Atomic diffusion in the FeAl alloy: A research via the kinetic Monte Carlo method
Keywords:Kinetic Monte Carlo method, Diffusion, Numerical simulations, Phase transitions
AbstractFor a binary alloy with an ordered structure B2, we research the atomic migration by means of kinetic Monte Carlo simulations, where the atomic migration results from the exchange of positions between an atom and a vacancy in a rigid lattice. The atomistic kinetic model we used is based on the jump rate theory and the residence time algorithm, wherein we consider the pair interactions between neighbours up to the next-nearest neighbours. Likewise, we determine the ratio of the diffusion coefficients as a function of temperature and investigate the antiphase boundary mobility in the last stages of the ordering process. Furthermore, we calculate the autocorrelation function, which reveals that, in the lattice, not only the vacancy makes highly correlated jumps at low temperatures but the atoms jump to positions of their sub-lattice at moderate temperatures.
J. K. Tien and J. Caulfield, Superalloys, Supercomposites and superceramics, Boston: Academic Press Inc., 1989.
G. Bester, B. Meyer, M. Fahnle, and C. L. Fu, “Dominant thermal defects in B2FeAl,” Materials Science and Engineering: A, vol. 323, pp. 487-490, 2002.
T. Haraguchi and M. Kogachi, “Point defect behavior in B2-type intermetallic compounds,” Materials Science and Engineering: A, vol. 329331, pp. 402-407, 2002.
R. Nakamura, K Takasawa, Y Yamazaki, and Y. Iijima, “Single-phase interdiffusion in the B2 type intermetallic compounds NiAl, CoAl and FeAl,” Intermetallics, vol. 10, pp. 195- 204, 2002.
O. Semenova, R. Krachler, and H. Ipser, "A generalized defect correlation model for B2 compounds," Solid State Sciences, vol. 10, pp. 1236-1244, 2008.
A. Hanc, J. Kansy, G. Dercz, and I. Jendrzejewska, "Point defect structure in B2- ordered FeAl alloys," Journal of Alloys and Compounds, vol. 480, pp. 84-86, 2009.
R. Felwish, G. Vogl, and B. Sepiol, "Elementary diffusion jump of iron atoms in intermetallic phases studied by Mossbauer spectroscopy II. From order to disorder," Acta Metallurgica et Materialia, vol. 43, pp. 2033-2039, 1995.
B. Sepiol, "Mössbauer Spectroscopy in Diffusion Studies", Defect and Diffusion Forum, vol. 125-126, pp. 1-18, 1995.
G. Vogl and B. Sepiol, "Elementary diffusion jump of iron atoms in intermetallic phases studied by Mossbauer spectroscopy I. FeAl close to 450 equiatomic stoichiometry," Acta Metallurgica et Materialia, vol. 42, pp. 3175- 3181, 1994.
A. T. Donaldson and R. D. Rawlings, "The diffusion of nickel and gallium in the intermetallic compound NiGa," Acta Metallurgica, vol. 24, pp. 285-291, 1976.
A. Lutze-Birk and H. Jacobi, "Diffusion of 114mIn in NiAl," Scripta Metallurgica, vol. 9, pp. 761-765, 1975.
H. Hahn, G. Frohberg, and H. Wever, "Self diffusion in the intermetallic B2 electron compound PdIn," Physica Status Solidi (a), vol. 79, 559-565, 1983.
P. Wynblatt, "Diffusion mechanisms in ordered body-centered cubic alloys," Acta Metallurgica, vol. 15, pp. 1453-1460, 1967.
E. W. Elcock and C. W. McCombie, "Vacancy Diffusion in Binary Ordered Alloys,” Physical Review, vol. 109, pp. 605, 1958.
C. R. Kao and Y.A. Chang, "On the composition dependencies of self-diffusion coefficients in B2 intermetallic compounds," Intermetallics, vol. 1, pp. 237-250, 1993.
N. A. Stolwijk, M. Van Gend and H. Bakker, "Self-diffusion in the intermetallic compound CoGa," Philosophical Magazine A, vol. 42, pp. 783-808, 1980.
J. L. Jordan and S. C. Deevi, "Vacancy formation and effects in FeAl,” Intermetallics, vol. 11, pp. 507-528, 2003.
J. H. Schneibel and L. M. Pike, "A technique for measuring thermal vacancy concentrations in stoichiometric FeAl," Intermetallics, vol. 12, pp. 85-90, 2004.
M. Athènes, P. Bellon and G. Martin, "Identification of novel diffusion cycles in B2 ordered phases by Monte Carlo simulation," Philosophical Magazine A, vol. 76, pp. 565- 585, 1997.
J. Kärger and D. M. Ruthven, "Diffusion in nanoporous materials: fundamental principles, insights and challenges," New Journal of Chemistry, vol. 40, pp. 4027, 2016.
J. Kärger, D. M. Ruthven and D. N. Theodorou, Diffusion in Nanoporous Materials Volume 1 & 2, 1st Edition, US: Wiley-VCH, 2012.
B. Tuck, Introduction to Diffusion in Semiconductors (IEE Monograph Series vol. 16), UK.: Peter Peregrinus Ltd., 1974.
E. V. Manrique Castillo, "Simulación Monte Carlo de la transición orden-desorden y la formación de agregados atómicos en las aleaciones modelos tridimensionales," in Licentiate Thesis, Lima, Peru, 2006.
R. J. Borg and G. J. Dienes, An Introduction to Solid State Diffusion, Boston: Academic Press, 1988.
P. G. Shewmon, Diffusion in Solids, US: McGraw-Hill Book Co., 1963.
E. V. Manrique Castillo, "Simulación Monte Carlo Cinético de la Difusión Atómica en la Aleación FeAl", MSc. Thesis, UNMSM, Lima, Peru, 2014.
K. Binder, Monte Carlo Methods in Condensed Matter, Berlin 495: Springer, 1992.
J. M. Hammersley and D. C. Handscomb, Monte Carlo Methods, New York: Wiley, 1967.
S. M. Kim, "Vacancy properties in ordered CoGa and FeAl," Journal of Physics and Chemistry of Solids, vol. 49, vol. 65-69, 1988.
S. H. Lim, G. E. Murch, and W. A. Oates, "Configurational thermodynamics of vacancy formation in solids by Monte Carlo simulation," Journal of Physics and Chemistry of Solids, vol. 53, pp. 175-180, 1992.
M. Doyama and J. S. Koehler, "Relation between the formation energy of a vacancy and the nearest neighbor interactions in pure metals and liquid metals," Acta Metallurgica, vol. 24, pp. 871-879, 1976.
C. P. Flynn, Point and Defects Diffusion, Oxford: Clarendon Press, 1972.
G. Martin, "Atomic mobility in Cahn’s diffusion model," Physical Review B, vol. 41, pp. 2279, 1990.
F. Soisson, A. Barbu, and G. Martin, "Monte Carlo simulations of copper precipitation in dilute iron-copper alloys during thermal ageing and under electron irradiation," Acta Metallurgica, vol. 44, pp. 3789-3800, 1996.
M. Athènes, P. Bellon, and G. Martin, "A Monte-Carlo study of B2 ordering and precipitation via vacancy mechanism in b.c.c. lattices," Acta Metallurgica, vol. 44, pp. 4739-4748, 1996.
H. Ackermann, G. Inden, and R. Kikuchi, "Tetrahedron approximation of the cluster variation method for b.c.c. alloys," Acta Metallurgica, vol. 37, pp. 1-7, 1989.
E. V. Manrique Castillo, J .Rojas Tapia, and E. Torres Tapia, "Estudio de la difusión atómica en el intermetálico FeAl mediante Monte Carlo cinético," Revista de Investigación de Física UNMSM 14, pp. 1-7, 2011.
W. Young and E. Elcock, "Monte Carlo studies of vacancy migration in binary ordered alloys: I," Proceedings of the Physical Society, vol. 89, pp. 735-746, 1966.
J. L. Bocquet, Report CEA-R4565, Commissariat à l’Energie Atomique, Gif-surYvette, 1974.
A. B. Bortz, M. H. Kalos, and J. L. Lebowitz, "New algorithm for Monte-Carlo simulations of Ising spin systems," Journal of Computational Physics, vol. 17, pp. 1018, 1975.
F. Haider, "Monte Carlo Study of the Phase Stability of Ordered FCC Phases Under Irradiation" IN: Ordering and Disordering in Alloys, edited by A. R. Yavari, Amsterdam: Elsevier, 1992.
G. S. Fishman, Monte Carlo: Concepts, Algorithms, and Applications, New York: Springer Verlag Inc., 1996.
H. Gould and J. Tobochnik, "Overcoming Critical Slowing Down," Computers in Physics, vol. 3, p. 82, 1989.
M. A. Novotny, "A new approach to an old algorithm for the Simulation of Ising-like Systems," Computer in Physics, vol. 9, p. 46, 1995.
J. M. Lanore, Report CEA-N4565, Commissariat à l’Energie Atomique, Gif-sur-Yvette, 1972.
H. Bakker, N. Stolwijk, L. P. Van der Meij and T. J. Zuurendonk, "Microstructural dependence of vacancy diffusion in ordered alloys," Nuclear Metallic, Metallic Society AIME (US), vol. 20, p. 96, 1976.
L. Zhao, R. Najafabadi, and D. J. Srolovitz, "Determination of vacancy and atomic diffusivities in solid solution alloys," Acta Metallurgica, vol. 44, pp. 2737-2749, 1996.
Y. W. Cui, R. Kato, T. Omori, I. Ohnuma, K. Oikawa, R. Kainuma, and K. Ishida, "Revisiting diffusion in FeAl intermetallics: Experimental determination and phenomenological treatment," Scripta Materialia, vol. 62, 189-197, 2010.
H. Mehrer, Computer Simulation of Liquids, Berlin: Springer-Verlag, 2007.
Y. Mishin and D. Farkas, "Atomistic simulation of point-defects and diffusion in B2 NiAl. Part II. Diffusion mechanisms," Philosophical Magazine A, vol. 75, pp. 187- 199, 1997.
M. K. Phani, J. L. Lebowitz, M. H. Kalos, and O. Penrose, "Kinetics of an OrderDisorder Transition," Review Letters, vol. 45, pp. 366, 1980.
S. M. Allen and J. W. Cahn, "A microscopic theory for antiphase boundary motion and its application to antiphase domain coarsening," Acta Metallurgica, vol. 27, pp. 1085-1095, 1979.
H. M. Eggersman, B. Sepiol, G. Vogl, and H. Mehrer, "Diffusion in the Intermetallic Phases of the Fe-Al system studied by Tracer and Mössbauer Techniques," Defect and Diffusion Forum, vol. 143-147, pp. 339, 1997.
G. Vogl, Mossbauer Spectroscopy Applied to Magnetism and Materials Science Vol. 2, New York: Plenum Press, 1996.
M. Bée, Quasielastic Neutron Scattering, Bristol: Adam Gilger, 1988.
B. Sepiol, A. Meyer, G. Vogl, R. Ruffer, A. I. Chumakov, and A. Q. R. Baron, "Time Domain Study of 57Fe Diffusion using Nuclear Forward Scattering of Synchrotron Radiation," Physical Review Letters, vol. 76, pp. 3220, 1996.
G. Vogl and B. Sepiol, "Elementary diffusion jump of iron atoms in intermetallic phases studied by Mossbauer spectroscopy I. FeAl close to equiatomic stoichiometry," Acta Metallurgica et Materialia, vol. 42, 3175- 3181, 1994.
B. Sepiol, C. Czihak, A. Meyer, G. Vogl, J. Metge, and R. Rüffer, "Synchrotron radiation study of diffusion in FeAl," Hyperfine Interactions, vol. 113, pp. 449-454, 1998.
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