Issues »  Volume 13, Issue 3

Statistical Thermodynamics of the Substitutional Short-Range Atomic Order and Kinematics of the Diffuse Scattering of Radiations in (Para)Magnetic F.C.C.-Ni–Fe Alloys

S. M. Bokoch$^{1,2}$, V. A. Tatarenko$^{3}$, I. V. Vernyhora$^{3,4}$

$^1$Institute for Advanced Materials Science and Innovative Technologies, 15 Sauletekio Ave., 10224 Vilnius, Lithuania
$^2$NIK Electronics, 34 Lesi Ukrayinky Blvd., 01133 Kyiv, Ukraine
$^3$G.V. Kurdyumov Institute for Metal Physics, NAS of Ukraine, 36 Academician Vernadsky Blvd., UA-03142 Kyiv, Ukraine
$^4$Institute of Applied Physics, NAS of Ukraine, 58 Petropavlivska Str., 40000 Sumy, Ukraine

Received: 07.03.2012; final version - 19.09.2012. Download: PDF

In imitation of f.c.c.-Ni—Fe alloy, the statistical-thermodynamic approach is applied for quantitative analysis of the thermal and composition—magnetic moment fluctuations’ influence on the kinematic diffuse-scattering intensity of radiations (X-rays or thermal neutrons) in magnetic alloys with the atomic short-range order (SRO). Within the temperature—concentration ($T-c$) domains of macroscopically ferromagnetic and paramagnetic states of f.c.c. alloy, the relation for the diffuse-scattering intensity distribution over the quasi-wave vectors (including the Bragg’s ‘fundamental’ point), depending on the total ‘mixing’ energies of atoms, are obtained within the scope of (i) the selfconsistent-field (SCF) and mean-SCF (MSCF) approximations as well as (ii) the simplest approximation by ‘interpolation’. The $2D$ patterns of (001)$^{*}$-type diffuse-scattering intensity distribution over a reciprocal space as well as the corresponding distributions (local configurations) of Fe and Ni atoms over the f.c.c.-lattice sites are modelled by a statistical Monte Carlo technique using the available experimental data on the Warren—Cowley SRO parameters extracted. Taking into account the magnetic (‘exchange’) interactions of atoms within the statistical thermodynamics of alloys with the atomic SRO, it is possible to clarify the significant ($T-c$)-deviations of the diffuse-scattering intensity from its values corresponding to classical relation by the Krivoglaz—Clapp—Moss (KCM) formula with constant interatomic-interaction parameters. The principal possibilities and validity of using the generalized form and main assumptions of the KCM formula under an analysis of the diffuse-scattering intensity in magnetic alloys are ascertained. One of the intriguing findings of a given work belongs to revealing a possibility for simple and quite accurate estimation of the total ‘mixing’ energies, including their magnetic and nonmagnetic contributions, by means of the experimental SRO intensities for magnetic alloys obtained with X-ray diffraction techniques only applied for synchrotron radiation instrumentation instead of conventional neutron scattering techniques, which are commonly used as a powerful probe in physics of magnetic materials. Obtained analytical and computational results on diffuse scattering characterization of (para)magnetic f.c.c.-Ni—Fe alloys are in a decent fit with all the reliable X-ray and thermal neutron diffraction data collected over years.

Keywords: f.c.c.-Ni—Fe alloys, interatomic interactions, magnetic impurity interactions, short-range atomic ordering, diffuse scattering, statistical thermodynamics, Monte Carlo simulation.

PACS: 05.10.Ln, 61.05.cf, 61.72.Bb, 64.60.De, 75.30.Et, 75.40.-s, 75.50.Bb

DOI: https://doi.org/10.15407/ufm.13.03.269

Citation: S. M. Bokoch, V. A. Tatarenko, and I. V. Vernyhora, Statistical Thermodynamics of the Substitutional Short-Range Atomic Order and Kinematics of the Diffuse Scattering of Radiations in (Para)Magnetic F.C.C.-Ni–Fe Alloys, Usp. Fiz. Met., 13, No. 3: 269—302 (2012), doi: 10.15407/ufm.13.03.269

References (88)  
  1. M. A. Krivoglaz and A. A. Smirnov, The Theory of Order–Disorder in Alloys (London: Macdonald: 1965).
  2. D. de Fontaine, Solid State Physics (Eds. H. Ehrenreich et al.) (New York: Academic Press: 1979), vol. 34, p. 73.
  3. F. Ducastelle, Order and Phase Stability in Alloys (New York: Elsevier: 1991).
  4. A. G. Khachaturyan, Progr. Mater. Sci., 22: 1 (1978). Crossref
  5. A. G. Khachaturyan, Theory of Structural Transformations in Solids (Mineola, NY: Dover Publications Inc.: 2008).
  6. M. A. Krivoglaz, X-Ray and Neutron Diffraction in Nonideal Crystals (Berlin: Springer: 1996). Crossref
  7. M. A. Krivoglaz, Diffuse Scattering of X-Rays and Thermal Neutrons by Fluctuational Inhomogeneities of Imperfect Crystals (Berlin: Springer: 1996). Crossref
  8. B. Schönfeld, Progr. Mater. Sci., 44, No. 5: 435 (1999). Crossref
  9. G. E. Ice and C. J. Sparks, Annu. Rev. Mater. Sci., 29: 25 (1999). Crossref
  10. M. A. Krivoglaz, Zh. Eksp. Teor. Fiz., 32: 1368 (1957).
  11. P. C. Clapp and S. C. Moss, Phys. Rev., 142, No. 2: 418 (1966). Crossref
  12. P. C. Clapp and S. C. Moss, Phys. Rev., 171, No. 3: 754 (1968). Crossref
  13. S. C. Moss and P. C. Clapp, Phys. Rev., 171, No. 3: 764 (1968). Crossref
  14. R. A. Tahir-Kheli, Phys. Rev., 188, No. 3: 1142 (1969). Crossref
  15. R. Kikuchi, Phys. Rev., 81, No. 6: 988 (1951). Crossref
  16. A. Finel, Statistics and Dynamics of Alloy Phase Transformations. NATO Advanced Studies Institute, Series B: Physics. Vol. 319 (Eds. P. E. A. Turchi and A. Gonis) (New York: Plenum: 1994), p. 495. Crossref
  17. J. M. Sanchez, V. Pierron-Bohnes, and F. Meja-Lira, Phys. Rev. B, 51, No. 6: 3429 (1995). Crossref
  18. R. Brout, Phase Transitions (New York: Benjamin: 1965). Crossref
  19. I. R. Yukhnoskii and Z.A. Gurskii, Quantum Statistical Theory of Disordered Systems (Kiev: Naukova Dumka: 1991) (in Russian).
  20. B. L. Gyorffy and G. M. Stocks, Phys. Rev. Lett., 50, No. 5: 374 (1983). Crossref
  21. J. B. Staunton and B.L. Gyorffy, Phys. Rev. Lett., 69, No. 2: 371 (1992). Crossref
  22. J. B. Staunton, Rep. Progr. Phys., 57, No. 12: 1289 (1994). Crossref
  23. J. B. Staunton, D. D. Johnson, and F. J. Pinski, Phys. Rev. B, 50, No. 3: 1450 (1994). Crossref
  24. D. D. Johnson, J. B. Staunton, and F. J. Pinski, Phys. Rev. B, 50, No. 3: 1473 (1994). Crossref
  25. F. J. Pinski, J. B. Staunton, and D. D. Johnson, Phys. Rev. B, 57, No. 24: 15177 (1998). Crossref
  26. J. B. Staunton, S. S. A. Razee, M. F. Ling, D. D. Johnson, and F. J. Pinski, J. Phys. D: Appl. Phys., 31, No. 19: 2355 (1998). Crossref
  27. D. A. Rowlands, J. B. Staunton, B. L. Gyorffy, E. Bruno, and B. Ginatempo, Phys. Rev. B, 72, No. 4: 045101 (2005). Crossref
  28. D. A. Rowlands, A. Ernst, B. L. Gyorffy, and J. B. Staunton, Phys. Rev. B, 73, No. 16: 165122 (2006). Crossref
  29. V. Gerold and J. Kern, Acta Metall., 35, No. 2: 393 (1987). Crossref
  30. F. Livet, Acta Metall., 35, No. 12: 2915 (1987). Crossref
  31. V. G. Vaks, N. E. Zein, and V. V. Kamyshenko, J. Phys. F: Metal Phys., 18, No. 8: 1641 (1988). Crossref
  32. V. G. Vaks, N. E. Zein, and V. V. Kamyshenko, J. Phys.: Condens. Matter, 1, No. 11: 2115 (1989). Crossref
  33. V. G. Vaks and V. V. Kamyshenko, J. Phys.: Condens. Matter, 3, No. 10: 1351 (1991). Crossref
  34. V. I. Tokar, Phys. Letters A, 110, No. 9: 453 (1985). Crossref
  35. T. A. Grishchenko, I. V. Masanskii, and V. I. Tokar, J. Phys.: Condens. Matter, 2, No. 21: 4769 (1990). Crossref
  36. V. I. Tokar, I. V. Masanskii, and T. A. Grishchenko, J. Phys.: Condens. Matter, 2, No. 50: 10199 (1990). Crossref
  37. I. V. Masanskii, V. I. Tokar, and T. A. Grishchenko, Phys. Rev. B, 44, No. 9: 4647 (1991). Crossref
  38. I. Tsatskis, Phil. Mag. Lett., 78, No. 5: 403 (1998). Crossref
  39. I. Tsatskis, J. Phys.: Condens. Matter, 10, No. 9: L145 (1998). Crossref
  40. I. Tsatskis and E. K. H. Salje, J. Phys.: Condens. Matter, 10, No. 17: 3791 (1998). Crossref
  41. I. Tsatskis, Phys. Letters A, 241, Nos. 1–2: 110 (1998). Crossref
  42. R. V. Chepulskii, J. Phys.: Condens. Matter, 10, No. 7: 1505 (1998). Crossref
  43. R. V. Chepulskii and V. N. Bugaev, J. Phys.: Condens. Matter, 10, No. 33: 7309 (1998). Crossref
  44. R. V. Chepulskii and V. N. Bugaev, J. Phys.: Condens. Matter, 10, No. 33: 7327 (1998). Crossref
  45. R. V. Chepulskii and V. N. Bugaev, J. Phys.: Condens. Matter, 10, No. 39: 8771 (1998). Crossref
  46. R. V. Chepulskii and V. N. Bugaev, J. Phys. Chem. Solids, 59, No. 9: 1469 (1998). Crossref
  47. R. V. Chepulskii, J. Phys. Chem. Solids, 59, No. 9: 1473 (1998). Crossref
  48. R. V. Chepulskii and V. N. Bugaev, Solid State Commun., 105, No. 10: 615 (1998). Crossref
  49. R. V. Chepulskii, J. Phys.: Condens. Matter, 11, No. 44: 8645 (1999). Crossref
  50. R. V. Chepulskii, J. Phys.: Condens. Matter, 11, No. 44: 8661 (1999). Crossref
  51. R. V. Chepulskii, Phys. Rev. B, 61, No. 13: 8606 (2000). Crossref
  52. R. V. Chepulskii, J. Phys.: Condens. Matter, 14, No. 8: L193 (2002). Crossref
  53. R. V. Chepulskii, J. B. Staunton, E. Bruno et al., Phys. Rev. B, 65, No. 6: 064201 (2002). Crossref
  54. R. V. Chepulskii, Phys. Rev. B, 69, No. 13: 134431 (2004). Crossref
  55. R. V. Chepulskii, Phys. Rev. B, 69, No. 13: 134432 (2004). Crossref
  56. V. A. Tatarenko, T. M. Radchenko, and V. M. Nadutov, Metallofiz. Noveishie Tekhnol., 25, No. 10: 1303 (2003) (in Ukrainian).
  57. V. A. Tatarenko and T. M. Radchenko, Intermetallics, 11, Nos. 11–12: 1319 (2003). Crossref
  58. V. A. Tatarenko, S. M. Bokoch, V. M. Nadutov, T. M. Radchenko, and Y. B. Park, Defect and Diffusion Forum, 280–281: 29 (2008).
  59. S. M. Bokoch and V. A. Tatarenko, Solid State Phenomena, 138: 303 (2008). Crossref
  60. S. M. Bokoch and V. A. Tatarenko, Uspehi Fiziki Metallov, 11, No. 4: 413 (2010). Crossref
  61. I. V. Vernyhora, V. A. Tatarenko, and S. M. Bokoch, ISRN Thermodynamics, 2012: ID 917836-1–11 (2012); doi:10.5402/2012/917836. Crossref
  62. J. S. Smart, Effective Field in Theories of Magnetism (Philadelphia: W. B. Saunders Company: 1966).
  63. D. Jiles, Introduction to Magnetism and Magnetic Materials (London: Charman & Hall: 1991). Crossref
  64. A. Aharoni, Introduction to the Theory of Ferromagnetism (New York: Oxford University Press: 2000).
  65. S. V. Semenovskaya, phys. stat. sol. (b), 64, No. 1: 291 (1974).
  66. S. M. Bokoch, M. P. Kulish, and T. D. Shatnii, Metallofiz. Noveishie Tekhnol., 26, No. 5: 627 (2004) (in Russian).
  67. S. M. Bokoch, M. P. Kulish, V. A. Tatarenko, and T. M. Radchenko, Proc. of the 1st International Conf. on Diffusion in Solids and Liquids–DSL-2005 (July 6–8, 2005, Aveiro), vol. 1, p. 57.
  68. S. M. Bokoch, N. P. Kulish, and V. A. Tatarenko, Fundamental'nyye Problemy Sovremennogo Materialovedeniya, 4: 78 (2007) (in Russian).
  69. S. H. Rahman, Acta Crystallogr. A, 49, No. 1: 56 (1993). Crossref
  70. S. H. Rahman, Acta Crystallogr. A, 49, No. 1: 68 (1993). Crossref
  71. S. H. Rahman and M. Rodewald, Acta Crystallogr. A, 51, No. 2: 153 (1995). Crossref
  72. K. Osaka and T. Takama, Acta Mater., 50, No. 6: 1289 (2002). Crossref
  73. S. Hata, S. Matsumura, N. Kuwano, and K. Oki, J. Surf. Analysis, 3: 401 (1997).
  74. S. Hata, H. Fujita, C. G. Schlesier, S. Matsumura, N. Kuwano, and K. Oki, Mater. Trans. JIM, 39, No. 1: 133 (1998). Crossref
  75. S. Hata, S. Matsumura, N. Kuwano, and K. Oki, Acta Mater., 46, No. 3: 881 (1998). Crossref
  76. S. Hata, S. Matsumura, N. Kuwano, K. Oki, and D. Shindo, Acta Mater., 46, No. 14: 4955 (1998). Crossref
  77. S. Hata, T. Mitate, N. Kuwano, S. Matsumura, D. Shindo, and K. Oki, Mater. Sci. Eng. A, 312, No. 1–2: 160 (2001). Crossref
  78. U. D. Kulkarni, Acta Mater., 52, No. 9: 2721 (2004). Crossref
  79. S. Lefebvre, F. Bley, M. Fayard, and M. Roth, Acta Metall., 29, No. 5: 749 (1981). Crossref
  80. P. Cenedese, F. Bley and S. Lefebvre, Mat. Res. Soc. Symp. Proc., 21, 351 (1984). Crossref
  81. X. Jiang, G. E. Ice, C. J. Sparks, L. Robertson, and P. Zschack, Phys. Rev. B, 54, No. 5: 3211 (1996). Crossref
  82. G. E. Ice, C. J. Sparks, A. Habenschuss, and L. B. Shaffer, Phys. Rev. Lett., 68, No. 6: 863 (1992). Crossref
  83. J. L. Robertson, G. E. Ice, C. J. Sparks, X. Jiang, P. Zschack, F. Bley, S. Lefebvre, and M. Bessiere, Phys. Rev. Lett., 82, No. 14: 2911 (1999). Crossref
  84. F. Bley, Z. Amilius, and S. Lefebvre, Acta Metall., 36, No. 7: 1643 (1988). Crossref
  85. S. Lefebvre, F. Bley, M. Bessiere, M. Fayard et al., Acta Crystallogr. A, 36, No. 1: 1 (1980). Crossref
  86. G. L. Squires, Introduction to the Theory of Thermal Neutron Scattering (Cambridge: Cambridge University Press: 1978).
  87. S. W. Lovesey, Theory of Neutron Scattering from Condensed Matter (New York: Oxford University Press: 1984), vols. 1, 2.
  88. Neutron Scattering from Magnetic Materials (Ed. T. Chatterji) (Amsterdam: Elsevier: 2006).
Cited By (1)
  1. P. V. Petrenko, N. P. Kulish, N. A. Mel’nikova and Yu. E. Grabovskii, Phys. Metals Metallogr. 117, 927 (2016).

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