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Reviews of topical problems


Microscopic theory of the lattice dynamics and the nature of the ferroelectric instability in crystals

,  a
a Lebedev Physical Institute, Russian Academy of Sciences, Leninsky prosp. 53, Moscow, 119991, Russian Federation

A brief review is given of model theories of the displacive structural instability in ferroelectrics. Particular attention is paid to the idea of compensation of the contributions of the short-range forces and the long-range internal field dipole forces to the square of the frequency of critical lattice vibrations. A vibronic theory of ferroelectricity is also discussed and its shortcomings are identified. A detailed analysis is made of the modern microscopic theory of lattice dynamics and exact expressions are derived for the force matrix governing the phonon spectrum of a crystal. The theory is discussed in the specific case of polar nonmetallic crystals. The example of semiconducting ferroelectrics from the group of IV--VI compounds is used to formulate rigorously the microscopic problem of the causes of the structural instability of such compounds on the basis of the exact expressions for the matrix of the force constants.

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Fulltext is also available at DOI: 10.1070/PU1988v031n01ABEH001946
PACS: 77.80.Dj, 77.80.Bh, 77.84.−s, 77.22.−d (all)
DOI: 10.1070/PU1988v031n01ABEH001946
URL: https://ufn.ru/en/articles/1988/1/a/
Citation: Kvyatkovskii O E, Maksimov E G "Microscopic theory of the lattice dynamics and the nature of the ferroelectric instability in crystals" Sov. Phys. Usp. 31 1–26 (1988)
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Оригинал: Квятковский О Е, Максимов Е Г «Микроскопическая теория динамики решетки и природа сегнетоэлектрической неустойчивости в кристаллах» УФН 154 3–48 (1988); DOI: 10.3367/UFNr.0154.198801a.0003

References (135) ↓ Cited by (28) Similar articles (20)

  1. Smolenskii G A, Bokov V A, Isupov V A i dr. Segnetoelektriki Antisegnetoelektriki 2-e izd. (L.: Nauka, 1971)
  2. Iona F, Shirane D Segnetoelektricheskie Kristally (M.: Mir, 1965)
  3. Blints F, Zheksh B Segnetoelektriki i Antisegnetoelektriki (M.: Mir, 1975)
  4. Lains M, Glass A Segentoelektriki i Rodstvennye Im Materialy (M.: Mir, 1981)
  5. Vaks V G Vvedenie v Mikroskopicheskuyu Teoriyu Segnetoelektrikov (M.: Nauka, 1973)
  6. Brus A, Kauli R Strukturnye Fazovye Perekhody (M.: Mir, 1984)
  7. Strokov B A, Levanyuk A P Fizicheskie Osnovy Segnetoelektricheskikh Yavlenii v Kristallakh (M.: Nauka, 1983)
  8. Ginzburg V L Zh. Eksp. Teor. Fiz. 15 739 (1945); Ginzburg V L Zh. Eksp. Teor. Fiz. 19 36 (1949); Ginzburg V L Usp. Fiz. Nauk 38 490 (1949); Ginzburg V L Trudy FIAN 180 3 (1987)
  9. Landau L D, Lifshits E M Elektrodinamika Sploshnykh Sred (M.: Nauka, 1982), Gl. 2
  10. Kurchatov I V Segnetoelektriki (M.-L.: GTTI, 1933); Kurchatov I V Izbrannye Trudy Vol. 1 (Pod red. A P Aleksandrova) (M.: Nauka, 1982) p. 281
  11. Fröhlich H Proc. R. Soc. London Ser. A 223 296 (1954); Fröhlich H Phys. Rev. 79 845 (1950)
  12. Mason W P, Matthias B T Phys. Rev. 74 1622 (1948)
  13. Vaks V G, Zinenko V I, Shneider V E Usp. Fiz. Nauk 141 629 (1983); Vaks V G, Zinenko V I, Shneider V E Sov. Phys. Usp. 26 1059 (1983)
  14. Ginzburg V L Fiz. Tverd. Tela 2 2031 (1960); Ginzburg V L Sov. Phys. Solid State 2 1824 (1961)
  15. Anderson P W Concepts In Solids (New York: Benjamin, 1963)
  16. Cochran W Phys. Rev. Lett. 3 412 (1959)
  17. Cochran W Adv. Phys. 9 387 (1960); Cochran W Adv. Phys. 10 401 (1961)
  18. Kwok P C, Miller P B Phys. Rev. 151 387 (1966)
  19. Vaks V G Zh. Eksp. Teor. Fiz. 54 910 (1968); Vaks V G Sov. Phys. JETP 27 486 (1968)
  20. Born M, Khuan Kun’ Dinamicheskaya Teoriya Kristallicheskikh Reshetok (M.: IL, 1958)
  21. Burstein E, Pinczuk A, Wallis R F J. Phys. Chem. Solids (32) 251 (1971)
  22. Bir G L, Pikus G E Simmetriya i Deformatsionnye Effekty v Poluprovodnikakh (M.: Nauka, 1972), Gl. 5
  23. Tolpygo K V Zh. Eksp. Teor. Fiz. 20 497 (1950)
  24. McKeehan L W Phys. Rev. 43 913 (1933); McKeehan L W Phys. Rev. 72 78 (1947)
  25. Luttinger J M, Tisza L Phys. Rev. 70 954 (1946); Luttinger J M, Tisza L Phys. Rev. 72 257 (1947)
  26. Skanavi G I Zh. Eksp. Teor. Fiz. 17 399 (1947)
  27. Shaskol’skaya M P (Red.) Akusticheskie Kristally (M.: Nauka, 1982)
  28. Skanavi G I Fizika Dielektrikov (M.-L.: Gostekhizdat, 1949)
  29. Slater J C Phys. Rev. 78 748 (1950)
  30. Cohen M H Phys. Rev. 84 368 (1951)
  31. Dvorak V, Janovec V Czech. J. Phys. B 12 461 (1962)
  32. Janovec V, Dvorak V Czech. J. Phys. B 13 905 (1963)
  33. Dvorak V Phys. Status Solidi 3 2235 (1963)
  34. Lucovsky G, Martin R M, Burstein E Phys. Rev. B 4 1367 (1971)
  35. Lucovsky G, Martin R M, Burstein E J. Nonmet. 1 137 (1973)
  36. Porod V, Vogl P Lecture Notes In Physics 152 247 (1982)
  37. Bersuker I V, Bekhter B G Fiz. Tverd. Tela 9 2652 (1967); Bersuker I V, Bekhter V G Sov. Phys. Solid State 9 2084 (1968)
  38. Kristoffel N, Konsin P Phys. Status Solidi 21 K39 (1967)
  39. Girshberg Ya G, Tamarchenko V I Fiz. Tverd. Tela 18 1066 (1976); Girshberg Ya G, Tamarchenko V I Sov. Phys. Solid State 18 609 (1976)
  40. Bersuker I V, Polinger V Z Vibronnye Vzaimodeistviya v Molekulakh i Kristallakh (M,: Nauka, 1983), Gl. 5
  41. Landau L D, Lifshits E M Kvantovaya Mekhanika (M.: Nauka, 1974)
  42. Brovman E G, Kagan E M Usp. Fiz. Nauk 112 369 (1974); Brovman E G, Kagan Yu M Sov. Phys. Usp. 17 125 (1974)
  43. Maksimov E G Trudy FIAN 86 101 (1975)
  44. Born M, Oppenheimer R Ann. Physik 84 457 (1927)
  45. Brovman E G, Kagan Yu M Zh. Eksp. Teor. Fiz. 52 557 (1967); Brovman E G, Kagan Yu M Sov. Phys. JETP 25 365 (1967)
  46. Chester G V Adv. Phys. 10 357 (1961)
  47. Sherrington D J. Phys. C 4 2771 (1971)
  48. Gurevich V L, Larkin A I, Firsov Yu A Fiz. Tverd. Tela 4 185 (1962); Gurevich V L, Larkin A I, Firsov Yu A Sov. Phys. Solid State 4 131 (1962)
  49. Maksimov E G Zh. Eksp. Teor. Fiz. 69 2236 (1975); Maksimov E G Sov. Phys. JETP 42 1138 (1975)
  50. Sham L J Modern Solid State Physics Vol. 2 (Eds R H Enns, R R Haering) (London: Gordon and Breach, 1969) p. 189
  51. Sham L J Phys. Rev. 188 1431 (1969)
  52. Pick R M, Cohen M H, Martin R M Phys. Rev. B 1 910 (1970)
  53. Johnson F A Proc. R. Soc. London A 310 79 (1969); Johnson F A Proc. R. Soc. London A 89 101; DeCicco P D, Johnson F A Proc. R. Soc. London A 310 111 (1969)
  54. Meissner G Z. Phys. 247 203 (1971)
  55. Landshoff R Z. Phys. 102 201 (1936); Landshoff R Phys. Rev. 52 246 (1937)
  56. Löwdin P O A Theoretical Investigation Into Some Properties Of Ionic Crystals (Uppsala: Heinman, 1948)
  57. Hohenberg P, Kohn W Phys. Rev. 136 B864 (1964)
  58. Kohn W, Sham L J Phys. Rev. 140 A1133 (1965)
  59. Lang N D Solid State Phys. 28 225 (1973)
  60. Callaway J, March N H Solid State Phys. 38 136 (1984)
  61. Lundqvist S, March N H (Eds) Theory Of The Inhomogeneous Electron Gas (New York: Plenum Press, 1983)
  62. Levy M Proc. Natl. Acad. Sci. USA 76 6062 (1979)
  63. Ceperley D Phys. Rev. B 18 3126 (1978); Ceperley D M, Alder B J Phys. Rev. Lett. 45 566 (1980)
  64. Kirzhnits D A, Lozovik Yu E, Shpatakovskaya G V Usp. Fiz. Nauk 117 3 (1975); Kirzhints D A, Lozovik Yu E, Shpatakovskaya G V Sov. Phys. Usp. 18 649 (1975)
  65. Gordon R G, Kim Y S J. Chem. Phys. 56 3122 (1972)
  66. Gaidaenko V I, Nikulin V K Chem. Phys. Lett. 7 360 (1970)
  67. Kim Y S, Gordon R G Phys. Rev. B 9 3548 (1974)
  68. Cohen A J, Gordon R G Phys. Rev. B 12 3228 (1975)
  69. Cohen A J, Gordon B C Phys. Rev. B 14 4593 (1976)
  70. Muhlhausen C, Gordon R G Phys. Rev. B 23 900 (1981)
  71. LeSar R, Gordon R G Phys. Rev. B 25 7221 (1982)
  72. Boyer L L Phys. Rev. Lett. 45 1858 (1980)
  73. Boyer L L Ferroelectrics 35 83 (1981)
  74. Boyer L L, Hardy J R Phys. Rev. B 24 2577 (1981)
  75. Flocken J W, Hardy J R, Boyer L L Ferroelectrics 55 793 (1984)
  76. Perdew J P, Zunger A Phys. Rev. B 23 5048 (1981)
  77. Sham L J Phys. Rev. B 7 4357 (1973)
  78. Shaginyan V R Solid State Commun. 55 9 (1985)
  79. Dolgov O V, Maksimov E G Usp. Fiz. Nauk 135 441 (1981); Dolgov O V, Maksimov E G Rev. Mod. Phys. 53 81 (1981)
  80. Cohen M L Phys. Ser. T1 5 (1982)
  81. Martin R M J. Phys. Paris 42 C6-617 (1981)
  82. Kunc K, Martin R M Physica B + C 117-118 511 (1983)
  83. Ab Initio Calculation of Phonon Spectra (Proc. CECAM Workshop, Antwerp, Belgium, 1981 (Eds J T Devreese, V E van Doren, P E van Camp) (New York: Plenum Press, 1983)
  84. Yin M T, Cohen M L Phys. Rev. B 25 7403 (1982)
  85. Froyen S, Cohen M L Phys. Rev. B 29 3770 (1984)
  86. Kunc K, Martin R M Phys. Rev. Lett. 48 406 (1982)
  87. Van Camp P E, Van Doren V E, Devreese J T Phys. Rev. B 25 4270 (1982)
  88. Resta R, Baldereschi A Phys. Rev. B 24 4839 (1981)
  89. Brillson L J, Brustein E, Maradudin A A, Stark T J. Phys. Chem. Solids 32 (Suppl. 1) 187 (1970)
  90. Lucovsky G, Keezer R C, Burstein E Solid State Commun. 5 439 (1967)
  91. Sham L J Phys. Rev. B 6 3581 (1972)
  92. Kharrison U Elektronnaya Struktura i Svoistva Tverdykh Tel Vol. 2 (M.: Mir, 1983), Chap. 14; Harrison W A Electronic Structure And The Properties Of Solids (San Francisco: W. H. Freeman, 1980), Chap. 14
  93. Volkov B A, Kushnir V P, Pankratov O A Fiz. Tverd. Tela 24 415 (1982); Volkov B A, Kushnir V P, Pankratov O A Sov. Phys. Solid State 24 235 (1982)
  94. Kvyatkovskii O E Fiz. Tverd. Tela 27 2673 (1985); Kvyatkovskii O E Sov. Phys. Solid State 27 1603 (1985)
  95. Adler S L Phys. Rev. 126 413 (1962)
  96. Szigeti B Trans. Faraday Soc. 45 155 (1949)
  97. Maksimov E G, Mazin I I Solid State Commun. 27 527 (1978)
  98. Paierls R Kvantovaya Teoriya Tverdykh Tel (M.: IL, 1956), Gl. 5
  99. Kawamura H Proc. Third Intern. Conf. on Physics of Narrow-Gap Semiconductors, Warsaw, 1977 (Eds J Rauluszkiewicz, M Gorska, E Kaczmarek) (Amsterdam: Elsevier, 1978) p. 7
  100. Penn D R Phys. Rev. 128 2093 (1962)
  101. Littlewood P B, Heine V J. Phys. C 12 4431 (1979)
  102. Slater J C, Koster G F Phys. Rev. 94 1498 (1954)
  103. Volkov B A, Pankratov O A Zh. Eksp. Teor. Fiz. 75 1362 (1978); Volkov B A, Pankratov O A Sov. Phys. JETP 48 687 (1978)
  104. Volkov B A, Pankratov O A, Sazonov A V Zh. Eksp. Teor. Fiz. 85 1395 (1983); Volkov B A, Pankratov O A, Sazonov A V Sov. Phys. JETP 58 809 (1983)
  105. Volkov B A, Kushnir V P Fiz. Tverd. Tela 25 1803 (1983); Volkov B A, Kushnir V P Sov. Phys. Solid State 25 1038 (1983)
  106. Cardona M, Vogl P Ferroelectrics 53 49 (1984)
  107. Volkov B A, Fal’kovskii L A Zh. Eksp. Teor. Fiz. 85 2135 (1983); Volkov B A, Fal’kovskii L A Sov. Phys. JETP 58 1239 (1983)
  108. Katayama S, Kawamura H Solid State Commun. 21 521 (1977)
  109. Tsu R, Howard W E, Esaki L Phys. Rev. 172 779 (1968)
  110. Bis R F, Dixon J R Phys. Rev. B 2 1004 (1970)
  111. Volkov B A, Kushnir V P Fiz. Tverd. Tela 24 3293 (1982); Volkov B A, Kushnir V P Sov. Phys. Solid State 24 1869 (1982)
  112. Abrikosov N Kh, Shelimova L E Poluprovodnikovye Materialy na Osnove Soedinenii A4B6 (M.: Nauka, 1975)
  113. Novikova S I, Shelimova L E Fiz. Tverd. Tela 9 1336 (1967); Novikova S I, Shelimova L E Sov. Phys. Solid State 9 1046 (1967)
  114. Sugai S, Murase K, Katayama S, Takaoka S, Nishi S, Kawamura H Solid State Commun. 24 407 (1977)
  115. Grassie A D C, Agapito J A, Gonzales P J. Phys. C 12 925 (1979)
  116. Schubert K, Fricke H Z. Metallkd. 44 457 (1953)
  117. Karbanov S G, Zlomanov V P, Novoselova A V Izv. AN SSSR. Ser. Neorganicheskie Materialy 5 1171 (1969); Karbanov S G, Zlomanov V P, Novoselova A V Izv. Inorg. Mater. 5 997 (1969)
  118. Novikova S I, Abrikosov N Kh, Shelimova L E, Karpinskii O G Fiz. Tverd. Tela 19 1171 (1977); Novikova S I, Abrikosov N Kh, Shelimova L E, Karpinskii O G Sov. Phys. Solid State 19 683 (1977)
  119. Hohler G (Ed.) Narrow-Gap Semiconductors (Springer Tracts in Modern Physics) Vol. 98 (Berlin: Springer-Verlag, 1983)
  120. Dynamical Properties Of IV-VI Compounds (Springer Tracts in Modern Physics) Vol. 99 (Berlin: Springer-Verlag, 1983)
  121. Kvyatkovskii O E Fiz. Tverd. Tela 28 983 (1986); Kvyatkovskii O E Sov. Phys. Solid State 28 548 (1986)
  122. Littlewood P B J. Phys. C 13 4855 (1980)
  123. Cohen M H, Falicov L M, Golin S IBM J. Res. Dev. 8 215 (1964)
  124. Cardona M, Greenaway D L Phys. Rev. 133 A1685 (1964)
  125. Lucovsky G, White R M Phys. Rev. B 8 660 (1973)
  126. Phillips J C Rev. Mod. Phys. 42 317 (1970)
  127. Heine V, Weaire D Solid State Phys. 24 249 (1970)
  128. Harrison W A Phys. Rev. B 14 702 (1976)
  129. Zemel J N, Jensen J D, Schoolar R B Phys. Rev. 140 A330 (1965)
  130. Pawley G S, Cochran W, Cowley R A, Dolling G Phys. Rev. Lett. 17 753 (1966)
  131. Khvostantsev L G, Sidorov V A, Shelimova L E, Abrikosov N Kh Phys. Status Solidi A 74 185 (1982)
  132. Cowley E R, Darby J K, Pawley G S J. Phys.C C 2 1916 (1969)
  133. Samara G A Comments Solid State Phys. 8 13 (1977)
  134. Bussmann-Holder A, Bilz H, Kress W J. Phys. Soc. Jpn. 49 (Suppl. A) 737 (1980)
  135. Migoni R, Bilz H, Bauerle D Phys. Rev. Lett. 37 1155 (1976)
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