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Long Period Structures in Alloys-Statistical Mechanics of the Annni Model and Related Concepts

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Alloy Phase Stability

Part of the book series: NATO ASI Series ((NSSE,volume 163))

Abstract

Results on the phase diagram of the axial next-nearest neighbour Ising (or ANNNI) model are reviewed and applications to strikingly similar findings on long-period superstructures in A3B alloys (like Al3Ti, Ag3Mg, and Cu3Pd) are discussed.

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References

  1. Fisher, M.E. and W. Selke, Phys. Rev. Lett. 44 (1980) 1502.

    Article  MathSciNet  ADS  Google Scholar 

  2. For previous reviews, see Bak, P., Rep, Prog. Phys. 45 (1982) 587

    Article  MathSciNet  ADS  Google Scholar 

  3. Fisher, M.E. and D.A. Huse, Melting, Localization, and Chaos. Kalia, R.K., Vashishta, P. (eds.) p. 259. New York: Elsevier 1982

    Google Scholar 

  4. Selke W., Modulated Structure Materials. Tsakalakos, T. (ed.) p. 23. Dordrecht, Boston, Lancaster: Martinus Nijhoff 1984; Yeomanns, J., preprint 1987.

    Google Scholar 

  5. de Fontaine, D. and J. Kulik, Acta Metall. 33 (1985) 145.

    Article  Google Scholar 

  6. Sato, H. and R.S. Toth, Alloying Behavior in Concentrated Solid Solutions. Massalski, T.B. (ed.) p. 295. New York: Gordon and Breach 1965.

    Google Scholar 

  7. Gyorffy, B.L. and G.M. Stocks, Phys. Rev. Lett. 50 (1983) 374.

    Article  ADS  Google Scholar 

  8. Elliott, R.J., Phys. Rev. 124 (1961) 346.

    Article  ADS  Google Scholar 

  9. Stephenson, J., Can. J. Phys. 48 (1970) 1724.

    Article  ADS  Google Scholar 

  10. Hornreich, R.M., R. Liebmann, H.G. Schuster and W. Selke, Z. Physik B 35 (1979) 91.

    Article  ADS  Google Scholar 

  11. Selke W., Z. Physik B 43 (1981) 335

    Article  MathSciNet  ADS  Google Scholar 

  12. Selke, W. and M.E. Fisher, Z. Physik B 40 (1980) 71

    Article  MathSciNet  ADS  Google Scholar 

  13. Barber, M.N. and W. Selke, J. Phys. A 15 (1982) L 617.

    Google Scholar 

  14. Recent references include, Oitmaa, J., J. Phys. A 18 (1985) 365

    Article  MathSciNet  ADS  Google Scholar 

  15. Finel, A. and D. de Fontaine, J. Stat. Phys. 43 (1986) 645

    Article  ADS  Google Scholar 

  16. Duxbury, P.M., J.M. Yeomans, and P.D. Beale, J. Phys. A 17 (1984) L 179

    Google Scholar 

  17. Saqi, M.A.S. and D.S. McKenzie, J. Phys. A 20 (1987) 471

    Article  ADS  Google Scholar 

  18. Rujan, P., W. Selke, and G. Uimin, Z. Physik B 65 (1986) 235.

    Article  ADS  Google Scholar 

  19. Selke, W., K. Binder and W. Kinzel, Surface Sci. 125 (1983) 74

    Article  ADS  Google Scholar 

  20. Rujan, P., W. Selke and G. Uimin, Z. Physik B 53 (1983) 221.

    Article  ADS  Google Scholar 

  21. Van Hove, M.A., W.H. Weinberg and C.M. Chan, Low-Energy Electron Diffraction. Heidelberg, Berlin, Tokyo, New York: Springer 1986

    Google Scholar 

  22. Zhadanov, V.P. and K.I. Zamarayev, Usp. Fiz. Nau. 149 (1986) 635.

    Article  Google Scholar 

  23. Redner, S. and H.E. Stanley, Phys. Rev. B 16 (1977) 4901

    Article  ADS  Google Scholar 

  24. Oitmaa, J., J. Phys. A 18 (1985) 365.

    Article  MathSciNet  ADS  Google Scholar 

  25. Fisher, M.E. and W. Selke, Philosophical Trans. R. Soc. 302 (1981) 1.

    Article  MathSciNet  ADS  Google Scholar 

  26. Selke, W. and M.E. Fisher, Phys. Rev, B 20 (1979) 257

    Article  ADS  Google Scholar 

  27. J. Magn. Magn. Mat. 15–18 (1980) 403.

    Article  Google Scholar 

  28. Selke, W., Z. Physik B 29 (1978) 133

    Article  ADS  Google Scholar 

  29. Kaski, K. and W. Selke, Phys. Rev. B 31 (1985) 3128.

    Article  ADS  Google Scholar 

  30. Hornreich, R.M., M. Luban and S. Shtrikman, Phys. Rev. Lett. 35 (1975) 1678.

    Article  ADS  Google Scholar 

  31. Rasmussen, E.B. and S.J. Knak Jensen, Phys. Rev. B 24 (1981) 2744

    Article  ADS  Google Scholar 

  32. Kawasaki, T., Prog. Theor. Phys. 71 (1984) 246.

    Article  ADS  Google Scholar 

  33. Szpilka, A.M. and M.E. Fisher, Phys. Rev. Lett. 57 (1986) 1044; Fisher M.E. and A.M. Szpilka, Phys. Rev. B (1987)

    Article  ADS  Google Scholar 

  34. for a related domain wall analysis using a harmonic approximation to the mean field equations at low temperatures keeping correctly only terms of lowest order, W2, see Villain, J. and M. Gordon, J. Phys. C 13 (1980) 3117.

    Article  ADS  Google Scholar 

  35. Selke, W. und P.M. Duxbury, Z. Physik B 57 (1984) 49

    Article  ADS  Google Scholar 

  36. Duxbury, P.M. and W. Selke, J. Phys. A 16 (1983) L 741.

    Article  Google Scholar 

  37. Bak, P. and J. von Boehm, Phys. Rev. B 21 (1980) 5297

    Article  MathSciNet  ADS  Google Scholar 

  38. Jensen, M.H. and P. Bak, Phys. Rev. B 27 (1983) 6853.

    Article  MathSciNet  ADS  Google Scholar 

  39. Aubry, S., Soliton and Condensed Matter Physics. Bishop, A.R., Schneider, T. (eds.) p. 264 Berlin, Heidelberg, New York: Springer 1978

    Google Scholar 

  40. similar ground state analyses on related models include Chou, W., and R.B. Griffiths, Phys. Rev. B 34 (1986) 6219

    Article  ADS  Google Scholar 

  41. Marchand, M., K. Hood and A. Caille, Phys. Rev. Lett. 58 (1987) 1660; Yokoi, C.S.O., L. Tang, and W. Chou, Preprint (1987).

    Article  ADS  Google Scholar 

  42. Aharony, A. and P. Bak, Phys. Rev. B 23 (1981) 4770.

    Article  ADS  Google Scholar 

  43. Siegert, M. and H.U. Everts, Z. Physik B 60 (1985) 265

    Article  ADS  Google Scholar 

  44. Siegert, M. and H.U. Everts, Z. Physik B 66 (1987) 227 and references therein.

    Article  ADS  Google Scholar 

  45. For other Potts models with competing interactions, see Peschel, I. and T.T. Truong, J. Stat. Phys. 45 (1986) 233.

    Article  MathSciNet  ADS  Google Scholar 

  46. For a review, see Weeks, J.D., Ordering in Strongly Fluctuating Condensed Matter Systems. Riste, T. (ed.) p. 293. New York: Plenum Press 1980.

    Google Scholar 

  47. Tentrup, T. and R. Siems, J. Phys. C 19 (1986) 3443.

    Article  ADS  Google Scholar 

  48. Domain wall properties of the ANNNI model are also considered in Widom, B., K.A. Dawson and M.D. Lipkin, Physica A 140 (1986) 26.

    Article  ADS  Google Scholar 

  49. For a review, see Janssen, T., Microscopic Theories of Incommensurate Crystal Phases. Blinc, R., Levanyuk, A.P. (eds.) p. 67. New York: Elsevier 1986.

    Google Scholar 

  50. Benkert, C., V. Heine and E.H. Simmons, Europhysics Lett. 3 (1987) 833.

    Article  ADS  Google Scholar 

  51. Selke W., J. Phys. C 14 (1981) L 17.

    Article  MathSciNet  ADS  Google Scholar 

  52. Selke W., M. Barreto and J. Yeomans, J. Phys. C 18 (1985) L 393

    Google Scholar 

  53. Barreto, M. and J. Yeomans, Physica A 134 (1985) 84

    Article  ADS  Google Scholar 

  54. see also Randa, J., Phys. Rev. B 32 (1985) 413.

    Article  ADS  Google Scholar 

  55. Yokoi, C.S.O., M.D. Coutinho-Filho and S.R. Salinas, Phys. Rev. B 24 (1981) 4047

    Article  ADS  Google Scholar 

  56. Smith, J. and J.M. Yeomans, J. Phys. C16 (1983) 5305

    Article  ADS  Google Scholar 

  57. Pokrovsky, V.L. and G.V. Uimin, Sov. Phys. Zh.E.T.F. 82 (1982) 1640

    Google Scholar 

  58. Szpilka, A.M., J. Phys. C 18 (1985) 569.

    Article  ADS  Google Scholar 

  59. Jensen, P.J., K.A. Penson and K.H. Bennemann, Phys. Rev. B 35 (1987) 7306.

    Article  ADS  Google Scholar 

  60. De Simone, T. and R.M. Stratt, Phys. Rev. B 32 (1985) 1537

    Article  ADS  Google Scholar 

  61. De Simone, T., R.M. Stratt and J. Tobochnik, Phys. Rev. B 32 (1985) 1549.

    Article  ADS  Google Scholar 

  62. Guymont, M., R. Portier and D. Gratias, Acta Cryst. A 36 (1980) 792.

    Article  Google Scholar 

  63. Broddin, D., G. Van Tendeloo, J. Van Landuyt, S. Amelinckx, R. Portier, M. Guymont and A. Loiseau, Phil. Mag. A 54 (1986) 395.

    Article  ADS  Google Scholar 

  64. Takeda, S., J. Kulik and D. de Fontaine, Preprint 1986; de Fontaine, D., A. Finel, S. Takeda and J. Kulik, Noble Metal Alloys. Massalski, T.B., Pearson, W.B., Benett, L.H. and Change, Y.A. (eds.) p. 49 (1986).

    Google Scholar 

  65. De Graef, M., D. Broddin, J. Van Humbeeck and L. Delaey, Proc. XIth Int. Congr. on Electron Microscopy, Kyoto (1986); De Graef, M. and D. Broddin, private communication.

    Google Scholar 

  66. Portier, R., D. Gratias, M. Guymont and W.M. Stobbs, Acta Cryst. A 36 (1980) 190.

    Article  Google Scholar 

  67. Fujino, Y., H. Sato, M. Hira-bayashi, E. Aoyagi and Y. Koyama, Phys. Rev. Lett. 58 (1987) 1012.

    Article  ADS  Google Scholar 

  68. Kulik, J., S. Takeda and D. de Fontaine, Acta Metall. 35 (1987) 1137.

    Article  Google Scholar 

  69. Van Tendeloo, G. and S. Amelinckx, Phys. Stat. Sol. A 43 (1977) 553.

    Article  ADS  Google Scholar 

  70. Loiseau, A., G. Van Tendeloo, R. Portier and F. Ducastelle, J. de Physique 46 (1985) 595

    Article  Google Scholar 

  71. Loiseau, A., Ph.D. thesis, O.N.E.R.A. (1985).

    Google Scholar 

  72. Fujiwara, K., J. Phys. Soc. Japan 12 (1957) 7.

    Article  Google Scholar 

  73. Van Tendeloo, G., these proceedings.

    Google Scholar 

  74. For example, Cahn, J.W. and R. Kikuchi, J. Phys. Chem. Solids 20 (1961) 9444.

    Article  Google Scholar 

  75. Kikuchi, R., and Cahn, J.W., J. Phys. Chem. Solids 23 (1962) 137

    Article  ADS  Google Scholar 

  76. Inden, G., S. Bruns and H. Ackermann, Phil. Mag. A 53 (1986) 87.

    Article  ADS  Google Scholar 

  77. Bieber, A. and F. Gautier, Z. Physik B 57 (1984) 335

    Article  ADS  Google Scholar 

  78. Bieber, A. and F. Gautier, Acta Metall. 34 (1986) 2291.

    Article  Google Scholar 

  79. Finel, A. and F. Ducastelle, Phase Transformations in Solids. Tsakalakos, T., (ed.) p. 293. New York: North Holland 1984

    Google Scholar 

  80. Sanchez, J.M. and D. de Fontaine, Structure and Bonding, Vol. II, p. 117, New York: Academic Press 1981

    Google Scholar 

  81. Ducastelle, F., Rech. Aerosp. 4 (1986) 11.

    Google Scholar 

  82. Binder, K., Festkörperprobleme XXVI (1986) 133.

    Google Scholar 

  83. Gerold, V. and J. Kern, Acta Metall. 35 (1987) 393

    Article  Google Scholar 

  84. Maysenhölder, W., Phys. Stat. Sol. B 139 (1987) 399.

    Article  ADS  Google Scholar 

  85. Schweika, W. and H.G. Haubold, Preprint (1987); Schweika, W., Ph.D. thesis, RWTH Aachen (1985)

    Google Scholar 

  86. Cheng, C., R.J. Needs, V. Heine and N. Churcher, Europhysics Lett. 3 (1987) 475.

    Article  ADS  Google Scholar 

  87. Huse, D.A., J.M. Yeomans and M.E. Fisher, Phys. Rev. B 23 (1981) 180

    Article  MathSciNet  ADS  Google Scholar 

  88. Selke, W. and F.Y. Wu, J. Phys. A 20 (1987) 703.

    Article  ADS  Google Scholar 

  89. Yokoi, C.S.O., M.J. de Oliveira, and S.R. Salinas, Phys. Rev. Lett. 54 (1985) 163

    Article  ADS  Google Scholar 

  90. Vannimenus, J., Z. Physik B 43 (1981) 141

    Article  ADS  Google Scholar 

  91. da Silva, C.R. and S. Coutinho, Phys. Rev. B 34 (1986) 7975

    Article  ADS  Google Scholar 

  92. Mariz, A.M., C. Tsallis, and E.L. Albuquerque, J. Stat. Phys. 40 (1985) 5777

    Article  MathSciNet  Google Scholar 

  93. Inawashiro, S., C.J. Thompson and G. Honda, J. Stat. Phys. 33 (1983) 419.

    Article  MathSciNet  ADS  Google Scholar 

  94. Rossat-Mignod, J., P. Burlet, J. Villain, H. Bartholin, W. Tscheng-Si and D. Florence, Phys. Rev. B16 (1977) 440

    Article  ADS  Google Scholar 

  95. Fischer P., B Lebech, G. Meier, B.D. Rainford and O. Vogt, J. Phys. C 11 (1978) 345

    Article  ADS  Google Scholar 

  96. Hälg, B. and A. Furrer, Phys. Rev. B 34 (1986) 6258.

    Article  ADS  Google Scholar 

  97. Müller, K.A., W. Berlinger, J.Y. Buzare and J.C. Fayet, Phys. Rev. B 21 (1980) 1763

    Article  ADS  Google Scholar 

  98. Currat, R., Multicritical Phenomena. Pynn, R., Skjeltrop, A. (eds.) p. 177. New York: Plenum Press.

    Google Scholar 

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Selke, W. (1989). Long Period Structures in Alloys-Statistical Mechanics of the Annni Model and Related Concepts. In: Stocks, G.M., Gonis, A. (eds) Alloy Phase Stability. NATO ASI Series, vol 163. Springer, Dordrecht. https://doi.org/10.1007/978-94-009-0915-1_16

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  • DOI: https://doi.org/10.1007/978-94-009-0915-1_16

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