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Non-commensurate (misfit) layer structures

  • E. Makovicky
  • B. G. Hyde
Conference paper
Part of the Structure and Bonding book series (STRUCTURE, volume 46)

Abstract

We consider incommensurate structures of the type which have two more or less independent, though modulated, sub-lattices derived from misfitting layers of two types, alternating regularly in the layer-stacking direction. These are the two-dimensional analogues of the so-called “chimney-ladder” structures (which are one-dimensional).

After an introductory discussion of such misfit structures, various terms that have previously been applied are reviewed, and degrees of incommensurability are used as the basis for a systematic nomenclature. The known structures of specific examples are then discussed: graphite intercalates; minerals with brucite-like layers as one component (koenenite, valleriite, tochilinites); silicates; heavy metal sulphides (cylindrite, incaite, franckeite, cannizzarite, lengenbachite, lanthanum-chromium sulphide); anion-excess, fluorite-related yttrium oxy-fluorides and related compounds.

A discussion of types of inter-layer bonding, layer types and layer matching is followed by a consideration of disorder in such structures, as well as symmetry aspects and some growth mechanisms. Structures transitional between this type of structure and commensurate structures, i.e. structures which are really non-commensurate layers joined at anti-phase boundaries which restore commensurability, are then considered and classified with a detailed consideration of known examples from inorganic chemistry and mineralogy. Finally, some broad, general conclusions are enumerated.

Keywords

Acta Cryst Layer Type Antiphase Boundary Hydroxide Layer Layer Match 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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References

  1. 1.
    Allmann, R.: Chimia 24, 99 (1970)Google Scholar
  2. 2.
    Allmann, R., Lohse, H. H. and Hellner, E.: Z. Kristallogr. 126, 7 (1968)CrossRefGoogle Scholar
  3. 3.
    Anderson, J. S.: J. Chem. Soc. Dalton, 1107 (1973)Google Scholar
  4. 4.
    Andersson, S. and Hyde, B. G.: J. Solid State Chem. 9, 92 (1974)CrossRefGoogle Scholar
  5. 5.
    Asher, R. C.: J. Inorg. Nucl. Chem. 10, 238 (1959)CrossRefGoogle Scholar
  6. 6.
    Bärnighausen, H.: Proc. 12th Rare Earth Res. Conf. (ed. C. E. Lundin) 1, 404 (1976). Denver: Univ. of DenverGoogle Scholar
  7. 7.
    Bärnighausen, H. and Haschke, J. M.: Inorg. Chem. 17, 18 (1978)CrossRefGoogle Scholar
  8. 8.
    Berner, R. A.: Science, 137, 669 (1962)Google Scholar
  9. 9.
    Bevan, D. J. M.: pp. 749–759 in Solid State Chemistry (ed. R. S. Roth and S. J. Schneider), N.B.S. Special Publ. 364. Washington, D. C.: U.S. Government Printing Office (1972)Google Scholar
  10. 10.
    Bevan, D. J. M., Hoskins, B. F. and Mohyla, J.: 3rd European Crystallography Meet., Zürich (1976)Google Scholar
  11. 11.
    Bevan, D. J. M. et al.: 11th Australian Crystallography Conf. Bendigo (Vic.), Febr. 1978Google Scholar
  12. 12.
    Bevan, D. J. M. and Mann, A. W.: Acta Cryst. B31, 1406 (1975)CrossRefGoogle Scholar
  13. 13.
    Bollmann, W.: Crystal defects and crystalline interfaces. Berlin: Springer-Verlag (1970)Google Scholar
  14. 14.
    Brebrick, R. F.: pp. 183–195 in The chemistry of extended defects in non-metallic solids (ed. L. Eyring and M. O'Keeffe). Amsterdam: North-Holland (1969)Google Scholar
  15. 15.
    Brouwer, R. and Jellinek, F.: J. de Phys., Colloque C7, 38, C7 (1977)Google Scholar
  16. 16.
    Bursill, L. A. and Hyde, B. G.: Progr. Solid State Chem. 7, 177 (1972a)CrossRefGoogle Scholar
  17. 17.
    Bursill, L. A. and Hyde, B. G.: Nature Phys. Sci. 240, 122 (1972b)Google Scholar
  18. 18.
    Caro, P. E. and Corbett, J. D.: J. Less-Common Metals 18, 1 (1969)CrossRefGoogle Scholar
  19. 19.
    Chukhrov, F. V. et al.: Abstract in 8th All-Union Conf. on X-ray analysis of Mineral Raw Materials. Symp. on Phase Analysis. Moscow: IGEM ANSSSR (1979)Google Scholar
  20. 20.
    Clapp, P. C.: pp. 663–668 in The chemistry of extended defects in non-metallic solids (ed. L. Eyring and M. O'Keeffe). Amsterdam: North-Holland (1969)Google Scholar
  21. 21.
    Cowley, J. M. and Ibers, J. A.: Acta Cryst. 9, 421 (1956)CrossRefGoogle Scholar
  22. 22.
    Daly, J. J. and Sanz, F.: Acta Cryst. B31, 620 (1975)CrossRefGoogle Scholar
  23. 23.
    de Ridder, R., van Tendeloo, G. and Amelinckx, S.: Phys. Stat. Sol. (a) 33, 383 (1976)Google Scholar
  24. 24.
    Dornberger-Schiff, K.: Lehrgang über OD-Strukturen (+ Anhang). Berlin: Akademie-Verlag (1966)Google Scholar
  25. 25.
    Drits, V. A. and Sakharov, B. A.: Trudy Geol. Inst. Akad. Nauk. SSSR. 295, 256 pp. Moscow: Nauka (1976)Google Scholar
  26. 26.
    Ďurovič, S.: Acta Cryst. B30, 2214 (1974)CrossRefGoogle Scholar
  27. 27.
    Evans, E. L. and Thomas, J. M.: J. Solid State Chem. 14, 99 (1975)CrossRefGoogle Scholar
  28. 28.
    Evans, H. T. and Allmann, R.: Z. Kristallogr. 127, 73 (1968)CrossRefGoogle Scholar
  29. 29.
    Galy, J. and Roth, R. S.: J. Solid State Chem. 7, 277 (1973)CrossRefGoogle Scholar
  30. 30.
    Graham, A. R., Thompson, R. M. and Berry, L. G.: Am. Miner. 38, 536 (1953)Google Scholar
  31. 31.
    Grey, I.: Acta Cryst. B31, 45 (1975)CrossRefGoogle Scholar
  32. 32.
    Guiderow, D.: Acta Cryst. B34, 1804 (1978)CrossRefGoogle Scholar
  33. 33.
    Harris, D. C., Cabri, L. J. and Stewart, J. M.: Am. Miner. 55, 2110 (1970)Google Scholar
  34. 34.
    Harris, D. C. and Vaughan, D. J.: Am. Miner. 57, 1037 (1972)Google Scholar
  35. 35.
    Hockstra, A., Spoelder, T. and Vos, A.: Acta Cryst. B28, 14 (1972)CrossRefGoogle Scholar
  36. 36.
    Haschke, J. M: Inorg. Chem. 15, 298 (1976)CrossRefGoogle Scholar
  37. 37.
    Hofmann, W.: Z. Kristallogr. 92A, 161 (1935)Google Scholar
  38. 38.
    Hoggins, J. T. and Steinfink, H.: Acta Cryst. B33, 673 (1977)CrossRefGoogle Scholar
  39. 39.
    Hohlwein, D. and Metz, W.: Z. Kristallogr. 139, 279 (1974)CrossRefGoogle Scholar
  40. 40.
    Holmberg, B.: Acta Chem. Scand. 20, 1082 (1966)CrossRefGoogle Scholar
  41. 41.
    Hooley, J. G.: Mater. Sci. Eng. 31, 17 (1977)CrossRefGoogle Scholar
  42. 42.
    Huhma, M. et al.: Bull Geol. Soc. Finland 45, 103 (1973)Google Scholar
  43. 43.
    Hyde, B. G. et al.: Ann. Rev. Mater. Sci. 4, 43 (1974)CrossRefGoogle Scholar
  44. 44.
    Hyde, B. G. et al.: Prog. Solid State Chem., 12, 273 (1979)CrossRefGoogle Scholar
  45. 45.
    Iishi, K. et al.: Am Miner. 55, 2107 (1970)Google Scholar
  46. 46.
    Jambor, J. L.: Geol. Survey Canada Paper 76-1 B, 65 (1976)Google Scholar
  47. 47.
    Jeitschko, W. and Parthé, E.: Acta Cryst. 22, 417 (1967)CrossRefGoogle Scholar
  48. 48.
    Jellinek, F.: p. 758 in Solid State Chemistry (ed. R. S. Roth and S. J. Schneider); N. B. S. Special Publ. 364. Washington, D. C.: U.S. Government Printing Office (1972)Google Scholar
  49. 49.
    Jesser, W. A. and Kuhlmann-Wilsdorf, D.: Phys. star. sol. 21, 533 (1967)Google Scholar
  50. 50.
    Johnson, A. W. S.: paper I C-2 in: Electron Diffraction and The Nature of Defects in Crystals. Melbourne (Australia): Austr. Academy of Science (1965)Google Scholar
  51. 51.
    Johnson, A. W. S.: Acta Cryst. 23, 770 (1967)CrossRefGoogle Scholar
  52. 52.
    Johnson, C. K.: Amer. Cryst. Assoc. Meeting Abstracts, Ser. 2, 4, 32 (1976)Google Scholar
  53. 53.
    Johnson, C. K. and Watson, Ch. R.: J. Chem. Phys. 64, 2271 (1976)CrossRefGoogle Scholar
  54. 54.
    Jung, W. and Juza, R.: Zeit. anorg. allg. Chem. 399, 129 (1973 a)CrossRefGoogle Scholar
  55. 55.
    Jung, W. and Juza, R.: Zeit. anorg. allg. Chem. 399, 148 (1973 b)CrossRefGoogle Scholar
  56. 56.
    Karup-Møller, S. and Makovicky, E.: Neues Jb. Miner. 136, 310 (1979)Google Scholar
  57. 57.
    Kato, K., Kawada, I. and Takahashi, T.: Acta Cryst. B33, 3437 (1977)CrossRefGoogle Scholar
  58. 58.
    Kupčik, V. and Veselá-Nováková, L.: Tschermaks Mineral. Petrogr. Mitt. 14, 55 (1970)CrossRefGoogle Scholar
  59. 59.
    La Placa, S. J. et al.: Solid State Comm. 17, 635 (1975)CrossRefGoogle Scholar
  60. 60.
    Liebau, F.: Acta Cryst. B24, 690 (1968)CrossRefGoogle Scholar
  61. 61.
    Löchner, U., Bärnighausen, H. and Corbett, J. D.: Inorg. Chem. 16, 2134 (1977)CrossRefGoogle Scholar
  62. 62.
    Lüke, H. and Eick, H. A.: Proc. 12th Rare Earth Res. Conf. (ed. C. E. Lundin) I, 424. Denver: Univ. of Denver (1976)Google Scholar
  63. 63.
    Mackay, A. L.: p. 27 in The harvest of a quiet eye (ed. M. Ebison). Bristol: The Institute of Physics. [Quoting G. L. (Comte de) Buffon (1783–1788) Histoire naturelle des minéraux III. Paris.] (1977)Google Scholar
  64. 64.
    Magnéli, A.: Acta Cryst. 6, 495 (1953)CrossRefGoogle Scholar
  65. 65.
    Makovicky, E.: unpublished MS, McGill Univ., Montreal (1970)Google Scholar
  66. 66.
    Makovicky, E.: Am. Miner. 56, 353 (1971 a)Google Scholar
  67. 67.
    Makovicky, E.: Neues Jb. Miner. Mh., 403 (1971 b)Google Scholar
  68. 68.
    Makovicky, E.: Neues Jb. Miner. Mh., 235 (1974 a)Google Scholar
  69. 69.
    Makovicky, E.: Fortschritte der Mineralogie 52, Bh. 2, 49 (1974 b)Google Scholar
  70. 70.
    Makovicky, E.: Neues Jb. Miner. Abh., 126, 304 (1976)Google Scholar
  71. 71.
    Makovicky, E.: Neues Jb. Miner. Abh., 131, 187 (1977)Google Scholar
  72. 72.
    Makovicky, E. and Karup-Møller, S.: Neues Jb. Miner. Abh., 130, 264; 131, 56 (1977)Google Scholar
  73. 73.
    Makovicky, E., Mumme, W. G. and Watts, J. A.: Canad. Miner. 15, 339 (1977)Google Scholar
  74. 74.
    Mann, A. W. and Bevan, D. J. M.: J. Solid State Chem. 5, 410 (1972)CrossRefGoogle Scholar
  75. 75.
    Matzat, E.: Acta Cryst. B35, 133 (1979)CrossRefGoogle Scholar
  76. 76.
    Megaw, H. D.: Crystal structures: a working approach. Philadelphia: Saunders (1973)Google Scholar
  77. 77.
    Metz, W. and Hohlwein, D.: Carbon, 13, 87 (1975)CrossRefGoogle Scholar
  78. 78.
    Metz, W. and Schulze, E. J.: Z. Kristallogr. 142, 409 (1975)CrossRefGoogle Scholar
  79. 79.
    Mohyla, J.: Thesis, The Flinders Univ. of South Australia (1979)Google Scholar
  80. 80.
    Mozgova, N. N., Borodayev, Yu. S. and Organova, N. I.: pp. 43–64 in Inhomogeneity in minerals and fine mineral mixtures (ed. F. V. Chukhrov and N. V. Petrovskaya). Moscow: Izd. Nauka (1977)Google Scholar
  81. 81.
    Mozgova, N. N., Borodayev, Yu. S. and Sveshnikova, O. L.: Dokl. Akad. Nauk U.S.S.R. 220, 191 (1975)Google Scholar
  82. 82.
    Mumme, W. G.: Am. Miner. 60, 548 (1975)Google Scholar
  83. 83.
    Mumme, W. G.: Am. Miner. 61, 839 (1976)Google Scholar
  84. 84.
    Muramatsu, Y., Nambu, N. and Takeuchi, T.: J. Japan Ass. Min. Petr. Econ. Geol. 70, 236 (1975)Google Scholar
  85. 85.
    Myers, R. J.: Thesis, Univ. of Melbourne (1976)Google Scholar
  86. 86.
    Nabarro, F. R. N.: Theory of crystal dislocations, pp. 32, 33. Oxford: Clarendon (1967)Google Scholar
  87. 87.
    Nickel, E. H. and Hudson, D. R.: Contrib. Mineral Petrol. 55, 265 (1976)CrossRefGoogle Scholar
  88. 88.
    Niizeki, N. and Buerger, M. J.: Z. Kristallogr. 109, 129 (1957)CrossRefGoogle Scholar
  89. 89.
    Nowacki, W.: Neues Jb. Miner. Mh., 69 (1968)Google Scholar
  90. 90.
    Nowacki, W. and Stalder, H. A.: Schweiz. Min. Petr. Mitt. 49, 97 (1969)Google Scholar
  91. 91.
    Nuffield, E. W.: Trans. Roy. Soc. Canada, 3rd Ser. 38, Sect. IV-Geol. Sci. and Mineral., 59 (1944)Google Scholar
  92. 92.
    Oftedal, I.: Z. Phys. Chem. 134, 301 (1928)Google Scholar
  93. 93.
    Okamura, K., Iwasaki, H. and Ogawa, S.: J. Phys. Soc. Japan, 21, 1616 (1966)CrossRefGoogle Scholar
  94. 94.
    Okamura, K., Iwasaki, H. and Ogawa, S.: J. Phys. Soc. Japan, 24, 569 (1968)CrossRefGoogle Scholar
  95. 95.
    O'Keeffe, M. and Hyde, B. G.: Phil. Trans. Roy. Soc. Lond., A 295, 553 (1979)CrossRefGoogle Scholar
  96. 96.
    Organova, N. I., Drits, V. A. and Dmitrik, A. L.: Kristallografiya, 17, 761 (1972)Google Scholar
  97. 97.
    Organova, N. I., Drits, V. A. and Dmitrik, A. L.: Kristallografiya, 18, 966 (1973 a)Google Scholar
  98. 98.
    Organova, N. I., Drits, V. A. and Dmitrik, A. L.: Dokl. Akad. Nauk SSSR 212, 192 (1973 b)Google Scholar
  99. 99.
    Organova, N. I., Drits, V. A. and Dmitrik, A. L.: Am Miner. 59, 190 (1974)Google Scholar
  100. 100.
    Organova, N. I. et al.: Zap. Vses. Min. Obschch., No. 4, 100 (1971)Google Scholar
  101. 100 a.
    Papiernik, R., Mercurio, D. and Frit, B.: Acta Cryst. B36, 1769 (1980)CrossRefGoogle Scholar
  102. 101.
    Roether, U.: Thesis, Univ. of Freiburg (1967)Google Scholar
  103. 102.
    Rösch, H. and Hellner, E.: Naturwiss. 46, 2 (1959)CrossRefGoogle Scholar
  104. 103.
    Roth, R. S. et al.: pp. 183–195 in Solid State Chemistry (ed. R. S. Roth and S. J. Schneider); N.B.S. Special Publ. 364. Washington, D. C.: U.S. Government Printing Office (1972)Google Scholar
  105. 104.
    Rüdorff, W. and Schulz, H.: Zeit. anorg. allg. Chem. 245, 121 (1940)CrossRefGoogle Scholar
  106. 105.
    Rüdorff, W. and Schulze, E.: Zeit. anorg. allg. Chem. 277, 156 (1954)CrossRefGoogle Scholar
  107. 106.
    Ruff, O. and Bretschneider, O.: Z. anorg. allg. Chem. 217, 1 (1934)CrossRefGoogle Scholar
  108. 107.
    Šćavničar, S.: Z. Kristallogr. 114, 85 (1960)CrossRefGoogle Scholar
  109. 108.
    Smith, D. K. and Newkirk, H. W.: Acta Cryst. 18, 983 (1965)CrossRefGoogle Scholar
  110. 109.
    Springer, G.: Neues Jb. Miner. Mh., 252 (1968)Google Scholar
  111. 110.
    Srikrishnan, T. and Nowacki, W.: Z. Kristallogr. 140, 114 (1974)CrossRefGoogle Scholar
  112. 111.
    Takagi, J. and Takeuchi, Y.: Acta Cryst. B28, 649 (1972)CrossRefGoogle Scholar
  113. 112.
    Takeda, H. and Donnay, J. D. H.: Acta Cryst. 19, 474 (1965)CrossRefGoogle Scholar
  114. 113.
    Takeuchi, Y. and Takagi, J.: Proc. Japan Acad. Sci. 50, 843 (1974)Google Scholar
  115. 114.
    Taylor, H. F. W.: Mineralogical Magazine (London), 39, 377 (1973)Google Scholar
  116. 115.
    van Tendeloo, G. et al.: Phys. Stat. Sol. (a) 25, 697 (1974)Google Scholar
  117. 116.
    Wadsley, A. D.: Acta Cryst. 5, 676 (1952)CrossRefGoogle Scholar
  118. 117.
    Wadsley, A. D.: Acta Cryst. 8, 165 (1955)CrossRefGoogle Scholar
  119. 118.
    Wolfe, C. W.: Am. Miner. 23, 790 (1938)Google Scholar
  120. 119.
    Zoltai, T.: Systematics of simple sulphide structures. Minneapolis: Univ. of Minnesota (1974)Google Scholar

Copyright information

© Springer-Verlag 1981

Authors and Affiliations

  • E. Makovicky
    • 1
  • B. G. Hyde
    • 2
  1. 1.Institute of MineralogyUniversity of CopenhagenCopenhagen KDenmark
  2. 2.Research School of ChemistryThe Australian National UniversityCanberra, A.C.T.Australia

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