Issues »  Volume 13, Issue 2

Modelling of Microstructural Transformations in the Systems Subject to Radiation Influence

D. O. Kharchenko$^{1}$, I. O. Lysenko$^{1}$, V. O. Kharchenko$^{1,2}$

$^1$Institute of Applied Physics, NAS of Ukraine, 58 Petropavlivska Str., 40000 Sumy, Ukraine
$^2$Institut für Physik, Universität Augsburg, Universitätsstraße 1, 86159 Augsburg, Deutschland

Received: 24.02.2012. Download: PDF

Formalism is developed for description of microstructure transformations and phase separation in systems under irradiation. Investigation is made within the scope of the crystal phase-field method. This approach allows one to simulate materials on the molecular-dynamics spatial scales but on the diffusive-dynamics temporal scales. Considering a model for a periodic one-component system driven by both competing stochastic fluxes–thermally-stimulated and external ballistic mixing flues of atoms, conditions of microstructure-transformations’ appearance are determined. Analysis of the system on a mesoscopic level for a binary equiatomic system is performed. Reentrant character of phase-separation process is revealed. For systems with transient dynamics, for instance, with incommensurable time scales of propagation of disturbances, which are characterized by the memory effects, at presence of fluctuations of lengths of jumps of the atoms knocked-on by high-energy particles, occurrence of pattern-selection processes is revealed.

Keywords: crystal system, ballistic diffusion, noise, spinodal decomposition, phase-field model of crystal.

PACS: 05.10.Gg, 05.40.-a, 05.65.+b, 61.72.Bb, 61.80.Az, 64.60.-i, 81.30.Mh

DOI: https://doi.org/10.15407/ufm.13.02.101

Citation: D. O. Kharchenko, I. O. Lysenko, and V. O. Kharchenko, Modelling of Microstructural Transformations in the Systems Subject to Radiation Influence, Usp. Fiz. Met., 13, No. 2: 101—187 (2012) (in Ukrainian), doi: 10.15407/ufm.13.02.101

References (108)  
  1. A. Onuki, Phase Transition Dynamics (Cambridge: Cambridge University Press: 2004).
  2. V. N. Voevodin, I. M. Neklyudov, Evolyutsiya strukturno-fazovogo sostoyaniya i radiatsionnaya stoykost' konstruktsionnykh materialov (Kiev: Naukova dumka: 2006).
  3. V. Y. Sugakov, Osnovy Synergetyky (Kyiv: Oberegi: 2001).
  4. W. Horsthemke and R. Lefever, Noise-Induced Transitions (Berlin: Springer-Verlag: 1984). Crossref
  5. J. Garcia-Ojalvo and J. M. Sancho, Noise in Spatially Extended Systems (New York: Springer-Verlag: 1999). Crossref
  6. A. I. Olemskoy, D. O. Kharchenko, Samoorganizatsiya samopodobnykh stokhasticheskikh sistem (Izhevsk–Moskva: NITs «Regulyarnaya i khaoticheskaya dinamika»: 2007).
  7. Dzh. Nikolis, I. Prigozhin, Samoorganizatsiya v neravnovesnykh sistemakh (Moskva : Mir: 1979).
  8. R. Enrique and P. Bellon, Phys. Rev. B, 60: 14649 (1999). Crossref
  9. J. Ye and P. Bellon, Phys. Rev. B, 70: 094104 (2004). Crossref
  10. G. Martin, Phys. Rev. B, 30: 1424 (1984). Crossref
  11. V. G. Vaks and V. V. Kamyshenko, Phys. Lett. A, 177: 269 (1993). Crossref
  12. S. Matsumara, Y. Tanaka, S. Miller, and C. Abromeit, J. Nucl. Instrum., 239: 42 (1996).
  13. R. Enrique and P. Bellon, Appl. Phys. Lett., 78: 4178 (2001). Crossref
  14. P. Krasnochtchekov, R.S. Averback, and P. Bellon, Phys. Rev. B, 72: 174102 (2005). Crossref
  15. T. Diaz de la Rubia, R. S. Averback, and H. Hsieh, J. Mater. Res., 4: 579 (1989). Crossref
  16. T. Diaz de la Rubia, R. S. Averback, R. Benedek, and W. E. King, Phys. Rev. Lett., 59: 1930 (1987). Crossref
  17. R. S. Averback, T. Diaz de la Rubia, and R. Benedek, Nucl. Instrum. Methods, B33: 693 (1988). Crossref
  18. G. H. Kinchin and R. S. Pease, Rep. Prog. Phys., 18: 1 (1955). Crossref
  19. R. S. Averback, R. Benedek, K. L. Merkle et al., J. Nucl. Mater., 113: 211 (1983). Crossref
  20. T. Diaz de la Rubia, A. Caro, and M. Spaczer, Phys. Rev. B, 47: 11483 (1993). Crossref
  21. S. Siegel, Phys. Rev., 75: 1823 (1949). Crossref
  22. A. R. Sweedler and D. E. Cox, Phys. Rev. B, 12: 147 (1975). Crossref
  23. L. R. Aronin, J. Appl. Phys., 25: 344 (1954). Crossref
  24. G. J. C. Carpenter and E. M. Shulson, J. Num. Mat., 73: 180 (1978).
  25. H. L. Glick, F. C. Brooks, W. F. Witzig, and W. E. Johnson, Phys. Rev., 87: 1074 (1952). Crossref
  26. J. Gilbert, Radiat. Eff., 20: 37 (1973). Crossref
  27. A. Ali, Phil. Mag. B, 37: 353 (1978). Crossref
  28. J. Koike, P. R. Okamoto, and M. Meshii, J. Non-Cryst. Solids, 106: 90 (1988). Crossref
  29. K. C. Russel, Prog. Mater. Sci., 28, No. 3–4: 229 (1984). Crossref
  30. F. Foisson and D. Duibisson, Met. Mat. Soc., 981 (1994).
  31. H. Yasuda, H. Mori, and J. G. Lee, Phys. Rev. B, 70: 214105 (2004). Crossref
  32. D. G. Morris, G. T. Brown, R. C. Piller, and R. E. Smallman, Acta Metall., 24: 21 (2008). Crossref
  33. M. Griffiths, J. Nucl. Mater., 159: 190 (1988). Crossref
  34. R. A. Enrique, K. Nordlund, R. S. Averback, and P. Bellon, J. Appl. Phys., 93: 2917 (2003). Crossref
  35. R. A. Enrique and P. Bellon, Phys. Rev. B, 63: 134111 (2001). Crossref
  36. P. K. MacKeown, Stochastic Simulation in Physics (Singapore: Springer-Verlag: 1997).
  37. J. S. Langer, Directions in Condensed Matter Physics (Singapore: World Scientific: 1986).
  38. K. R. Elder, N. Provatas, J. Berry et al., Phys. Rev. B, 75: 064107 (2007). Crossref
  39. J. Berry, K. R. Elder, and M. Grant, Phys. Rev. E, 77: 061506 (2008). Crossref
  40. A. Jaatinen, C. V. Achim, K. R. Elder, and T. Ala-Nissila, Phys. Rev. E, 80: 031602(10) (2009). Crossref
  41. K. R. Elder, M. Katakowski, M. Haataja, and M. Grant, Phys. Rev. Lett., 88: 245701 (2002). Crossref
  42. K. R. Elder and M. Grant, Phys. Rev. E, 70: 051605 (2004). Crossref
  43. J. Berry, M. Garnt, and K. R. Elder, Phys. Rev. E, 73: 031609 (2006). Crossref
  44. J. Swift and P. C. Hohenberg, Phys. Rev. A, 15: 319 (1977). Crossref
  45. B. von Haeften, G. Izús, S. Mangioni et al., arXiv:nlin, 0309029.
  46. K. R. Elder, M. Katakowski, M. Haataja, and M. Grant, Phys. Rev. Lett., 88: 245701 (2002). Crossref
  47. P. Stefanovich, M. Haataja, and N. Provatas, Phys. Rev. Lett., 96: 225504(4) (2006).
  48. D. Kharchenko, P. Galenko, and V. Lebedev, Usp. Fiz. Met., 10: 27 (2009). Crossref
  49. R. A. Enrique and P. Bellon, Phys. Rev. B, 63: 134111 (2001). Crossref
  50. J. Ye and P. Bellon, Phys. Rev. B, 70: 094104 (2004). Crossref
  51. V. I. Dubinko, A. V. Tur, and V. V. Yanovsky, Radiat. Eff., 112: 233 (1990). Crossref
  52. J. Garcia-Ojalvo, A. M. Lacasta, J. M. Sancho, and R. Toral, Europhys. Lett., 42: 125 (1998). Crossref
  53. M. Ibanes, J. Garcia-Ojalvo, R. Toral, and J. M. Sancho, Phys. Rev. E, 60: 3597 (1999). Crossref
  54. H. Risken, The Fokker–Planck Equation (Berlin: Springer-Verlag: 1984).
  55. C. W. Gardiner, Handbook of Stochastic Methods (Berlin–Heidelberg–New-York–Tokyo: Springer-Verlag: 1985).
  56. D. O. Kharchenko, A. V. Dvornichenko, and I. O. Lysenko, Ukr. Phys. Journ., 53: 917 (2008).
  57. J. Buceta, M. Ibanes, J. M. Sancho, and K. Lindenberg, Phys. Rev. E, 67: 021113 (2003). Crossref
  58. K. Wood, J. Buceta, and K. Lindenberg, Phys. Rev. E, 73: 022101 (2006). Crossref
  59. D. Kharchenko, I. Lysenko, and V. Kharchenko, Physica A, 389: 3356 (2010). Crossref
  60. U. M. Marconi, A. Puglisi, L. Rondoni, and A. Vulpiani, Phys. Rep., 461: 111 (2008). Crossref
  61. L. D. Landau, E. M. Lifshits, Statisticheskaya fizika. Tom V (Moskva: Nauka: 1976).
  62. A. A. Ponomarov, V. I. Miroshnichenko, and A. G. Ponomarev, Nucl. Instrum. Methods Phys. Res. B, 267, Iss. 12–13: 2041 (2009). Crossref
  63. M. Ibanes, J. Garcia-Ojalvo, R. Toral, and J. M. Sancho, Lecture Notes in Physics, 557: 247 (Eds. J. A. Freund and T. Poschel) (Berlin: Springer-Verlag: 2000).
  64. E. A. Novikov, ZhETF, 20: 1290 (1965).
  65. K. V. Gardiner, Stokhasticheskie metody v estestvennykh naukakh (Moskva: Mir: 1986).
  66. N. G. Van Kampen, Stokhasticheskie protsessy v fizike i khimii (Moskva: Vysshaya shkola: 1990).
  67. D. O. Kharchenko and A. V. Dvornichenko, Physica A, 387: 5342 (2008). Crossref
  68. J. M. R. Parrondo, C. Van der Broeck, J. Buceta, and F. J. de la Rubia, Physica A, 224: 153 (1996). Crossref
  69. J. D. Gunton, M. San Miguel, and P. S. Sahni, In: Phase Transtions and Critical Phenomena (Eds. C. Domb and J. L. Lebowitz) (New York: Academic Press: 1983).
  70. G. Schmitz, J. C. Ewert, F. Harbsmeier et al., Phys. Rev. B, 63: 224113 (2001). Crossref
  71. J. Ye and P. Bellon, Phys. Rev. B, 70: 094104 (2004). Crossref
  72. J. Ye and P. Bellon, Phys. Rev. B, 70: 094105 (2004). Crossref
  73. D. O. Kharchenko and A. V. Dvornichenko, Eur. Phys. J. B, 61: 95 (2008). Crossref
  74. G. E. P. Box and M. E. Müller, Ann. Math. Stat., 29: 610 (1958). Crossref
  75. D. O. Kharchenko, V. O. Kharchenko, and I. O. Lysenko, Cent. Eur. J. Phys., 9: 698 (2011).
  76. D. D. Joseph and L. Preziosi, Rev. Mod. Phys., 61: 41 (1989). Crossref
  77. G. Repke, Neravnovesnaya statisticheskaya mekhanika (Moskva: Mir: 1990).
  78. D. Jou, J. Casas Vazquez, and G. Lebon, Extended Irreversible Thermodynamics (Berlin: Springer-Verlag: 2001). Crossref
  79. P. Galenko, D. Danilov, and V. Lebedev, Phys. Rev. E, 79: 051110 (2009). Crossref
  80. J. A. P. Ramos, E. Granato, S. C. Ying et al., Phys. Rev. E, 81: 011121(7) (2010).
  81. K.-A. Wu, A. Adland, and A. Karma, Phys. Rev. E, 81: 061601(15) (2010).
  82. D. O. Kharchenko, I. O. Lysenko, and S. V. Kokhan, Eur. Phys. J. B, 76: 37 (2010). Crossref
  83. D. O. Kharchenko, І. O. Lisenko, V. O. Kharchenko, Metallofiz. Noveishie Tekhnol., 32, No. 6: 783 (2010).
  84. A. G. Khachaturyan, Theory of Structural Transformations in Solids (New York: Wiley: 1983).
  85. V. P. Skripov, A. V. Skripov, UFN, 128: 193 (1979). Crossref
  86. W. J. Moberly Chan, D. P. Adams, M. J. Aziz et al., MRS Bulletin, 32: 424 (2007). Crossref
  87. C. L. Emmott and A. J. Bray, Phys. Rev. E, 59: 213 (1999). Crossref
  88. J. W. Cahn and J. E. Hilliard, J. Chem. Phys., 28: 258 (1958). Crossref
  89. C. W. Gardiner, Handbook of Stochastic Methods (Berlin–Heidelberg–New York: Springer-Verlag: 1985).
  90. D. O. Kharchenko and I. A. Knyaz', Eur. Phys. J. B, 32: 375 (2003). Crossref
  91. A. I. Olemskoi, D. O. Kharchenko, and I. A. Knyaz', Phys. Rev. E, 71: 041101 (2005). Crossref
  92. M. Ibanes, J. Garcia-Ojalvo, R. Toral, and J. M. Sancho, Phys. Rev. Lett., 87: 020601 (2001). Crossref
  93. I. M. Lifshitz and V. V. Slyozov, J. Phys. Chem. Solids, 19: 35 (1961). Crossref
  94. G. Martin and P. Bellon, Solid State Phys., 50: 189 (1996). Crossref
  95. P. K. Galenko, D. O. Kharchenko, and I. O. Lysenko, Physica A, 389: 3443 (2010). Crossref
  96. P. Galenko and D. Jou, Physica A, 388: 3113 (2009). Crossref
  97. D. Jou, J. Casas-Vazquez, and G. Lebon, Rep. Prog. Phys., 51: 1005 (1988). Crossref
  98. D. Joseph and L. Preziosi, Rev. Mod. Phys., 61: 41 (1989). Crossref
  99. J. W. Cahn and J. E. Hilliard, J. Chem. Phys., 28: 258 (1958). Crossref
  100. J. W. Cahn, Acta Metall., 9: 795 (1961). Crossref
  101. H. E. Cook, Acta Metall., 18: 297 (1970). Crossref
  102. P. Galenko and V. Lebedev, Phys. Lett. A, 372: 985 (2008). Crossref
  103. N. Lecoq, H. Zapolsky, and P. Galenko, Eur. Phys. J. Spec. Top., 177: 165 (2009). Crossref
  104. D. O. Kharchenko, I. O. Lisenko, V. O. Kharchenko, Ukr. Fiz. Zhurnal, 55: 1226 (2010).
  105. K. Binder and P. Fratzl, Phase Transformations in Materials (Eds. G. Kostorz) (Weinheim–New York–Chichester–Brisbane–Singapore–Tokyo: Wiley-VCH: 2001).
  106. Y. Yackle and M. Piesoth, Z. Phys. B, 72: 25 (1988). Crossref
  107. K. Binder, Festkörperprobleme—Advances in Solid State Physics (Eds. P. Grosse) (Braunschweig: Vieweg: 1986).
  108. G. Martin, Phys. Rev. B, 41: 2279 (1990). Crossref
Cited By (3)
  1. Dmitrii O. Kharchenko and Vasyl O. Kharchenko, Radiation Effects and Defects in Solids 171, 819 (2016).
  2. D.O. Kharchenko, V.O. Kharchenko and A.I. Bashtova, Ukr. J. Phys. 61, 265 (2016).
  3. V. O. Kharchenko, I. O. Lysenko, O. M. Shchokotova, A. I. Bashtova et al., Usp. Fiz. Met. 18, 295 (2017).

© 2013–2018 "G.V. Kurdyumov Institute for Metal Physics"