Mackay, A.L., Geometrical Principles of the Self-Assembly of Nanoparticles, Fiz. Khim. Stekla, 2008, vol. 34, no. 1, pp. 3–10 [Glass. Phys. Chem. (Engl. transl.) 2008, vol. 34, no. 1, pp. 1–8].Google Scholar
  18. 18.
    Mackay, A.L. and Klinowski, J., Towards a Grammar of Inorganic Structures, Comput. Math. Appl. B, 1986, vol. 12, pp. 803–824.CrossRefMathSciNetGoogle Scholar
  19. 19.
    Mackay, A.L., Generalised Crystallography, THEOCHEM, 1995, vol. 336, pp. 293–303.CrossRefGoogle Scholar
  20. 20.
    Gamow, G., Rich, A., and Ycas, M., The Problem of Information Transfer from Nucleic Acids to Protein, Adv. Biol. Med. Phys., 1959, vol. 4, pp. 41–51.Google Scholar

Copyright information

© Pleiades Publishing, Ltd. 2010

Authors and Affiliations

  • V. Ya. Shevchenko
    • 1
  • S. V. Krivovichev
    • 2
  • A. L. Mackay
    • 3
  1. 1.Grebenshchikov Institute of Silicate ChemistryRussian Academy of SciencesSt. PetersburgRussia
  2. 2.Department of Crystallography, Faculty of GeologySt. Petersburg State UniversitySt. PetersburgRussia
  3. 3.School of Crystallography, Birkbeck CollegeUniversity of LondonLondonUK

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