Skip to main content
Log in

Towards the ab initio based theory of phase transformations in iron and steel

  • Structure, Phase Transformations, and Diffusion
  • Published:
Physics of Metals and Metallography Aims and scope Submit manuscript

Abstract

Despite of the appearance of numerous new materials, the iron based alloys and steels continue to play an essential role in modern technology. The properties of a steel are determined by its structural state (ferrite, cementite, pearlite, bainite, martensite, and their combination) that is formed under thermal treatment as a result of the shear lattice reconstruction γ (fcc) → α (bcc) and carbon diffusion redistribution. We present a review on a recent progress in the development of a quantitative theory of the phase transformations and microstructure formation in steel that is based on an ab initio parameterization of the Ginzburg–Landau free energy functional. The results of computer modeling describe the regular change of transformation scenario under cooling from ferritic (nucleation and diffusion-controlled growth of the α phase) to martensitic (the shear lattice instability γ → α). It has been shown that the increase in short-range magnetic order with decreasing the temperature plays a key role in the change of transformation scenarios. Phase-field modeling in the framework of a discussed approach demonstrates the typical transformation patterns.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Similar content being viewed by others

References

  1. O. Kwon, “What’s new in steel?” Nature Mater. 6, 713 (2007).

    Article  Google Scholar 

  2. G. V. Kurdjumov, L. M. Utevski, and R. I. Entin, Transformation in Iron and Steel (Nauka, Moscow, 1977) [in Russian].

  3. V. M. Schastlivtsev, D. A. Mirzaev, and I. L. Yakovleva, Pearlite in Carbon Steels (Ural. Otd. Ross. Akad. Nauk, Ekaterinburg, 2006) [in Russian].

  4. H. K. D. H. Bhadeshia, Bainite in Steel (IOM Commun, London, 2001).

  5. W. C. Leslie and E. Hornbogen, “Physical metallurgy of steels,” in Physical Metallurgy, Ed. by R. W. Cahn and P. Haasen (Nort-Holland, New York, 1983), Vol. 2, pp. 1555–1620.

    Google Scholar 

  6. H. K. D. H. Bhadeshia and R. W. K. Honeycombe, Steels: Microstructure and Properties (Butterworth–Heinemann, Oxford, 1995), 3rd ed.

    Google Scholar 

  7. S. V. Okatov, A. R. Kuznetsov, Yu. N. Gornostyrev, V. N. Urtsev, and M. I. Katsnelson, “Effect of magnetic state on the γ–a transition in iron: First-principles calculations of the Bain transformation path,” Phys. Rev. B: Condens. Matter Mater. Phys. 79, 094111 (2009).

    Article  Google Scholar 

  8. S. V. Okatov, Yu. N. Gornostyrev, A. I. Lichtenstein, and M. I. Katsnelson, “Magnetoelastic coupling in γ-iron,” Phys. Rev. B: Condens. Matter Mater. Phys. 84, 214422 (2011).

    Article  Google Scholar 

  9. K. O. Rasmussen, T. Lookman, A. Saxena, A. R. Bishop, R. C. Albers, and S. R. Shenoy, “Threedimensional elastic compatibility and varieties of twins in martensites,” Phys. Rev. Lett. 87, 055704 (2001).

    Article  Google Scholar 

  10. M. Bouville and R. Ahluwalia, “Interplay between diffusive and displacive phase transformations: Timetemperature- transformation diagrams and microstructures,” Phys. Rev. Lett. 97, 055701 (2006).

    Article  Google Scholar 

  11. S. R. Shenoy, T. Lookman, A. Saxena, and A. R. Bishop, “Martensitic textures: Multiscale consequences of elastic compatibility,” Phys. Rev. B: Condens. Matter Mater. Phys. 60, 537–541 (1999).

    Article  Google Scholar 

  12. I. K. Razumov, Yu. N. Gornostyrev, and M. I. Katsnelson, “Effect of magnetism on kinetics of γ–a transformation and pattern formation in iron,” J. Phys.: Cond. Mat. 25, 135401 (2013).

    Google Scholar 

  13. I. K. Razumov, D. V. Boukhvalov, M. V. Petrik, V. N. Urtsev, A. V. Shmakov, M. I. Katsnelson, and Yu. N. Gornostyrev, “Role of magnetic degrees of freedom in a scenario of phase transformations in steel,” Phys. Rev. B: Condens. Matter Mater. Phys. 90, 094101 (2014).

    Article  Google Scholar 

  14. I. K. Razumov, Yu. N. Gornostyrev, and M. I. Katsnelson, “Autocatalytic mechanism of pearlite transformation,” Phys. Rev. Lett. (in press).

  15. M. L. Bernshtein, G. V. Kurdjumov, V. S. Mes’kin, A. A. Popov, V. D. Sadovsky, Yu. A. Skakov, V. M. Schastlivtsev, Yu. N. Taran, L. M. Utevsky, and R. I. Entin, “The iron–carbon,” in Metallurgy and Heat Treatment of Steel and Cast Iron, Ed. by A. G. Rakhshtadt, L. M. Kaputkina, S. D. Prokoshkin, and A. V. Supov (Intermet Engineering, Moscow, 2005), Vol. 3 [in Russian].

    Google Scholar 

  16. H. Okamoto, “The C–Fe (Carbon–iron) system,” J. Phase Equilib. 13, 543–565 (1992); Eisenhüttenw. 32, 251–260 (1961).

    Article  Google Scholar 

  17. L. Kaufman, S. V. Radcliffe, and M. Cohen, in Decomposition of Austenite by Diffusional Processes, Ed. by V. F. Zackay and H. I. Aaronson (Interscience, New York, 1962).

  18. C. Liu, Z. Zao, D. O. Northwood, and Y. Liu, “A new empirical formula for the calculation of Ms temperatures in pure iron and super-low carbon alloy steels,” J. Mater. Process. Technol. 113, 556–562 (2001).

    Article  Google Scholar 

  19. L. C. D. Fielding, “The bainite controversy,” Mater. Sci. Technol. 29, 383–399 (2013).

    Article  Google Scholar 

  20. H. K. D. H. Bhadeshia and L.-E. Svensson, “Modelling the evolution of microstructure in steel weld metal,” in Mathematical Modelling of Weld Phenomena, Ed. by H. Cerjak and K. E. Eastering (Inst. Mater., London, 1993), pp. 109–182.

    Google Scholar 

  21. C. Zener, “Kinetics of decomposition of an austenite,” Trans. AIME 167, 550–595 (1946).

    Google Scholar 

  22. G. V. Kurdjumov, “Non-diffusional (martensitic) transitions in alloys,” Dokl. Akad. Nauk SSSR 60, 1543–1546 (1948).

    Google Scholar 

  23. M. Cohen, E. S. Machlin, and V. G. Paranjpe, “Thermodynamics of the martensitic transformation,” in Thermodynamics in Physical Metallurgy (Am. Soc. Metals, Cleveland, 1950).

    Google Scholar 

  24. C. H. Shih, B. H. Averbach, and M. Cohen, “Some characteristics of the isothermal martensitic transformation,” Trans. AIME (J. Metals) 203, 183–187 (1955).

    Google Scholar 

  25. R. E. Cech and D. J. Turnbull, “Heterogeneous nucleation of the martensite transformation,” Trans. AIME 206, 124–132 (1956).

    Google Scholar 

  26. E. C. Bain, “The nature of martensite,” Trans. AIME 70, 25–46 (1924).

    Google Scholar 

  27. G. V. Kurdjumov and G. Sachs, “Over the mechanisms of steel hardening,” Z. Phys. 64, 325–343 (1930).

    Article  Google Scholar 

  28. G. R. Barsch and J. A. Krumhansl, “Twin boundaries in ferroelastic media without interface dislocations,” Phys. Rev. Lett. 53, 1069–1072 (1984).

    Article  Google Scholar 

  29. J. A. Krumhansl and R. J. Gooding, “Structural phase transitions with little phonon softening and first-order character,” Phys. Rev. B: Condens. Matter 39, 3047–3056 (1989).

    Article  Google Scholar 

  30. W. Hume-Rothery, “Properties and conditions of formation of intermetallic compounds,” J. Inst. Met. 35, 295–361 (1926).

    Google Scholar 

  31. M. I. Katsnelson, I. Naumov, and A. V. Trefilov, “Singularities of the electronic structure and premartensitic anomalies of lattice properties in beta-phases of metals and alloys,” Phase Trans. 49, 143–191 (1994).

    Article  Google Scholar 

  32. D. de Fontaine and R. Kikuchi, “Bragg-Williams and other models of the omega phase transformation,” Acta Metall. 22, 1139–1146 (1974).

    Article  Google Scholar 

  33. H. E. Cook, “On first-order structural phase transitions,” Acta Metall. 23, 1027–1054 (1975).

    Article  Google Scholar 

  34. J. Neuhaus, W. Petry, and A. Krimmel, “Phonon softening and martensitic transformation in a-Fe,” Physica B 234–236, 897–899 (1997).

    Article  Google Scholar 

  35. I. Leonov, A. I. Poteryaev, V. I. Anisimov, and D. Vollhardt, “Calculated phonon spectra of paramagnetic iron at the a phase transition,” Phys. Rev. B: Condens. Matter Mater. Phys. 85, 020401 (2012).

    Article  Google Scholar 

  36. F. Kormann, A. Dick, B. Grabovski, T. Hickel, and J. Neugebauer, “Atomic forces at finite magnetic temperatures: Phonons in paramagnetic iron,” Phys. Rev. B: Condens. Matter Mater. Phys. 85, 125104 (2012).

    Article  Google Scholar 

  37. C. Zener, Elasticity and Anelasticity of Metals (Univ. Chicago, Chicago, 1948).

    Google Scholar 

  38. L. Kaufman, E. V. Clougherty, and R. J. Weiss, “Lattice stability of metals. 3. Iron,” Acta Metall. 11, 323–335 (1963).

    Article  Google Scholar 

  39. H. Hasegawa and D. G. Pettifor, “Microscopic theory of the temperature–pressure phase diagram of iron,” Phys. Rev. Lett. 50, 130–133 (1983).

    Article  Google Scholar 

  40. D. W. Boukhvalov, Yu. N. Gornostyrev, M. I. Katsnelson, and A. I. Lichtenstein, “Magnetism and local distortions near carbon impurity in γ–iron,” Phys. Rev. Lett. 99, 247205 (2007).

    Article  Google Scholar 

  41. A. Hultrgen, “Isothermal transformation of austenite,” Trans. ASM 39, 915–1005 (1947).

    Google Scholar 

  42. M. Hillert, Paraequilibrium. Technical report (Swedish Inst. Metals Res., Stockholm, Sweden, 1953).

    Google Scholar 

  43. E. P. Klier and T. Lyman, “The Bainite Reaction in Hypoeutectoid Steels,” Trans. AIME. Met. Technol. 158, 394–422 (1944).

    Google Scholar 

  44. T. Ko and S. A. Cottrell, “The formation of bainite,” J. Iron. Steel Inst. 17, 307–313 (1952).

    Google Scholar 

  45. M. Hillert, The Growth of Ferrite, Bainite and Martensite. Internal Report (Swedish Inst. Metals Res., Stockholm, Sweden, 1960).

  46. J. Hultgren, J. Iron. Steel Inst. 114, 421–422 (1926).

    Google Scholar 

  47. J. W. Christian, “The origins of surface relief effects in phase transformations,” in Decomposition of Austenite by Diffusional Processes, Ed. by V. F. Zackay and H. I. Aaronson (AIME, New York, 1962), pp. 371–386.

    Google Scholar 

  48. M. Hillert, L. Hoglund, and J. Agren, “Role of carbon and alloying elements in the formation of bainitic ferrite,” Metall. Mater. Trans. A 35, 3693–3700 (2004).

    Article  Google Scholar 

  49. H. I. Aaronson, The Mechanism of Phase Transformations in Crystalline Solids (The Institute of Metals, London, 1969).

    Google Scholar 

  50. F.-W. Ling and D. E. Laughlin, “The kinetics of transformation in Zn–Al superplastic alloys,” Metall. Trans. A 10, 921–928 (1979).

    Article  Google Scholar 

  51. A. T. Adorno, A. V. Benedetti, R. Silva, A. G. Da, and M. Blanco, “Influence of the Al content on the phase transformation in Cu–Al–Ag Alloys,” Eclectica Quimica 28, 33–38 (2003).

    Article  Google Scholar 

  52. A. Das, W. Gust, and E. J. Mittemeijer, “Eutectoid transformation in Au–39 at. % In,” J. Mater. Sci. Tech. 16, 593–598 (2000).

    Article  Google Scholar 

  53. R. Abbaschian, L. Abbaschian, and R. Reed-Hill, Physical Metallurgy Principles. SI Version (Cengage Learning, Stamford, 2009).

    Google Scholar 

  54. M. V. Kral, M. A. Mangan, and G. Spanos, “Threedimensional analysis of mcrostructures,” Mater. Character. 45, 17–23 (2000).

    Article  Google Scholar 

  55. M. D. Graef, M. V. Kral, and M. Hillert, “A modern 3D view of an old perlite colony,” J. Metals 58, 25–28 (2006).

    Google Scholar 

  56. J. W. Cahn and J. E. Hilliard, “Free energy of a nonuniform system. I. Interfacial free energy,” J. Chem. Phys. 28, 258–267 (1958).

    Article  Google Scholar 

  57. H. K. D. H. Bhadeshia, “Carbon-carbon interactions in iron,” J. Mater. Sci. 39, 3949–3955 (2004).

    Article  Google Scholar 

  58. A. V. Ponomareva, Yu. N. Gornostyrev, and I. A. Abrikosov, “Energy of interaction between carbon impurities in paramagnetic γ–iron,” JETP 120, 716–724 (2015).

    Article  Google Scholar 

  59. M. Hillert, “Solid state phase transformation,” Jenkontorets Annaler 141, 757–790 (1957).

    Google Scholar 

  60. D. Turnbull, “Theory of cellular precipitation,” Acta Metall. 3, 55–63 (1955).

    Article  Google Scholar 

  61. B. E. Sundquist, “The edgewise growth of pearlite,” Acta Metall. 16, 1413–1422 (1968).

    Article  Google Scholar 

  62. V. G. Vaks and A. Yu. Stroev, “Kinetics of the eutectoid colony growth in a solid solution for simple alloy models,” J. Exp. Theor. Phys. 107, 90–101 (2008).

    Article  Google Scholar 

  63. V. G. Vaks, A. Y. Stroev, V. N. Urtsev, and A. V. Shmakov, “Experimental and theoretical study of the formation and growth of pearlite colonies in eutectoid steels,” J. Exp. Theor. Phys. 112, 961–978 (2011).

    Article  Google Scholar 

  64. A. Yamanaka, T. Yamamoto, T. Takaki, and Y. Tomita, “MultiPhase-field study for pearlite transformation with grain boundary diffusion,” Proc. 4th Int. Conf. Multiscale Mater. Model. (MMM2008), Florida, USA, 2008.

    Google Scholar 

  65. K. Ankit, A. Choudhury, C. Qin, S. Schulz, M. McDaniel, and B. Nestler, “Theoretical and numerical study of lamellar eutectoid growth influenced by volume diffusion,” Acta Mater. 61, 4245–4253 (2003).

    Article  Google Scholar 

  66. R. F. Mehl and A. Dube, “The eutectoid reaction,” in Phase Transformation in Solids, Ed. by J. E. Mayer, R. Smoluchowski, and W. A. Weyl (Wiley, New York, 1951), pp. 545–582.

    Google Scholar 

  67. G. V. Smith and R. F. Mehl, “Lattice relationships in decomposition of austenite to pearlite, bainite and martensite,” Trans. AIME 150, 211–226 (1942).

    Google Scholar 

  68. M. E. Nicholson, “On the nucleation of pearlite,” J. Metals 6, 1071–1074 (1954).

    Google Scholar 

  69. K. N. Tu and D. Turnbull, “Morphology and structure of tin lamellae formed by cellular precipitation,” Acta Metall. 17, 1263–1279 (1969).

    Article  Google Scholar 

  70. M. Hillert, “The formation of pearlite,” in Decomposition of Austenite by Diffusional Processes, Ed. by V. F. Zackay and H. I. Aaronson (Interscience, New York, 1962), pp. 197–237.

    Google Scholar 

  71. A. S. Pandit and H. K. D. H. Bhadeshia, “Divorced pearlite in steels,” Proc. Royal Soc. A 468, 2767–2778 (2012).

    Article  Google Scholar 

  72. J. D. Verhoeven and E. D. Gibson, “The divorced eutectoid transformation in steel,” Metall. Mater. Trans. A 29, 1181–1189 (1998).

    Article  Google Scholar 

  73. T. Oyama, O. D. Sherby, J. Wadworth, and B. Walser, “Application of the divorced eutectoid transformation to the development of fine-grained, spheroidized structures in ultrahigh carbon steels,” Scr. Metall. 18, 799–804 (1984).

    Article  Google Scholar 

  74. K. Ankit, R. Mukherjee, T. Mittnacht, and B. Nestler, “Deviations from cooperative growth mode during eutectoid transformation: Insights from phase field approach,” Acta Mater. 81, 204–209 (2014).

    Article  Google Scholar 

  75. K. Ankit, R. Mukherjee, and B. Nestler, “Deviations from cooperative growth mode during eutectoid transformation: Mechanisms of polycrystalline eutectoid evolution in Fe–C steels,” Acta Mater. 97, 316–324 (2015).

    Article  Google Scholar 

  76. V. G. Vaks and K. Yu. Khromov, “On the theory of austenite–cementite phase equilibria in steels,” JETP 106, 265–279 (2008).

    Article  Google Scholar 

  77. X. Zhang, T. Hickel, J. Rogal, S. Fahler, R. Drautz, and J. Neugebauer, “Structural transformations among austenite, ferrite and cementite in Fe–C alloys: A unified theory based on ab initio simulations,” Acta Mater. 99, 281–289 (2015).

    Article  Google Scholar 

  78. H. I. Aaronson, “Atomic mechanisms of diffusional nucleation and growth and comparisons with their counterparts in shear transformations,” Metall. Trans. A, 241, 241–276 (1993).

    Article  Google Scholar 

  79. A. Ali and H. K. D. H. Bhadeshia, “Nucleation of widmanstätten ferrite,” Mater. Sci. Technol. 6, 781–784 (1990).

    Article  Google Scholar 

  80. A. Yamanaka, T. Takaki, and Y. Tomita, “Phase-field simulation of austenite to ferrite transformation and widmanstatten ferrite formation in Fe–C alloy,” Mater. Trans. 47, 2725–2731 (2006).

    Article  Google Scholar 

  81. L. Q. Chen and A. G. Khachaturyan, “Dynamics of simultaneous ordering and phase-separation and effect of long-range,” Phys. Rev. Lett. 70, 1477–1480 (1993).

    Article  Google Scholar 

  82. S. M. Allen and J. W. Cahn, “Mechanisms of phase transformations within the miscibility gap of Fe-rich Fe–Al alloys,” Acta Metall. 24, 425–437 (1976).

    Article  Google Scholar 

  83. A. J. Bray, “Theory of phase-ordering kinetics,” Adv. Phys. 43, 357–459 (1994).

    Article  Google Scholar 

  84. F. Falk, “Model free-energy, mechanics and thermodynamics of shape-memory alloys,” Acta Metall. 28, 1773–1780 (1980).

    Article  Google Scholar 

  85. A. Onuki, “Pretransitional effects at structural phase transitions,” J. Phys. Soc. Jpn. 68, 5–8 (1999).

    Article  Google Scholar 

  86. S. Kartha, J. A. Krumhansl, J. P. Sethna, and L. K. Wickham, “Disorder-driven pretransitional tweed pattern in martensitic transformations,” Phys. Rev. B: Condens. Matter 52, 803–822 (1995).

    Article  Google Scholar 

  87. M. Baus and R. Lovett, “Generalization of the stress tensor to nonuniform fluids and solids and its relation to Saint-Venant’s strain compatibility conditions,” Phys. Rev. Lett. 65, 1781–1783 (1990).

    Article  Google Scholar 

  88. A. G. Khachaturyan, Theory of Structural Transformations in Solids (Nauka, Moscow, 1974; Wiley, New York, 1983; Dover, New York, 2008).

    Google Scholar 

  89. K. de Bell, A. B. MacIsaac, and J. P. Whitehead, “Dipolar effects in magnetic thin films and quasi-twodimensional systems,” Rev. Mod. Phys. 72, 225–257 (2000).

    Article  Google Scholar 

  90. J. Schmalian and P. G. Wolynes, “Stripe glasses: Selfgenerated randomness in a uniformly frustrated system,” Phys. Rev. Lett. 85, 836–839 (2000).

    Article  Google Scholar 

  91. E. A. Jagla, “Numerical simulations of two-dimensional magnetic domain patterns,” Phys. Rev. E: Stat., Nonlin., Soft Matter Phys. 70, 046204 (2004).

    Article  Google Scholar 

  92. V. J. Emery and S. A. Kivelson, “Frustrated electronic phase separation and high-temperature superconductors,” Physica A 209, 597–621 (1993).

    Article  Google Scholar 

  93. D. Kivelson, S. A. Kivelson, X. Zhao, Z. Nussinov, and G. Tarjus, “Statistical mechanics and its applications,” Physica A 219, 27–38 (1995).

    Article  Google Scholar 

  94. Z. Nussinov, J. Rudnick, S. A. Kivelson, and L. N. Chayes, “Avoided critical behavior in O(n) systems,” Phys. Rev. Lett. 83, 472–475 (1999).

    Article  Google Scholar 

  95. P. A. Prudkovskii, A. N. Rubtsov, and M. I. Katsnelson, “Topological defects, pattern evolution, and hysteresis in thin magnetic films,” Europhys. Lett. 73, 104–109 (2006).

    Article  Google Scholar 

  96. I. K. Razumov, Yu. N. Gornostyrev, and M. I. Katsnelson, “Intrinsic nanoscale inhomogeneity in ordering systems due to elastic-mediated interactions,” Europhys. Lett. 80, 66001 (2007).

    Article  Google Scholar 

  97. R. Brucas, H. Hafermann, M. I. Katsnelson, I. L. Soroka, O. Eriksson, and B. Hjörvarsson, “Magnetization and domain structure of bcc Fe81Ni19/Co(001),” Phys. Rev. B: Condens. Matter Mater. Phys. 69, 064411 (2004).

    Article  Google Scholar 

  98. L. D. Landau and E. M. Lifschitz, Theory of Elasticity (Nauka, Moscow, 1987; Pergamon, Oxford, 1986, 1993).

    Google Scholar 

  99. G. R. Barsch and J. A. Krumhansl, “Nonlinear and nonlocal continuum model of transformation precursors in martensites,” Metall. Trans. A 19, 761–775 (1988).

    Article  Google Scholar 

  100. E. Jiang and E. A. Carter, “Carbon dissolution and diffusion in ferrite and austenite from first principles,” Phys. Rev. B: Condens. Matter Mater. Phys. 67, 214103 (2003).

    Article  Google Scholar 

  101. J. A. Lobo and G. H. Geiger, “Thermodynamics of carbon in austenite and Fe–Mo austenite,” Metall. Trans. A 7, 1359–1364 (1976).

    Article  Google Scholar 

  102. B. M. Mogutnov, I. A. Tomilin, and L. A. Shvartsman, Thermodynamics of Carbon-Iron Alloys (Metallurgy, Moscow, 1972).

    Google Scholar 

  103. W. Kurz and D. J. Fisher, Fundamentals of Solidification (Trans. Tech., Aedermannsdorf, Switzerland, 1992), 3rd. ed.

    Google Scholar 

  104. U. Hecht, L. Gránásy, T. Pusztai, B. Böttger, M. Apel, V. Witusiewicz, L. Ratke, J. de Wilde, L. Froyen, D. Camel, B. Drevet, G. Faivre, S. G. Fries, B. Legendre, and S. Rex, “Multiphase solidification in multicomponent alloys,” Mater. Sci. Eng. Rep. 46, 1–49 (2004).

    Article  Google Scholar 

  105. R. Folch and M. Plapp, “Quantitative phase-field modeling of two-phase growth,” Phys. Rev. E: Stat., Nonlin., Soft Matter Phys. 72, 011602 (2005).

    Article  Google Scholar 

  106. B. Nestler and A. A. Wheeler, “A multi-phase-field model of eutectic and peritectic alloys: Numerical simulation of growth structures,” Phys. D (Amsterdam) 138, 114–133 (2000).

    Article  Google Scholar 

  107. W. J. Boettinger, J. A. Warren, C. Beckermann, and A. Karma, “Phase-field simulation of solidification,” Ann. Rev. Mater. 32, 163–194 (2002).

    Article  Google Scholar 

  108. K. R. Elder, F. Drolet, J. M. Kosterlitz, and M. Grant, “Stochastic eutectic growth,” Phys. Rev. Lett. 72, 677–680 (1994).

    Article  Google Scholar 

  109. F. Drolet, K. R. Elder, M. Grant, and J. M. Kosterlitz, “Phase-field modeling of eutectic growth,” Phys. Rev. E: Stat., Nonlin., Soft Matter Phys. 61, 6705–6720 (2000).

    Article  Google Scholar 

  110. M. Greenwood, N. Ofori-Opoku, J. Rottler, and N. Provatas, “Modeling structural transformations in binary alloys with phase field crystals,” Phys. Rev. B: Condens. Matter Mater. Phys. 84, 064104 (2011).

    Article  Google Scholar 

  111. J. Kundin, D. Raabe, and H. Emmerich, “A phasefield model for incoherent martensitic transformations including plastic accommodation processes in the austenite,” J. Mech. Phys. Solids 59, 2082–2102 (2011).

    Article  Google Scholar 

  112. A. Malik, H. K. Yeddu, G. Amberg, A. Borgenstam, and J. Agren, “Three dimensional elasto-plastic phase field simulation of martensitic transformation in polycrystal,” Mater. Sci. Eng., A 556, 221–232 (2012).

    Article  Google Scholar 

  113. H. K. Yeddu, A. Borgenstam, and J. Agren, “Stressassisted martensitic transformations in steels: A 3-D phase-field study,” Acta Mater. 61, 2595–2606 (2013).

    Article  Google Scholar 

  114. V. I. Levitas and M. Javanbakht, “Interaction between phase transformations and dslocations at the nanoscale,” J. Mech. Phys. Solids 82, 287–319 (2015).

    Article  Google Scholar 

  115. A. L. Roitburd and D. E. Temkin, “Plastic deformation and thermodynamic hysteresis at phase transformation in solids,” Sov. Phys. Solid State 28, 432–443 (1986).

    Google Scholar 

  116. I. M. Kaganova and A. L. Roitburd, “Effect of plastic deformation on the equilibrium shape of a new phase inclusion and thermodynamic hysteresis,” Sov. Phys. Solid State 31, 545–550 (1989).

    Google Scholar 

  117. V. I. Levitas, A. V. Idesman, G. B. Olson, and E. Stein, “Numerical modeling of martensite growth in elastoplastic material,” Philos. Mag. A 82, 429–462 (2002).

    Article  Google Scholar 

  118. F. D. Fisher and G. Reisner, “A criterion for the martensitic transformation of a microregion in an elasticplastic material,” Acta Mater. 46, 2095–2102 (1998).

    Article  Google Scholar 

  119. J. S. Smart, Effective Field Theories of Magnetism (Saunders, London, 1966; Mir, Moscow, 1968).

    Google Scholar 

  120. F. Körmann, A. Dick, B. Grabowski, B. Hallstedt, T. Hickel, and J. Neugebauer, “Free energy of bcc iron: Integrated ab initio derivation of vibrational, electronic, and magnetic contributions,” Phys. Rev. B: Condens. Matter Mater. Phys. 78, 033102 (2008).

    Article  Google Scholar 

  121. J. M. Ziman, Models of Disorder (University Press, Cambridge, 1979).

    Google Scholar 

  122. W. F. Smith and J. Hashemi, Foundations of Materials Science and Engineering (McGraw-Hill, Allas, USA, 2005), 4th ed.

    Google Scholar 

  123. M. Yu. Lavrentiev, D. Nguyen-Manh, and S. L. Dudarev, “Magnetic cluster expansion model for bcc–fcc transitions in Fe and Fe–Cr alloys,” Phys. Rev. B: Condens. Matter Mater. Phys. 81, 184202 (2010).

    Article  Google Scholar 

  124. Q. Chen and B. Sundman, “Modeling of thermodynamic properties for bcc, fcc, liquid, and amorphous iron,” J. Phase Equilibria 22, 631–643 (2001).

    Article  Google Scholar 

  125. J. S. Darken and R. W. Gurry, “Free energy of formation of cementite and the solubility of cementite in austenite,” Trans. AIME 191, 1015–1018 (1951).

    Google Scholar 

  126. A. Dick, F. Körmann, T. Hickel, and J. Neugebauer, “Ab initio based determination of thermodynamic properties of cementite including vibronic, magnetic, and electronic excitations,” Phys. Rev. B: Condens. Matter Mater. Phys. 84, 125101 (2011).

    Article  Google Scholar 

  127. L. Battezzati, M. Baricco, and S. Curiotto, “Non-stoichiometric cementite by rapid solidification of cast iron,” Acta Mater. 53, 1849–1856 (2005).

    Article  Google Scholar 

  128. Landolt–Börnstein, Numerical Data and Functional Relationships in Science and Technology, New Series, Group III: Crystal and Solid State Physics, V. 26, Diffusion in Metals and Alloys, Ed. by H. Mehrer (Springer- Verlag, Berlin, 1990).

  129. B. Ozturk, “The diffusion coefficient of carbon in cementite, Fe3C, at 450°C,” Solid State Ionics 12, 145–151 (1984).

    Article  Google Scholar 

  130. A. Hultgren, “Isothermal transformation of austenite,” ASM Trans. 39, 915–1005 (1947).

    Google Scholar 

  131. M. M. Aranda, R. Rementeria, C. Capdevila, and R. E. Hackenberg, “Can pearlite form outside of the Hultgren extrapolation of the Ae3 and Acm phase boundaries?” Met. Mat. Trans. A 47, 649–660 (2016).

    Article  Google Scholar 

  132. J. W. Christian, “Thermodynamics and kinetics of martensite,” Proc. Int. Conf. on Martensitic Transformations (ICOMAT 79), Boston, USA, Ed. by G. B. Olson and M. Cohen, pp. 220–234.

  133. V. A. Lobodyuk and E. I. Estrin, “Isothermal martensitic transformations,” Phys.-Usp. 48, 713–732 (2005).

    Article  Google Scholar 

  134. I. Manna, S. K. Pabi, and W. Gust, “Discontinuous reaction in solids,” Int. Mater. Rev. 46, 53–91 (2001).

    Article  Google Scholar 

  135. S. Bensaada, H. Mazouz, and M. T. Bouziane, “Discontinuous precipitation and dissolution in Cu–4.6 at % In alloy under effect of plastic deformation and the temperature,” Mater. Sci. App. 2, 1471–1479 (2011).

    Google Scholar 

  136. E. Hornbogen, “Systematics of cellular precipitation reactions,” Metall. Mater. Trans. B 3, 2717–2727 (1972).

    Article  Google Scholar 

  137. H. Ramanarayan and T. Abinandanan, “Grain boundary effects on spinodal decomposition. II. Discontinuous microstructures,” Acta Mater. 52, 921–930 (2004).

    Article  Google Scholar 

  138. I. K. Razumov, “The simulation of the growth of colonies in the spinodal decomposition of metastable phases,” Russ. J. Phys. Chem. A 83, 1682–1688 (2009).

    Article  Google Scholar 

  139. I. K. Razumov, “Influence of lattice relaxation on the kinetics of spinodal decomposition of solid solutions,” J. Eng. Phys. Thermophys. 82, 635–641 (2009).

    Article  Google Scholar 

  140. C. S. Smith, “Microstructure,” Trans. Am. Soc. Metals 45, 533–575 (1953).

    Google Scholar 

  141. V. D. Sadovskii, N. M. Rodigin, L. V. Smirnov, G. M. Filonchik, and I. G. Fakidov, “On magnetic field effect on martensitic transformation in steel,” Fiz. Metal. Metalloved. 12, 302–304 (1961).

    Google Scholar 

  142. E. A. Fokina and E. A. Zawadskii, “The effect of magnetic field on martensitic transformation in seel,” Fiz. Metal. Metalloved. 16, 311–313 (1963).

    Google Scholar 

  143. V. D. Sadovskii, L. V. Smirnov, and E. A. Fokina, “Steel quenching in magnetic field,” Fiz. Metal. Metalloved. 24, 918–939 (1967).

    Google Scholar 

  144. P. A. Malinen, V. D. Sadovskii, L. V. Smirnov, and E. A. Fokina, “On principles of the pulsed magnetic field effect on martensitic transformations in steel and alloys,” Fiz. Met. Metalloved. 23, 535–542 (1967).

    Google Scholar 

  145. M. A. Krivoglaz, V. D. Sadovskii, L. V. Smirnov, and E. A. Fokina, Steel Quenching in Magnetic Field (Nauka, Moscow, 1977) [in Russian].

    Google Scholar 

  146. E. I. Estrin, “Magnetic field effect on martensitic transformation,” Fiz. Met. Metalloved. 19, 929–932 (1965).

    Google Scholar 

  147. M. Shimotomai and K. Maruta, “Aligned two-phase structures in Fe–C alloys,” Scr. Mater. 42, 499–503 (2000).

    Article  Google Scholar 

  148. M. Shimotomai, K. Maruta, K. Mine, and M. Matsui, ”Formation of aligned two-phase microstructures by applying a magnetic field during the austenite to ferrite transformation in steels,” Acta Mater. 51, 2921–2932 (2003).

  149. Y. D. Zhang, N. Gey, C. S. He, X. Zhao, L. Zuo, and C. Esling, “High temperature tempering behaviors in a structural steel under high magnetic field,” Acta Mater. 52, 3467–3474 (2004).

    Article  Google Scholar 

  150. Y. D. Zhang, C. Esling, X. Zhao, and L. Zuo, “Solid state phase transformations under high magnetic fields in a medium carbon steel,” Mater. Sci. Forum 495–497, 1131–1140 (2005).

    Article  Google Scholar 

  151. M. A. Krivoglaz and V. D. Sadovskii, “On strong magnetic field effect on phase transformations,” Fiz. Met. Metalloved. 18, 502–505 (1964).

    Google Scholar 

  152. I. A. Abrikosov, A. V. Ponomareva, P. Steneteg, S. A. Barannikova, and B. Alling, “Recent progress in simulations of the paramagnetic state of magnetic materials,” Current Opinion in Solid State Mater. Sci. 20, 85–106 (2016).

    Article  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to I. K. Razumov.

Additional information

Published in Russian in Fizika Metallov i Metallovedenie, 2017, Vol. 118, No. 4, pp. 380–408.

The article is published in the original.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Razumov, I.K., Gornostyrev, Y.N. & Katsnelson, M.I. Towards the ab initio based theory of phase transformations in iron and steel. Phys. Metals Metallogr. 118, 362–388 (2017). https://doi.org/10.1134/S0031918X16130032

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1134/S0031918X16130032

Keywords

Navigation