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Equilibrium

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Part of the book series: Springer Series in Solid-State Sciences ((SSSOL,volume 36))

Abstract

Crystal growth and decrystallization (evaporation, melting, dissolution, etching, etc.) take place under the influence of a thermodynamic driving force determined by deviations in temperature, pressure, concentration, and external field intensity from their equilibrium values. Growth and decrystallization occur on interfaces whose structure and properties are close to equilibrium. Thus the basic principles governing phase equilibrium, driving force, and equilibrium interface structure and properties should be considered before entering into the kinetics of phase transformation. These aspects of equilibrium form the subject of this chapter.

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References

  1. L.D. Landau, E.M. Lifshits: Statisticheskaya fizika ( Nauka, Moscow 1964 )

    Google Scholar 

  2. L.D. Landau, E.M. Lifshits: Statistical Physics, 2nd ed. ( Pergamon, London 1969 )

    Google Scholar 

  3. F. Rosenberger: Fundamentals of Crystal Growth I. Macroscopic Equilibrium and Transport Concepts; Springer Ser. Solid-State Sci., Vol. 5 ( Springer, Berlin, Heidelberg, New York 1981 )

    Google Scholar 

  4. O. Söhnel, J. Garside: J. Cryst. Growth 46, 238 (1979)

    Article  Google Scholar 

  5. J.W. Mullin: The Chemical Engineer, June, 1973, p. 316

    Google Scholar 

  6. A.V. Shubnikov, N.N. Sheftal(eds.): Rost kristaZZov, T.2 (Izd-vo Akad. Nauk SSSR, Moscow 1959) [English transl.: Growth of Crystals. Vol.2 (Consultants Bureau, New York 1959)]

    Google Scholar 

  7. V.Ya. Khaimov-Mal’kov: In [Ref.1.3a, p.5] [English transl.: “The Thermodynamics of Crystallization Pressure”, in Ref.1.3a, p.3]

    Google Scholar 

  8. V.Ya. Khaimov-Mal’kov: In [Ref.1.3a, p.17] [English transl.: “Experimental Measurement of Crystallization Pressure”, in Ref.1.3a, p.14]

    Google Scholar 

  9. V.Ya. Khaimov-Mal’kov: In [Ref.1.3a, p.26] [English transl.: “The Growth Conditions of Crystals in Contact with Large Obstacles”, in Ref.1.3a, p.20]

    Google Scholar 

  10. Yu.S. Barash, V.L. Ginzburg: Usp. Fiz. Nauk 116,5 (1975) [English transl.: Electromagnetic fluctuations in matter and molecular (Van der Waals) forces between them. Sov. Phys. Usp./8, 305 (1975)]

    Google Scholar 

  11. B.V. Derjaguin, I.I. Abrikosova, E.M. Lifshits: Molekulyarnoe prityazhenie kondensirovannykh tel (Molecular attraction of condensed bodies). Usp. Fiz. Nauk 64, 493 (1958)

    Google Scholar 

  12. I.E. Dzyaloshinsky, E.M. Lifshits, L.P. Pitayevsky: Usp. Fiz. Nauk 73,381 (1961) [English transl.: General theory of Van der Waals forces. Sov. Phys. Usp.4, 153 (1961)]

    Google Scholar 

  13. E. Kaldis, H.J. Scheel (eds.): 1976 Crystal Growth and Materials: Review Papers of the First European Conference on Crystal Growth ECCG-1, Zurich, Sept. 1976 ( North-Holland, Amsterdam 1977 )

    Google Scholar 

  14. A.A. Chernov, D.E. Temkin: “Capture of Inclusions in Crystal Growth”, in [Ref.1.7a, p.3]

    Google Scholar 

  15. R.G. Horn, J.N. Israelashvili: J. Chem. Phys. 75, 1400 (1981)

    Article  CAS  Google Scholar 

  16. C.W. Correns: Discuss. Faraday Soc. No. 5, 267 (1949)

    Google Scholar 

  17. P. Hartman: In Rost kristallov, T.7,ed. by N.N. Sheftal’ (Nauka, Moscow 1967) p.8 [English transl.: “The Dependence of Crystal Morphology on Crystal Structure”, in Growth of Crystals, Vol.7 (Consultants Bureau, New York 1969) p.3]

    Google Scholar 

  18. B. Honigmann: Gleichgewichts— und Wachstumsformen von Kristallen ( Steinkopf, Darmstadt 1958 )

    Google Scholar 

  19. P. Hartman: “Le coté cristallographique de l’adsorption vu par le changement de faciés”, in Adsorption et croissance cristalline, Colloq. Int. CNRS, No.152 (Edition du Centre National de la Recherche Scientifique, Paris 1965 ) p. 477, 506

    Google Scholar 

  20. P. Hartman: “Structure and Morphology”, in Crystal Growth: An Introduction, ed. by P. Hartman ( North-Holland, Amsterdam 1973 ) p. 367

    Google Scholar 

  21. Ya.E. Geguzin, N.N. Ovcharenko: Usp. Fiz. Nauk 76,283 (1962) [English transl.: Surface energy and processes on solid surfaces. Soy. Phys. Usp.5, 129 (1962)]

    Google Scholar 

  22. N. Eustatopulos, J.-C. Joud: “Interfacial Tension and Adsorption of Metallic Systems”, Current Topics Mat. Sci., Vol.4 ( North-Holland, Amsterdam 1979 ) p. 281

    Google Scholar 

  23. V.I. Marchenko, A.Ya. Parshin: Zh. Eksp. Teor. Fiz.79, 257 (1980) [English transl.: Soy. Phys. JETP 52,129 (1980)]

    Google Scholar 

  24. A.F. Andreyev, Yu.A. Kosevich: Zh. Eksp. Teor. Fiz.81, 1435 (1981) 1.15 I.N. Stransky, R. Kaischew: K teorii rosta kristallov i obrazovaniya kristallicheskikh zarodyshei (On the theory of crystal growth and nucleation), Usp. Fiz. Nauk 21, 408 (1939)

    Google Scholar 

  25. Ch. Kittel: Introduction to Solid State Physics, 4th ed. ( Wiley, New York 1971 )

    Google Scholar 

  26. W.K. Burton, N. Cabrera, F.C. Frank: The growth of crystals and the equilibrium structure of their surfaces. Philos. Trans. R. Soc. London A243, 299 (1951)

    Article  Google Scholar 

  27. A.A. Chernov: Usp. Fiz. Nauk 73, 277 (1961) [English transl.: The spiral growth of crystals. Soy. Phys. Usp.4, 116 (1961)]

    Google Scholar 

  28. S.F. Bedair: Surf. Sci. 42, 595 (1974)

    Article  CAS  Google Scholar 

  29. S. Hok, M. Drechsler: Surf. Sci. 107, 262 (1981)

    Article  Google Scholar 

  30. T.N. Kompaniyets: Zh. Tekh. Fiz. 46, 1361 (1976)

    Google Scholar 

  31. R.C. Weast (ed.): Handbook of Chemistry and Physics, 56th ed. ( CRC, Cleveland, Ohio 1975 )

    Google Scholar 

  32. A.A. Chernov, N.S. Papkov: Kristallografiya 25,1002 (1980) [English transl.: Soy. Phys. Crystallogr.25, 572 (1980)]

    Google Scholar 

  33. A.A. Chernov, M.P. Ruzaikin: J. Cryst. Growth 45, 73 (1978); 52, 185 (1981)

    Google Scholar 

  34. A.A. Chernov: Equilibrium adsorption and some interfacial growth processes in gaseous solutions and CVD systems. J. Jp. Assoc. Cryst. Growth 5, 227 (1978)

    Google Scholar 

  35. R. Cadoret: “Application of the Theory of the Rate Processes in the CVD of GaAs”, Current Topics Mat. Sci., Vol.5 ( North-Holland, Amsterdam 1980 ) p. 218

    Google Scholar 

  36. A.A. Chernov, M.P. Ruzaikin, N.S. Papkov: Poverkhn. Fiz. Khim. Mekh.I, 94 (1982)

    Google Scholar 

  37. F. Hottier, R. Cadoret: J. Cryst. Growth 52, 199 (1981)

    Article  CAS  Google Scholar 

  38. F. Hottier, J.B. Theeten: J. Cryst. Growth 48, 644 (1980)

    Article  CAS  Google Scholar 

  39. J. Bloem, L.J. Gilling: “Chemical Vapour Deposition of Silicon”, Current Topics Mat. Sci., Vol.1 ( North-Holland, Amsterdam 1978 ) p. 147

    Google Scholar 

  40. J. Bloem, W.A.P. Claassen: J. Cryst. Growth 49, 435 (1980)

    Article  CAS  Google Scholar 

  41. W.A.P. Claassen, J. Bloem: J. Cryst. Growth 50, 803 (1980); 51, 443 (1981)

    Article  CAS  Google Scholar 

  42. J. Bloem, W.A.P. Claassen, W.G.J.N. Valkenburg: J. Cryst. Growth 57, 177 (1982)

    Article  CAS  Google Scholar 

  43. J. Bloem: J. Cryst. Growth 50, 581 (1980)

    Article  CAS  Google Scholar 

  44. V.V. Voronkov: Kristallografiya 11,284 (1966) [English transl.: Sov. Phys. Crystallogr.1i, 259 (1966)]

    Google Scholar 

  45. G.H. Gilmer, J.D. Weeks: J. Chem. Phys. 68, 950 (1978)

    Article  CAS  Google Scholar 

  46. H.J. Leamy, G.H. Gilmer, K.A. Jackson: Statistical Thermodynamics of Clean Surfaces, in Surface of Materials, Vol. 1, ed. by J.M. Blakely ( Academic, New York 1975 ) p. 121

    Google Scholar 

  47. H.J. Leamy, K.A. Jackson: J. Appl. Phys. 42, 2121 (1971)

    Article  CAS  Google Scholar 

  48. G.H. Gilmer: J. Cryst. Growth 42, 3 (1977)

    Article  CAS  Google Scholar 

  49. J.Q. Broughton, G.H. Gilmer, J.D. Weeks: J. Chem. Phys.75, 5128 (1981); Phys. Rev. B25, 4651 (1982)

    Google Scholar 

  50. J.M. Phillips, L.W. Bruch, R.D. Murphy: J. Chem. Phys. 75, 5097 (1981)

    Article  CAS  Google Scholar 

  51. M.R. Mruzik, S.H. Garofalini, G.M. Pound: Surf. Sci. 103, 353 (1981)

    Article  CAS  Google Scholar 

  52. Y. Hiwatari, E. Stoll, T. Schneider: J. Chem. Phys. 68, 3401 (1978)

    Article  Google Scholar 

  53. J.Q. Brougton, A. Bonissent, F.F. Abraham: J. Chem. Phys. 74, 4029 (1981)

    Article  Google Scholar 

  54. A. Bonissent, F. Abraham: J. Chem. Phys. 74, 1306 (1981)

    Article  CAS  Google Scholar 

  55. A. Bonissent: Structure of Solid-Liquid Interface. Crystals, Vol.9 (Springer, Berlin, Heidelberg, New York 1983 ) p. 1

    Google Scholar 

  56. D.E. Temkin: “0 molekulyarnoi sherokhovatosti granitsy kristall—rasplav” (On Molecular Roughness of the Crystal—Melt Interface), in Mekhanism i kinetika kristallizatsii (Mechanism and Kinetics of Crystallization), ed. by N.N. Sirota ( Nauka i Tekhnika, Minsk 1964 ) p. 86

    Google Scholar 

  57. R.H. Doremus, B.W. Roberts, D. Turnbull (eds.): Growth and Perfection of Crystals ( Wiley, New York 1958 )

    Google Scholar 

  58. K.A. Jackson: “Interface Structure”, in [Ref.1.29a, pp.319, 324]

    Google Scholar 

  59. A.A. Chernov (ed.): Rost kristallov, T.11 (Izd-vo EGU, Erevan 1975) [English transl.: Growth of Crystals, Vol.11 (Consultants Bureau, New York 1979)]

    Google Scholar 

  60. K.A. Jackson: In [Ref.1.30a, p.116] [English transi.: “Computer Modelling of Crystal Growth Processes”, jn Ref.1.30a, p.115]

    Google Scholar 

  61. D. Turnbull: J. Appl. Phys. 21, 1022 (1950)

    Article  CAS  Google Scholar 

  62. V.V. Voronkov, A.A. Chernov: Structure of crystal ideal solution interface. J. Phys. Chem. Solids Suppl./, 593 (1967); Kristallografiya 11,662 (1966) [English transl.: Sov. Phys. Cryst. 11,571 (1967)]

    Google Scholar 

  63. H.W. Kerr, W.C. Winegard: Eutectic solidification. J. Phys. Chem. Solids Suppl./, 179 (1967)

    Google Scholar 

  64. V.V. Podolinsky, V.G. Drykin: 6th Int. Conf. Cryst. Growth, Extended Abstracts, Vol.2, USSR Academy of Sciences, Moscow 1980, p. 77

    Google Scholar 

  65. A.F. Andreev, A.Ya. Parshin: Zh. Eksp. Teor. Fiz.75, 1511 (1978) [English transl.: Sov. Phys. JETP 48,763 (1978)]

    Google Scholar 

  66. K.O. Keshishev, A.Ya. Parshin, A.V. Babkin: Zh. Eksp. Teor. Fiz.80, 716 (1981) [English transi.: Sov. Phys. JETP 53,362 (1981)]; Zh. Eksp. Teor. Fiz. Pis’ma Red.30, 63 (1979) [English transi.: Sov. Phys. JETP Lett.30, 56 (1979)]

    Google Scholar 

  67. S. Balibar, D.O. Edward, C. Laroche: Phys. Rev. Lett. 42, 782 (1979)

    Article  CAS  Google Scholar 

  68. J. Landau, S.G. Lipson, M.M. Määttänen, L.S. Balfour, D.O. Edwards: Phys. Rev. Lett. 45, 31 (1980)

    Article  CAS  Google Scholar 

  69. C. Herring: “The Use of Classical Macroscopic Concepts in Surface-Energy Problems”, in Structure and Properties of Solid Surfaces, ed. by E.R. Gourer, C.J. Smith (University of Chicago Press, Chicago 1953) PP. 5, 72

    Google Scholar 

  70. C. Herring: “Surface Tension as a Motivation for Sintering”, in The Physics on Powder Metallurgy ( McGraw-Hill, New York 1951 ) p. 143

    Google Scholar 

  71. G.G. Lemmlein: Dokl. Akad. Nauk SSSR 98, 973 (1954)

    CAS  Google Scholar 

  72. G.G. Lemmlein: Morfologiya i genesis kristallov (Crystal Morphology and Genesis) ( Nauka, Moscow 1973 )

    Google Scholar 

  73. M.O. Kliya: Kristallografiya 1, 577 (1956)

    CAS  Google Scholar 

  74. J.C. Heyraud, J.J. Metois: J. Cryst. Growth 50, 571 (1980)

    Article  CAS  Google Scholar 

  75. J.J. Metois, J.C. Heyraud: J. Cryst. Growth 57, 487 (1982)

    Article  CAS  Google Scholar 

  76. J.C. Heyraud, J.J. Metois: Acta Meta11. 28, 1789 (1980)

    Article  CAS  Google Scholar 

  77. M. Drechsler, J.F. Nicholas: J. Phys. Chem. Solids 28, 2609 (1967)

    Article  CAS  Google Scholar 

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Chernov, A.A. (1984). Equilibrium. In: Modern Crystallography III. Springer Series in Solid-State Sciences, vol 36. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-81835-6_1

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  • DOI: https://doi.org/10.1007/978-3-642-81835-6_1

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