Isotopes in Solids

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


The modern view of solid-state physics is based on the presentation of elementary excitations, having mass, quasiimpuls, electrical charge and so on. According to this presentation the elementary excitations of the non-metallic materials are electrons (holes), excitons (polaritons) and phonons. The latter are the elementary excitations of the crystal lattice, the dynamics of which is described in harmonic approximation as is well known, the base of such view on solids is the multiparticle approach. In this view, the quasiparticles of solids are ideal gas, which describe the behavior of the system, e.g. noninteracting electrons. We should take into account such an approach to consider the theory of elementary excitations as a suitable model for the application of the common methods of quantum mechanics for the solution of the solid-state physics task. In this chapter we consider not only the manifestations of the isotope effect on different solids, but also the new accurate results, showing the quantitative changes of different characteristics of phonons and electrons (excitons) in solids with isotopic substitution. The isotopic effect becomes more pronounced when dealing with solids. For example, on substitution of H with D the change in energy of the electron transition in solid state (e.g. LiH ) is two orders of magnitude larger than in atomic hydrogen. Using elementary excitations to describe the complicated motion of many particles has turned out to be an extraordinarily useful device in contemporary physics, and it is the view of a solid which we describe in this chapter.


Isotope Effect Mixed Crystal Elementary Excitation Isotopic Substitution Coherent Potential Approximation 
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.


  1. 1.
    D. Pines, Elementary Excitations in Solids (W.A. Benjamin, Inc., New York, 1963)Google Scholar
  2. 2.
    S.I. Pekar, Crystaloptics and Addition Waves (Kiev, Naukova Dumka, 1982) (in Russian)Google Scholar
  3. 3.
    G.P. Srivastava, The Physics of Phonons (Hilger, Bristol, 1990)Google Scholar
  4. 4.
    V.G. Plekhanov, Isotopetronics-New Directions of Nanoscience, ArXiv, phys./1007.5386Google Scholar
  5. 5.
    V.G. Plekhanov, Isotopic and disorder effects in large exciton spectroscopy. Physcs–Uspekhi (Moscow) 40, 553–579 (1997)Google Scholar
  6. 6.
    J. Callaway, Energy Band Structure (Academic Press, New York, 1964)Google Scholar
  7. 7.
    R.M. Martin, Electronic Structure—Basic Theory and Practical Methods (Cambridge University Press, Cambridge, 2004)Google Scholar
  8. 8.
    N.W. Ashcroft, N.D. Mermin, Solid State Physics (Holt, Reinhart and Winston, New York, 1976)Google Scholar
  9. 9.
    J.M. Ziman, Electrons and Phonons (Oxford University Press, London, 1963)Google Scholar
  10. 10.
    V.G. Plekhanov, Giant Isotope Effect in Solids (Stefan University Press, La Jola, 2004)Google Scholar
  11. 11.
    N.F. Mott, R.V. Gurney, Electron Processes in Ionic Crystals (Clarendon Press, Oxford, 1948)Google Scholar
  12. 12.
    J. Slater, The Self-Consistent Field for Molecules and Solids (McGraw-Hill, New York, 1975)Google Scholar
  13. 13.
    W.B. Fowler, Influence of electronic polarization on the optical properties of insulators. Phys. Rev. 151, 657–667 (1966)Google Scholar
  14. 14.
    D.H. Ewing, F. Seitz, On the electronic constitution of crystals: LiF and LiH. Phys. Rev. 50, 760–777 (1936)Google Scholar
  15. 15.
    F. Perrot, Bulk properties of lithium hydride up to 100 Mbar. Phys. Stat. Sol. (b) 77, 517–525 (1976)Google Scholar
  16. 16.
    G.S. Zavt, K. Kalder et al., Electron excitation and luminescence LiH single crystals, Fiz. Tverd. Tela (St. Petersburg) 18, 2724–2730 (1976) (in Russian).Google Scholar
  17. 17.
    N.I. Kulikov, Electron structure, state equation and phase transitions insulator—metal in hydride lithium, ibid, 20, 2027–2035 (1978) (in Russian)Google Scholar
  18. 18.
    G. Grosso, G.P. Parravichini, Hartree-Fock energy bands by the orthogonalized-plane-wave method: lithium hydride results. Phys Rev. B20, 2366–2372 (1979)Google Scholar
  19. 19.
    S. Baroni, G.P. Parravichini, G. Pezzica, Quasiparticle band structure of lithium hydride. Phys. Rev. B32, 4077–4087 (1985)Google Scholar
  20. 20.
    A.B. Kunz, D.J. Mikish, Electronic structure of LiH and NaH, ibid, B11, 1700–1704 (1975)Google Scholar
  21. 21.
    T.A. Betenekova, I.N. Shabanova, F.F. Gavrilov, The structure of valence band in lithium hydride, Fiz. Tverd. Tela 20, 2470–2477 (1978) (in Russian)Google Scholar
  22. 22.
    K. Ichikawa, N. Susuki, K. Tsutsumi, Photoelectron spectroscopic study of LiH. J. Phys. Soc. Japan 50, 3650–3654 (1981)Google Scholar
  23. 23.
    R.A. Kink, M.F. Kink, T.A. Soovik, Reflection spectra of lithium hydride crystals in 4–25 eV at 5 K. Nucl. Instrum. Methods Phys. Res. A261, 138–140 (1987)Google Scholar
  24. 24.
    V.G. Plekhanov, V.I. Altukhov, Determination of exciton and exciton–phonon interaction parameters via resonant secondary emission of insulators. Sov. Phys. Solid State 23, 439–447 (1981)Google Scholar
  25. 25.
    V.G. Plekhanov, Nuclear Technology of the Creation of Quantum Dots in Graphene, (Science Transactient of SHI, Tallinn, 2011), pp. 66–71Google Scholar
  26. 26.
    A.A. Blistanov, in Acoustic Crystals: Handbook, ed. by M.T. Shchaskol’skaya (Nauka, Moscow, 1982) (in Russian)Google Scholar
  27. 27.
    C. Kittel, Introduction to Solid State Physics (Wiley, New York, 1986)Google Scholar
  28. 28.
    R. Wyckoff, Crystal Structures (Interscience, New York, 1963)Google Scholar
  29. 29.
    M.L. Cohen, J. Chelikowsky, Electronic Properties and Optical Properties of Semiconductors, 2nd ed. Springer Series Solid-State Science, Vol. 75 (Springer, Berlin, 1989)Google Scholar
  30. 30.
    J.I. Pankove, Optical Processes in Semiconductors (Prentice-Hall Englewood Cliffs, New Jersey, 1971)Google Scholar
  31. 31.
    V.G. Plekhanov, Elementary excitations in isotope mixed crystals. Phys. Reports 410, 1–235 (2005)Google Scholar
  32. 32.
    L.D. Landau, E.M. Lifshitz, Quantum Mechanics (Nonrelativistic Theory) (Pergamon Press, New York, 1977)Google Scholar
  33. 33.
    R. Loudon, The Raman effect in crystals. Adv. Phys. 13, 423–488 (1964)Google Scholar
  34. 34.
    R.A. Cowley, Anharmonicity, J. Phys. (Paris). 26, 659–664 (1965)Google Scholar
  35. 35.
    R.A. Cowley, Anharmonic crystals, Rep. Prog. Phys. 31, 123–166 (1968)Google Scholar
  36. 36.
    R.A. Cowley, in Anharmonicity, ed. by A. Anderson. Raman Effect, (Marcel Dekker, New York, 1971)Google Scholar
  37. 37.
    M.A. Eliashevich, Mechanics of the vibrations of molecules, Uspekhi Fiz. Nauk (Moscow) 48, 482–544 (1946) (in Russian)Google Scholar
  38. 38.
    D.A. Long, Raman Spectroscopy (McGraw-Hill Inc., London, 1977)Google Scholar
  39. 39.
    J.L. Birman, in Space Group Symmetry, Handbuch fur Physik, vol. 25/2b (Springer, Berlin, 1974)Google Scholar
  40. 40.
    M. Cardona, M.L.W. Thewalt, Isotope effect on the optical spectra of semiconductors. Rev. Mod. Phys. 77, 1173–1224 (2005)Google Scholar
  41. 41.
    V.F. Agekyan, A.M. Asnin, V.M. Kryukov et al., Isotope effect in germanium, Fiz. Tverd. tela (St. Petersburg) 31, 101–104 (1989) (in Russian)Google Scholar
  42. 42.
    M. Lax, E. Burstein, Infrared lattice absorption in ionic and homopolar crystals. Phys. Rev. 97, 39–52 (1955)Google Scholar
  43. 43.
    H.D. Fuchs, P. Etchegoin, M. Cardona et al., Vibrational band modes in germanium: isotopic—disorder induced Raman scattering. Phys. Rev. Let. 70, 1715–1718 (1993)Google Scholar
  44. 44.
    H. Hanzawa, N. Umemura, Y. Nisida, H. Kanda, Disorder effect of nitrogen impurities, irradiation induced defects and \(^{13}\)C composition on the Raman spectrum in synthetic I\(^{b}\) diamond. Phys. Rev. B54, 3793–3799 (1996)Google Scholar
  45. 45.
    V.G. Plekhanov, Isotope Effects in Solid State Physics, in Semiconductors and Semimetals, vol. 68, ed. by R.K. Willardson, E. Weber (Academic Press, San Diego, 2001)Google Scholar
  46. 46.
    V.G. Plekhanov, Isotope effect in lattice dynamics. Physics-Uspekhi (Moscow) 46, 689–715 (2003)Google Scholar
  47. 47.
    R.M. Chrenko, \(^{13}\)C-doped diamond: Raman spectra. Appl. Phys. 63, 5873–5875 (1988)Google Scholar
  48. 48.
    K.C. Hass, M.A. Tamor, T.R. Anthony, W.F. Banholzer, Effect of isotopic disorder on the phonon spectrum of diamond. Phys. Rev. B44, 12046–12053 (1991)Google Scholar
  49. 49.
    S.H. Solin, A.K. Ramdas, Raman spectrum of diamond. Phys. Rev. B1, 1687–1699 (1970)Google Scholar
  50. 50.
    V.G. Plekhanov, Isotope effect on the lattice dynamics. Mater. Sci. Eng. R35, 139–237 (2001)Google Scholar
  51. 51.
    V.G. Plekhanov, Lattice—dynamics of isotope—mixed crystals, ArXiv cond–mat/1007.5125 (2010).Google Scholar
  52. 52.
    R.J. Elliott, J.A. Krumhansl, P.L. Leath, The thery and properties of randomly disordered crystals and physical systems. Rev. Mod. Phys. 46, 465–542 (1974)Google Scholar
  53. 53.
    I.F. Chang, S.S. Mitra, Long-wavelength of optical phonons in mixed crystals. Adv. Phys. 20, 360–404 (1971)Google Scholar
  54. 54.
    I.P. Ipatova, Universal parameters in mixed crystals, in [120] Ch. p. 1–34, 1988Google Scholar
  55. 55.
    V.G. Plekhanov, Lattice dynamics of isotopically mixed crystals, Opt. spectrosc. (St. Petersburg) 82, 95–24 (1997)Google Scholar
  56. 56.
    V.G. Plekhanov, Experimental evidence of strong phonon scattering in isotopical disordered systems: the case LiH\(_{x}\)D\(_{1-x}\). Phys. Rev. B51, 8874–8878 (1995)Google Scholar
  57. 57.
    V.G. Plekhanov, Fundamentals and applications of isotope effect in modern technology, J. Nucl. Sci. Technol. (Japan) 43, 375–381 (2006). ArXiv: cond–mat/0807.2521 (2008)Google Scholar
  58. 58.
    G. Herzberg, Molecular Spectra and Molecular Structure (D. van Nostrand, New York, 1951)Google Scholar
  59. 59.
    A.F. Kapustinsky, L.M. Shamovsky, K.S. Bayushkina, Thermochemistry of isotopes. Acta Physicochim. (USSR) 7, 799–810 (1937)Google Scholar
  60. 60.
    V.G. Plekhanov, T.A. Betenekova, V.A. Pustovarov et al., Excitons and some peculiarities of exciton–phonon interactions. Sov. Phys. Solid State 18, 1422–1424 (1976)Google Scholar
  61. 61.
    V.G. Plekhanov, Wannier—Mott excitons in isotope—disordered crystals. Rep. Prog. Phys. 61, 1045–1095 (1998)Google Scholar
  62. 62.
    F.I. Kreingol’d, K.F. Lider, M.B. Shabaeva, Influence of isotope substitution sulfur on the exciton spectrum in CdS crystal, Fiz. Tverd. Tela (St. Petersburg) 26, 3940–3941 (1984) (in Russian)Google Scholar
  63. 63.
    Y. Onodera, Y. Toyozawa, Persistence and amalgamation types in the electronic structure of mixed crystals. J. Phys. Soc. Japan 24, 341–355 (1968)Google Scholar
  64. 64.
    Y. Toyozawa, Optical Processes in Solids, (Cambridge University Press, Cambridge, 2003)Google Scholar
  65. 65.
    F.I. Kreingol’d, K.F. Lider, K.I. Solov’ev, Isotope shift of exciton line in absorption spectrum Cu\(_{2}\)O, JETP Lett. (Moscow) 23, 679–681 (1976) (in Russian)Google Scholar
  66. 66.
    F.I. Kreingol’d, K.F. Lider, V.F. Sapega, Influence of isotope substitution on the exciton spectrum in Cu\(_{2}\)O crystal, Fiz. Tverd. Tela (St. Petersburg) 19, 3158–3160 (1977) (in Russian)Google Scholar
  67. 67.
    F.I. Kreingol’d, B.S. Kulinkin, Influence of isotope substitution on the forbidden gap of ZnO crystals, ibid, 28, 3164–3166 (1986) (in Russian).Google Scholar
  68. 68.
    F.I. Kreingol’d, Dependence of band gap ZnO on zero-point energy, ibid, 20, 3138–3140 (1978) (in Russian)Google Scholar
  69. 69.
    J.M. Zhang, T. Ruf, R. Lauck et al., Sulfur isotope effect on the excitonic spectra of CdS. Phys. Rev. B57, 9716–9722 (1998)Google Scholar
  70. 70.
    T.A. Meyer, M.L.W. Thewalt, R. Lauck et al., Sulfur isotope effect on the excitonic spectra of CdS. Phys. Rev. B69, 115214–115215 (2004)Google Scholar
  71. 71.
    G.L. Bir, G.E. Picus, Symmetry and Deformation in Semiconductors (Science, Moscow, 1972) (in Russian)Google Scholar
  72. 72.
    D.G. Thomas (ed.), II–VI Semiconducting Comounds (Benjamin, New York, 1967)Google Scholar
  73. 73.
    L.F. Lastras-Martinez, T. Ruf, M. Konuma et al., Isotopic effect on the dielectric response of Si around the E\(_{1}\) gap, Phys. Rev. B61, 12946–12951 (2000)Google Scholar
  74. 74.
    D. Karaskaja, M.L.W. Thewalt, T. Ruf et al., Photoluminescence studies of isotopically—enriched silicon: Isotopic effects on indirect electronic band gap and phonon energies. Solid State Commun. 123, 87–92 (2003)Google Scholar
  75. 75.
    S. Tsoi, H. Alowadhi, X. Lu et al., Electron–phonon renormalization of electronic band gaps of semiconductors: Isotopically enriched silicon. Phys. Rev. B70, 193201–193204 (2004)Google Scholar
  76. 76.
    A.K. Ramdas, S. Rodriguez, S. Tsoi et al., Electronic band gap of semiconductors as influenced by their isotopic composition. Solid State Commun. 133, 709–714 (2005)Google Scholar
  77. 77.
    S. Tsoi, S. Rodriguez, A.K. Ramdas et al., Isotopic dependence of the E\(_{0}\) and E\(_{1}\) direct gaps in the electronic band structure of Si. Phys. Rev. B72, 153203–153204 (2005)Google Scholar
  78. 78.
    H. Kim, S. Rodriguez, T.R. Anthony, Electronic transitions of holes bound to boron acceptors in isotopically controlled diamond. Solid State Commun. 102, 861–865 (1997)Google Scholar
  79. 79.
    M. Cardona, Dependence of the excitation energies of boron in diamond on isotopic mass. Solid State Commun. 121, 7–8 (2002)Google Scholar
  80. 80.
    A.A. Klochikhin, V.G. Plekhanov, Isotope effect on the Wannier—Mott exciton levels. Sov. Phys. Solid state 22, 342–344 (1980)Google Scholar
  81. 81.
    V.G. Plekhanov, Direct observation of the effect of isotope-induced-disorder on exciton binding energy in LiH\(_{x}\)D\(_{1-x}\) mixed crystals. J. Phys. Condens. Matter 19, 086221–086229 (2007)Google Scholar
  82. 82.
    P.G. Klemens, Thermal conductivity and lattice vibrational modes, in Solid state Physics: Advances in Research and Applications, vol. 7, ed. by F. Seitz, D. Turnbull (Academic Press, New York, 1958)Google Scholar
  83. 83.
    M.G. Holland, Thermal Conductivity, in Physics of III–V Compounds (Semiconductors and Semimetals), vol. 2, ed. by R.K. Willardson, A.C. Beer (Academic Press, New York, 1966)Google Scholar
  84. 84.
    Y.S. Toulookian, R.W. Powel, C.Y. Ho, P.G. Klemens, Thermal Conductivity Metallic Elements and Alloys. in Thermophysical Properties of Materials, vol. 1 (IFI Plenum Press, New York–Washington, 1970)Google Scholar
  85. 85.
    R.Z. Berman, Thermal Conduction in Solids (Clarendon Press, Oxford, 1976)Google Scholar
  86. 86.
    J. Callaway, Model for lattice thermal conductivity at low temperatures. Phys. Rev. 113, 1046–1051 (1959)Google Scholar
  87. 87.
    R. Peierls, Quantum Theory of Solids (Clarendon Press, Oxford, 1955)Google Scholar
  88. 88.
    J.M. Ziman, Models of Disorder (Cambridge University Press, Cambridge, 1979)Google Scholar
  89. 89.
    I. Ya, Pomeranchuk, About thermal conductivity of dielectrics. J. Phys. (USSR) 6, 237–246 (1942)Google Scholar
  90. 90.
    T.H. Geballe, G.W. Hull, Isotopic and other types of thermal resistance in germanium. Phys. Rev. 110, 773–775 (1958)Google Scholar
  91. 91.
    D.G. Onn, A. Witek, Y.Z. Qiu et al., Some aspect of the thermal conductivity of isotopically enriched diamond single crystals. Phys. Rev. Lett. 68, 2806–2809 (1992)Google Scholar
  92. 92.
    J.R. Olson, R.O. Pohl, J.W. Vandersande et al., Thermal conductivity of diamond between 170 and 1200 K and the isotopic effect, Phys. Rev. B47, 14850–14856 (1993)Google Scholar
  93. 93.
    L. Wei, P.K. Kuo, R.L. Thomas, Thermal conductivity of isotopically modified single crystal diamond. Phys. Rev. Lett. 79, 3764–3767 (1993)Google Scholar
  94. 94.
    P. Debye, The Debye theory of specific heat, Ann. Phys. (Leipzig) 4, 39, 789–803 (1912)Google Scholar
  95. 95.
    M. Cardona, R.K. Kremer, M. Sanati et al., Measurements of the heat capacity of diamond with different isotopic composition. Solid State Commun. 133, 465–468 (2005)Google Scholar
  96. 96.
    V.G. Plekhanov, Isotope—Mixed Crystals: Fundamentals and Applications (Bentham, e-books, 2011) (ICBN: 978-1-60805-091-8)Google Scholar
  97. 97.
    M. Asen-Palmer, K. Bartkowsky, E. Gmelin et al., Thermal conductivity of germanium crystals with different isotopic composition, Phys. Rev. B56, 9431–9447 (1997)Google Scholar
  98. 98.
    W.C. Capinski, H.J. Maris, M. Asen-Palmer et al., Thermal conductivity of isotopically enriched Si, Appl. Phys. Lett. 71, 2109–2111 (1997)Google Scholar
  99. 99.
    W.C. Capinski, H.J. Maris, S. Tamura, Analysis of the effect of isotope scattering on the thermal conductivity of crystalline silicon. Phys. Rev. B59, 10105–10110 (1999)Google Scholar
  100. 100.
    T. Ruf, R.W. Henn, M. Asen-Palmer et al., Thermal conductivity of isotopically enriched silicon, Solid State Commun. 115, 243–247 (2000); Erratum 127, 257 (2003)Google Scholar
  101. 101.
    A.P. Zhernov, A.V. Inyushkin, Kinetic coefficients in isotopically disordered crystals. Physics-Uspekhi (Moscow) 45, 573–599 (2002)Google Scholar
  102. 102.
    V.G. Plekhanov, Isotope engineering. Physics-Uspekhi (Moscow) 43, 1147–1154 (2000)Google Scholar
  103. 103.
    M. Omini, A. Sparavigna, Heat transport in dielectric solids with diamond structure. Nuovo Cimento D19, 1537–1563 (1997)Google Scholar
  104. 104.
    A. Sparavigna, Influence of isotope scattering on the thermal conductivity of diamond, Phys. Rev. B65, 064305-1–064305-5 (2002), ibid, B67, 144305–4 (2003)Google Scholar
  105. 105.
    K.C. Hass, M.A. Tamor, T.R. Anthony, W.F. Banholzer, Lattice dynamics and Raman spectra of isotopically mixed diamond. Phys. Rev. B45, 7171–7182 (1992)Google Scholar
  106. 106.
    H.D. Fuchs, C.H. Grein, C. Thomsen et al., Comparison of the phonon spectra \(^{70}\)Ge and natural Ge crystals: Effect of isotopic disorder, ibid, B43, 4835–4841 (1991)Google Scholar
  107. 107.
    D.T. Wang, A. Gobel, J. Zegenhagen et al., Raman scattering on \(\alpha \)-Sn: dependence on isotopic composition, ibid, B56, 13167–13172 (1997)Google Scholar
  108. 108.
    S. Tamura, Isotope scattering of dispersive phonons in Ge. Phys. Rev. B27, 858–866 (1983)Google Scholar
  109. 109.
    S. Tamura, Isotope scattering of large-wave-vector phonons in GaAs and inSb: deformation-dipole and overlap-shell models, ibid, B30, 849–854 (1984)Google Scholar
  110. 110.
    F. Widulle, J. Serrano, M. Cardona, Disorder—induced phonon self-energy of semiconductors with binary isotopic composition. Phys. Rev. B65, 075206–075210 (2002)Google Scholar
  111. 111.
    J. Spitzer, P. Etchegoin, W.F. Banholzer et al., Isotopic disorder induced Raman scattering in diamond. Solid State Commun. 88, 509–514 (1993)Google Scholar
  112. 112.
    R. Vogelgesand, A.K. Ramdas, T.R. Anthony, Brillouin and Raman scattering in natural and isotopically controlled diamond. Phys. Rev. B54, 3989–3999 (1996)Google Scholar
  113. 113.
    F. Widulle, T. Ruf, V.I. Ozhogin et al., Isotope effect in elemental semiconductors: A Raman study of silicon. Solid State Commun. 118, 1–22 (2001)Google Scholar
  114. 114.
    N. Vast, S. Baroni, Effect of disorder on the Raman spectra of crystals: Theory and ab initio calculations for diamond and germanium. Phys. Rev. B61, 9387–9391 (2000)Google Scholar
  115. 115.
    N. Vast, S. Baroni, Effect of disorder on the Raman spectra of crystals: Theory and ab initio calculations for diamond and germanium. Comput. Matr. Sci. 17, 395–399 (2000)Google Scholar
  116. 116.
    S. Rohmfeld, M. Hundhausen, L. Ley, Isotope-disorder-induced line broadening of phonons in the Raman spectra of SiC. Phys. Rev. Lett. 86, 826–829 (2001)Google Scholar
  117. 117.
    V.G. Plekhanov, V.I. Altukhov, Light scattering in LiH crystals with LO phonons emission. J. Raman Spectrosc. 16, 358–365 (1985)Google Scholar
  118. 118.
    V.G. Plekhanov, Comparative study of isotope and chemical effects on the exciton states in LiH crystals. Prog. Solid State Chem. 29, 71–177 (2001)Google Scholar
  119. 119.
    V.G. Plekhanov, Isotope-induced energy-spectrum renormalization of the Wannier– Mott exciton in LiH crystals. Phys. Rev. B54, 3869–3877 (1996)Google Scholar
  120. 120.
    R.J. Elliott, I.P. Ipatove (eds.), Optical Properties of Mixed Crystals (North-Holland, Amsterdam, 1988)Google Scholar
  121. 121.
    C. Parks, A.K. Ramdas, S. Rodriguez et al., Electronic band structure of isotopically pure germanium, Phys. Rev. B49, 14244–14260 (1994)Google Scholar
  122. 122.
    G. Davies, J. Hartung, V. Ozhogin et al., Effects of isotope disorder on phonons in germanium determined from bound exciton luminescence. Semicond. Sci. Technol. 8, 127–130 (1993)Google Scholar
  123. 123.
    S. Permogorov, A. Reznitsky, Effect of disorder on the optical spectra of wide-gap II–VI semiconductor solid solutions. J. Luminescence 52, 201–223 (1992)Google Scholar
  124. 124.
    S. Permogorov, A. Klochikhin, A. Reznitsky, Disorder—induced exciton localization in 2D wide—gape semiconductor solid solutions, ibid, 100, 243–257 (2002)Google Scholar
  125. 125.
    A.L. Efros, M.E. Raikh, Effect of composion disorder on the electronic properties in semiconducting mixed crystals, in [116]. Ch. 5, 133–177 (1988)Google Scholar
  126. 126.
    I.M. Lifshitz, Selected Works (Science, Moscow, 1987) (in Russian)Google Scholar
  127. 127.
    V.A. Kanehisa, R.J. Elliott, Effect of disorder on exciton binding energy in semiconductor alloys. Phys. Rev. B35, 2228–2236 (1987)Google Scholar
  128. 128.
    N.F. Schwabe, R.J. Elliott, Approximation of excitonic absorption in disordered systems using a composition–component–weighted coherent–potential approximation, ibid, B54, 5318–5329 (1996)Google Scholar
  129. 129.
    H.A. Bethe, E. Salpiter, Quantum Theory of One and Two Electron Atoms (Academic Press, New York, 1957)Google Scholar
  130. 130.
    R.J. Nelson, N. Holonjak, W. Groves, Free—exciton transitions in the optical absorption spectra of GaAs\(_{1-x}\)P\(_{x}\). Phys. Rev. B13, 5415–5419 (1976)Google Scholar
  131. 131.
    S.D. Mahanti, C.M. Varma, Effective electron—hole interactions in polar semiconductors, ibid, B6, 2209–2226 (1972)Google Scholar
  132. 132.
    S.D. Mahanti, Excitons in semiconducting alloys, ibid, B10, 1384–1390 (1974)Google Scholar
  133. 133.
    J. Hama, N. Kawakami, Pressure induced insulator—metal transiton in solid LiH. Phys. Lett. A126, 348–352 (1988)Google Scholar
  134. 134.
    V.G. Plekhanov, Experimental manifestation of the effect of disorder on exciton binding energy in mixed crystals, Phys. Rev. B53, 9558–9560 (1996–I)Google Scholar
  135. 135.
    V.G. Plekhanov, N.V. Plekhanov, Isotope dependence of band-gap energy. Phys. Lett. A313, 231–237 (2003)Google Scholar
  136. 136.
    H. Rechenberg, Historical Remarks on Zero-Point Energy and the Casimir Effect, in The Casimir Effect 50 Years later, ed. by M. Bordag (World Scientific, Singapore, 1999) p. 10–19Google Scholar
  137. 137.
    M. Planck, Über die begrundung des gesetz der Schwarzen strahlung. Ann. Phys. 37, 642–656 (1912)Google Scholar
  138. 138.
    W. Nernst, F.A. Lindeman, Z. Elektrochem. Angew. Phys. Chem. 17, 817 (1911) (cited in [136])Google Scholar
  139. 139.
    A. Einstein, O. Stern, Einige argumente fur die annahme einer molekularen agitation beim absoluten null punkt. Ann. Phys. 40, 551 (1913)Google Scholar
  140. 140.
    H.Y. Fan, Temperature dependence of the energy gap in semiconductors. Phys. Rev. 82, 900–905 (1951)Google Scholar
  141. 141.
    S. Zollner, M. Cardona and S. Gopalan, Isotope and temperature shifts of direct and indirect band gaps in diamond-type semiconductors, ibid, B45, 3376–3385 (1992)Google Scholar
  142. 142.
    G. Baym, Lectures on Quantum Mechanics (Benjamin, New York, 1968), p. 98Google Scholar
  143. 143.
    K.A. Milton, The Casimir effect: Recent controversis and progress. J. Phys. A: Math. Gen. 37, R209–R277 (2004)Google Scholar
  144. 144.
    S.K. Lamoreaux, The Casimir force: Background, experiments and applications. Rep. Prog. Phys. 68, 201–236 (2009)Google Scholar
  145. 145.
    P. Lautenschlager, M. Garriga, L. Vina et al., Temperature dependence of the dielectric function and interband critical points in silicon. Phys. Rev. B36, 4821–4830 (1987)Google Scholar
  146. 146.
    V.G. Plekhanov, Comparative investigation of isotopic and temperature effects involving excitons in LiH\(_{x}\)D\(_{1-x}\) crystals, Phys. Solid State (St. Petersburg) 35, 1493–1499 (1993)Google Scholar
  147. 147.
    A.P. Zhernov, Isotope composition dependence of energy bands in semiconductors, Fiz. Tverd. Tela (St. Petersburg) 44, 992–1000 (2002) (in Russian)Google Scholar
  148. 148.
    P.W. Milonni, The Quantum Vacuum: An Introduction to Quantum Elctrodynamics (Academic Press, New York, 1994)Google Scholar
  149. 149.
    P.W. Milonni and M.-L. Shih, Zero-point energy in early quantum theory, Am. J. Phys. 59, 684–698 (1991)Google Scholar
  150. 150.
    T.H. Boyer, The classical vacuum (zero-point energy), Sci. Am. Mag, pp. 70–78, (Aug, 1985) Google Scholar
  151. 151.
    P. Yam, Exploiting zero-point energy, ibd, December 1997, pp. 82–85Google Scholar
  152. 152.
    H. Puthoff, Quantum fluctuations of empty space: a new Rosetta stone in physics,
  153. 153.
    W. Nerst, Über einen versuch von quantentheorietischen Betrachtungen zuruckzukehren. Verhandl. Deut. Phys. Ges. 18, 83–91 (1916)Google Scholar
  154. 154.
    P.A.M. Dirac, The Principle of Quantum Mechanics (Clarendon Press, Oxford, 1995)Google Scholar
  155. 155.
    A. Peres, Quantum Theory: Concepts and Methods (Kluwer Academic Publ, Dodrech, 1994)Google Scholar
  156. 156.
    B. Haisch, A. Rueda, Y. Dobyns, Insrtial mass and the quantum vacuum fields. Ann. der Phys. 10, 393–414 (2001)Google Scholar
  157. 157.
    T.H. Boyer, Random electrodynamics: The theory of classical electrodynamics with classical electromagnetic zero-point radiation, Phys. Rev. D11, 790–808 (1975)Google Scholar
  158. 158.
    T.H. Boyer, Random Electrodynamics: The Theory of Classical Electrodynamics with Classical Electromagnetic Zero-Point Radiation, in Foundations of Radiation and Quantum Electrodynamics, ed. by A.O. Barut ( Plenum Press, New York, 1980)Google Scholar
  159. 159.
    L. de la Peña and A.M. Cetto, The Quantum Dice: An Introduction to Stochastic Electrodynamics (Kluwer, Dodrecht, 1996)Google Scholar
  160. 160.
    B. Kosyakov, Introduction to the Classical Theory of Particles and Fields (Springer, Heidelberg, 2007)Google Scholar
  161. 161.
    E. Schrödinger, Über die kroftefreie Bewegung in dr relativoschen Quantemmechanics, Sitz. Preus. Akad. Wiss. Phys. Math. K1 24, 418–428 (1930); 3, 1–10 (1931)Google Scholar
  162. 162.
    K. Huang, On the zitterbewegung of the Dirac electron. Am. J. Phys. 20, 479–487 (1952)Google Scholar
  163. 163.
    A. Barut, N. Zanghi, Classical model on the Dirac Electron. Phys. Rev. Lett. 52, 2003–2006 (1984)Google Scholar
  164. 164.
    H.E. Puthoff, Groung—state of hydrogen as a zero-point-fluctuation-detrmined state. Phys. Rev. D35, 3266–3269 (1987)Google Scholar
  165. 165.
    D.C. Cole, Yi. Zou, Quantum mechanical ground state og hydrogen obtained from classical electrodynamics, Phys. Lett. A317, 14–20 (2003)Google Scholar
  166. 166.
    E.W. Davis, V.L. Teofilo, B. Haisch at al., Review of experimental concepts for studying the quantum vacuum field, in Space Technology and Applications International Forum, SPAIF - 2006, ed. by El-Genk, 2006, pp. 1390–1401Google Scholar
  167. 167.
    V.G. Plekhanov, Manifestation and origin of the isotope effec, ArXiv: phys/0907.2024 (2009), (review)Google Scholar
  168. 168.
    H.E. Puthhoff, Source of vacuum electromagnetic zero-point energy. Phys. Rev. A40, 4857–4862 (1989)Google Scholar
  169. 169.
    P.W. Milonni, Semiclassical and quantum electrodynamical approaches in nonrelativistic radiation theory. Phys. Rep. 25, 1–81 (1976)Google Scholar
  170. 170.
    M. Jammewr, Concepts of Mass in Contemporary Physics and Philosophy, (Harvard University Press, Cambridge, 1961)Google Scholar
  171. 171.
    E. Mach, Mechanics (Saint-Petersburg, 1909) (in Russian)Google Scholar
  172. 172.
    H.E. Puthoff, Gravity as a zero-point-fluctuation force. Phys. Rev. A39, 2333–2342 (1989)Google Scholar
  173. 173.
    A.D. Sakharov, Vacuum quantum fluctuation in curved space and the theory of gravitation, Dokl. Akad, Nauk SSSR. Sov. Phys. Dokl. 12, 1040–1042 (1968)Google Scholar
  174. 174.
    M. Planck, The Theory of Heat Radiation (Blackinston, London, 1914)Google Scholar
  175. 175.
    B. Haisch and A. Rueda, The Zero-Point Field and Inertia, in Causality and Locality in Modern Physics, ed. by G. Hunter, S. Jeffers, J.-P. Vieger, (Kluwer Academic Publishers, Dodrecht, 1998) pp. 171–178Google Scholar
  176. 176.
    A. Rueda, B. Haisch, Gravity and the quantum vacuum inertia hypothesis. Ann. der Phys. 14, 479–498 (2005)Google Scholar
  177. 177.
    B. Haisch, A. Rueda, H.E. Puthoff, Inertia as a zero-point-field Lorentz force. Phys. Rev. A49, 678–694 (1994)Google Scholar
  178. 178.
    T.D. Lee, Particle Physics and Introduction to Field Theory (Harwood Academic, London, 1988)Google Scholar
  179. 179.
    H.E. Puthoff, S.R. Little, M. Ibison, Engineering the zero-point field and polarizable vacuum for interstellar flight. IBIS 55, 137–144 (2002)Google Scholar
  180. 180.
    C.W. Turtur, Two paradoxes of the existence of electric charge, ArXiv:phys/0710.3253 (2007)Google Scholar
  181. 181.
    R.L. Forward, Extracting electrical energy from the vacuum by cohesion foliated conductors. Phys. Rev. B30, 1700–1702 (1984)Google Scholar
  182. 182.
    H.B.G. Casimir, On the attraction between two perfectly conducting plates. Proc. K. Ned. Akad. Wet. 51, 793–801 (1948)Google Scholar
  183. 183.
    P.W. Milonni, R.J. Cook, M.E. Goggin, Radiation pressure from the vacuum: Physical interpretation of the Casimir force. Phys. Rev. A38, 1621–1623 (1988)Google Scholar
  184. 184.
    D.C. Cole, H.E. Puthoff, Extracting energy and the heat from the vacuum. Phys. Rev. E48, 1562–1565 (1993)Google Scholar
  185. 185.
    A. Rueda, B. Haisch, D.C. Cole, Vacuum zero-point field pressure instabiity in astrophysical plasmas and the formation of cosmic voids. Astrophys. J. 445, 7–16 (1995)Google Scholar
  186. 186.
    I.Tu. Sokolov, The Casimir effect is a possible source of cosmic energy. Phys. Lett. A223, 163–166 (1996)Google Scholar
  187. 187.
    C.E. Carlson, T. Goldman and J. Peres-Mercader, Gamma-ray burst, neutron atar quales, and the Casimir effect, Europhys. Lett. 36, 637–642 (1996)Google Scholar
  188. 188.
    F.B. Mead, Jr., J. Nachamkin, System for converting electromagnetic radiation energy to electrical energy, US Patent No 5,590.031, issued Dec. 31, 1996Google Scholar
  189. 189.
    F. Ya. Khalili, Zero-point oscillations, zero-point fluctuations, and fluctuations of zero-point oscillations, Physics-Uspekhi (Moscow) 173, 301–316 (2003) (in Russian)Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2013

Authors and Affiliations

  1. 1. Department Mathematics and PhysicsComputer Science CollegeTallinnEstonia

Personalised recommendations