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Segregation

Chapter
Part of the Springer Series in Solid-State Sciences book series (SSSOL, volume 5)

Abstract

The discussion of phase transitions in Chapters 3 and 4 has shown that only monocomponent and congruently melting or vaporizing multicomponent systems, respectively, remain unchanged in composition during solidification or crystallization. In all other systems the composition of the solid differs from that of the coexisting fluid (liquid or vapor) even in equilibrium. This phenomenon is called segregation or redistribution. In this chapter we will be mainly concerned with “impurities”, i.e., concentrations of solutes of, say, a few percent and below. We will, however, emphasize the consequences of adding large concentrations of components (solvents, inert gases) for the formal description of segregation dynamics.

Keywords

Zone Melting Zone Length Solute Distribution Diffusion Boundary Layer Molten Zone 
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. 6.1
    C.P. Thurmond, J.D. Struthers: Equilibrium thermochemistry of solid and liquid alloys of germanium and silicon. J. Phys. Chem. 57, 831 (1953)Google Scholar
  2. 6.2
    K. Lehovec: Thermodynamics of binary semiconductor-metal alloys. J. Phys. Chem. Solids 23, 695 (1962)Google Scholar
  3. 6.3
    K. Weiser: Theoretical calculation of distribution coefficients of im-purities in germanium and silicon, heats of solid solution. J. Phys. Chem. Solids 7, 118 (1958)Google Scholar
  4. 6.4
    R.N. Hall: Variation of the distribution coefficient and solid solubili-ty with temperature. J. Phys. Chem. Solids 3, 63 (1957)Google Scholar
  5. 6.5
    J.C. Brice: The Growth of Crystals from the Melt ( North-Holland, Amster-dam 1965 )Google Scholar
  6. 6.6
    M. Ikeya, N. Itoh, T. Suita: Distribution coefficients of various im-purities in alkali halides. Japan. J. Appl. Phys. 7, 837 (1968)Google Scholar
  7. 6.7
    U. Gross: Zonenschmelzen von Alkalihalogeniden. Thesis, University of Stuttgart (1970)Google Scholar
  8. 6.8
    T.B. Douglas: Calculated heats of dilute solid solution among the alka-li halides other than cesium salts. J. Chem. Phys. 45, 4571 (1966)Google Scholar
  9. 6.9
    M. Blander: Some calculations for a one-dimensional salt mixture. J.Chem. Phys. 34, 697 (1961)Google Scholar
  10. 6.10
    A.P. Ratner: On the theory of the distribution of electrolytes between a solid crystalline and a liquid phase. J. Chem. Phys. 1, 789 (1933)Google Scholar
  11. 6.11
    F. Vaslow, G.E. Boyd: Thermodynamics of coprecipitation: dilute solid solutions of AgBr in AgCl. J. Am. Chem. Soc. 74, 4691 (1952)Google Scholar
  12. 6.12
    F. Rosenberger, H.G. Riveros: Segregation in alkali halide crystallization. J. Chem. Phys. 60, 668 (1974)Google Scholar
  13. 6.13
    F.A. Kröger: The Chemistry of Imperfect Crystals, Vol. 1 (North-Holland, Amsterdam 1973 ) pp. 5–6Google Scholar
  14. 6.14
    J.C. Brice: The Growth of Crystals from Liquids ( North-Holland, Amsterdam 1973 )Google Scholar
  15. 6.15
    F. Rosenberger: “Purification of Alkali Halides”, in Ultrapurity, ed. by M. Zief, R. Speights ( Marcel Dekker, New York 1972 )Google Scholar
  16. 6.16
    W.L. McIntire: Trace element partition coefficients. Geochim. Cosmochim. Acta 27, 1209 (1963)Google Scholar
  17. 6.17
    H.H. Schock: Bestimmung sehr kleiner Verteilungs-Koeffizienten von Cs, Na and Ba zwischen Lösung and KC1-Einkristallen mittels radio-aktiver Isotope. Contr. Mineral. and Petrol. 13, 161 (1966)Google Scholar
  18. 6.18
    J.C. Brice: “Phase Relationships in Semiconductors”, in Atomic Diffu-sion in Semiconductors, ed. by D. Shaw ( Plenum Press, London 1973 )Google Scholar
  19. 6.19
    F.A. Kröger: The Chemistry of Imperfect Crystals, Vol. 2 ( North-Holland, Amsterdam 1973 )Google Scholar
  20. 6.20
    C. Wagner: Physical chemistry of ionic crystals involving small concentrations of foreign substances. J. Phys. Chem. 57, 738 (1953)Google Scholar
  21. 6.21
    W.D. Edwards: The interaction between oxygen and boron in liquid germanium. J. Appl. Phys. 39, 1784 (1968)Google Scholar
  22. 6.22
    K. Nassau, G.M. Loiacono: Calcium tungstate-III, trivalent rare earth substitution. J. Phys. Chem. Solids 24, 1503 (1963)Google Scholar
  23. 6.23
    R.A. Laudise: The Growth of Single Crystals ( Prentice Hall, Englewood Cliffs, NJ 1970 )Google Scholar
  24. 6.24
    J.C. Brice: Some thermodynamic aspects of the growth of strained crystals. J. Crystal Growth 28, 249 (1975)Google Scholar
  25. 6.25
    W.A. Wilcox: ‘The Role of Mass Transfer in Crystallization Processes“ in Preparation and Properties of Solid State Materials, ed. by R.A. Lefever ( Marcel Dekker, New York 1971 )Google Scholar
  26. 6.26
    W.R. Wilcox: Crystallization flow. J. Crystal Growth 12, 93 (1972)Google Scholar
  27. 6.27
    J.A. Burton, R.C. Prim, W.P. Slichter: The distribution of solute in crystals grown from the melt. Part I. Theoretical. J. Chem. Phys. 21, 1987 (1953)Google Scholar
  28. 6.28
    W.R. Wilcox: “Mass Transfer in Fractional Solidification”, in Fractional Solidification, ed. by M. Zief, W.R. Wilcox ( Marcel Dekker, New York 1967 )Google Scholar
  29. 6.29
    J.A. Burton, E.D. Kolb, W.P. Slichter, J.D. Struthers: The distribution of solute in crystals grown from the melt. Part II. Experimental. J. Chem. Phys. 21, 1991 (1953)Google Scholar
  30. 6.30
    W.G. Cochran: The flow due to a rotating disk. Proc. Cambr. Phil. Soc. 30, 365 (1934)Google Scholar
  31. 6.31
    J.C. Brice, P.A.C. Whiffin: Solute striae in pulled crystals of zinc tungstate. Brit. J. Appl. Phys. 18, 581 (1967)Google Scholar
  32. 6.32
    M.C. Flemings: Solidification Processing ( McGraw-Hill, New York 1974 )Google Scholar
  33. 6.33
    H. Kelting, H. Witt: Ober KCl Kristalle mit Zusätzen von Erdalkalichloriden. Z. Physik 126, 697 (1949)Google Scholar
  34. 6.34
    G.A. Andreev, B.P. Aleksandrov: Flotation study of the distribution of singly charged impurities in NaCl. Sov. Phys. Solid State 7, 135 (1965)Google Scholar
  35. 6.35
    R.H. McFee: Foreign ion rejection in the growth of sodium chloride crystals from the melt. J. Chem. Phys. 15, 856 (1947)Google Scholar
  36. 6.36
    M. Krumnacker, W. Lange: Investigation of the concentration ratios at the solid-liquid interface. Kristall and Technik 4, 207 (1969)Google Scholar
  37. 6.37
    W.G. Pfann: Zone Melting, 2nd ed. ( Wiley, New York 1966 )Google Scholar
  38. 6.38
    M. Zief, W.R. Wilcox (ed.): Fractional Solidification ( Marcel Dekker, New York 1967 )Google Scholar
  39. 6.39
    W.G. Pfann: Principles of zone melting. Trans. Am. Inst. Mining Met. Engrs. 194, 747 (1952)Google Scholar
  40. 6.40
    A.F. Witt, H.C. Gatos, M. Lichtensteiger, M.C. Lavine, C.J. Herman: Crystal growth and steady-state segregation under zero gravity: InSb. J. Electrochem. Soc. 122, 267 (1975)Google Scholar
  41. 6.41
    F.V. Dean, J.R. Kerr, A. Hellawell: Factors affecting the solute distri bution during the normal freezing of lead-antimony alloys. J. Inst. Metals 90, 234 (1962)Google Scholar
  42. 6.42
    C.E. Shoemaker, R.L. Smith: “Survey of Inorganic Materials”, in Fractional Solidification, ed. by M. Zief, W.R. Wilcox ( Marcel Dekker, New York 1967 )Google Scholar
  43. 6.43
    H. Schildknecht: Zone Melting ( Verlag Chemie-Academic Press, New York 1966 )Google Scholar
  44. 6.44
    J.S. Shah: “Zone Melting and Applied Techniques”, in Crystal Growth, ed. by B.R. Pamplin ( Pergamon Press, Oxford 1975 )Google Scholar
  45. 6.45
    D. Fischer: A study on zone refining: solid-phase impurity diffusion and the influence of separating the impure end. J. Appl. Phys. 44, 1977 (1973)Google Scholar
  46. 6.46
    V.Ya. Khaimov-Malk’ov: Distribution of volatile impurities in various methods of crystallization from melts: KI-T1I system. J. Crystal Growth 35, 302 (1976)Google Scholar
  47. 6.
    W.R. Wilcox: “Heat Transfer in Fractional Solidification”, in [6.38]Google Scholar
  48. 6.48
    K.M. Kim, A.F. Witt, H.C. Gatos: Segregation behavior in a stationary vertical zone with converging interfaces: pressure induced segregation effects. J. Electrochem. Soc. 121, 448 (1974)Google Scholar
  49. 6.49
    F. Rosenberger: Preparation of alkali halide single crystals of highest purity by zone refining. Mat. Res. Bull. 1, 123 (1966)Google Scholar
  50. 6.50
    F. Rosenberger: “Preparation of ultrapure alkali halide single crystals”, in Crystal Growth, ed. by H.S. Peiser ( Pergamon Press, Oxford 1966 ) p. 141Google Scholar
  51. 6.51
    K.-Th. Wilke: Methoden der KristalZzüchtung ( VEB Deutscher Verlag der Wissenschaften, Berlin 1963 )Google Scholar
  52. 6.52
    A.Z. Knittel: Vapour growth of crystals with a steady state source. J. Crystal Growth 26, 33 (1974)Google Scholar
  53. 6.53
    S.V. Airapetyants, G.I. Shmelev: Method for growing uniform monocrys-tals of alloyed semiconductor materials, solid solutions, and inter-metallic compounds of a given composition determined by the composition of the melt. Sov. Phys. Solid State 2, 689 (1960)Google Scholar
  54. 6.54
    E.N. Da C. Andrade, R. Roscoe: Glide in metal single crystals. Proc. Phys. Soc. (London) 49, 152 (1973)Google Scholar
  55. 6.55
    L.G. Van Uitert, W.A. Bonner, W.H. Grodkiewicz, L. Pitroski, G.J. Zydzik: Garnets for bubble domain devices. Mat. Res. Bull. 5, 825 (1970)Google Scholar
  56. 6.56
    J.R. Carruthers and A.F. Witt: “Transient Segregation Effects in Czochralski Growth”, in Crystal Growth and Characterization, Proceedings of the ISSCG2 Springschool, Japan, 1974, ed. by R. Ueda, J.B. Mullin (North-Holland, Amsterdam 1975 )Google Scholar
  57. 6.57
    K.M. Kim, A.F. Witt, H.C. Gatos: Crystal growth from the melt under destabilizing thermal gradients. J. Electrochem. Soc. 119, 1218 (1972)Google Scholar
  58. 6.58
    A.F. Witt, M. Lichtensteiger, H.C. Gatos: Experimental approach to the quantitative determination of dopant segregation during crystal growth on a microscale: Ga doped Ge. J. Electrochem. Soc. 120, 1119 (1973)Google Scholar
  59. 6.59
    J.T. Yue, F.W. Volt: Influence of gravity-free solidification on solute microsegregation. J. Crystal Growth 29, 329 (1975)Google Scholar
  60. 6.60
    J.T. Yue, private communication (1976)Google Scholar
  61. 6.61
    H. Beleites, F. Fröhlich: Autoradiographic investigation on the incorporation of Ca ions in KC1 crystals during Kyropoulos growth. Kristall and Technik 12, 1329 (1972)Google Scholar
  62. 6.62
    J.-Y. Boniort, C. Brehm, G. Desplanches, J.-Y. Barraud, P. Margotin: Crystal growth of strontium barium niobate BaxSrl_xNb206. J. Crystal Growth 30, 357 (1975)Google Scholar
  63. 6.63
    R.L. Barns: A survey of precision lattice parameter measurements as a tool for the characterization of single-crystal materials. Mat. Res. Bull. 2, 273 (1967)Google Scholar
  64. 6.64
    A.B. Chase, W.R. Wilcox: Temperature fluctuations and striations in flux crystal growth. J. Am. Ceram. Soc. 50, 332 (1967)Google Scholar
  65. 6.65
    B.M. Wanklyn: “Practical Aspects of Flux Growth by Spontaneous Nucleation”, in Crystal Growth, ed. by B.R. Pamplin ( Pergamon Press, Oxford 1975 )Google Scholar
  66. 6.66
    A.A. Chernov, V.E. Khadzhi: Trapping of colloidal inclusions in the growth of quartz crystals. J. Crystal Growth 3, 4, 641 (1968)Google Scholar
  67. 6.67
    B.J. Curtis, J.P. Dismukes: Effects of natural and forced convection in vapor phase growth systems. J. Crystal Growth 17, 128 (1972)Google Scholar
  68. 6.68
    J.P. Dismuskes, B.J. Curtis: in Semiconductor Silicon, ed. by H.R. Huff, R.R. Burgess ( The Electrochemical Society, Princeton, N J 1973 ) p. 258Google Scholar
  69. 6.69
    J.C. Marinace: Epitaxial vapor growth of Ge single crystals in a closed-cycle process, IBM J. Res. Develop. 4, 248 (1960)Google Scholar
  70. 6.70
    A. Meyer: Gastransport und Charakterisierung von Einkristallen aus CdCr2S4, FeCr2S4 und Cdl_xFexCr2S4. Paper at DGKK Meeting, Freiburg (1972)Google Scholar
  71. 6.71
    E. Fitzer: Dynamische Instabilitäten bei heterogenen Gas/FeststoffReaktionen. Chemie-Ing.-Tech. 41, 331 (1969)Google Scholar
  72. 6.72
    W. Fritz: Oscillations during hot wall pyrolysis. High Temp. - High Press. 2, 291 (1970)Google Scholar
  73. 6.73
    W.G. Pfann, K.E. Benson, J.H. Wernick: Some aspects of Peltier heating at liquid-solid interfaces in germanium. J. Electronics 2, 597 (1957)Google Scholar
  74. 6.74
    H. Bethge, F. Fröhlich: Über die bei der Kristallzüchtung nach dem Nacken-Kyropoulos-Verfahren auftretenden Wachstumsformen und die Herstellung von Alkalihalogenid-Bikristallen. phys. stat. sol. 3, 55 (1963)Google Scholar
  75. 6.75
    M. Kumagawa, A.F. Witt, M. Lichtensteiger, F.C. Gatos: Current-controlled growth and dopant modulation in liquid phase epitaxy. J. Electrochem.Soc. 12n, 583 (1973)Google Scholar
  76. 6.76
    D.J. Lawrence, L.F. Eastman: Electric current controlled growth and doping modulation in GaAs liquid phase epitaxy. J. Crystal Growth 30, 267 (1975)Google Scholar
  77. 6.77
    A. Räuber: Doping modulation by electric currents in lithium niobate during crystal growth. Mat. Res. Bull. 11, 497 (1976)Google Scholar
  78. 6.78
    J.P.M. Damen, J.M. Robertson: Induced non-periodic growth striations in flux-grown magnetic oxide single crystals. J. Crystal Growth 16, 50 (1972)Google Scholar
  79. 6.79
    L. Malicskô, L. Jeszensky: Ober den Einbau von Zusätzen in KC1 Einkristalle bei der Züchtung aus Blei-und Zinnhaltigen Wässrigen Lösungen. J. Crystal Growth 7, 13 (1970)Google Scholar
  80. 6.80
    G.A. Andreev: Distribution of Impurities in Crystallization of NaC1,KC1 and KBr from Aqueous Solutions. Sov. Phys. Cryst. 12, 82 (1967)Google Scholar
  81. 6.81
    V.G. Smith, W.A. Tiller, J.W. Rutter: A mathematical analysis of solute redistribution during solidification. Can. J. Physics 33, 723 (1955)Google Scholar
  82. 6.82
    W.R. Wilcox: Incomplete liquid mixing in crystal growth from the melt. J. Appl. Phys. 35, 636 (1964)Google Scholar
  83. 6.83
    D.T.J. Hurle, E. Jakeman, E.R. Pike: Striated solute distributions produced by temperature oscillations during crystal growth from the melt. J. Crystal Growth 3, 4, 633 (1968)Google Scholar
  84. 6.84
    J.R. Carruthers: Solute incorporation during cyclic solidification of silicon. Can. Met. Quart. 5, 55 (1966)Google Scholar
  85. 6.85
    W.P. Slichter, J.A. Burton: “The Distribution of Solute Elements: Transient Conditions”, in Transistor Technology,ed. by H.E. Bridgers,J.H. Scaff, J.N. Shive (Van Nbstrand, Princeton NJ 1958) Chap. 6Google Scholar
  86. 6.86
    K.J. Berg, F. Fröhlich, M. Schmuntzsch: Berechnung der Verteilungs-funktion für einen periodisch veränderlichen Verteilungskoeffizienten beim Kristallwachstum nach dem Kyropoulos-Verfahren. Kristall and Technik 9, 1349 (1974)Google Scholar
  87. 6.87
    D.T.J. Hurle, E. Jakeman: Effects of fluctuations on the measurement of distribution coefficients by directional solidification. J. Crystal Growth 5, 227 (1969)Google Scholar
  88. 6.88
    J.R. Carruthers: “Crystal Growth from the Melt”, in Treatise on Solid State Chemistry,ed. by N.B. Hannay, Vol. 5 (Plenum Press, New York 1975) Chap. 7Google Scholar
  89. 6.89
    D.T.J. Hurle: “Melt Growth”, in Crystal Growth, ed. by P. Hartmann ( North-Holland, Amsterdam 1973 )Google Scholar
  90. 6.90
    J.B. Mullin, K.F. Hulme: Orientation-dependent distribution coeffi-cients in melt-grown InSb crystals. J. Phys. Chem. Solids 17, 1 (1960)Google Scholar
  91. 6.91
    J.A.M. Dikhoff: Gross-sectional resistivity variations in germanium single crystals. Solid State Electron. 1, 202 (1960)Google Scholar
  92. 6.92
    A.F. Witt, H.C. Gatos: Impurity striations in InSb as revealed by interference contrast microscopy. J. Electrochem. Soc. 113, 808 (1966)Google Scholar
  93. 6.93
    K. Morizane, A.F. Witt, H.C. Gatos: Growth characteristics and impuri-ty incorporation during facet growth. J. Electrochem. Soc. 115, 747 (1968)Google Scholar
  94. 6.94
    R. Singh, A.F. Witt, H.C. Gatos: Application of the Peltier effect for the determination of crystal growth rates. J. Electrochem. Soc. 115, 112 (1968)Google Scholar
  95. 6.95
    R.N. Hall: Segregation of impurities during the growth of germanium and silicon crystals. J. Phys. Chem. 57, 836 (1953)Google Scholar
  96. 6.96
    A. Trainor, B.E. Bartlett: A possible mechanism of crystal growth from the melt and its application to the problem of anomalous segregation at crystal facets. Solid State Electron. 2, 106 (1961)Google Scholar
  97. 6.97
    P.J. Holmes: A competitive adsorption model of steady state growth of a crystal from a lightly-doped melt. J. Phys. Chem. Solids 24, 1239 (1963)Google Scholar
  98. 6.98
    A.A. Chernov: “Excess Impurity Trapping During Crystal Growth”, in Growth of Crystals (Rost Kristallov), ed. by A.V. Shubnikov, N.N. Sheftal, Vol. 3 ( Consultants Bureau, New York 1962 ) p. 35Google Scholar
  99. 6.99
    J.C. Brice, P.A.C. Whiffin: The temperature distribution in pulled ger-manium crystals during growth. Solid State Electron. 7, 183 (1964)Google Scholar
  100. 6.100
    T. Abe: The growth of Si single crystals from the melt and impurity incorporation mechanisms. J. Crystal Growth 24 /25, 463 (1974)Google Scholar
  101. 6.101
    H.C. Gatos, M.C. Lavine: Characteristics of the fill surfaces of the III-V intermetallic compounds. J. Electrochem. Soc. 107, 427 (1960)Google Scholar
  102. 6.102
    E.V. Skudnova, M.S. Mirgalovskaya: Partition coefficient of sulfur in indium antimonide. Inorg. Materials 1, 165 (1965)Google Scholar
  103. 6.103
    H. Beneking, W. Vits: Proc. 2nd Int. Symp. on Gallium Arsenide, Inst. Phys. Soc. Conf. Ser. No. 7, 96–100Google Scholar
  104. 6.104
    A.F. Witt, M. Lichtensteiger, H.C. Gatos: Application of interface demarcation to the study of facet growth and segregation: germanium. J. Electrochem. Soc. 121, 787 (1974)Google Scholar
  105. 6.105
    R.N. Hall: p-n junctions produced by growth rate variation. Phys. Rev. 88, 139 (1952)Google Scholar
  106. 6.106
    G.F. Dobrzhanskii, 0.L. Kreinin, L.E. Nikolaeva, K.M. Rozin, M.P. Shaskol’skaya: Anisotropy of impurity introduction into CsBr single crystals. Sov. Phys.-Crystallogr. 16, 581 (1962)Google Scholar
  107. 6.107
    J.A. Spittle, M.D. Hunt, R.W. Smith: Orientation dependence of the partition coefficient in zinc-base alloy single crystals. J. Crystal Growth 3, 4, 647 (1968)Google Scholar
  108. 6.108
    A.A. Kralina, \i.A. Sazonova: The influence of orientation of growth directions on the impurity distribution in nickel single crystals and on their substructure. Sov. Phys. Cryst. 22, #4 (1977)Google Scholar
  109. 6.109
    A.F. Witt, H.C. Gatos: Homogeneous impurity incorporation during crys- tal growth from the melt. J. Electrochem. Soc. 116, 511 (1969)Google Scholar
  110. 6.110
    F.V. Williams: The effect of orientation on the electrical properties of epitaxial gallium arsenide. J. Electrochem. Soc. 111, 886 (1964)Google Scholar
  111. 6.111
    L. Malicskb, L. Jeszensky: Investigations on inhomogeneous impurity distribution caused by growth centers. J. Crystal Growth 15, 243 (1972)Google Scholar
  112. 6.112
    W. Kleber: Ober den Einlagerungsmechanismus bei Adsorptionsmischkristallen, Z. Phys. Chemie 212, 222 (1959)Google Scholar
  113. 6.113
    U. Steinike: Zur Bildung von Adsorptionsmischkristallen. Kristall und Technik, 6, 7 (1971)Google Scholar
  114. 6.114
    M.M. Lukina, L.A. Chernyaev: Intake of iron in hydrothermal zincite crystals. Sov. Phys. Cryst. 13, 979 (1969)Google Scholar

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© Springer-Verlag Berlin Heidelberg 1979

Authors and Affiliations

  1. 1.Department of Physics and Department of Materials Science and EngineeringUniversity of UtahSalt Lake CityUSA

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