Issues $\rightarrow$ Volume 26, Issue 1 (2025)

Parameterization of Diffusion Characteristics of Atomic-Order Relaxation Kinetics in Ni–Al Alloys

TATARENKO V.A., RADCHENKO T.M., NAUMUK A.Yu., and MORDYUK B.M.

G.V. Kurdyumov Institute for Metal Physics of the N.A.S. of Ukraine, 36 Academician Vernadsky Blvd., UA-03142 Kyiv, Ukraine

Received 04.11.2024, final version 11.11.2024 Download PDF logo PDF

Abstract
To study diffusion characteristics in substitutional f.c.c.-Ni–Al alloys, we review, analyse, and use the kinetic models, in which the relaxation of correlation parameters for the atomic distribution causes the time dependence of both the diffuse-scattering intensity I and the residual electrical resistivity ρ. Using the parameterization of the available literature data about the measurement of the residual electrical resistivity during the isothermal annealing of alloys, the most characteristic relaxation times of ρ after quenching of the alloys and its equilibrium value ρ∞ are estimated. The maximum characteristic relaxation time of the atomic order of such alloys is determined, and the curves of the time dependence of the normalized change in intensity ΔI are predicted based on the hypothesis of the coincidence of the largest characteristic relaxation times for I and ρ. The relaxation process is accompanied by both the increase in the number of clusters with the presence of short-range order in their structure and the degree of their order that is consistent with both the results of computer modelling of local atomic ordering using the Monte Carlo method and the model of inhomogeneous short-range order.

Keywords: Ni–Al solid solution, atomic jumps, diffusion, short-range order, relaxation, diffuse scattering, residual resistivity.

DOI: https://doi.org/10.15407/ufm.26.01.***

Citation: V.A. Tatarenko, T.M. Radchenko, A.Yu. Naumuk, and B.M. Mordyuk, Parameterization of Diffusion Characteristics of Atomic-Order Relaxation Kinetics in Ni–Al Alloys, Progress in Physics of Metals, 26, No. 1: ***–*** (2025)

References  
  1. А.G. Khachaturyan, Fiz. Tverd. Tela, 9, No. 9: 2594 (1967) (in Russian).
  2. А.G. Khachaturyan, Fiz. Tverd. Tela, 11, No. 12: 3534 (1969) (in Russian).
  3. М.А. Krivoglaz, Zh. Eksp. Tepr. Fiz., 40, No. 6: 1812 (1961) (in Russian).
  4. A.G. Khachaturyan, Theory of Structural Transformations in Solids (Mineola, NY: Dover Publications, Inc.: 2008).
  5. V.A. Tatarenko, O.V. Sobol’, D.S. Leonov, Yu.A. Kunyts’kyy, and S.M. Bokoch, Statistical thermodynamics and physical kinetics of structural changes of quasi-binary solid solutions based on the close-packed simple lattices (according to the data about evolution of a pattern of scattering of waves of various kinds), Usp. Fiz. Met., 12, No. 1: 1 (2011) (in Ukrainian); https://doi.org/10.15407/ufm.12.01.001
  6. L.S. Darken, AIME Transactions, 175: 184 (1948).
  7. М.А. Krivoglaz, Theory of X-Ray and Thermal Neutron Scattering by Real Crystals (New York: Springer: 1969).
  8. H.E. Cook, The kinetics of clustering and short-range order in stable solid solutions, J. Phys. Chem. Solids, 30, No. 10: 2427 (1969); https://doi.org/10.1016/0022-3697(69)90067-5
  9. P.R. Okamoto and G. Thomas, On short range order and micro-domains in the Ni4Mo system, Acta Metall., 19, No. 8: 825 (1971); https://doi.org/10.1016/0001-6160(71)90139-8
  10. S.K. Das, P.R. Okamoto, P.M.J. Fischer, and G. Thomas, Short range order in Ni–Mo, Au–Cr, Au–V and Au–Mn alloys, Acta Metall., 21, No. 7: 913 (1971).
  11. S. Hata, H. Fujita, C.G. Schlesier, S. Matsumura, N. Kuwano, and K. Oki, Materials Transaction: The Jpn. Institute of Metals, 39, No. 1: 133 (1998); https://doi.org/10.2320/matertrans1989.39.133
  12. S. Hata, S. Matsumura, N. Kuwano, K. Oki, and D. Shindo, Acta Mater., 46, No. 14: 4955 (1998); https://doi.org/10.1016/S1359-6454(98)00180-3
  13. S. Hata, D. Shindo, N. Kuwano, S. Matsumura, and K. Oki, Monte Carlo study of ordering processes in fcc-based Ni–Mo Alloys, Materials Transaction: The Jpn. Institute of Metals, 39, No. 9: 914 (1998); https://doi.org/10.2320/matertrans1989.39.914
  14. S. Hata, D. Shindo, T. Mitate, N. Kuwano, S. Matsumura, and K. Oki, HRTEM image contrast of short range order in Ni4Mo, Micron, 31, No. 5: 533 (2000); https://doi.org/10.1016/S0968-4328(99)00134-1
  15. S. Hata and S. Matsumura, 合金の短範囲規則状態の微視的構造, The Crystallographic Society of Jpn., 44, No. 4: 225 (2002); https://doi.org/10.5940/jcrsj.44.225
  16. D. de Fontaine, k-space symmetry rules for order–disorder reactions, Acta Metall., 23, No. 5: 553 (1975); https://doi.org/10.1016/0001-6160(75)90096-6
  17. H.E. Cook, Continuous transformations, Mater. Sci. Eng., 25: 127 (1976); https://doi.org/10.1016/0025-5416(76)90059-8
  18. D. de Fontaine, Solid State Physics (Еds. H. Ehrenreich, F. Seits, and D. Turnbull) (New York: Academic Press.: 1979), vol. 34, p. 73.
  19. H. Chen and J.B. Cohen, Measurements of the ordering instability in binary alloys, Acta Metall., 27, No. 2: 603 (1979); https://doi.org/10.1016/0001-6160(79)90012-9
  20. H. Chen and J.B. Cohen, Pretransition phenomena in first-order order–disorder transitions, Metallurg. Mater. Trans. A, 12, No. 4: 575 (1981); https://doi.org/10.1007/BF02649731
  21. U.D. Kulkarni and S. Banerjee, Phase separation during the early stages of ordering in Mi3Mo, Acta Metall., 36, No. 2: 413 (1998); https://doi.org/10.1016/0001-6160(88)90017-X
  22. S. Banerjee, U.D. Kulkarni, and K. Urban, Initial stages of ordering in Ni3Mo — thermal and irradiation ordering experiments, Acta Metall., 37, No. 1: 35 (1989); https://doi.org/10.1016/0001-6160(89)90264-2
  23. A. Arya, S. Banerjee, G.P. Das, I. Dasgupta, T. Saha-Dasgupta, and A. Mookerjee, A first-principles thermodynamic approach to ordering in Ni–Mo alloys, Acta Mater., 49, No. 17: 3575 (2001); https://doi.org/10.1016/S1359-6454(01)00235-X
  24. A. Arya, G.K. Dey, V.K. Vasudevan, and S. Banerjee, Effect of chromium addition on the ordering behaviour of Ni–Mo alloy: experimental results vs. electronic structure calculations, Acta Mater., 50, No. 14: 3301 (2002); https://doi.org/10.1016/S1359-6454(02)00093-9
  25. A. Mookerjee, T. Saha-Dasgupta, I. Dasgupta, A. Arya, S. Banerjee, and G. P. Das, A first-principles thermodynamic approach to ordering in binary alloys, Bulletin of Materials Science, 26, No. 1: 79 (2003); https://doi.org/10.1007/BF02712791
  26. H.E. Cook, Brownian motion in spinodal decomposition, Acta Metall., 18, No. 3: 297 (1970); https://doi.org/10.1016/0001-6160(70)90144-6
  27. H.E. Cook, D. de Fontaine, and J.E. Hillard, A model for diffusion on cubic lattices and its application to the early stages of ordering, Acta Metall., 17, No. 6: 765 (1969); https://doi.org/10.1016/0001-6160(69)90083-2
  28. V.А. Tatarenko and T.M. Radchenko, Parameters of the short-range order relaxation kinetics and interactions of atoms in binary substitutional f.c.c. solid solutions from the data of time evolution of diffuse scattering of radiation, Metallofiz Noveishie Technol., 24, No. 10: 1335 (2002).
  29. S.M. Bokoch, N.P. Kulish, T.M. Radchenko, S.P. Repetskij, and V.A. Tatarenko, Parameters of a relaxation of an electrical resistance and diffuse scattering in binary substitutional solutions fcc-Ni–Mo, Metallofiz. Noveishie Tekhnol., 24, No. 5: 691 (2002) (in Russian).
  30. М.М. Naumova, S.V. Semenovskaya, and Ya.S. Umanskiy, Fiz. Tverd. Tela, 12, No. 4: 976 (1970) (in Russian).
  31. F. Bley, Z. Amilius, and S. Lefebvre, Wave vector dependent kinetics of short-range ordering in 62Ni0.765Fe0.235, studied by neutron diffuse scattering, Acta Metall., 36, No. 7: 1643 (1988); https://doi.org/10.1016/0001-6160(88)90231-3
  32. М.М. Naumova and S.V. Semenovskaya, Fiz. Tverd. Tela, 13, No. 12: 3632 (1970) (in Russian).
  33. H. Chen and J. Cohen, A comparison of experiment and the theory of continuous ordering, Supplément au J. de Physique Colloques, 38, No. 7: 314 (1977); https://doi.org/10.1051/jphyscol:1977762
  34. S. Banerjee, K. Urban, and M. Wilkens, Order–disorder transformation in Ni4Mo under electron irradiation in a high-voltage electron microscope, Acta Metall., 32, No. 3: 299 (1984); https://doi.org/10.1016/0001-6160(84)90103-2
  35. S.M. Bokoch, M.P. Kulish, T.M. Radchenko, and V.A. Tatarenko, Kinetics of short-range ordering of substitutional solid solutions (according to data on a scattering of various kinds of waves). I. Microscopic parameters of migration of atoms within f.c.c.-Ni–Mo in Fourier-representation, Metallofiz. Noveishie Tekhnol., 26, No. 3: 387 (2004) (in Russian).
  36. T.M. Radchenko and V.A. Tatarenko, Fe–Ni alloys at high pressures and temperatures: statistical thermodynamics and kinetics of the L12 or D019 atomic order, Usp. Fiz. Met., 9, No. 1: 1 (2008) (in Ukrainian); https://doi.org/10.15407/ufm.09.01.001
  37. T.M. Radchenko, V.A. Tatarenko, S.M. Bokoch, and M.P. Kulish, Microscopic approach to the evaluation of diffusion coefficients for substitutional f.c.c. solid solutions, Proc. of the 1st Int’l Conf. on Diffusion in Solids and Liquids—‘DSL-2005’ (Aveiro, Portugal, 6–8 July, 2005) (Еds. A. Öchsner, J. Grácio, and F. Barlat) (Aveiro: University of Aveiro: 2005), vol. 2, р. 591.
  38. S.M. Bokoch, M.P. Kulish, V.A. Tatarenko, and T.M. Radchenko, Kinetics of short-range ordering of substitutional solid solutions (according to data on a scattering of various kinds of waves). II. Parameters of atomic microdiffusion within f.c.c.-Ni–Mo, Metallofiz. Noveishie Tekhnol., 26, No. 4: 541 (2004) (in Russian).
  39. V.A. Tatarenko and T.M. Radchenko, The application of radiation diffuse scattering to the calculation of phase diagrams of f.c.c. substitutional alloys, Intermetallics, 11, Nos. 11–12: 1319 (2003); https://doi.org/10.1016/S0966-9795(03)00174-2
  40. V.A. Tatarenko, T.M. Radchenko, and V.M. Nadutov, Parameters of interatomic interaction in a substitutional alloy f.c.c. Ni–Fe according to experimental data about the magnetic characteristics and equilibrium values of intensity of a diffuse scattering of radiations, Metallofiz. Noveishie Tekhnol., 25, No. 10: 1303 (2003) (in Ukrainian).
  41. L.-Q. Chen and A.G. Khachaturyan, Formation of virtual ordered states along a phase-decomposition path, Phys. Rev. B, 44, No. 9: 4681 (1991); https://doi.org/10.1103/PhysRevB.44.4681
  42. L.-Q. Chen and A.G. Khachaturyan, Kinetics of Ordering Transformations in Metals (Еds. H. Chen and V.K. Vasudevan) (Warrendale, Pennsylvania: TMS: 1992), р. 197.
  43. L.-Q. Chen and A. G. Khachaturyan, Kinetics of virtual phase formation during precipitation of ordered intermetallics, Phys. Rev. B, 46, No. 10: 5899 (1992); https://doi.org/10.1103/PhysRevB.46.5899
  44. R. Poduri and L.-Q. Chen, Computer simulation of the kinetics of order-disorder and phase separation during precipitation of δ′ (Al3Li) in Al–Li alloys, Acta Mater., 45, No. 1: 245 (1997); https://doi.org/10.1016/S1359-6454(96)00137-1
  45. R. Poduri and L.-Q. Chen, Acta Mater., 46, No. 5: 1719 (1998); https://doi.org/10.1016/S1359-6454(97)00335-2
  46. Y. Wang, D. Banerjee, C.C. Su, and A.G. Khachaturyan, Computer simulation of atomic ordering and compositional clustering in the pseudobinary Ni3Al–Ni3V system, Acta Mater., 46, No. 9: 2983 (1998); https://doi.org/10.1016/S1359-6454(98)00015-9
  47. G. Rubin and A.G. Khachaturyan, Three-dimensional model of precipitation of ordered intermetallics, Acta Mater., 47, No. 7: 1995 (1999); https://doi.org/10.1016/S1359-6454(99)00107-X
  48. V.A. Tatarenko and T.M. Radchenko, Diffusive relaxation of short-range order parameters and the time evolution of diffuse radiation scattering in solid solutions, Defect Diffus. Forum, 194–199, Pt. 1: 183 (2001); https://doi.org/10.4028/www.scientific.net/DDF.194-199.183
  49. V.A. Tatarenko, S.M. Bokoch, V.M. Nadutov, T.M. Radchenko, and Y.B. Park, Semi-empirical parameterization of interatomic interactions and kinetics of the atomic ordering in Ni–Fe–C permalloys and elinvars, Defect Diffus. Forum, 280–281: 29–78 (2008); https://doi.org/10.4028/www.scientific.net/DDF.280-281.29
  50. E.P. Feldman, L.I. Stefanovich, and K.V. Gumennik, Izv. RAN. Ser.: Fiz., 70, No.: 1048 (2006) (in Russian).
  51. T.M. Radchenko and V.A. Tatarenko, Atomic-ordering kinetics and diffusivities in Ni–Fe permalloy, Defect Diffus. Forum, 273–276: 525 (2008); https://doi.org/10.4028/www.scientific.net/DDF.273-276.525
  52. T.M. Radchenko, V.A. Tatarenko, and S.M. Bokoch, Diffusivities and kinetics of short-range and long-range orderings in Ni–Fe permalloys, Metallofiz. Noveishie Tekhnol., 28, No. 12: 1699 (2006).
  53. V.A. Tatarenko and T.M. Radchenko, Direct and indirect methods of the analysis of interatomic interaction and kinetics of a relaxation of the short-range order in close-packed substitutional (interstitial) solid solutions, Usp. Fiz. Met., 3, No. 2: 111 (2002) (in Ukrainian); https://doi.org/10.15407/ufm.03.02.111
  54. V.A. Tatarenko, T.M. Radchenko, A.Yu. Naumuk, and B.M. Mordyuk, Statistical-thermodynamic models of the Ni–Al-based ordering Phases (L12, L10, B2): role of magnetic Ni-atoms’ contribution, Prog. Phys. Met., 25, No. 1: 3 (2024); https://doi.org/10.15407/ufm.25.01.003
  55. N.S. Stoloff, Physical and mechanical metallurgy of Ni3Al and its alloys, Int. Mater. Rev., 34, No. 4: 153 (1989); https://doi.org/10.1179/imr.1989.34.1.153
  56. О.V. Savin, N.N. Stepanova, Yu.N. Akshentsev, B.А. Baum, B.А. Sazonova, and Yu.E. Turhan, Fiz. Met. Metalloved., 88, No. 4: 69 (1999) (in Russian).
  57. О.V. Savin, N.N. Stepanova, Yu.N. Akshentsev, B.А. Baum, and Е.Е. Baryshev, Fiz. Met. Metalloved., 90, No. 1: 66 (2000) (in Russian).
  58. А.А. Katsnelson and P.Sh. Dazhaev, Izv. VUZov SSSR. Ser.: Fiz., No. 4: 23 (1970) (in Russian).
  59. А.А. Katsnelson, А.М. Silonov, and V.М. Silonov, Fiz. Met. Metalloved., 33, No. 6: 1267 (1972) (in Russian).
  60. S.M. Bokoch, D.S. Leonov, M.P. Kulish, V.A. Tatarenko, and Yu.A. Kunitsky, Influence of relaxation of the atomic order in f.c.c.-Ni–Al alloys on X-ray diffuse scattering, phys. status solidi A, 206, No. 8: 1766 (2009); https://doi.org/10.1002/pssa.200881604
  61. S.M. Bokoch, D.S. Leonov, M.P. Kulish, V.A. Tatarenko, and Yu.A. Kunitsky, Influence of a relaxation of the atomic order in fcc-Ni–Al alloys on X-ray diffuse scattering, electrical resistance and microhardness, Metallofiz. Noveishie Tekhnol., 30, No. 12: 1677 (2008).
  62. D.S. Leonov, T.M. Radchenko, V.A. Tatarenko, and Yu.A. Kunitskiy, Kinetics parameters of atomic migration and diffuse scattering of radiations within the f.c.c.-Ni–Al alloys, Defect Diffus. Forum, 273–276: 520 (2008); https://doi.org/10.4028/www.scientific.net/DDF.273-276.520
  63. D.S. Leonov, T.M. Radchenko, V.A. Tatarenko, and Yu.A. Kunitsky, Kinetic parameters of migration of atoms and relaxation of scattering of different-type waves in the ordering fcc-Ni–Al alloy, Metallofiz. Noveishie Tekhnol., 29, No. 12: 1587 (2007) (in Russian).
  64. V.V. Lizunov, I.M. Melnyk, T.M. Radchenko, S.P. Repetsky, V.A. Tatarenko, Influence of strong electron–electron correlations on the electrical conduction and magnetic properties of substitutional alloys as advanced functional spintronic materials, Functional Magnetic and Spintronic Nanomaterials, NATO Science for Peace and Security Series B: Physics and Biophysics (Eds. I. Vladymyrskyi, B. Hillebrands, A. Serha, D. Makarov, and O. Prokopenko) (Dordrecht: Springer: 2024), Ch. 1, p. 1; https://doi.org/10.1007/978-94-024-2254-2_1
  65. E.G. Len, I.M. Melnyk, S.P. Repetsky, V.V. Lizunov, and V.A. Tatarenko, Electronic structure and temperature dependence of the linear size of the nanoscale magnetic domains in a disordered bcc-Fe–Co alloy, Materialwiss. Werkstofftech., 42, No. 1: 47 (2011); https://doi.org/10.1002/mawe.201100729
  66. S.P. Repetsky, E.G. Len, and V.V. Lizunov, Energy spectrum of electrons and magnetic susceptibility of Fe–Co alloy, Metallofiz. Noveishie Tekhnol., 28, No. 9: 1143 (2006).
  67. T.M. Radchenko, O.S. Gatsenko, V.V. Lizunov, and V.A. Tatarenko, Research trends and statistical-thermodynamic modeling the α″-Fe16N2-based phase for permanent magnets, Fundamentals of Low-Dimensional Magnets, 1st Edition (Eds. R.K. Gupta, S.R. Mishra, and T.A. Nguyen) (Taylor & Francis–CRC Press: 2022), Ch. 18, p. 343; https://doi.org/10.1201/9781003197492-18
  68. V.V. Slezov, Theory of Diffusive Decomposition of Solid Solutions (Chichester: Harwood Academic: 1995).

Creative Commons License
This work is licensed under a Creative Commons Attribution-NoDerivatives 4.0 International License
© G. V. Kurdyumov Institute for Metal Physics of the N.A.S. of Ukraine,