In Volumes 1 and 2 of this treatise detailed accounts have been given of the various types of defects that occur in solids. We are particularly concerned in this chapter with the point defects because it is to their mobility that the phenomenon of diffusion in solids is largely due. The most important of the point defects in this connection are vacancies and interstitials and more complex types derived from these, such as divacancies, split interstitials, etc. By processes of thermal activation, vacancies can migrate by exchanging places with neighboring atoms or ions. Similarly, interstitial atoms can migrate by moving from one interstitial site to another interstitial site. Alternatively, they can migrate by the interstitialcy mechanism whereby an interstitial atom moves onto a neighboring lattice site and displaces the atom on that site into another interstitial position. The net result of defect mobility, whether of vacancies or interstitials, is that the atoms of a solid are in a state of continual migration from site to site throughout the crystal. It follows that when there are variations in composition within a solid a relative mass transport can occur of the different types of atoms present which tends to level out these variations, and it is this process that we call “diffusion.”


Isotope Effect Ionic Crystal Chemical Diffusion Impurity Diffusion Jump Frequency 
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  1. 1.
    R. M. Barrer, Diffusion in and through Solids, MacMillan (1951).Google Scholar
  2. 2.
    W. Seith, Diffusion in Metallen, Springer Verlag, Berlin (1955).Google Scholar
  3. 3.
    W. Jost, Diffusion in Solids, Liquids and Gases, Academic Press, New York (1960).Google Scholar
  4. 4.
    P. G. Shewmon, Diffusion in Solids, McGraw-Hill, New York (1963).Google Scholar
  5. 5.
    J. Crank, Mathematics of Diffusion, Oxford Univ. Press, London (1956).Google Scholar
  6. 6.
    Y. Adda and J. Philibert, La Diffusion dans les Solides, Presses Universitaires de Paris (1966).Google Scholar
  7. 7.
    S. R. de Groot and P. Mazur, Non-Equilibrium Thermodynamics, North-Holland, Amsterdam (1962).Google Scholar
  8. 8.
    J. S. Kirkaldy, Diffusion in multicomponent metallic systems, Can. J. Phys. 35, 435 (1957).CrossRefGoogle Scholar
  9. 9.
    A. D. Le Claire, Diffusion in metals, in Progress in Metal Physics, Pergamon Press, London, Vol. 1 (1949), Vol. 4 (1953).Google Scholar
  10. 10.
    D. Lazarus, Diffusion in metals, Solid State Phys. 10, 71 (1960).CrossRefGoogle Scholar
  11. 11.
    D. Lazarus, Intermetallic diffusion, in Energetics in Metallurgical Phenomena, Vol. 1, Gordon and Breach (1965).Google Scholar
  12. 12.
    N. Peterson, Diffusion in metals, Solid State Phys. 22, 409 (1968).CrossRefGoogle Scholar
  13. 13.
    R. E. Howard and A. B. Lidiard, Matter transport in solids, Rep. Progr. Phys. 27, 161 (1964).CrossRefGoogle Scholar
  14. 14.
    P. Kofstad, Nonstoichiometry, Diffusion and Electrical Conductivity in Binary Metal Oxides, Wiley, New York (1972).Google Scholar
  15. 15.
    F. A. Kröger, The Chemistry of Imperfect Crystals, North-Holland, Amsterdam (1964).Google Scholar
  16. 16..
    Atom Movements, American Society for Metals, Cleveland, Ohio (1951).Google Scholar
  17. 17.
    C. T. Tomizuka, in Methods in Experimental Physics, Academic Press, New York, (1959), Vol. 5.Google Scholar
  18. 18.
    J. S. Kirkaldy and D. G. Fedak, Nonplanar interfaces in two phase ternary diffusion couples, Trans. Met. Soc. AIME 224, 490 (1962).Google Scholar
  19. 19.
    D. K. Dawson and L. W. Barr, Measurement of anionic diffusion in KBr by isotope exchange, Proc. Brit. Ceram. Soc. 9, 171 (1967).Google Scholar
  20. 20.
    H. S. Carslaw and J. C. Yaeger, Conduction of Heat in Solids, Oxford Univ. Press, London (1957).Google Scholar
  21. 21.
    A. S. Nowick and B. S. Berry, Anelastic Relaxation in Crystalline Solids, Academic Press (1972).Google Scholar
  22. 22.
    C. A. Wert, Damping of interstitial atoms in b.c.c. metals, J. Phys. Chem. Solids 31, 1771 (1970).CrossRefGoogle Scholar
  23. 23.
    G. Schumann, J. Völkl, and G. Alefeld, Relaxation process due to long range diffusion for high diffusivities in solids, Phys. Rev. Letters 21, 891 (1968).CrossRefGoogle Scholar
  24. 24.
    A. Seeger, D. Wolf, and H. Mehrer, Analysis of tracer and nuclear magnetic resonance measurements of self-diffusion in Al, Phys. Stat. Sol. (b) 48, 481 (1971).CrossRefGoogle Scholar
  25. 25.
    D. L. Johnson, New method of obtaining volume, grain boundary and surface diffusion coefficients from sintering data, J. Appl. Phys. 40, 192 (1969).CrossRefGoogle Scholar
  26. 26..
    J. G. Mullen, Mössbauer studies of atomic transport in solids and liquids, in Ref. 75.Google Scholar
  27. 26a.
    T. Springer, Quasi-Elastic Neutron Scattering for the Investigation of Diffusive Motion in Solids and Liquids, Springer Tracts in Modern Physics, Vol. 64, Springer, New York (1972).Google Scholar
  28. 27.
    A. D. Le Claire, The analysis of grain boundary diffusion measurements, Brit. J. Appl. Phys. 14, 351 (1963).CrossRefGoogle Scholar
  29. 28.
    R. W. Balluffi, Dislocation self-diffusion in f.c.c. metals—A review, Phys. Stat. Sol. 42, 11(1970).Google Scholar
  30. 29.
    H. Gleiter and B. Chalmers, High angle grain boundaries, in Progress in Materials Science, Vol. 16, Pergamon Press (1972), Chapter 4.Google Scholar
  31. 30.
    E. W. Hart, On the role of dislocations in bulk diffusion, Acta Met. 5, 597 (1957).CrossRefGoogle Scholar
  32. 30a.
    A. J. Mortlock, The effect of segregation on the solute diffusion enhancement due to the presence of dislocations, Acta Met. 8, 132 (1960).CrossRefGoogle Scholar
  33. 31.
    G. Neumann and G. M. Neumann, Surface Self-Diffusion of Metals, Trans. Tech. Publ., Ohio (1972).Google Scholar
  34. 32.
    J. M. Blakeley, Surface Diffusion, Progr. in Materials Science, Vol. 10, Pergamon Press (1963).Google Scholar
  35. 33.
    L. S. Darken, Diffusion of carbon in austenite with a discontinuity in composition, Trans. AIME 180, 430 (1949).Google Scholar
  36. 34.
    J. E. Reynolds, B. L. Averbach, and M. Cohen, Self-diffusion and interdiffusion in AuNi Alloys, Acta Met. 5, 29 (1957);CrossRefGoogle Scholar
  37. 34a.
    J. R. Manning, Tracer diffusion in a chemical concentration gradient in AgCd, Phys. Rev. 116, 69 (1959).CrossRefGoogle Scholar
  38. 35.
    J. R. Manning, Diffusion Kinetics in Crystals, Van Nostrand (1968).Google Scholar
  39. 36.
    J. R. Manning, Vacancy wind effect in diffusion and deviation from thermodynamic equilibrium conditions, Can. J. Phys. 46, 2633 (1968).CrossRefGoogle Scholar
  40. 37.
    R. O. Meyer, Phys. Rev. 181, 1086 (1969);CrossRefGoogle Scholar
  41. 37a.
    M. H. Greene et al., Phys. Stat. Sol 5(a), 365 (1971);CrossRefGoogle Scholar
  42. 37b.
    M. J. Dallwitz, Acta Met. 20, 1229 (1972).CrossRefGoogle Scholar
  43. 38.
    D. J. Schmatz, H. A. Damian, and H. I. Aaronson, J. Appl. Phys. 37, 1741 (1966).CrossRefGoogle Scholar
  44. 39.
    A. Kohn et al., Acta Met. 18, 163 (1970).CrossRefGoogle Scholar
  45. 40.
    A. D. Le Claire, Correlation effects in diffusion in solids, in Physical Chemistry, Vol. X, Academic Press, New York and London (1970), Chapter 5.Google Scholar
  46. 41.
    M. J. Jones and A. D. Le Claire, Solvent self-diffusion in dilute b.c.c. solid solutions, Phil. Mag. 26, 1191(1972).CrossRefGoogle Scholar
  47. 42.
    A. B. Lidiard, Ionic conductivity in Handbuch der Physik, Vol. XX, Springer Verlag, Berlin (1957).Google Scholar
  48. 43.
    W. Van Gool (ed.), Fast Ion Transport in Solids, North-Holland, Amsterdam (1973).Google Scholar
  49. 44.
    L. W. Barr and A. B. Lidiard, Defects in ionic crystals, in Physical Chemistry, Vol. X, Academic Press, New York and London (1970), Chapter 7.Google Scholar
  50. 45.
    J. Hladik (ed.), Physics of Electrolytes, Vol. 1, Transport Processes in Solid Electrolytes and Electrodes, Academic Press, New York and London (1972).Google Scholar
  51. 46.
    M. D. Weber and R. J. Friauf, Interstitialcy motion in the silver halides, J. Phys. Chem. Solids 30, 407 (1969).CrossRefGoogle Scholar
  52. 47.
    C. P. Flynn, Point Defects and Diffusion, Clarendon Press, Oxford (1972).Google Scholar
  53. 48.
    G. H. Vineyard, Frequency factors and isotope effects in solid state rate processes, J. Phys. Chem. Solids 3, 121 (1957).CrossRefGoogle Scholar
  54. 49.
    S. A. Rice, Dynamical theory of diffusion in crystals, Phys. Rev. 112, 804 (1958).CrossRefGoogle Scholar
  55. 50.
    C. A. Wert, Diffusion coefficient of C in Fe, Phys. Rev. 79, 601 (1950).CrossRefGoogle Scholar
  56. 51.
    M. D. Feit, Some formal aspects of a dynamical theory of diffusion, Phys. Rev. 133, 1223 (1971).Google Scholar
  57. 52.
    M. D. Feit, Dynamical theory of diffusion. II. Comparison with rate theory and the impurity isotope effect, Phys. Rev. B 5, 2145 (1972).CrossRefGoogle Scholar
  58. 53.
    C. P. Flynn and M. Stoneham, Quantum theory of diffusion with applications to light interstitials in metals, Phys. Rev. 131, 3966 (1970).Google Scholar
  59. 54.
    J. N. Sherwood (ed.), Diffusion processes, Gordon and Breach, London (1971).Google Scholar
  60. 55.
    A. P. Batra, Anisotropic isotopic effect for diffusion of Zn and Cd in Zn, Phys. Rev. 159, 487 (1967).CrossRefGoogle Scholar
  61. 56.
    N. L. Peterson, L. W. Barr, and A. D. Le Claire, Isotope effect for Ag diffusion in AgBr and AgCl, J. Physics C 6, 2020 (1973).CrossRefGoogle Scholar
  62. 57.
    S. J. Rothman et al., Temperature dependence of the isotope effect for diffusion of Na in NaCl, J. Phys. Chem. Solids 33, 1061 (1972).CrossRefGoogle Scholar
  63. 58.
    W. K. Cheo, N. L. Peterson, and W. T. Reeves, Isotope effect for cation self-diffusion in CoO crystals, Phys. Rev. 186, 887 (1969).CrossRefGoogle Scholar
  64. 59.
    M. L. Volpe, N. L. Peterson, and J. Reddy, Isotope effect for cation self-diffusion in single crystals of NiO, Phys. Rev. B 3, 1417 (1971).CrossRefGoogle Scholar
  65. 60.
    J. N. Mundy, Effect of pressure on the isotope effect in sodium self-diffusion, Phys. Rev. 133, 2431 (1971).Google Scholar
  66. 61.
    S. J. Rothman, N. L. Peterson, and J. T. Robinson, Isotope effect for self-diffusion in single crystals of Ag, Phys. Stat. Sol. 39, 635 (1970).CrossRefGoogle Scholar
  67. 62.
    H. B. Huntington, M. D. Feit, and D. Lortz, Dynamic studies of vacancy motion, Crystal Lattice Defects 1, 193 (1970).Google Scholar
  68. 63.
    B. N. Narabari Achar, Lattice dynamical theory of the diffusion process. I. Isotope effect in cubic metals, Phys. Rev. 132, 3848 (1970).Google Scholar
  69. 64.
    H. I. Aaronson (ed.), Diffusion, American Society of Metals, Ohio (1974).Google Scholar
  70. 65.
    A. S. Nowick and J. J. Burton (eds.), Diffusion in Solids. Recent Developments, Academic Press, New York (1974).Google Scholar
  71. 66.
    A Seeger et al. (eds.), Vacancies and Interstitials in Metals, North-Holland, Amsterdam (1970).Google Scholar
  72. 67.
    D. Lazarus and N. H. Nachtrieb, in Solids Under Pressure, McGraw-Hill, New York (1963).Google Scholar
  73. 68.
    C. Smithells (ed.), Metals Reference Book, Butterworths, London, 4th ed., Vol. 2 (1967); 5th ed. (1974).Google Scholar
  74. 69.
    P. J. Harrop, Self-diffusion data in simple oxides, J. Mat. Sci. 3, 206 (1968).CrossRefGoogle Scholar
  75. 70.
    B. L. Sharma, Diffusion in Semiconductors, Trans. Tech. Publications, Cleveland, Ohio (1970).Google Scholar
  76. 71.
    D. Shaw (ed.), Atomic Diffusion in Semiconductors, Plenum Press, London and New York (1973).Google Scholar
  77. 72.
    P. Suptitz and J. Teltow, Transport of matter in simple ionic crystals (cubic halides), Phys. Stat. Sol. 23, 9 (1967).CrossRefGoogle Scholar
  78. 73.
    F. H. Wöhlbier, Diffusion Data (1967–1973) (quarterly); now Diffusion and Defect Data (1974) (Trans. Tech. Publications, Cleveland, Ohio).Google Scholar
  79. 74..
    Diffusion in bcc Metals, American Society for Metals, Cleveland, Ohio (1965).Google Scholar
  80. 75.
    A. Lodding and T. Lagerwall (eds.), Atom Transport in solids and liquids, Verlag Z. Naturforsch. Tubingen, Germany (1971).Google Scholar

Copyright information

© Bell Telephone Laboratories, Incorporated 1976

Authors and Affiliations

  • A. D. Le Claire
    • 1
  1. 1.Atomic Energy Research EstablishmentHarwellEngland

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