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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.

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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)
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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

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  35. Sorokin M V, Ahmad I et al 2022 19th International Bhurban Conference on Applied Sciences and Technology (IBCAST), (2022) p. 10
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  38. Gumarov A I, Yanilkin I V et al Materials Letters 305 130783 (2021)
  39. 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
  40. Volosnikov D V, Povolotsky I I et al High Temp 59 (2-6) 283 (2021)
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  42. Osipovich K, Vorontsov A et al Metals 11 (8) 1151 (2021)
  43. Basko M M Appl. Math. Mech.-Engl. Ed. 42 (6) 871 (2021)
  44. Galimzyanov B N, Doronina M A, Mokshin A V Journal Of Non-Crystalline Solids 572 121102 (2021)
  45. Igolnikov A A, Rutin S B, Skripov P V Thermochimica Acta 695 178815 (2021)
  46. Shilkina L A, Nagaenko A V et al Journal Of Alloys And Compounds 866 158871 (2021)
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  48. Davydov S, Gorlenko A Science intensive technologies in mechanical engineering 2020 (2) 28 (2020)
  49. Blagonravov L A, Silina T I Moscow Univ. Phys. 75 (4) 363 (2020)
  50. Lyakhov G A, Shcherbakov I A, Shermeneva M A Phys. Wave Phen. 28 (3) 236 (2020)
  51. Vasin M G, Lebedev V G Journal Of Non-Crystalline Solids 543 120131 (2020)
  52. Kumar A, Narayanam Ch et al Phys. Rev. E 100 (6) (2019)
  53. Spivak L V, Shchepina N E Tech. Phys. 64 (9) 1319 (2019)
  54. Spivak L V, Shchepina N E Phys. Solid State 61 (8) 1347 (2019)
  55. Steyn-Ross M L, Steyn-Ross D A et al Phys. Rev. E 99 (1) (2019)
  56. Blagonravov L A, Laptinskaya T V Russ. J. Phys. Chem. 93 (7) 1270 (2019)
  57. Narayanam Ch, Kumar A et al J. Phys. Chem. C 123 (22) 13958 (2019)
  58. Radkevich E V, Vasil’eva O A, Sidorov M I Dokl. Math. 100 (3) 571 (2019)
  59. Lebedev V G, Obukhov A A, Vasin M G Journal Of Non-Crystalline Solids 505 414 (2019)
  60. Lebedev V G, Galenko P K J. Exp. Theor. Phys. 129 (1) 86 (2019)
  61. Spivak L V, Shchepina N E Phys. Solid State 60 (12) 2598 (2018)
  62. Basko M M Physics Of Fluids 30 (12) 123306 (2018)
  63. Levin D M, Kolmakov Yu N DDF 383 74 (2018)
  64. Li Ya, Li Ch et al Journal Of Thermal Stresses 41 (10-12) 1364 (2018)
  65. L’vov P E, Svetukhin V V Modelling Simul. Mater. Sci. Eng. 26 (4) 045001 (2018)
  66. Kharchenko D O, Kharchenko V O et al Physica A: Statistical Mechanics And Its Applications 486 497 (2017)
  67. Davydov S V, Petrov E V Tech. Phys. 62 (8) 1207 (2017)
  68. Zhang G, Yang T et al Phys. Rev. E 96 (3) (2017)
  69. L’vov P E, Svetukhin V V Modelling Simul. Mater. Sci. Eng. 25 (7) 075006 (2017)
  70. Avdeev A A Bubble Systems Mathematical Engineering Chapter 8 (2016) p. 265
  71. Bordonskiy G S Tech. Phys. 61 (8) 1250 (2016)
  72. Davydov S Yu, Lebedev A A et al Tech. Phys. Lett. 42 (12) 1153 (2016)
  73. Lyakhova N B, Shkirin A V, Lyakhov G A Phys. Wave Phen. 24 (2) 142 (2016)
  74. Balashov V A, Savenkov E B KIAM Prepr. (13) 1 (2016)
  75. Bunkin N F, Shkirin A V et al The Journal of Chemical Physics 145 (18) (2016)
  76. Bunkin N F, Lyakhov G A et al Phys. Wave Phen. 23 (4) 241 (2015)
  77. Kushchev S B, Bosykh M A et al Inorg Mater 51 (7) 673 (2015)
  78. Shikin V Physica B: Condensed Matter 460 126 (2015)
  79. L’vov P E, Svetukhin V V Phys. Solid State 57 (6) 1213 (2015)
  80. Davydov S Yu, Lebedev A A Semiconductors 48 (6) 701 (2014)
  81. Khomenkova L, An Y -T et al Physica B: Condensed Matter 453 100 (2014)
  82. Semenov A A, Woo C H Journal Of Nuclear Materials 454 (1-3) 60 (2014)
  83. L’vov P E, Svetukhin V V Phys. Solid State 56 (9) 1889 (2014)
  84. Lebedev A A, Zamoryanskaya M V et al Journal Of Crystal Growth 396 100 (2014)
  85. Lebedev A A, Zamoryanskaya M V et al MSF 778-780 247 (2014)
  86. Nakoryakov V E, Tsoi A N et al Thermophys. Aeromech. 21 (3) 279 (2014)
  87. Zhang G, Liu G et al RSC Adv. 4 (14) 7068 (2014)
  88. Zhang G, Qiao G The Journal of Chemical Physics 139 (13) (2013)
  89. Lebedev A A, Zamorianskaya M V et al Semiconductors 47 (11) 1539 (2013)
  90. Belovolova L V, Vinogradov E A, Glushkov M V Phys. Wave Phen. 21 (3) 190 (2013)
  91. L’vov P E, Svetukhin V V Phys. Solid State 55 (11) 2374 (2013)
  92. Wagner R, Kampmann R, Voorhees P W Materials Science and Technology 1 (2013)
  93. Xiao Z H, Semenov A A et al Journal Of Nuclear Materials 439 (1-3) 25 (2013)
  94. Semenov A A, Woo C H Acta Materialia 60 (17) 6112 (2012)
  95. Zhukov V T, Zaitsev N A et al Math Models Comput Simul 4 (4) 440 (2012)
  96. Baten’kin M A, Mensov S N Polym. Sci. Ser. B 54 (9-10) 496 (2012)
  97. L’vov P E, Svetukhin V V Phys. Solid State 54 (11) 2285 (2012)
  98. Kharchenko D O, Lysenko I O, Kharchenko V O Usp. Fiz. Met. 13 (2) 101 (2012)
  99. Ionin A A, Kudryashov S I et al Jetp Lett. 94 (10) 753 (2012)
  100. Vasilevskaya T N, Andreev N S Phys. Solid State 53 (11) 2250 (2011)
  101. Rykov Yu G, Zaitsev N A Math Models Comput Simul 3 (4) 468 (2011)
  102. Ionin A A, Kudryashov S I et al Jetp Lett. 94 (4) 266 (2011)
  103. Nakoryakov V E, Zakharov V E et al J. Engin. Thermophys. 20 (4) 335 (2011)
  104. Semenov A A, Woo C H Journal Of Nuclear Materials 411 (1-3) 144 (2011)
  105. Maslov V P Math Notes 90 (3-4) 533 (2011)
  106. Belovolova L V, Glushkov M V, Vinogradov E A BIOPHYSICS 56 (2) 181 (2011)
  107. Yukalov V I Symmetry 2 (1) 40 (2010)
  108. Galenko P K, Kharchenko D, Lysenko I Physica A: Statistical Mechanics And Its Applications 389 (17) 3443 (2010)
  109. Kinetics of First‐Order Phase Transitions 1 (2009) p. 399
  110. Mirgorod Yu, Borshch N A et al Russ J Appl Chem 82 (8) 1357 (2009)
  111. Galenko P, Jou D Physica A: Statistical Mechanics And Its Applications 388 (15-16) 3113 (2009)
  112. Lecoq N, Zapolsky H, Galenko P Eur. Phys. J. Spec. Top. 177 (1) 165 (2009)
  113. Mao S Transport in Laser Microfabrication 1 6 (2009) p. 146
  114. Indeĭtsev D A, Osipova E V Phys. Solid State 51 (9) 1901 (2009)
  115. Abylkalykova R B, Tazhibaeva G B et al Bull. Russ. Acad. Sci. Phys. 73 (11) 1542 (2009)
  116. Kharchenko D O, Galenko P K, Lebedev V G Usp. Fiz. Met. 10 (1) 27 (2009)
  117. Kukadiya S B, Chan P K, Mehrvar M Macro Theory & Simulations 18 (2) 97 (2009)
  118. Mebed A M, Abd-Elrahman M I et al Phase Transitions 82 (8) 587 (2009)
  119. Wu B Journal of Applied Physics 105 (5) (2009)
  120. Galenko P, Lebedev V Physics Letters A 372 (7) 985 (2008)
  121. Critical Behavior of Non‐Ideal Systems 1 (2008) p. 229
  122. Abyzov A S, Schmelzer J W P The Journal of Chemical Physics 127 (11) (2007)
  123. Sobol’ O V Phys. Solid State 49 (6) 1161 (2007)
  124. Schmelzer J W P, Abyzov A S J. Engin. Thermophys. 16 (3) 119 (2007)
  125. Galenko P, Lebedev V Philosophical Magazine Letters 87 (11) 821 (2007)
  126. Galenko P K, Lebedev V G Jetp Lett. 86 (7) 458 (2007)
  127. Andreev S N, Samokhin A A, Smurov I Applied Surface Science 252 (13) 4506 (2006)
  128. Borman V D, Zenkevich A V et al J. Exp. Theor. Phys. 103 (6) 850 (2006)
  129. Cheng Ch, Xu X Phys. Rev. B 72 (16) (2005)
  130. Vidal F, Johnston T W et al Phys. Rev. B 70 (18) (2004)
  131. Baidakov V G Dokl. Phys. 49 (1) 15 (2004)
  132. Xu X, Cheng Ch, Chowdhury I H Journal of Heat Transfer 126 (5) 727 (2004)
  133. Xu X 37th AIAA Thermophysics Conference, (2004)
  134. Xu X MRS Proc. 850 (2004)
  135. Kortsenshtein N M, Samuilov E V Doklady Physical Chemistry 392 (1-3) 243 (2003)
  136. Gapontsev V L, Kondrat’ev V V Dokl. Phys. 47 (8) 576 (2002)
  137. Vidal F, Laville S et al Spectrochimica Acta Part B: Atomic Spectroscopy 56 (6) 973 (2001)
  138. Vidal F, Johnston T W et al Phys. Rev. Lett. 86 (12) 2573 (2001)
  139. Skripov V P Uspekhi Fizicheskikh Nauk 170 (5) 559 (2000)
  140. Borman V D, Zenkevich A V et al Jetp Lett. 72 (3) 148 (2000)
  141. Merzhanov A G, Rumanov E N Rev. Mod. Phys. 71 (4) 1173 (1999)
  142. Ivanov A O, Zubarev A Yu Physica A: Statistical Mechanics And Its Applications 251 (3-4) 348 (1998)
  143. Sokolowski-Tinten K, Bialkowski J et al Phys. Rev. Lett. 81 (1) 224 (1998)
  144. Parizel N, Kempkes F et al Polymer 39 (2) 291 (1998)
  145. Borman V D, Lebedinskii Yu Yu, Troyan V I J. Exp. Theor. Phys. 87 (1) 133 (1998)
  146. Kukushkin S A, Osipov A V J. Exp. Theor. Phys. 86 (6) 1201 (1998)
  147. Mahato M C, Jayannavar A M Physica A: Statistical Mechanics And Its Applications 248 (1-2) 138 (1998)
  148. Fraerman A A, Mel’nikov A S et al Phys. Rev. B 55 (10) 6316 (1997)
  149. Chan P K, Rey A D Macromolecules 30 (7) 2135 (1997)
  150. Bunkin N F, Lobeyev A V Colloids And Surfaces A: Physicochemical And Engineering Aspects 129-130 33 (1997)
  151. Goryachev S B Computer Simulation in Materials Science Chapter 2 (1996) p. 17
  152. Bunkin N F, Lobeyev A V The Journal of Chemical Physics 104 (17) 6659 (1996)
  153. Chan P K, Rey A D Macromolecules 29 (27) 8934 (1996)
  154. Dass Sh, Johri G, Pandey L Pramana - J. Phys 47 (6) 447 (1996)
  155. Blyakhman Yu, Polushkin N I et al Phys. Rev. B 52 (14) 10303 (1995)
  156. Chan P K, Rey A D Computational Materials Science 3 (3) 377 (1995)
  157. Chan P K, Rey A D Macro Theory & Simulations 4 (5) 873 (1995)
  158. Mahato M C, Shenoy S R Phys. Rev. E 50 (4) 2503 (1994)
  159. Belevtsev B I, Komnik Yu F, Vatsuk L A Physica Status Solidi (b) 183 (1) 175 (1994)
  160. Goryachev S B Phys. Rev. Lett. 72 (12) 1850 (1994)
  161. Starovoitov V N J Appl Mech Tech Phys 35 (6) 891 (1994)
  162. Gülen S C Journal of Non-Equilibrium Thermodynamics 19 (4) (1994)
  163. Torres F E, Troian S M Colloids And Surfaces A: Physicochemical And Engineering Aspects 89 (2-3) 227 (1994)
  164. Mahato M C, Shenoy S R J Stat Phys 73 (1-2) 123 (1993)
  165. Journal of Non-Equilibrium Thermodynamics 18 (3) (1993)
  166. Martynyuk M M Int J Thermophys 14 (3) 457 (1993)
  167. Belevtsev B I, Fomin A V, Yatsuk L A Soviet Journal of Low Temperature Physics 18 (11) 883 (1992)
  168. Mahato M C, Shenoy S R Physica A: Statistical Mechanics And Its Applications 186 (1-2) 220 (1992)
  169. Boiko V G, Mogel’ Kh I et al Uspekhi Fizicheskikh Nauk 161 (02) 77 (1991)
  170. Blowey J F, Elliott C M Eur. J. Appl. Math 2 (3) 233 (1991)
  171. Calzetta E Annals Of Physics 190 (1) 32 (1989)
  172. Chvoj Z, Kožíšek Z, Šesták J Thermochimica Acta 153 349 (1989)
  173. Pego R L Proceedings of the Royal Society of London. A. Mathematical and Physical Sciences 422 (1863) 261 (1989)
  174. Elliott C M Mathematical Models for Phase Change Problems Chapter 3 (1989) p. 35
  175. Mitlin V S, Manevich L I Polymer Science U.S.S.R. 30 (1) 8 (1988)
  176. Mirgorod Yu A J Struct Chem 27 (3) 418 (1986)
  177. Grant M, San M M et al Phys. Rev. B 31 (5) 3027 (1985)
  178. Shibanov Yu D, Godovsky Yu K Colloid & Polymer Sci 263 (3) 202 (1985)
  179. Belevtsev B I, Komnik Yu F, Yatsuk L A Soviet Journal of Low Temperature Physics 11 (2) 102 (1985)
  180. Heermann D W Z. Physik B - Condensed Matter 61 (3) 311 (1985)
  181. Binder K Phys. Rev. A 29 (1) 341 (1984)
  182. Furusaka M, Ishikawa Y et al Physica B+C 120 (1-3) 383 (1983)
  183. Gunton J D Springer Series In Solid-State Sciences Vol. Magnetic Phase TransitionsKinetics of First-Order Phase Transitions48 Chapter 9 (1983) p. 154
  184. Wonneberger W Z. Physik B - Condensed Matter 46 (1) 73 (1982)
  185. Ryzhkov V I, Ryzhkova E F, Bobyr’ A M Soviet Physics Journal 24 (12) 1112 (1981)
  186. Mogel’ Kh -I, Chalyi A V Soviet Physics Journal 24 (3) 266 (1981)
  187. Coutsias E, Huberman B A Phys. Rev. B 24 (5) 2592 (1981)
  188. Titov V V Phys. Stat. Sol. (a) 63 (1) 11 (1981)
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