Issues

 / 

1974

 / 

February

  

Reviews of topical problems


Phonons in nontransition metals

,  a
a National Research Centre ‘Kurchatov Institute’, pl. akad. Kurchatova 1, Moscow, 123182, Russian Federation

The article reviews the present status of the microscopic theory of non-transition-metal lattice vibrations. A regular scheme is described, which makes it possible to analyze in detail the role of the electrons in the formation of the phonon spectrum of metals. It is based on a consistent utilization of a small parameter $V_\mathbf{K}/\varepsilon F$, corresponding to the effective weakness of the interaction between the conduction electron and the ion core ($V_\mathbf{K}$ is the Fourier component of this interaction with a momentum transfer equal to one of the reciprocal-lattice vectors). Expansion of the electron-ion energy of the system in terms of this parameter yields, besides the pair interactions that are traditional for metals, also automatically the effective three-particle etc. unpaired inter-ion forces. It is shown that the unpaired forces play an important and sometimes decisive role in a number of questions, such as lattice stability, compressibility, the Cauchy relations for the elastic moduli, and singularities in the phonon spectrum. The theoretical analysis is illustrated by calculations of the static and dynamic properties of metals, and by comparison with experiment, using Na, Mg, Al, and $\beta$-Sn as examples.

Fulltext pdf (1.5 MB)
Fulltext is also available at DOI: 10.1070/PU1974v017n02ABEH004329
PACS: 63.20.Dj
DOI: 10.1070/PU1974v017n02ABEH004329
URL: https://ufn.ru/en/articles/1974/2/a/
Citation: Brovman E G, Kagan Yu M "Phonons in nontransition metals" Sov. Phys. Usp. 17 125–152 (1974)
BibTexBibNote ® (generic)BibNote ® (RIS)MedlineRefWorks

Îðèãèíàë: Áðîâìàí Å Ã, Êàãàí Þ Ì «Ôîíîíû â íåïåðåõîäíûõ ìåòàëëàõ» ÓÔÍ 112 369–426 (1974); DOI: 10.3367/UFNr.0112.197403a.0369

Cited by (162) ↓ Similar articles (20)

  1. Kagan M Lecture Notes In Physics Vol. Lecture Notes of Professor Yuri Kagan in Theoretical Solid-State PhysicsLecture 11. Neutron Scattering on Crystals1048 Chapter 11 (2026) p. 181
  2. Kagan M Lecture Notes In Physics Vol. Lecture Notes of Professor Yuri Kagan in Theoretical Solid-State PhysicsLecture 7. Density of the Phonon States. Debye Approximation1048 Chapter 7 (2026) p. 107
  3. Kagan M Lecture Notes In Physics Vol. Lecture Notes of Professor Yuri Kagan in Theoretical Solid-State PhysicsLecture 17. Correlation Energy for the Interaction of Electrons with Opposite Spins1048 Chapter 17 (2026) p. 309
  4. Kagan M Lecture Notes In Physics Vol. Lecture Notes of Professor Yuri Kagan in Theoretical Solid-State PhysicsLecture 10. Mossbauer Effect: Diagonal Processes with Respect to Phonon Occupation Numbers1048 Chapter 10 (2026) p. 167
  5. Kagan M Lecture Notes In Physics Vol. Lecture Notes of Professor Yuri Kagan in Theoretical Solid-State PhysicsLecture 9. Phonon Distribution Function: Specific Heat of the Crystal1048 Chapter 9 (2026) p. 149
  6. Kagan M Lecture Notes In Physics Vol. Lecture Notes of Professor Yuri Kagan in Theoretical Solid-State PhysicsLecture 15. Basic Interactions in Metals: Ion–Ion and Electron–Ion Interaction1048 Chapter 15 (2026) p. 275
  7. Kagan M Lecture Notes In Physics Vol. Lecture Notes of Professor Yuri Kagan in Theoretical Solid-State PhysicsLecture 8. Phonon Spectrum in Crystals with Pairwise Interaction: Quantization of the Lattice Vibrations1048 Chapter 8 (2026) p. 129
  8. Kagan M Lecture Notes In Physics Vol. Lecture Notes of Professor Yuri Kagan in Theoretical Solid-State PhysicsLecture 18. Charge Screening in Metals in the Random Phase Approximation1048 Chapter 18 (2026) p. 325
  9. Gabovich A M, Kuznetsov V I, Voitenko A I Low Temperature Physics 51 (7) 821 (2025)
  10. Sadovskii M V J Supercond Nov Magn 38 (6) (2025)
  11. Badrtdinov D I, Katsnelson M I, Rudenko A N Phys. Rev. B 110 (6) (2024)
  12. Sadovskii M V Phys. Usp. 65 (07) 724 (2022)
  13. Benedek G, Bernasconi M et al Springer Handbook of Surface Science Springer Handbooks Chapter 23 (2020) p. 737
  14. Chubukov A V, Abanov A et al Annals Of Physics 417 168190 (2020)
  15. Shvets V  T Metallofiz. Noveishie Tekhnol. 42 (7) 901 (2020)
  16. Shvets V T Phys. Metals Metallogr. 121 (1) 1 (2020)
  17. Degtyarenko N N, Grishakov K S, Mazur E A Jetp Lett. 109 (6) 410 (2019)
  18. Skinner G C G, Paxton A T, Moriarty J A Phys. Rev. B 99 (21) (2019)
  19. Gulian M, Melkonyan G, Kasthurirengan S Quantum Stud.: Math. Found. 5 (1) 89 (2018)
  20. Shalaeva E V, Medvedeva N I et al Philosophical Magazine 97 (13) 1024 (2017)
  21. Degtyarenko N N, Mazur E A, Grishakov K S Solid State Communications 262 33 (2017)
  22. Hu H, Wu X et al Journal Of Alloys And Compounds 666 185 (2016)
  23. Shvets V  T Metallofiz. Noveishie Tekhnol. 36 (10) 1287 (2016)
  24. Sidnov K P, Belov D S et al Journal Of Alloys And Compounds 688 534 (2016)
  25. Dmitriev S V, Korznikova E A et al Uspekhi Fizicheskikh Nauk 186 (5) 471 (2016)
  26. Shvets V T Phys. Metals Metallogr. 116 (4) 328 (2015)
  27. Bobrov V B, Zagorodny A G, Trigger S A Low Temperature Physics 41 (11) 901 (2015)
  28. Ponomareva A V, Vekilov Yu Kh, Abrikosov I A Journal Of Alloys And Compounds 586 S274 (2014)
  29. Gabovich A M, Kuznetsov V I Eur. J. Phys. 34 (2) 371 (2013)
  30. Osipenko I A, Kukin O V et al Phys. Solid State 55 (12) 2405 (2013)
  31. Shvets V T, Kozitskii S V Phys. Solid State 55 (4) 681 (2013)
  32. Shvets V T J. Exp. Theor. Phys. 116 (1) 159 (2013)
  33. Shvets V T, Kozytskiy S V Ukr. J. Phys. 58 (05) 458 (2013)
  34. Osipenko I A, Kukin O V, Gufan A Yu Bull. Russ. Acad. Sci. Phys. 77 (7) 913 (2013)
  35. Gufan A Yu, Kukin O V et al Phys. Solid State 54 (4) 820 (2012)
  36. Shvets V T Phys. Metals Metallogr. 113 (10) 927 (2012)
  37. Ponomareva A V, Isaev E I et al Phys. Rev. B 85 (14) (2012)
  38. Shvets’ V T, Kozits’kii S V, Shvets’ T V Ukr. J. Phys. 57 (1) 35 (2012)
  39. Shvets V T, Kozitskii S V, Shvets T V High Temp 50 (2) 194 (2012)
  40. Shvets V T Jetp Lett. 95 (1) 29 (2012)
  41. Gufan Yu M, Kukin O V, Smolin A Yu Bull. Russ. Acad. Sci. Phys. 75 (9) 1267 (2011)
  42. Condensed Matter Physics 1 (2010) p. 341
  43. Gabovich A M, Voitenko A I et al Advances In Condensed Matter Physics 2010 1 (2010)
  44. Egorov V S Uspekhi Fizicheskikh Nauk 180 (8) 785 (2010)
  45. Ebeling W, Blaschke D et al J. Phys. A: Math. Theor. 42 (21) 214033 (2009)
  46. Shvets V T Carbon Nanomaterials in Clean Energy Hydrogen Systems NATO Science For Peace And Security Series C: Environmental Security Chapter 77 (2009) p. 615
  47. Tarenkov V Yu, D’yachenko A I et al Phys. Solid State 51 (9) 1778 (2009)
  48. Ebeling W, Redmer R et al Contrib. Plasma Phys. 48 (9-10) 670 (2008)
  49. Shvets V T Phys. Metals Metallogr. 103 (4) 330 (2007)
  50. Shvets V T J. Exp. Theor. Phys. 104 (4) 655 (2007)
  51. Deligöz E, Çiftci Ya, Çolakoğlu K Materials Letters 59 (17) 2166 (2005)
  52. Kontsevoi O Y, Gornostyrev Yu N, Freeman A J JOM 57 (3) 43 (2005)
  53. Maksimov E G, Magnitskaya M V, Fortov V E Uspekhi Fizicheskikh Nauk 175 (8) 793 (2005)
  54. Ermolaev A M, Rashba G I Low Temperature Physics 29 (11) 945 (2003)
  55. Gabovich A M, Voitenko A I, Ausloos M Physics Reports 367 (6) 583 (2002)
  56. Egorov V S, Lykov P V J. Exp. Theor. Phys. 94 (1) 162 (2002)
  57. Nonequilibrium Electrons and Phonons in Superconductors Selected Topics In Superconductivity Chapter 3 (2002) p. 67
  58. Shvets V T High Temperature 39 (1) 49 (2001)
  59. Pélissier J L, Wetta N Physica A: Statistical Mechanics And Its Applications 289 (3-4) 459 (2001)
  60. Gabovich A M, Voitenko A I et al Supercond. Sci. Technol. 14 (4) R1 (2001)
  61. Dorfman S, Liubich V et al J. Phys.: Condens. Matter 13 (31) 6719 (2001)
  62. Fuks D, Dorfman S et al Int J Of Quantum Chemistry 85 (4-5) 354 (2001)
  63. Pogosov V V, Kurbatsky V P J. Exp. Theor. Phys. 92 (2) 304 (2001)
  64. Gornostyrev Yu N, Katsnelson M I et al Phys. Rev. B 62 (12) 7802 (2000)
  65. Karakozov A E, Maksimov E G J. Exp. Theor. Phys. 88 (5) 987 (1999)
  66. Fedorov A S Phys. Solid State 41 (2) 213 (1999)
  67. Revinskii A F Semiconductors 32 (9) 917 (1998)
  68. Strauch D, Pavone P et al Advances In Solid State Physics Vol. Advances in Solid State Physics 37Ab initio lattice dynamics: Methods, results, and applications37 Chapter 7 (1998) p. 99
  69. Colakoğlu K, Colak H et al Nouv Cim D 20 (12) 1863 (1998)
  70. Strauch D, Pavone P et al Advances in Solid State Physics / Festkörperprobleme Chapter 7 (1998) p. 99
  71. Zhernov A P J. Exp. Theor. Phys. 87 (6) 1172 (1998)
  72. Katsnelson M I, Sigalas M et al Philosophical Magazine B 75 (3) 407 (1997)
  73. Katsnelson M I, Naumov I I et al Philosophical Magazine B 75 (3) 389 (1997)
  74. Krivoglaz M A X-Ray and Neutron Diffraction in Nonideal Crystals Chapter 2 (1996) p. 75
  75. Krivolaz M A Diffuse Scattering of X-Rays and Neutrons by Fluctuations Chapter 2 (1996) p. 51
  76. Ponedilok G V, Savenko V P Physica Status Solidi (b) 184 (2) 433 (1994)
  77. Khodel V A, Shaginyan V R, Khodel V V Physics Reports 249 (1-2) 1 (1994)
  78. Shvets V T Materials Science And Engineering: B 26 (2-3) 141 (1994)
  79. Katsnelson M I, Naumov I I, Trefilov A V Phase Transitions 49 (1-3) 143 (1994)
  80. Kovalenko N P, Krasny Yu P, Mikho V V Journal Of Molecular Liquids 58 45 (1993)
  81. Malozovsky Y M, Fan J D Physics Letters A 184 (1) 136 (1993)
  82. Okoye C M I, Pal S Physica B: Condensed Matter 183 (3) 279 (1993)
  83. Kodess B N, Rakhmanov S Ya Solid State Communications 87 (7) 631 (1993)
  84. Aronov I E, Fal’ko V L Physics Reports 221 (2-3) 81 (1992)
  85. Gornostyrev Yu N, Katsnelson M I et al Physica Status Solidi (b) 164 (1) 185 (1991)
  86. Ebina K, Kaburagi M Surface Science 242 (1-3) 124 (1991)
  87. Idiodi J O A Physica Status Solidi (b) 166 (2) 369 (1991)
  88. Kovalenko N P, Krasny Yu P Physica B: Condensed Matter 162 (2) 115 (1990)
  89. EBINA Kuniyoshi, KABURAGI Makoto Strongly Coupled Plasma Physics (1990) p. 397
  90. Mohapatra M, Tolpadi S Pramana - J Phys 35 (2) 159 (1990)
  91. Sandalov I S, Filatjev V I Physica B: Condensed Matter 162 (2) 139 (1990)
  92. EBINA Kuniyoshi, KABURAGI Makoto Strongly Coupled Plasma Physics (1990) p. 397
  93. Fomichev S V, Katsnelson M I et al Physica Status Solidi (b) 161 (1) 153 (1990)
  94. Greenberg B A, Katsnelson M I et al Physica Status Solidi (b) 158 (2) 441 (1990)
  95. Vaks V G, Katsnelson M I et al J. Phys.: Condens. Matter 1 (32) 5319 (1989)
  96. GOROBCHENKO V D, KOHN V N, MAKSIMOV E G Modern Problems In Condensed Matter Sciences Vol. The Dielectric Function of Condensed SystemsThe Dielectric Function of the Homogeneous Electron Gas24 (1989) p. 87
  97. Tyuterev V G Soviet Physics Journal 32 (6) 479 (1989)
  98. Vonsovsky S V, Katsnelson M I Springer Series In Solid-State Sciences Vol. Quantum Solid-State PhysicsMany-Particle Effects73 Chapter 5 (1989) p. 396
  99. Ebina K, Miyagi H Physics Letters A 142 (4-5) 237 (1989)
  100. Vaks V G, Samolyuk G D, Trefilov A V Physics Letters A 127 (1) 37 (1988)
  101. Prakash D, Upadhyaya J C Journal Of Physics And Chemistry Of Solids 49 (1) 91 (1988)
  102. Vaks V G, Trefilov A V J. Phys. F: Met. Phys. 18 (2) 213 (1988)
  103. Prakash D, Upadhyaya J C Physica Status Solidi (b) 148 (2) (1988)
  104. Zhernov A P, Kulagina T N Physica Status Solidi (b) 147 (1) 149 (1988)
  105. Kovalenko N P, Krasnyi Yu P et al Soviet Journal of Low Temperature Physics 13 (9) 535 (1987)
  106. Harrison R J Condensed Matter Theories Chapter 21 (1986) p. 207
  107. Orlov V G Journal Of Magnetism And Magnetic Materials 61 (3) 337 (1986)
  108. Bogdanov V I, Fuks D L Physica Status Solidi (b) 131 (2) 495 (1985)
  109. Grechnev G E Soviet Journal of Low Temperature Physics 11 (1) 55 (1985)
  110. Moraitis G, Khalifeh J, Demangeat C Journal Of The Less Common Metals 101 203 (1984)
  111. Kovalenko N P, Kuzmina L M Physica Status Solidi (b) 124 (2) 537 (1984)
  112. Reznik I M, Tolpygo K B J Struct Chem 24 (4) 501 (1984)
  113. Fielek B L J. Phys. F: Met. Phys. 14 (1) 61 (1984)
  114. Ebeling W, Fortov V E et al Experientia Supplementum Vol. Transport Properties of Dense PlasmasReferences47 Chapter 7 (1984) p. 168
  115. Kowalenko N P, Krasny Yu P Experientia Supplementum Vol. Transport Properties of Dense PlasmasTheory of Equilibrium and Kinetic Properties of Liquid Metals47 Chapter 5 (1984) p. 127
  116. Dementyev V M, Kozlov E V, Kolodeznaya S F MRS Proc. 39 (1984)
  117. Ebina K Progress Of Theoretical Physics 69 (6) 1686 (1983)
  118. Kapitonov V S, Popov V N J Math Sci 23 (4) 2421 (1983)
  119. John W Ergebnisse in der Elektronentheorie der Metalle Chapter 10 (1983) p. 375
  120. Karakhtanov V S, Maksimov E G Solid State Communications 48 (1) 85 (1983)
  121. Bratkovsky A M, Vaks V G, Trefilov A V J. Phys. F: Met. Phys. 13 (12) 2517 (1983)
  122. Ebina K, Nagara H, Miyagi H Progress Of Theoretical Physics 68 (3) 781 (1982)
  123. Kozlov � V, Dement’ev V M Soviet Physics Journal 25 (12) 1122 (1982)
  124. Bratkovsky A M, Vaks V G et al J. Phys. F: Met. Phys. 12 (7) 1293 (1982)
  125. Vonsovsky S V, Izyumov Yu A, Kurmaev E Z Springer Series In Solid-State Sciences Vol. Superconductivity of Transition MetalsSuperconductivity in Transition Metals27 Chapter 4 (1982) p. 179
  126. Zarochentsev E V, Teplov S V Physica Status Solidi (b) 113 (1) 259 (1982)
  127. Bogdanov V I, Ruban A V, Fuks D L Physica Status Solidi (b) 110 (2) 431 (1982)
  128. Vonsovsky S V, Izyumov Yu A, Kurmaev E Z Springer Series In Solid-State Sciences Vol. Superconductivity of Transition MetalsIntroduction27 Chapter 1 (1982) p. 1
  129. Smirnov V A, Kiselev Yu V, Kozlov � V Soviet Physics Journal 25 (3) 213 (1982)
  130. Christoph V, Kuzemsky A L, Frauenheim T Crystalline Electric Field Effects in f-Electron Magnetism Chapter 24 (1982) p. 219
  131. Ebina K Progress Of Theoretical Physics 67 (2) 475 (1982)
  132. Stupfel B, Gautier F J. Phys. F: Met. Phys. 12 (8) 1577 (1982)
  133. Khwaja F A, Razmi M S K Physica Status Solidi (b) 104 (2) 727 (1981)
  134. Augst G R Physica Status Solidi (b) 104 (1) 357 (1981)
  135. Fielek B L J. Phys. F: Met. Phys. 11 (10) 2021 (1981)
  136. Zarochentsev E V, Teplov S V Solid State Communications 33 (11) 1107 (1980)
  137. Shvets V T Theor Math Phys 42 (2) 178 (1980)
  138. Vaks V G, Kravchuk S P, Trefilov A V J. Phys. F: Met. Phys. 10 (11) 2325 (1980)
  139. Nakamura T, Nagara H, Miyagi H Progress Of Theoretical Physics 63 (2) 368 (1980)
  140. Katsnelson A A, Silonov V M, Khwaja F A Physica Status Solidi (b) 91 (1) 11 (1979)
  141. Postnikov V S, Postnikov V V, Fedorov V M Physica Status Solidi (b) 92 (1) 347 (1979)
  142. Vaks V G, Zein N E et al Physica Status Solidi (b) 96 (2) 857 (1979)
  143. Vaks V G, Zarochentsev E V et al Physica Status Solidi (b) 85 (1) 63 (1978)
  144. Fielek B L J. Phys. F: Met. Phys. 8 (4) 577 (1978)
  145. Hammerberg J Journal Of Physics And Chemistry Of Solids 39 (6) 617 (1978)
  146. Zarochentsev E V, Teplov S V, Safronov V P Soviet Journal of Low Temperature Physics 4 (3) 187 (1978)
  147. Chakravarty S, Ashcroft N W Phys. Rev. B 18 (9) 4588 (1978)
  148. Kaner É A, Chebotarev L V, Uvimana É Soviet Journal of Low Temperature Physics 4 (9) 574 (1978)
  149. Kagan Yu, Pushkarev V V, Holas A Solid State Communications 27 (4) 335 (1978)
  150. Vaks V G, Zarochentsev E V et al Physica Status Solidi (b) 85 (2) 749 (1978)
  151. Bigun G I Theor Math Phys 37 (1) 915 (1978)
  152. Zarochentsev E V, Safronov V P, Trefilov A V Soviet Journal of Low Temperature Physics 3 (2) 100 (1977)
  153. Krasko G L, Makhnovetskii A B Physica Status Solidi (b) 80 (2) 713 (1977)
  154. Lazarev B G, Kaner E A, Chebotarev L V Soviet Journal of Low Temperature Physics 3 (6) 394 (1977)
  155. Cusack S, March N H et al J. Phys. F: Met. Phys. 6 (5) 749 (1976)
  156. Stepanov V G, Kozhevnikov V F Journal Of Engineering Physics 30 (5) 567 (1976)
  157. Schulz H, Hüfner S Solid State Communications 20 (9) 827 (1976)
  158. Solt G, Kollár J Solid State Communications 16 (4) 453 (1975)
  159. Solt G, Kollár J Physica Status Solidi (b) 71 (2) 769 (1975)
  160. Krasko G L, Makhnovetskii A B Physica Status Solidi (b) 66 (1) 349 (1974)
  161. Belenkii A Ya, Krasko G L Physica Status Solidi (b) 65 (1) 73 (1974)
  162. Krasko G L, Makhnovetskii A B Physica Status Solidi (b) 65 (2) 869 (1974)

© 1918–2026 Uspekhi Fizicheskikh Nauk
Email: ufn@ufn.ru Editorial office contacts About the journal Terms and conditions