УКАЗАТЕЛЬ √ 2000

Указатель документов описания первоисточников (УКАЗАТЕЛЬ - 2000)

Кристаллография

Сборники ВЦ РАН

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UDC 548.1

Mathematical Modelling of Composite Objects Part II. Responsible editor V.R.Khachaturov Moscow: Comp. Centre of RAS, 2000. 123 pp.

ISBN 5-201-14739-9 (яз. англ.)

УДК 548.1

Математическое моделирование композиционных объектов. Часть II. Сб. статей. Отв. ред.: доктор физ.-матем. наук В.Р. Хачатуров М.: ВЦ РАН, 2000. 123 с. ISBN 5-201-14739-9

Аннотация

This collection of works develops methods for solving the general reciprocal problem of condensed matter put forth in the previous collection of works - the determination of the set of chemical elements and corresponding types of crystalline lattices in searching for materials with preassigned properties. Appropriate methods and algorithms are developed, concrete methods for solving this problem for some specific classes of substances are presented.

Referees: I.B.Kurakin and A.P.Prudnikov

Articles presented in this collection of works have been supported by Russian Fund for Fundamental Studies, grant No.95-01-01003.

Contents

С. 3-5

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INTRODUCTION

С. 6-22

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ENUMERATION OF ALL POSSIBLE CRYSTALLINE STRUCTURES FOR A GIVEN CHEMICAL FORMULA AND SYMMETRY ILLUSTRATED BY PEROVSKIT CASE

V.R. Khachaturov, K.K.Abgaryan,A.V.Bakaev, R.V.Galiulin, V.I.Kabanovich

Ключевые слова: кристаллические структуры, группа симметрии, заданная химическая формула, кристаллографические формулы, перовскит.

Key words: crystalline structures, symmetry group, given chemical formulae, crystallographic formulae, perovskit.

References

1. Galiulin R.V., Khachaturov V.R. Algorithm for determination of crystalline structures with a given chemical formula // Coll. Mathematical modelling of composite objects, Moscow: CC RAS, 1994.

2. Winestein В.К. et al, Modern Crystallography. Volume 2, Crystal Structure, Moscow:═ Nauka, 1979.

References 21-22

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С. 23-32

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CALCULATION OF OPTICAL PROPERTIES OF SOLID MATTER IN THE TIGHT-BINDING APPROXIMATION

A.V. Bakaev, V.I. Kabanovich

Ключевые слова: твердое вещество, оптические свойства, электронная проводимость, электромагнитное излучение, поглощение, абсорбция, оптический спектр, структура каменной соли, галит, сильная связь.

Key words: solid matter, optical properties, electronic conductivity, electromagnetic radiation, absorption, optical spectrum, rock salt structure, tight binding.

References

1. Animalu A. Quantum theory of crystalline solid matter, Moscow: Mir, 1981.

2. Ballentine L.E. and Hammerberg J.E. The recursion method with a non-orthogonal basis // Can. J. Phys., 1984, vol. 62, no. 2, p. 692.

References p.32

С. 33-41

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A MODULE FOR CALCULATION OF ALL CRYSTALLOGRAPHICAL STRUCTURES HAVING THE GIVEN CHEMICAL FORMULA

A.V. Vlasov

Ключевые слова: кристаллографические структуры, химическая формула, структурная химическая формула, федоровская группа.

Key words: crystallograpical structures, chemical formula, structural chemical formula, Fyodorov (Fedorov) group.

References

1. Galiulin R.V., Khachaturov V.R. Algorithm for determination of crystalline structures with a given chemical formula // Mathematical modelling of composite objects, Moscow: CC RAS, 1994, p.32.

2. Galiulin R.V. Fyodorov groups - the universal law of the nature // Nature, 1991, vol. 214, no. 3, pp.515-524.

3. Galiulin R.V. Lections on geometric foundations of crystallography, Chelyabinsk: Chelyabinsk State University, 1989.

References p.41

С. 42-102

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DELONE SYSTEMS IN RIEMANN SPACE AS DISCRETE MATHEMATICAL MODELS OF SOLID MATTER

R.V. Galiulin

Ключевые слова: твердое вещество, системы Делоне, триангуляция Делоне, регулярные системы, преобразование симметрии, группы симметрии, решетки, дискретная математическая модель.

Key words: solid matter, Delone systems, Delone triangulation, regular systems, symmetry transformation, symmetry group, lattices, discrete mathematical model.

References

1. Delone B.N., Geometry of positive quadratic forms // UFN, 1937, vol.3, no. 2, p. 300.

2. Galiulin R.V., Delone systems // Crystallography, 1980, vol. 25, no. 4, pp. 901-907.

3. Preparata F., Shaymos M., Computational geometry, Moscow: Mir, 1989.

4. Burns J. The principles of crystallography // Scientific American, 1986, vol.255, no I, p. 100.

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5. Konovalov O.V., Galiulin R.V., To more exact definition of the concept of "Symmetry element" // Crystallography, 1989, vol.34, no. 3, pp.731-732.

6. Galiulin R.V., Sigarev S.E., On stability of minerals with holohedric Fedorov groups // Reports of AS USSR, 1987, vol. 293, no. I, PP.99-100.

7. Galiulin R.V., Crystallographic geometry, Moscow: Nauka, 1984.

8. Delone B.N., Dolbilin N.P., Shtogrin M.I., Galiulin R.V., Delone Systems // Reports of AS USSR, 1976, vol.227, no. I, pp.19-21.

9. Engel R., Geometrical Crystallography, Dordrecht: Kluwer, 1985.

10. Galiulin R.V., How crystals are structured // Kvant, 1983, vol. II, pp.10-17.

11. Galiulin R.V., Regular systems // Nature, 1991, vol. 12, pp.20-36.

12. Galiulin R.V., Ideal crystals in spaces of constant curvature // Crystallography, 1994, vol.39, no. 4, pp. 581-585.

13. Galiulin R.V., Lectures on geometric backgrounds of crystallography, Chelyabinsk: Chelyabinsk University, 1989.

14. Galiulin R.V., Holohedric varieties of simple forms of crystals // Crystallography, 1979, vol-24, no. 4, pp. 661-665.

15. International Tables for Crystallography. Vol.A, Dordrecht: Kluwer, 1989.

16. Bokyi G.B., Number of physically distinct simple forms of crystals // Proc. of crystallography laboratory of AS of USSR, 1940, no. 2, pp.13-37.

17. Delone B.N., 24 sorts of crystalline lattices // Science and humanity, Moscow: Mir, 1980.

18. International Tables for═ X-Ray═ Crystallography, Birmingem, 1952.

19. Mathematical modelling of compositional objects // Moscow: CC RAS, 1994.

20. Vernadskyi V.I., Paragenesis of chemical elements in earth's crust // Journal of 12th congress of russian naturalists, 1909-1910, pp. 73-91.

21. Khachaturov V.R., Mirzoyan N.A., Solution to the problem of computational programming by ray-method // Moscow, CC AS USSR, 1987.

22. Danzer L., International Fedorov conference, devoted to 100 anniversary of the derivation of Fedorov groups, Leningrad, 1991.

23. Homyakov A.P., Systems of natural and synthetic compaunds as intersecting sets. // Notes of AII-Rus.Min.Soc., 1994, vol. 123, no. 4, pp. 40-43.

24. Sardarov S.S., Cyclicity of variations of the crystalline structure of minerals in Galactic years // Abstracts of the 12-th European Crystallographic Meeting, Moscow, 1989.

25. Danzer L., A family of 3D-Spacefillers not permitting any periodic or quasiperiodic tiling // Aperiodic' 94, pp. 11-17.

26. Makarov V.S., On one nonregular partition of n-dimensional Lobachevskyi space with congruent polyhedrons // Proceedings of Steklov mathematical institute, 1991, vol.l96, no. 2, PP.93-97.

27. Shtogrin M.I., Regular partitions of Dirichlet-Voronoy for the second triclinic group. // Proceedings of Steklov mathematical institute, 1973, vol.l23, no. 4, p. 567.

28. Makarov P.V., On Kelvin partitions of three-dimensional Lobachevskyi space with regular polyhedrons // UMN, 1990, vol.45, no. I, PP.179-180.

29. Mc-Kay A.L., On pentagonal snowflakes // Crystallography, 1981, vol.26, no. 5, pp.910-919.

30. Antonuk P.N., Galiulm R.V., Makarov V.S., Quasicrystal as ideal crystal of Lobachevskyi space. // Nature, 1993, vol.7, pp.28-31.

31. Kuzmenkov L.S., Growth of structures conserving similitude (Theory of A.A.VIasov) // Processes of real growth of crystals, Moscow: Nauka, 1977, pp. 221-227.

32. Eletskyi A.V.,.Smirnov В.M., Fullerens and carbon structures // UFN, 1995, vol.l656 no. 9, pp.977-1009.

33. Ivanenko D.D., Galiulm R.V., Quasicrystal model of the universe // Proceedings of 17th seminar on high energy physics and field theory, Protvino, 1995, pp. 80-86.

34. A.A.Logunov, Relativistic gravitation theory // Nature, 1987, vol. 210, no. I, pp. 36-47.

35. Efremov Yu.N., Centres of star formations in galactics, Moscow: Nauka, 1989.

36. Fedorov E.S.,Perfictionism // Proc. of the St.Petersburg biological laboratory, 1906, vol.8, no. I, pp.25-65; issue 2, PP.9-67.

References 98-102

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С. 103-122

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DETERMINATION OF CHEMICAL COMPOSITION AND CONDITIONS OF THERMIC PROCESSING TO OBTAIN STEEL WITH PREASSIGNED PROPERTIES

S.N.Bobrov, V.R.Khachaturov

Ключевые слова: технология металлов, сталь, технология упрочнения (укрепления), сталь с предписанными свойствами.

Key words: technology of metals, steel, strengthening technology, steel with preassigned properties.

References

1. Arzamasov B.N., Material Science. Textbook for high technical educational institutions, Moscow: Mashinostroenie, 1986.

2. Sorokin V.G., Volosnikova A.V., Viatkin S.A., et al, Handbook of steels and alloys, ed. by V.G.Sorokin, Moscow: Mashinostroenie, 1989.

3. Arzsmasov B.N., Brodstrem B.A., Bushe N.A. et al., Construction materials. Reference book, ed. by B.N.Arzsmasov, Moscow: Mashinostroenie, 1990.

4. Tylkin M.A., Reference book of thermist, Moscow: Metallurgy, 1981.

5. Khachaturov V.R., Methods of mathematical modeling of compositional objects // Mathematical modelling of compositional objects, Moscow: CC RAS, 1994.

6. Novikov I.I. et al., Material Science. Thermic processing and roentgenography, Moscow: MISAA, 1994.

References p.122

К 20698

Mathematical modelling of composite object a. Pt.II / Rus. Acad. of sci.Computing center; Khachaturov V.R. (ed.).-M.:Computing centre of the Rus.acad.of sci.,2000.- 123 p.- Текст англ. √Паралл. загл.: Математическое моделирование композиционных объектов. Ч.II. Библиогр. в конце работ.

I.3агл. II.Rus.acad.of sci.Compuґting centre.III.Ed.