SELF-DIFFUSION OF BCC INTERSTITIAL ALLOY FeSi
DOI:
https://doi.org/10.18173/2354-1059.2025-0036Keywords:
FeSi, self-diffusion, activation energy, pre-exponential factor, self-diffusion coefficientAbstract
In this work, we present analytical formulations for self-diffusion parameters, namely the activation energy, pre-exponential factor, and self-diffusion coefficient as functions of temperature, pressure, interstitial atom concentration, and strain in a BCC interstitial binary alloy, derived using the statistical moment method (SMM). These theoretical models are utilized to perform numerical simulations for the FeSi alloy. The computed SMM values for FeSi are compared with those obtained for pure Fe. The SMM results for Fe show strong consistency with existing experimental measurements and alternative computational data. The additional SMM findings are novel and offer predictions that can guide future experimental investigations.
References
[1] Danilchenko VE, Mazanko VF, Filatov AV & Iakovlev VE, (2015). The effect of cyclic martensitic transformations on diffusion of cobalt atoms in Fe 18 wt.% Mn 2 wt.% Si alloy. Nanoscale Research Letters, 10, 178.
[2] Bevz VP, Bondar VI & Danilchenko VE, (2008). Diffusion regularities of carbon atoms in iron phase hardened alloy. Metallofizika i Noveishie Tekhnologii, 30(10), 1307–1314.
[3] Brick VB, Kumok LM, Nikolin BI & Falchenko VM, (1981). Effect of phase transformations on the diffusion mobility of atoms in iron and cobalt alloys. Metally, 4, 131–135.
[4] Brick VB, (1985). Diffusion and phase transformations in metals and alloys. Kiev: Naukova Dumka.
[5] Crank J, (1980). The mathematics of diffusion (2nd ed.). Oxford University Press.
[6] Mironov VM, Mironova TF, Koval YN, Gertsriken DS & Alekseeva VV, (2006). Diffusion processes in metals and alloys under martensitic transformations. Vestnik Samara State University, 3, 34.
[7] Aziz MJ, (1997). Thermodynamics of diffusion under pressure and stress: Relation to point defect mechanisms. Applied Physics Letters, 70(21), 2810–2812.
[8] Vu VH, Do DT & Nguyen TH, (2007). Effect of stress on defect diffusion in metals. HNUE Journal of Science: Natural Science, 52(1), 13–18.
[9] Nguyen HT & Vu VH, (1988). Investigation of the thermodynamic properties of anharmonic crystals by the momentum method (I): General results for FCC crystals. Physica Status Solidi (b), 149, 511.
[10] Nguyen HT & Vu VH, (1990). Investigation of the thermodynamic properties of anharmonic crystals by the momentum method (III): Thermodynamic properties of the crystals at various pressures. Physica Status Solidi (b), 162, 371.
[11] Hoang VT & Vu VH, (1999). Influence of anharmonicity on the diffusion of vacancies by the moment method. In Proceedings of the 3rd International Workshop on Materials (IWOMS 99), Hanoi, November 2–4, 939–942.
[12] Vu VH, Hoang VT & Do DT, (1999). Study of self-diffusion in alloys by statistical moment method: Anharmonicity effects. Communications in Physics, 9(4), 232–241.
[13] Masuda JK, Vu VH & Hoang VT, (1999). Self diffusion theory of vacancies in anharmonic crystals. Proceedings of the NCST of Vietnam, 11(2), 39–44.
[14] Vu VH, Hoang VT & Masuda JK, (2000). Study of self-diffusion in metals by statistical moment method: Anharmonicity effects. Journal of the Physical Society of Japan, 69(8), 2691–2699.
[15] Vu VH, Lee J, Masuda JK & Phan TTH, (2006). Study of self-diffusion in silicon at high pressure. Journal of the Physical Society of Japan, 75(2), 024601.
[16] Hoang VT, (2000). Diffusion theory of metals and alloys (PhD Thesis). Hanoi National University of Education.
[17] Nguyen QH, Dinh QV, Le HV & Nguyen VP, (2016). Study on diffusion theory of interstitial alloy AB with BCC structure. HNUE Journal of Science: Natural Science, 61(4), 3–9.
[18] Nguyen QH, Bui DT, Dinh QV & Le HV, (2016). Diffusion of interstitial atoms in interstitial alloys FeSi and FeH with BCC structure under pressure. Scientific Journal of Hanoi Metropolitan University, 61(8), 48–56.
[19] Nguyen QH, Nguyen DH & Nguyen HN, (2020). Study on the diffusion theory of BCC substitutional alloy AB with interstitial atom C. HNUE Journal of Science: Natural Science, 65(3), 31–38.
[20] Nguyen QH, Phan TTL, Nguyen TV & Nguyen NL, (2020). The diffusion in FCC binary interstitial alloy. HNUE Journal of Science: Natural Science, 65(10), 18–23.
[21] Goldschmidt HJ, (1967). Interstitial Alloys. London: Butterworth.
[22] Shibazaki Y, Nishida K, Higo Y, Igarashi M, Tahara M, Sakamaki T & Ohtani E, (2016). Compressional and shear wave velocities for polycrystalline BCC Fe up to 6.3 GPa and 800 K. American Mineralogist, 101(5), 1150–1160.
[23] Takeuchi S, (1969). Solid-solution strengthening in single crystals of iron alloys. Journal of the Physical Society of Japan, 27, 929–940.
[24] Melnykov M & Davidchack RI, (2018). Characterization of melting properties of several Fe–C model potentials. Computational Materials Science, 144, 273–279.
[25] Lau TT, Fürst CJ, Lin X, Gale JD, Yip S & Van Vliet KJ, (2007). Many-body potential for point defect clusters in Fe–C alloys. Physical Review Letters, 98(21), 215501.
[26] Liyanage LS, Kim SG, Houze J, Kim S, Tschopp MA, Baskes MI & Horstemeyer MF, (2014). Structural, elastic and thermal properties of cementite (Fe₄C) calculated using a modified embedded atom method. Physical Review B, 89, 094102.
[27] Nguyen QH & et al., (2020). On the melting of defective FCC interstitial alloy α–FeC under pressure up to 100 GPa. Journal of Electronic Materials, 49, 910–916.
[28] Pépin CM, Dewaele A, Geneste G, Loubeyre P & Mezouar M, (2014). New iron hydrides under high pressure. Physical Review Letters, 113(26), 265504.
[29] Terasaki H, Ohtani E, Sakai T, Kamada S, Asanuma H, Shibazaki Y & Funakoshi KI, (2012). Stability of FeNi hydride after reaction between Fe–Ni alloy and δ-AlOOH up to 1.2 Mbar. Physics of the Earth and Planetary Interiors, 194–195, 18–24.
[30] Psiachos D, Hammerschmidt T & Drautz R, (2011). Ab initio study of the modification of elastic properties of α-iron by hydrostatic strain and hydrogen interstitials. Acta Materialia, 59(11), 4255–4263.
[31] Lee BJ & Jang JW, (2007). A modified embedded-atom method interatomic potential for the FeH system. Acta Materialia, 55, 6779–6788.
[32] Odkhuu D, Yun WS & Hong SC, (2012). Electronic origin of the negligible magnetostriction of an electric steel Fe1–xSix alloy: A density-functional study. Journal of Applied Physics, 111(6), 063911.
[33] Zhang J, Su C & Liu Y, (2020). First-principles study of bcc Fe–Cr–Si binary and ternary random alloys from special quasi-random structure. Physica B: Condensed Matter, 586, 412085.
[34] Kümmerle EA, Badura K, Sepiol B, Mehrer H & Schaefer HE, (1995). Thermal formation of vacancies in Fe3Si. Physical Review B, 52, R6947–R6950.
[35] Zhao KM, Jiang G & Wang L, (2011). Electronic and thermodynamic properties of B2–FeSi from first principles. Physica B: Condensed Matter, 406(3), 363–367.
[36] Guo Z, Yuan W, Sun Y & Cai Z, (2000). Thermodynamic assessment of the Si–Ta and Si–W systems. Journal of Phase Equilibria and Diffusion, 30(5), 564–570.
[37] Nguyen QH, Nguyen DH, Nguyen TD & Cao VL, (2021). Study on the melting temperature, jumps of volume, enthalpy and entropy at melting point, and Debye temperature for the BCC defective and perfect interstitial alloy WSi under pressure. Journal of Composites Science, 5(6), 153.
[38] Aziz MJ, (2001). Stress effects on defects and dopant diffusion in Si. Materials Science in Semiconductor Processing, 4(5), 397–403.
[39] Lazarus D, (1983). Diffusion in Metals and Alloys. In Kedves FJ & Beke PL (Eds.).
[40] Iijima Y, Kimura K & Hirano K, (1988). Self-diffusion and isotope effect in α-iron. Acta Metallurgica, 36(12), 2811–2820.
[41] Lubbehusen M & Mehrer H, (1990). Self-diffusion in α-iron: The influence of dislocations and the effect of the magnetic phase transition. Acta Metallurgica et Materialia, 38(2), 283–292.
[42] Zhang B, (2014). Calculation of self-diffusion coefficients in iron. AIP Advances, 4, 017128.
[43] Magomedov MN, (1987). Calculation of temperature Debye and parameter Grüneisen. Zhurnal Fizicheskoi Khimii, 61(4), 1003–1009.
[44] Magomedov MN, (2011). Activated-process parameters for diamond, silicon and germanium crystals. Russian Microelectronics, 40(8), 567–573.
