RSS feeds
РусскийEnglish
Issue 9, 2026
Volume year page
Issues Authors PACS Subscription For authors

Issues

 / 

1979

 / 

June

←  →

Reviews of topical problems


Spinodal decomposition (phase transitions via unstable states)

 a,
a Institute of Thermal Physics, Ural Branch of the Russian Academy of Sciences, Pervomaiskaya str. 91, Ekaterinburg, 620219, Russian Federation

Considerable deviations from equilibrium conditions are observed for nonstatic, first-order phase transitions. In some cases, unstable (labile) phase states may precede the onset of the phase transition. The relaxation of the system is then accompanied by an enhancement of random inhomogeneities and the appearance of a modulated intermediate structure. This mechanism of the initial stage of a phase transition is called spinodal decomposition (SD). Theoretical and experimental studies of SD in two-component systems are reviewed in this paper. Thermodynamic stability and the possibility of SD in one-component liquid-vapor systems and an alternative nucleation mechanism are discussed. The phenomenological theory of SD is based on the Ginzburg-Landau expression for the free energy of an inhomogeneous system. A linearized diffusion equation is derived, for which thermodynamically unstable states have exponentially increasing solutions for the Fourier components of composition. Subsequent refinements of SD theory take into account thermal fluctuations and involve the derivation of the kinetic equation for the distribution functional. Diffraction methods are the most effective in the experimental study of SD in alloys, glasses, and binary liquid mixtures. So far, the agreement between theory and experiment must be regarded as only qualitative.

Fulltext pdf (2.3 MB)
Fulltext is also available at DOI: 10.1070/PU1979v022n06ABEH005571
PACS: 64.60.−i, 64.70.Fx, 64.80.Eb (all)
DOI: 10.1070/PU1979v022n06ABEH005571
URL: https://ufn.ru/en/articles/1979/6/a/
Citation: Skripov V P, Skripov A V "Spinodal decomposition (phase transitions via unstable states)" Sov. Phys. Usp. 22 389–410 (1979)
BibTexBibNote ® (generic)BibNote ® (RIS)MedlineRefWorks

Оригинал: Скрипов В П, Скрипов А В «Спинодальный распад (Фазовый переход с участием неустойчивых состояний)» УФН 128 193–231 (1979); DOI: 10.3367/UFNr.0128.197906a.0193

Cited by (199) ↓ Similar articles (20)

  1. Wang J, Nde Ju et al Phys. Rev. Research 8 (3) (2026)
  2. ’i’?’?’?’?’?’?ch ’M ’E, ’i’?’?ут’?’?’? ’B ’E ’? ’?р ’zр’?’?’?’?’?ы ’?’?sh’?’?’?стр’?’?’?’?ya ’? ’?’?т’?’?’?т’?’?’?ts’?’? 2 (4c) 4 (2026)
  3. Radkevich E V, Ragutkin A V et al J. Mach. Manuf. Reliab. 55 (1) 1 (2026)
  4. Huang Ya, Liu Z et al Acta Mech. Solida Sin. (2026)
  5. Gunes E, Kalay Y E Materials Characterization 239 116744 (2026)
  6. Wang Sh, Sheng H, Zhou G Appl. Phys. A 132 (9) (2026)
  7. Zhang X, Woodgate C D et al Acta Materialia 307 121965 (2026)
  8. Hingangavkar G M Next Research 4 101224 (2026)
  9. Kovalchuk V I, Zabashta Yu F, Bulavin L A Ukr. J. Phys. 71 (6) 529 (2026)
  10. Alhamdani N, Wasfi M K Al-Kitab J. Pure Sci. 10 (01) 110 (2026)
  11. Radkevich E V, Ragutkin A V et al Tech. Phys. 70 (9) 339 (2025)
  12. Radkevich E V, Stavrovsky M E et al Rossijskij Tehnologičeskij žurnal 13 (4) 107 (2025)
  13. Radkevich E V, Rykov Yu G Lobachevskii J Math 46 (11) 5639 (2025)
  14. Budkov Yu A, Kalikin N N, Brandyshev P E The Journal of Chemical Physics 163 (2) (2025)
  15. Melkikh A, Rutin S et al FHMT 23 (3) 721 (2025)
  16. Frielinghaus H, Gommes C J J Appl Crystallogr 58 (5) 1553 (2025)
  17. Radkevich E V, Stavrovskii M E et al Russ. Metall. 2025 (5) 966 (2025)
  18. Zhao Yu, Rajkowski M et al Acta Materialia 298 121400 (2025)
  19. Radkevich E V, Ragutkin A V et al Tech. Phys. 70 (9) 353 (2025)
  20. Denisenko Yu I Russ Microelectron 54 (8) 1360 (2025)
  21. Vasiliev A L, Trunkin I N et al Crystallogr. Rep. 70 (6) 908 (2025)
  22. Kuznetsov D, Kuznetsova E et al Nanomaterials 15 (19) 1466 (2025)
  23. Martovitskii V P, Nikitin M V, Pokrovskii V Ya Jetp Lett. 120 (1) 38 (2024)
  24. Igol’nikov A A, Ryutin S B, Skripov P V J Appl Mech Tech Phy 65 (4) 771 (2024)
  25. Kamo Y, Matsumoto A Molecules 29 (9) 2059 (2024)
  26. Botchev M A, Fahurdinov I A, Savenkov E B Comput. Math. And Math. Phys. 64 (8) 1726 (2024) [Botchev M A, Fakhurdinov I A, Savenkov E B Žurnal Vyčislitelʹnoj Matematiki I Matematičeskoj Fiziki 64 (8) 1366 (2024)]
  27. Igolnikov A, Skripov P Energies 16 (5) 2109 (2023)
  28. Parmar V, Singh S et al Optics & Laser Technology 165 109575 (2023)
  29. Buchin E Yu, Denisenko Yu I Glass Phys Chem 49 (5) 535 (2023)
  30. Volosnikov D V, Povolotskiy I I, Skripov P V J. Engin. Thermophys. 32 (1) 1 (2023)
  31. Ranjbarrad S, Chan P K Can J Chem Eng 101 (10) 5743 (2023)
  32. Kravchenko N Yu, Kovtunov S S Discrete And Continuous Models 31 (1) 75 (2023)
  33. Lebedev V G, Shklyaev K Y et al Calphad 83 102615 (2023)
  34. Igolnikov A, Rutin S, Skripov P Applied Thermal Engineering 215 118904 (2022)
  35. Gumarov A I, Yanilkin I V et al Appl Magn Reson 53 (6) 875 (2022)
  36. Skripov P Energies 15 (12) 4440 (2022)
  37. Sorokin M V, Ahmad I et al 2022 19th International Bhurban Conference on Applied Sciences and Technology (IBCAST), (2022) p. 10
  38. Poluektov Yu M, Soroka A A Phase Transitions 95 (4) 267 (2022)
  39. Zhang G, Qin Zh et al Computational Materials Science 213 111659 (2022)
  40. Sibirev N V, Berdnikov Yu S et al Semiconductors 56 (1) 14 (2022)
  41. Skripov P V, Igolnikov A A et al International Journal Of Heat And Mass Transfer 184 122290 (2022)
  42. Ranjbarrad S, Chan P K Polymers 14 (20) 4345 (2022)
  43. Saurov A N, L’vov P E et al J. Mater. Chem. C 10 (15) 5864 (2022)
  44. Son L D Bull. Russ. Acad. Sci. Phys. 86 (2) 145 (2022)
  45. Zemtsova N D Crystallogr. Rep. 67 (2) 236 (2022)
  46. Boytsova O V, Makarevich O N et al Inorg Mater 58 (7) 673 (2022)
  47. Shrivastava Sh Progress In Biophysics And Molecular Biology 162 111 (2021)
  48. Galimzyanov B N, Doronina M A, Mokshin A V Journal Of Non-Crystalline Solids 572 121102 (2021)
  49. Shilkina L A, Nagaenko A V et al Journal Of Alloys And Compounds 866 158871 (2021)
  50. Igolnikov A A, Rutin S B, Skripov P V Thermochimica Acta 695 178815 (2021)
  51. Gumarov A I, Yanilkin I V et al Materials Letters 305 130783 (2021)
  52. Kovalchuk V Condens. Matter Phys. 24 (4) 43601 (2021)
  53. Volosnikov D V, Povolotsky I I et al High Temp 59 (2-6) 283 (2021)
  54. Skripov P V, Yampol’skiy A D, Rutin S B Handbook of Research on Advancements in Supercritical Fluids Applications for Sustainable Energy Systems Advances In Chemical And Materials Engineering chapter 12 (2021) p. 424
  55. Basko M M Appl. Math. Mech.-Engl. Ed. 42 (6) 871 (2021)
  56. Osipovich K, Vorontsov A et al Metals 11 (8) 1151 (2021)
  57. Vasin M G, Lebedev V G Journal Of Non-Crystalline Solids 543 120131 (2020)
  58. (THE 2ND INTERNATIONAL CONFERENCE ON PHYSICAL INSTRUMENTATION AND ADVANCED MATERIALS 2019) Vol. THE 2ND INTERNATIONAL CONFERENCE ON PHYSICAL INSTRUMENTATION AND ADVANCED MATERIALS 2019Non-stationary heat transfer beyond diffusion spinodal of a solutionS. B.RutinP. V.SkripovA. A.Igolnikov2314 (2020) p. 030046
  59. Blagonravov L A, Silina T I Moscow Univ. Phys. 75 (4) 363 (2020)
  60. Lyakhov G A, Shcherbakov I A, Shermeneva M A Phys. Wave Phen. 28 (3) 236 (2020)
  61. Davydov S, Gorlenko A Science intensive technologies in mechanical engineering 2020 (2) 28 (2020)
  62. Lebedev V G, Obukhov A A, Vasin M G Journal Of Non-Crystalline Solids 505 414 (2019)
  63. Spivak L V, Shchepina N E Phys. Solid State 61 (8) 1347 (2019)
  64. Lebedev V G, Galenko P K J. Exp. Theor. Phys. 129 (1) 86 (2019)
  65. Spivak L V, Shchepina N E Tech. Phys. 64 (9) 1319 (2019)
  66. Narayanam Ch, Kumar A et al J. Phys. Chem. C 123 (22) 13958 (2019)
  67. Blagonravov L A, Laptinskaya T V Russ. J. Phys. Chem. 93 (7) 1270 (2019)
  68. Steyn-Ross M L, Steyn-Ross D A et al Phys. Rev. E 99 (1) (2019)
  69. Kumar A, Narayanam Ch et al Phys. Rev. E 100 (6) (2019)
  70. Radkevich E V, Vasil’eva O A, Sidorov M I Dokl. Math. 100 (3) 571 (2019)
  71. Levin D M, Kolmakov Yu N DDF 383 74 (2018)
  72. Basko M M Physics Of Fluids 30 (12) 123306 (2018)
  73. Li Ya, Li Ch et al Journal Of Thermal Stresses 41 (10-12) 1364 (2018)
  74. Spivak L V, Shchepina N E Phys. Solid State 60 (12) 2598 (2018)
  75. L’vov P E, Svetukhin V V Modelling Simul. Mater. Sci. Eng. 26 (4) 045001 (2018)
  76. Frolov A M, Kraynova G S, Dolzhikov S V J. Surf. Investig. 11 (2) 339 (2017)
  77. L’vov P E, Svetukhin V V Modelling Simul. Mater. Sci. Eng. 25 (7) 075006 (2017)
  78. Davydov S V, Petrov E V Tech. Phys. 62 (8) 1207 (2017)
  79. Zhang G, Yang T et al Phys. Rev. E 96 (3) (2017)
  80. Kharchenko D O, Kharchenko V O et al Physica A: Statistical Mechanics And Its Applications 486 497 (2017)
  81. Bordonskiy G S Tech. Phys. 61 (8) 1250 (2016)
  82. Lyakhova N B, Shkirin A V, Lyakhov G A Phys. Wave Phen. 24 (2) 142 (2016)
  83. Bunkin N F, Shkirin A V et al The Journal of Chemical Physics 145 (18) (2016)
  84. Davydov S Yu, Lebedev A A et al Tech. Phys. Lett. 42 (12) 1153 (2016)
  85. Avdeev A A Bubble Systems Mathematical Engineering Chapter 8 (2016) p. 265
  86. Balashov V A, Savenkov E B KIAM Prepr. (13) 1 (2016)
  87. L’vov P E, Svetukhin V V Phys. Solid State 57 (6) 1213 (2015)
  88. Bunkin N F, Lyakhov G A et al Phys. Wave Phen. 23 (4) 241 (2015)
  89. Kushchev S B, Bosykh M A et al Inorg Mater 51 (7) 673 (2015)
  90. Shikin V Physica B: Condensed Matter 460 126 (2015)
  91. Lebedev A A, Zamoryanskaya M V et al MSF 778-780 247 (2014)
  92. Davydov S Yu, Lebedev A A Semiconductors 48 (6) 701 (2014)
  93. Nakoryakov V E, Tsoi A N et al Thermophys. Aeromech. 21 (3) 279 (2014)
  94. Lebedev A A, Zamoryanskaya M V et al Journal Of Crystal Growth 396 100 (2014)
  95. L’vov P E, Svetukhin V V Phys. Solid State 56 (9) 1889 (2014)
  96. Khomenkova L, An Y -T et al Physica B: Condensed Matter 453 100 (2014)
  97. Semenov A A, Woo C H Journal Of Nuclear Materials 454 (1-3) 60 (2014)
  98. Zhang G, Liu G et al RSC Adv. 4 (14) 7068 (2014)
  99. Wagner R, Kampmann R, Voorhees P W Materials Science and Technology 1 (2013)
  100. Belovolova L V, Vinogradov E A, Glushkov M V Phys. Wave Phen. 21 (3) 190 (2013)
  101. Lebedev A A, Zamorianskaya M V et al Semiconductors 47 (11) 1539 (2013)
  102. L’vov P E, Svetukhin V V Phys. Solid State 55 (11) 2374 (2013)
  103. Zhang G, Qiao G The Journal of Chemical Physics 139 (13) (2013)
  104. Xiao Z H, Semenov A A et al Journal Of Nuclear Materials 439 (1-3) 25 (2013)
  105. L’vov P E, Svetukhin V V Phys. Solid State 54 (11) 2285 (2012)
  106. Ionin A A, Kudryashov S I et al Jetp Lett. 94 (10) 753 (2012)
  107. Baten’kin M A, Mensov S N Polym. Sci. Ser. B 54 (9-10) 496 (2012)
  108. Kharchenko D O, Lysenko I O, Kharchenko V O Usp. Fiz. Met. 13 (2) 101 (2012)
  109. Zhukov V T, Zaitsev N A et al Math Models Comput Simul 4 (4) 440 (2012)
  110. Semenov A A, Woo C H Acta Materialia 60 (17) 6112 (2012)
  111. Ionin A A, Kudryashov S I et al Jetp Lett. 94 (4) 266 (2011)
  112. Vasilevskaya T N, Andreev N S Phys. Solid State 53 (11) 2250 (2011)
  113. Belovolova L V, Glushkov M V, Vinogradov E A BIOPHYSICS 56 (2) 181 (2011)
  114. Semenov A A, Woo C H Journal Of Nuclear Materials 411 (1-3) 144 (2011)
  115. Rykov Yu G, Zaitsev N A Math Models Comput Simul 3 (4) 468 (2011)
  116. Nakoryakov V E, Zakharov V E et al J. Engin. Thermophys. 20 (4) 335 (2011)
  117. Maslov V P Math Notes 90 (3-4) (2011)
  118. Galenko P K, Kharchenko D, Lysenko I Physica A: Statistical Mechanics And Its Applications 389 (17) 3443 (2010)
  119. Yukalov V I Symmetry 2 (1) 40 (2010)
  120. Kukadiya S B, Chan P K, Mehrvar M Macro Theory & Simulations 18 (2) 97 (2009)
  121. Mebed A M, Abd-Elrahman M I et al Phase Transitions 82 (8) 587 (2009)
  122. Wu B Journal of Applied Physics 105 (5) (2009)
  123. Kharchenko D O, Galenko P K, Lebedev V G Usp. Fiz. Met. 10 (1) 27 (2009)
  124. Mao S Transport in Laser Microfabrication 1 6 (2009) p. 146
  125. Kinetics of First??BOrder Phase Transitions 1 (2009) p. 399
  126. Mirgorod Yu, Borshch N A et al Russ J Appl Chem 82 (8) 1357 (2009)
  127. Inde?etsev D A, Osipova E V Phys. Solid State 51 (9) 1901 (2009)
  128. Galenko P, Jou D Physica A: Statistical Mechanics And Its Applications 388 (15-16) 3113 (2009)
  129. Lecoq N, Zapolsky H, Galenko P Eur. Phys. J. Spec. Top. 177 (1) 165 (2009)
  130. Abylkalykova R B, Tazhibaeva G B et al Bull. Russ. Acad. Sci. Phys. 73 (11) (2009)
  131. Galenko P, Lebedev V Physics Letters A 372 (7) 985 (2008)
  132. Critical Behavior of Non??BIdeal Systems 1 (2008) p. 229
  133. Abyzov A S, Schmelzer Jürn W P The Journal of Chemical Physics 127 (11) (2007)
  134. Galenko P K, Lebedev V G Jetp Lett. 86 (7) 458 (2007)
  135. Sobol’ O V Phys. Solid State 49 (6) 1161 (2007)
  136. Schmelzer J W P, Abyzov A S J. Engin. Thermophys. 16 (3) 119 (2007)
  137. Galenko P, Lebedev V Philosophical Magazine Letters 87 (11) 821 (2007)
  138. Borman V D, Zenkevich A V et al J. Exp. Theor. Phys. 103 (6) 850 (2006)
  139. Andreev S N, Samokhin A A, Smurov I Applied Surface Science 252 (13) 4506 (2006)
  140. Cheng Ch, Xu X Phys. Rev. B 72 (16) (2005)
  141. Xu X 37th AIAA Thermophysics Conference, (2004)
  142. Xu X MRS Proc. 850 (2004)
  143. Vidal F, Johnston T W et al Phys. Rev. B 70 (18) (2004)
  144. Xu X, Cheng Ch, Chowdhury I H Journal of Heat Transfer 126 (5) 727 (2004)
  145. Baidakov V G Dokl. Phys. 49 (1) 15 (2004)
  146. Kortsenshtein N M, Samuilov E V Doklady Physical Chemistry 392 (1-3) 243 (2003)
  147. Gapontsev V L, Kondrat’ev V V Dokl. Phys. 47 (8) 576 (2002)
  148. Vidal F, Johnston T W et al Phys. Rev. Lett. 86 (12) 2573 (2001)
  149. Vidal F, Laville S et al Spectrochimica Acta Part B: Atomic Spectroscopy 56 (6) 973 (2001)
  150. Skripov V P Uspekhi Fizicheskikh Nauk 170 (5) 559 (2000)
  151. Borman V D, Zenkevich A V et al Jetp Lett. 72 (3) 148 (2000)
  152. Merzhanov A G, Rumanov E N Rev. Mod. Phys. 71 (4) 1173 (1999)
  153. Sokolowski-Tinten K, Bialkowski J et al Phys. Rev. Lett. 81 (1) 224 (1998)
  154. Parizel N, Kempkes F et al Polymer 39 (2) 291 (1998)
  155. Mahato M C, Jayannavar A M Physica A: Statistical Mechanics And Its Applications 248 (1-2) 138 (1998)
  156. Borman V D, Lebedinskii Yu Yu, Troyan V I J. Exp. Theor. Phys. 87 (1) 133 (1998)
  157. Ivanov A O, Zubarev A Yu Physica A: Statistical Mechanics And Its Applications 251 (3-4) 348 (1998)
  158. Kukushkin S A, Osipov A V J. Exp. Theor. Phys. 86 (6) 1201 (1998)
  159. Chan P K, Rey A D Macromolecules 30 (7) 2135 (1997)
  160. Fraerman A A, Mel’nikov A S et al Phys. Rev. B 55 (10) 6316 (1997)
  161. Bunkin N F, Lobeyev A V Colloids And Surfaces A: Physicochemical And Engineering Aspects 129-130 33 (1997)
  162. Chan P K, Rey A D Macromolecules 29 (27) 8934 (1996)
  163. Goryachev S B Computer Simulation in Materials Science Chapter 2 (1996) p. 17
  164. Bunkin N F, Lobeyev A V The Journal of Chemical Physics 104 (17) 6659 (1996)
  165. Dass Sh, Johri G, Pandey L Pramana - J. Phys 47 (6) 447 (1996)
  166. Chan P K, Rey A D Macro Theory & Simulations 4 (5) 873 (1995)
  167. Chan P K, Rey A D Computational Materials Science 3 (3) 377 (1995)
  168. Blyakhman Yu, Polushkin N I et al Phys. Rev. B 52 (14) 10303 (1995)
  169. Gülen S C Journal of Non-Equilibrium Thermodynamics 19 (4) (1994)
  170. Torres F E, Troian S M Colloids And Surfaces A: Physicochemical And Engineering Aspects 89 (2-3) 227 (1994)
  171. Mahato M C, Shenoy S R Phys. Rev. E 50 (4) 2503 (1994)
  172. Goryachev S B Phys. Rev. Lett. 72 (12) 1850 (1994)
  173. Starovoitov V N J Appl Mech Tech Phys 35 (6) 891 (1994)
  174. Belevtsev B I, Komnik Yu F, Vatsuk L A Physica Status Solidi (b) 183 (1) 175 (1994)
  175. Mahato M C, Shenoy S R J Stat Phys 73 (1-2) 123 (1993)
  176. Martynyuk M M Int J Thermophys 14 (3) 457 (1993)
  177. Journal of Non-Equilibrium Thermodynamics 18 (3) (1993)
  178. Mahato M C, Shenoy S R Physica A: Statistical Mechanics And Its Applications 186 (1-2) 220 (1992)
  179. Belevtsev B I, Fomin A V, Yatsuk L A Soviet Journal of Low Temperature Physics 18 (11) 883 (1992)
  180. Blowey J F, Elliott C M Eur. J. Appl. Math 2 (3) 233 (1991)
  181. Boiko V G, Mogel’ Kh I et al ’pс’?’?kh’? ф’?’?’?ch’?с’?’?kh ’?’?у’? 161 (02) 77 (1991)
  182. Calzetta E Annals Of Physics 190 (1) 32 (1989)
  183. Pego R L Proceedings of the Royal Society of London. A. Mathematical and Physical Sciences 422 (1863) 261 (1989)
  184. Elliott C M Mathematical Models for Phase Change Problems Chapter 3 (1989) p. 35
  185. Chvoj Z, Kož?e?lek Z, ?iest?lk J Thermochimica Acta 153 349 (1989)
  186. Mitlin V S, Manevich L I Polymer Science U.S.S.R. 30 (1) 8 (1988)
  187. Mirgorod Yu A J Struct Chem 27 (3) 418 (1986)
  188. Heermann D W Z. Physik B - Condensed Matter 61 (3) 311 (1985)
  189. Grant M, San M M et al Phys. Rev. B 31 (5) 3027 (1985)
  190. Shibanov Yu D, Godovsky Yu K Colloid & Polymer Sci 263 (3) 202 (1985)
  191. Belevtsev B I, Komnik Yu F, Yatsuk L A Soviet Journal of Low Temperature Physics 11 (2) 102 (1985)
  192. Binder K Phys. Rev. A 29 (1) 341 (1984)
  193. Furusaka M, Ishikawa Y et al Physica B+C 120 (1-3) 383 (1983)
  194. Gunton J D Springer Series In Solid-State Sciences Vol. Magnetic Phase TransitionsKinetics of First-Order Phase Transitions48 Chapter 9 (1983) p. 154
  195. Wonneberger W Z. Physik B - Condensed Matter 46 (1) 73 (1982)
  196. Coutsias E, Huberman B A Phys. Rev. B 24 (5) 2592 (1981)
  197. Titov V V Phys. Stat. Sol. (a) 63 (1) 11 (1981)
  198. Ryzhkov V I, Ryzhkova E F, Bobyr’ A M Soviet Physics Journal 24 (12) 1112 (1981)
  199. Mogel’ Kh -I, Chalyi A V Soviet Physics Journal 24 (3) 266 (1981)
© 1918–2026 Uspekhi Fizicheskikh Nauk
Email: ufn@ufn.ru Editorial office contacts About the journal Terms and conditions