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Isotopes in Condensed Matter pp 151–206Cite as

Effects Related to Isotopic Disorder in Solids

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Part of the book series: Springer Series in Materials Science ((SSMATERIALS,volume 162))

Abstract

Interest in diffusion is as old as metallurgy or ceramics. The first measurement of diffusion in the solid state was made by Roberts-Austen [1]. Many measurements, especially of chemical diffusion in metals, were made in the 1930s; the field was reviewed by Jost [2] and Seith [3]. Diffusion research increased after World War II; the increase was motivated by the connection among diffusion, defects and radiation damage and helped by the availability of many artificial radiotracers. These researchers were the first to attempt to identify the basic underlying atomistics mechanisms responsible for mass transport through solids by a quantitative investigations and theoretical analysis of the activation energies required for diffusion by exchange, interstitial and vacancy mechanisms in solids. Prior to this time, there had been little concern with treating diffusional phenomena on a microscopic basis, and most research was concerned with fairly crude observation of overall bulk transfer processes at junctions between regions with strong compositional differences. It was at this time that suggestions on how to carry out high precision, highly reproducible diffusion experiments were first put forward [4, 5].

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References

  1. W.C. Roberts-Austen, Bakerian Lecture: On the diffusion of metals, Philos Trans. Royal. Soc. (London) A 187, 383–415, (1896)

    Google Scholar 

  2. W. Jost, Diffusion in Solids, Liquids, Gas (Academic Press, New York, 1952)

    Google Scholar 

  3. W. Seith, Diffusion in Metallen (Springer, Berlin, 1954)

    Google Scholar 

  4. L. Slifkin, D. Lazarus, C.T. Tomisuka, Self-diffusion in pure polycrystalline silver. J. Appl. Phys. 23, 1032–1034 (1952)

    Article  CAS  Google Scholar 

  5. C.T. Tomizuka, in Diffusion Methods of Experimental Physics, ed. by K. Lark-Horrowitz, V.A. Johnson, vol. 6, Part A (Academic Press, New York, 1959), pp. 364–413

    Google Scholar 

  6. N.F. Mott, R.F. Gurney, Electronic Processes in Ionic Crystals (Clarendon Press, Oxford, 1948)

    Google Scholar 

  7. J.H. Crawford Jr., L.M. Slifkin (eds.), Point Defects in Solids, vol. 1–2 (Plenum Press, London, 1975)

    Google Scholar 

  8. A.S. Nowick, J.J. Burton (eds.), Diffusion in Solids: Recent Developments (Academic Press, New York, 1975)

    Google Scholar 

  9. G.E. Murch, A.S. Nowick (eds.), Diffusion in Crystalline Solids (Academic Press, New York, 1984)

    Google Scholar 

  10. H. Mehrer, in Diffusion in Solids, Fundamentals Methods, Materials, Diffusion-Controlled Processes, vol. 155 (Springer, Berlin, 2007)

    Google Scholar 

  11. P. Heitjans, J. Kärger (eds.), Diffusion in Condensed Matter Methods Materials, Models (Springer, Berlin, 2008)

    Google Scholar 

  12. V.G. Plekhanov, Applications of isotope effect in solids. J. Mater. Sci. 38, 3341–3429 (2003)

    Article  CAS  Google Scholar 

  13. J.R. Manning, Diffusion of Atoms in Crystals (Princeton, New Jersey, 1968)

    Google Scholar 

  14. J. Crank, The Mathematics of Diffusion (Oxford University Press, New York, 1975)

    Google Scholar 

  15. D. Wolf, Spin Temperature and Nuclear-Spin Relaxation in Matter: Basic Principles and Applications (Oxford University Press, New York, 1979)

    Google Scholar 

  16. V.G. Plekhanov, Applications of Isotopic Effects in Solids (Springer-Verlag, Berlin, 2004)

    Book  Google Scholar 

  17. H.S. Carslaw, C. Jaeger, Conduction Heat in Solids (Oxford University Press, New York, 1959)

    Google Scholar 

  18. S.J. Rothman, The measurement of tracer diffusion coefficients in solids, in [9], chap. 1, p. 1–61

    Google Scholar 

  19. N.L. Pterson, W.K. Chen, Cation self-diffusion and the isotope effect in \({\rm Mn}_{\delta } {\rm O}\), in [8], Chap. 2, pp. 115–157. J. Phys. Chem. Solids 43, 29–38 (1982)

    Google Scholar 

  20. W. Frank, U. Gösele, H. Mehrer et al., Diffusion in silicon and germanium, in [9], Chap. 2, pp. 63–141

    Google Scholar 

  21. D.E. Aboltyn, Ya.E. Karis, V.G. Plekhanov, Experimental manifestation of the role of phonons in the formation and motion of point defects in alkali halide crystals. Sov. Phys. Solid State 22, 510–511 (1980)

    Google Scholar 

  22. A. Seager, K.P. Chik, Diffusion mechanisms and point defects in silicon and germanium. Phys. Stat. Solidi 29, 455–542 (1068)

    Article  Google Scholar 

  23. R.N. Ghashtagor, diffusion in tellurium. I. Anisotropy and impurity effects. Phys. Rev. 155, 598–602 (1967)

    Article  Google Scholar 

  24. M. Werner, H. Mehrer, H. Siethoft, Self-diffusion and antimony diffusion in tellurium, J. Phys. C: Solid State Phys. 16, 6185–6197 (1983)

    Google Scholar 

  25. P. Bratter, H. Gobrecht, Self-diffusion in selenium. Phys. Status Solidi 37, 869–878 (1970)

    Article  Google Scholar 

  26. D.M. Holloway, Applications of depth profiling by Auger sputter techniques. J. Vac. Sci. Technol. 12, 392–399 (1975)

    Article  CAS  Google Scholar 

  27. J.W. Mayer, J.M. Poate, in Thin Film Interdiffusion and Reactions, ed. by N.B. Urli, J.B. Corbett (Springer, Berlin, 1981)

    Google Scholar 

  28. R. Behrisch, Introduction and overview in Sputtering by Particle Bombardment, II, ed. by R. Behrisch (Springer, Berlin, 1981), Chap. 1, pp. 1–10

    Google Scholar 

  29. B. Chapman, Glow Dicharge Processes (Wiley, New York, 1980)

    Google Scholar 

  30. R.D. Reader, H.R. Kauffman, Optimization of an electron-bombardmention source for ion machining. J. Vac. Sci. Technol. 12, 1344–1347 (1975)

    Article  Google Scholar 

  31. J.N. Mundy, S.J. Rothman, An apparatus for microsectioning diffusion samples by sputtering, Ibid, A 1, 74–78 (1983)

    Google Scholar 

  32. D. Gupta, R.R.C. Tsui, A universal microsectioning technique for diffusion. Appl. hys. Lett. 17, 294–297 (1970)

    Article  CAS  Google Scholar 

  33. H. Liebl, Secondary-ion mass spectrometry and its use in depth profiling. J. Vac. Sci. Technol. 12, 385–399 (1975)

    Article  CAS  Google Scholar 

  34. W. Reuter, J.E.E. Baglin, Secondary-ion mass spectrometry and Rutherford backscattering spectroscopy for the analysis of thin films, Ibid, 18, 282–288 (1981)

    Google Scholar 

  35. M.-P. Macht, V. Naundorf, Direct measurement of small diffusion coefficients with secondary mass spectroscopy, J. Appl. Phys. 53, 7551–7558 (1982)

    Google Scholar 

  36. G.J. Slusser, J.S. Slattery, Secondary-ion mass spectrometry analysis of semiconductor layers. J. Vac. Sci. Technol. 18, 301–304 (1981)

    Article  CAS  Google Scholar 

  37. D.S. Catlett, J.N. Spencer, G.J. Vogt, Hydrogen transport in lithium hydride as a function of pressure. J. Chem. Phys. 58, 3432–3438 (1973)

    Article  CAS  Google Scholar 

  38. J.N. Spencer, D.S. Catlett, G.J. Vogt, Hydrogen transport in lithium hydrides a function of temperature, Ibid, 59, 1314–1318 (1973)

    Google Scholar 

  39. V.B. Ptashnik, TYu. Dunaeva, Self-diffusion of lithium and hydrogen ions in lithium hydride single crystals. Fiz. Tverd. Tela 19, 1643–1647 (1977)

    CAS  Google Scholar 

  40. Yu.M. Baikov, V.B. Ptashnik, T.Yu. Dunaeva, Influence of isotope composition of hydrogen on the electric conductivity of solid lithium hydride, Fiz. Tverd. Tela. 20, 1244–1246 (1978) (in Russian)

    Google Scholar 

  41. T.A. Dellin, G.J. Dienes, C.R. Rischer et al., Low-temperature volume expansion of LiH-LiT. Phys. Rev. B 1, 1745–1753 (1970)

    Article  Google Scholar 

  42. F.E. Pretzel, D.T. Vier, E.G. Szklarz et al., Los Alamos Sci. Lab. Rep. LA 2463 (1961) cited in [40]

    Google Scholar 

  43. H. Letaw Jr, W.M. Portnoy, L. Slifkin, Self-diffusion in germanium. Phys. Rev. 102, 636–639 (1956)

    Article  CAS  Google Scholar 

  44. M.W. Valenta, C. Ramasastry, Effect of heavy doping on the self-diffusion of germanium, Ibid, 106, 73–75 (1957)

    Google Scholar 

  45. D.R. Campbell, Isotope effect for self-diffusion in Ge, Ibid, B 12, 2318–2324 (1975)

    Google Scholar 

  46. G. Vogel, H. Hettich, H. Mehrer, Self-diffusion in intrinsic germanium and effects of doping on self-diffusion in germanium. J. Phys. C: Solid State Phys. 16, 6197–6208 (1983)

    Article  CAS  Google Scholar 

  47. A. Seeger, W. Frank, On the theory of the diffusion of gold into dislocated silicon wavers. Appl. Phys. A 27, 171–176 (1982)

    Article  Google Scholar 

  48. H.D. Fuchs, W. Walukiewicz, W. Dondl et al., Germanium \(^{70}{\rm Ge/}^{74}\) Ge isotope heterostructures: an approach to self-diffusion studies. Phys. Rev. B51, 16817–16821 (1995)

    Google Scholar 

  49. Beke D.L. (ed.), Diffusion in Semiconductors and Non-Metallic Solids, Landolt-Börnstein, New Series, Group III, vol. 33A, (Springer, Berlin, 1998)

    Google Scholar 

  50. M. Schulz (ed.), Impurities and Defects in Group IV Elements, IV–IV and III–V Compounds, Landolt-Börnstein, New Series, Group III, vol. 41A2, Part \(\alpha \), (Springer, Berlin, 2002)

    Google Scholar 

  51. M. Schulz (ed.), Impurities and Defects in Group IV Elements, IV–IV and III–V Compounds, Landolt-Börnstein, New Series, Group III, vol. 41A2, Part \(\beta \), (Springer, Berlin, 2003)

    Google Scholar 

  52. H. Bracht, N.A. Stolwijk, Solubility in Silicon and Germanium, Landolt-Börnstein, New Series, Group III, vol. 41A2, Part \(\alpha \), (Springer, Berlin, 2002)

    Google Scholar 

  53. N.A. Stolwijk, H. Bracht, Diffusion in Silicon, Germanium and Their Alloys, Landolt-Börnstein, New Series, Group III, vol. 33A (Springer, Berlin, 1998)

    Google Scholar 

  54. J. Spitzer, T. Ruf, W. Dondl et al., Raman scattering by optical phonons in isotopic \(^{70}({\rm Ge})_{n}^{74}({\rm Ge})_{n}\) superlattice. Phys. Rev. Lett. 72, 1565–1568 (1994)

    Article  CAS  Google Scholar 

  55. H.D. Fuchs, K.M. Itoh, E.E. Haller, Isotopically controlled germanium: A new medium for the study of carrier scattering by neutral impurities. Philos. Mag. B 70, 661–670 (1994)

    Article  CAS  Google Scholar 

  56. H. Bracht, H.H. Silvester, Self- and foreign-atom diffusion in semiconductor isotope heterostructures. II Experimental results for silicon, Phys. Rev. B 75, 035211/1–21, (2007)

    Google Scholar 

  57. H. Bracht, Self- and foreign-atom diffusion in semiconductor isotope heterostructures. I. Continuum theoretical calculations, Ibid, B 75, 035210/1–16, (2007)

    Google Scholar 

  58. G. Leibfried, W. Ludwig, in Theory of Anharmonic Effects in Crystals Solid State Physics, ed. by F. Seitz, D. Turnbull (Academic Press, New York, 1961) p. 275–445

    Google Scholar 

  59. N.W. Aschcroft, N. David Mermin, Solid State Physics (Harcourt Brace College Publishers, New York, 1975)

    Google Scholar 

  60. G.P. Srivastawa, The Physics of Phonons (Hilger, Bristol, 1990)

    Google Scholar 

  61. I.E. Tamm, Eine Bemerkung zur Diracschen Theorie der Lichtenstroung und Dispersion. Zs. Phys. 62, 705–708 (1930)

    Article  Google Scholar 

  62. M. Blackman, in The specific heat of solids Handbuch der Physik, ed. by S. Flüge, Vol 7, Pt. 1 (Springer-Verlag, Berlin, 1955) p. 325–367

    Google Scholar 

  63. P. Klemens, in Thermal Conductivity and Lattice Vibrational Modes Solid State Physics, ed. by F. Seitz, D. Turnbull, Vol. 7 (Academic Press, New York, 1959) p. 1–98

    Google Scholar 

  64. P. Debye, The Debye theory of specific heat, Ann. Phys. (Leipzig) 39(4) 789–803 (1912)

    Google Scholar 

  65. L.D. Landau, E.M. Lifshitz, Statistical Physics (Pergamon Press, New York, 1968)

    Google Scholar 

  66. V.G. Plekhanov, Isotope effect on the lattice dynamics of crystals. Mater. Sci.& Eng. R 35, 139–237 (2001)

    Article  Google Scholar 

  67. D.F. Gibbons, Thermal expansion of some crystals with the diamond structure. Phys. Rev. 112, 136–140 (1958)

    Article  CAS  Google Scholar 

  68. D.N. Batchelor, R.O. Simons, Lattice constants and thermal expansivities of silicon and calcium ftuoride between 6 and 322K. J. Chem. Phys. 41, 2324–2330 (1964)

    Article  Google Scholar 

  69. A.S. Okhotin, A.S. Pushkarski, V.V. Gorbachev, Thermophysical Properties of Semiconductors (Moscow (Atom Publ House, London, 1972). (in Russian)

    Google Scholar 

  70. S.I. Novikova, Thermal Expansion of Solids (Science, Moscow, 1974) (in Russian)

    Google Scholar 

  71. G. Dolling, R.A. Cowley, The thermodynamic and optical properties of germanium, silicon, diamond and gallium arsenide. Proc. Phys. Soc. 88, 463–494 (1966)

    Article  CAS  Google Scholar 

  72. V.G. Plekhanov, Elementary excitations in isotope-mixed crystals. Phys. Reports 410, 1–235 (2005)

    Article  CAS  Google Scholar 

  73. T.H. Baron, J.G. Collins, G.K. White, Thermal expansion of solids at low temperatures. Adv. Phys. 29, 609–730 (1980)

    Article  Google Scholar 

  74. V.I. Ozhogin, A.V. Inyushkin, A.N. Taldenkov, et al., Isotope effect for thermal expansion coefficient of germanium, JETP (Moscow) 115, 243–248 (1999) (in Russian)

    Google Scholar 

  75. H. Jex, Thermal expansion and mode Gruneisen parameters of LiH and LiD. J. Phys. Chem. Solids 35, 1221–1223 (1974)

    Article  CAS  Google Scholar 

  76. B.W. James, H. Kherandish, The low temperature variation of the elastic constants of LiH and LiD. J. Phys. C: Solid State Phys. 15, 6321–6339 (1982)

    Article  CAS  Google Scholar 

  77. D. Gerlich, C.S. Smith, The pressure and temperature derivatives of the elastic module of lithium hydride. J. Phys. Chem Solids 35, 1587–1592 (1974)

    Article  CAS  Google Scholar 

  78. J.J. Fontanella, D.E. Schuele, Low temperature Gruneisen parameter of RbI from elasticity data, Ibid 31, 647–654 (1970)

    Google Scholar 

  79. J.R. Hardy, A.M. Karo, The Lattice Dynamics and Statics of Alkali Halide Crystals (Plenum Press, New York, 1979)

    Book  Google Scholar 

  80. V.G. Plekhanov, Isotope-Mixed Crystals: Fundamentals and Applications, Bentham, e-books, (2011). ISBN 978-1-60805-091-8

    Google Scholar 

  81. S. Haussuhl, I. Skorczyk, Elastische und thermoelastische Eigenschaften von LiH und LiD einkristallen. Zs. Krist. 130, 340–345 (1969)

    Article  Google Scholar 

  82. A.R. Ubellohde, The Molten State of Substances (Metallurgy, Moscow, 1982) (in Russian)

    Google Scholar 

  83. G.L. Anderson, G. Nasise, K. Phillipson et al., Isotopic effects on the thermal expansion of lithium hydride. J. Phys. Chem. Solids 31, 613–618 (1970)

    Article  CAS  Google Scholar 

  84. R.B. Von Dreele, J.G. Morgan, S.M. Stishov, Thermal expansion and equation of state of KCN of different isotopic composition, JETP (Moscow) 114, 2182–2186 (1998) (in Russian)

    Google Scholar 

  85. A.P. Zhernov, Thermal expansion of germanium crystal lattice with different isotope composition, Fiz. Tverd. Tela (St. Petersburg) 40, 1829–1831 (1998)

    Google Scholar 

  86. A. P. Zhirnov, Statistical displacement about isotope impurities and remain resistance, JETP (Moscow) 114, 2153–2165 (1998) (in Russian)

    Google Scholar 

  87. I.G. Kuleev, I.I. Kuleev, Influence normal processes of phonon–phonon scattering on maximum values of thermal conductivity isotope pure Si crystal, JETP (Moscow) 122, 558–569 (2002) (in Russian)

    Google Scholar 

  88. V.I. Tyutyunnik, Effect of isotope substitution on thermal expansion of LiH crystal. Phys. Status Solidi (b) 172, 539–543 (1992)

    Article  CAS  Google Scholar 

  89. V.S. Kogan, Isotope effect in structuring properties. Sov. Phys. Uspekhi 5, 579–618 (1963)

    Article  Google Scholar 

  90. M. Planck, Zur Theorie der Wämestrahlung. Ann Phys. 336, 758–768 (1910)

    Article  Google Scholar 

  91. Ch. Kittel, Thermal Physics (Wiley, New York, 1969)

    Google Scholar 

  92. M. Born, K. Huang, Dynamical Theory of Crystal Lattice (Oxford University Press, Oxford, 1988)

    Google Scholar 

  93. V.G. Plekhanov, Isotope effect in lattice dynamics, Physics-Uspekhi (Moscow) 46, 689–717 (2003); Lattice dynamics of isotope-mixed crystals, ArXiv:cond-mat/1007.5125

    Google Scholar 

  94. P. Günter, Ann. Phys. 63, 476 (1920) cited in [97]

    Google Scholar 

  95. V.N. Kostryukov, The capacity of LiH between 3.7 and 295K, Zh. Fiz. Khim. (Moscow) 35, 1759–1762 (1961) (in Russian)

    Google Scholar 

  96. V.G. Plekhanov, Lattice dynamics of isotopically mixed crystals, Opt. Spectr. (St. Petersburg) 82, 95–124 (1997)

    Google Scholar 

  97. G. Yates, G.H. Wostenholm, J.K. Bingham, The specific heat of \(^{7}{\rm LiH} {\rm and} ^{7}{\rm LiD}\) at low temperature. J. Phys. C: Solid state Phys. 7, 1769–1778 (1974)

    Article  CAS  Google Scholar 

  98. M.W. Guinan, C.F. Cline, Room temperature elastic constants of \(^{7}{\rm LiH} {\rm and} ^{7}{\rm LiD}\). J. Nonmetals 1, 11–15 (1972)

    CAS  Google Scholar 

  99. D.P. Schumacher, Polymorphies transition of LiH. Phys. Rev. 126, 1679–1684 (1962)

    Article  CAS  Google Scholar 

  100. K.-F. Berggren, A pseudopotential approach to crystalline lithium hydride, J. Phys. C: Solid State Phys. 2, 802–815 (1969)

    Google Scholar 

  101. F.F. Voronov, V.A. Goncharov, Compressions of lithium hydride, Fiz. Tverd. Tela (St. Petersburg) 8, 1643–1645 (1966) (in Russian)

    Google Scholar 

  102. D.R. Stephens, E.M. Lilley, Compressions of isotopes lithium hydride. J. Appl. Phys. 39, 177–180 (1968)

    Article  CAS  Google Scholar 

  103. Q. Johnson, A.C. Mitchel, Search for the NaCl and CsCl transition in LiH by flash X-ray diffraction. Acta Cryst. A31, S241–S245 (1975)

    Google Scholar 

  104. Y. Kondo, K.J. Asaumi, Effect of pressure on the direct gap of LiH. J. Phys. Soc. Japan 57, 367–371 (1988)

    Article  CAS  Google Scholar 

  105. K. Chandehari, A. Ruoff, Band gap and index refraction of CsH to 25 GPa. Solid State Commun. 95, 385–388 (1995)

    Article  Google Scholar 

  106. W. Schnelle, E. Gmelin, Heat capacity of germanium crystals with different isotopic composition. J. Phys: Condens. Matter 13, 6087–6094 (2001)

    Article  CAS  Google Scholar 

  107. M. Sanati, S.K. Estreicher, Specific heat and entropy of GaN, Ibid 16, L327–L331 (2004)

    Google Scholar 

  108. U. Piestergen, in Heat capacity and Debye temperature Semiconductors and Semimetals, ed. by R.K. Willardson, A.C. Beer, Vol. 2 (Academic Press, New York, 1966) p. 49–62

    Google Scholar 

  109. G. London, The difference in molecular volume of isotopes. Z. Phys. Chem. Neue Folge 16, 3021–3029 (1958)

    Article  Google Scholar 

  110. A.R. Ruffa, Thermal expansion and zero-point displacement in isotopic lithium hydride. Phys. Rev. B 27, 1321–1325 (1983)

    Article  CAS  Google Scholar 

  111. E.E. Shpil’rain, K.A. Yakimovich, T.N. Mel’mikova, Thermal Properties of Lithium Hydride, Deuteride and Tritide and Their Solutions (Energoatomizdat, Moscow, 1983) (in Russian)

    Google Scholar 

  112. A.A. Berezin, A.M. Ibragim, Effects of the diversity of stable isotopes on properties of materials. Mater. Chem. Phys. 19, 420–437 (1988)

    Article  Google Scholar 

  113. D.K. Smith, H.R. Leider, Low-temperature thermal expansion of LiH. J. Appl. Crystal. 1, 246–249 (1968)

    Article  CAS  Google Scholar 

  114. H. Holloway, K.C. Hass, M.A. Tamor et al., Isotopic dependence of lattice constants of diamond. Phys. Rev. B44, 7123–7126 (1991)

    Google Scholar 

  115. H. Holloway, K.C. Hass, M.A. Tamor et al., Isotopic dependence of lattice constants of diamond. Phys. Rev. B 45, 6353E (1992)

    Article  Google Scholar 

  116. P. Pavone, S. Baroni, Dependence of the crystal lattice constant on isotopic composition. Solid State Commun. 90, 295–297 (1994)

    Article  CAS  Google Scholar 

  117. R.C. Bushert, A.E. Merlin, S. Pace et al., Effect of isotope concentration on the lattice parameter of germanium perfect crystals. Phys. Rev. B 38, 5219–5221 (1988)

    Article  Google Scholar 

  118. J.C. Noya, C.P. Hrrero, R. Ramirez, Isotope dependence of the lattice parameter of germanium from path-integral Monte Carlo simulations. Phys. Rev. B 56, 237–243 (1997)

    Article  CAS  Google Scholar 

  119. C.P. Herrero, Dependence of the silicon lattice constant on isotopic mass. Phys. Status Solidi (b) 220, 857–867 (2000)

    Article  CAS  Google Scholar 

  120. Y. Ma, J.S. Tse, Ab initio detrmination of crystal lattice constant and thermal expansion for germanium isotopes. Solid State Commun. 143, 161–165 (2007)

    Article  CAS  Google Scholar 

  121. W. Banholzer, T. Anthony, Diamond properties as a function of isotopic composition. Thin Solid Films 212, 1–10 (1992)

    Article  CAS  Google Scholar 

  122. W.B. Zimmerman, Lattice constant dependence on isotopic composition in the \(^{7}\)Li(H, D) system. Phys. Rev. B5, 4704–4707 (1972)

    Google Scholar 

  123. T. Yamanaka, S. Morimoto, H. Kanda, Influence of the isotope ratio on the lattice constant of diamond, Ibid B49, 9341–9343 (1994)

    Google Scholar 

  124. R. Vogelgesang, A.K. Ramdas, S. Rodriguez et al., Brillouin and Raman in natural and isotopically controlled diamond. Phys. Rev. B 54, 3989–3999 (1996)

    Article  CAS  Google Scholar 

  125. N. Garo, A. Cantarero, T. Ruf et al., Dependence of the lattice parameters and energy gap of zinc-blende-type semiconductors on isotopic mass. Phys. Rev. B 54, 4732–7440 (1996)

    Google Scholar 

  126. A. Debernardi, M. Cardona, Isotopic effect on the lattice constant in compound semiconductors by perturbation theory: An ab initio calculation. Phys. Rev. B 54, 11305–11310 (1996)

    Article  CAS  Google Scholar 

  127. H. Bilz, W. Kress, Phonon Dispersion Relations in Insulators (Springer, Berlin, 1979)

    Book  Google Scholar 

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Plekhanov, V. (2013). Effects Related to Isotopic Disorder in Solids. In: Isotopes in Condensed Matter. Springer Series in Materials Science, vol 162. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-28723-7_5

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