Atomic mobilities and diffusivities in the fcc, L12 and B2 phases of the Ni-Al system
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Lijun Zhang
, Yong Du , Qing Chen , Ingo Steinbach und Baiyun Huang
Abstract
A phenomenological model was utilized to describe diffusivities in the γ (fcc) /γü (L12) and A2/B2 phases of the NiüAl system. An effective strategy, which takes the homogeneity range and defect concentration into account, was developed in the present work to optimize the atomic mobilities of γü phase. Such a strategy results in a dramatic decrease in the number of atomic mobility parameters to be evaluated for the L12 phase. The measured composition- and temperature- dependent diffusivities in the NiüAl system have been well replicated by the present mobility descriptions. For the L12 phase, comprehensive comparisons show that with fewer model parameters the presently obtained mobilities yield a better fit to experimental diffusivities, compared with previous assessments. The mobility descriptions are further validated by comparing calculated and measured concentration profiles for various diffusion couples. The time-dependent Al composition profile for the annealed vapor Al / γ couple is accurately described for the first time.
References
[1] J.-O.Anderson, T.Helander, L.Höglund, P.Shi, B.Sundman: CALPHAD26 (2002) 273.10.1016/S0364-5916(02)00037-8Suche in Google Scholar
[2] J.-O.Andersson, L.Höglund, B.Jönsson, J.Ågren, in: G.R.Prudy (Ed.), Fundamentals and applications of ternary diffusion, Pergamon Press, New York (1990) 153.10.1016/B978-0-08-040412-7.50023-2Suche in Google Scholar
[3] A.Engström, L.Höglund, J.Ågren: Metall. Mater. Trans. A25 (1994) 1127.10.1007/BF02652288Suche in Google Scholar
[4] U.R.Kattner, W.J.Böttinger, S.R.Coriell: Z. Metallkd.87 (1996) 522.Suche in Google Scholar
[5] B.J.Lee: Scripta Mater.40 (1999) 573.10.1016/S1359-6462(98)00497-7Suche in Google Scholar
[6] T.Helander, J.Ågren: Acta Mater.47 (1999) 1141.10.1016/S1359-6454(99)00010-5Suche in Google Scholar
[7] L.Zhang, Y.Du, Y.Ouyang, H.Xu, X.-G.Lu, Y.Liu, Y.Kong, J.Wang: Acta Mater.56 (2008) 3940.10.1016/j.actamat.2008.04.017Suche in Google Scholar
[8] I.Steinbach, M.Apel: Phys. D217 (2006) 153.10.1016/j.physd.2006.04.001Suche in Google Scholar
[9] I.Steinbach, M.Apel: Acta Mater.55 (2007) 4817.10.1016/j.actamat.2007.05.013Suche in Google Scholar
[10] I.Steinbach: Acta Mater.57 (2009) 2640.10.1016/j.actamat.2009.02.004Suche in Google Scholar
[11] I.Steinbach: Mod. Sim. Mat. Sci. Eng.17 (2009) 073001.10.1088/0965-0393/17/7/073001Suche in Google Scholar
[12] S.G.Fries, B.Böttger, J.Eiken, I.Steinbach: Int. J. Mater. Res.100 (2009) 128.Suche in Google Scholar
[13] I.Steinbach, B.Böttger, J.Eiken, N.Warnken, S.G.Fries: J. Phase Equilib. Diffus.28 (2007) 101.10.1007/s11669-006-9009-2Suche in Google Scholar
[14] Q.Chen, N.Ma, K.Wu, Y.Wang: Scripta Mater.50 (2004) 471.10.1016/j.scriptamat.2003.10.032Suche in Google Scholar
[15] R.Zhang, T.Jing, W.Jie, B.Liu: Acta Mater.54 (2006) 2235.10.1016/j.actamat.2006.01.029Suche in Google Scholar
[16] A.Engström, J.Ågren: Z. Metallkd.87 (1996) 92.Suche in Google Scholar
[17] L.A.Girifalco: J. Phys. Chem. Solids25 (1964) 323.10.1016/0022-3697(64)90111-8Suche in Google Scholar
[18] H.Wei, G.Hou, X.Sun, H.Guan, Z.Hu: J. Alloys Compd.454 (2008) 400.10.1016/j.jallcom.2006.12.119Suche in Google Scholar
[19] Y.Liu, D.Liang: J. Alloys Compd.459 (2008) L5.10.1016/j.jallcom.2007.04.256Suche in Google Scholar
[20] C.E.Campbell: Acta Mater.56 (2008) 4277.10.1016/j.actamat.2008.04.061Suche in Google Scholar
[21] C.E.Campbell: Private Communication, NIST, USA (2009).Suche in Google Scholar
[22] B.Jönsson: Z. Metallkd.85 (1994) 502.10.1515/ijmr-1994-850708Suche in Google Scholar
[23] Y.W.Cui, K.Oikawa, R.Kainuma, K.Ishida: J. Phase Equilib. Diffus.27 (2006) 333.Suche in Google Scholar
[24] F.Y.Fradin, T.J.Rowland: Appl. Phys. Lett.11 (1967) 207.10.1063/1.1755100Suche in Google Scholar
[25] J.Burke, T.R.Ramachandran: Metall. Trans.3 (1972) 147.10.1007/BF02680593Suche in Google Scholar
[26] T.S.Lundy, J.F.Murdock: J. Appl. Phys.33 (1962) 1671.10.1063/1.1728808Suche in Google Scholar
[27] T.G.Stoebe, R.D.GulliverII, T.O.Ogurtani, R.A.Huggins: Acta Metall.13 (1965) 701.10.1016/0001-6160(65)90135-5Suche in Google Scholar
[28] P.M.Beyeler, Y.Adda: J. Phys.29 (1968) 345.Suche in Google Scholar
[29] R.Messer, S.Dais, D.Wolf, in: P.S. Allen, E.R. Andrew, C.A. Bates (Eds.), Proceedings of 18th Ampere Congress, North-Holland Publishing, Amsterdam (1975) 327.Suche in Google Scholar
[30] T.E.Volin, R.W.Balluffi: Phys. Stat. Sol.25 (1968) 163.10.1002/pssb.19680250116Suche in Google Scholar
[31] N.Dupin, I.Ansara, B.Sundman: CALPHAD25 (2001) 279.10.1016/S0364-5916(01)00049-9Suche in Google Scholar
[32] J.-O.Andersson, J.Ågren: J. Appl. Phys.72 (1992) 1350.10.1063/1.351745Suche in Google Scholar
[33] N.Eyring: J. Chem. Phys.3 (1935) 107.10.1063/1.1749604Suche in Google Scholar
[34] B.Jönsson: Z. Metallkd.85 (1994) 498.10.1515/ijmr-1994-850707Suche in Google Scholar
[35] B.Jönsson: Z. Metallkd.83 (1992) 349.10.1515/ijmr-1992-830512Suche in Google Scholar
[36] J.Ågren: Curr. Opin. Solid State Mater. Sci.1 (1996) 355.10.1016/S1359-0286(96)80025-8Suche in Google Scholar
[37] Z.Tôkei, J.Bernardini, P.Gas, D.L.Beke: Acta Mater45 (1997) 541.10.1016/S1359-6454(96)00196-6Suche in Google Scholar
[38] H.Burgess, R.Smoluchowski: J. Appl. Phys.26 (1955) 491.10.1063/1.1722026Suche in Google Scholar
[39] R.E.Hoffman, F.W.Pikus, R.A.Ward: J. Metals8 (1956) 483.Suche in Google Scholar
[40] J.E.Reynolds, B.L.Averbach, M.Cohen, J.E.Hilliard: Acta Metall.5 (1957) 29.10.1016/0001-6160(57)90152-9Suche in Google Scholar
[41] J.R.MacEwan, J.U.MacEwan, L.Yaffe: Can. J. Chem.37 (1959) 1623.10.1139/v59-236Suche in Google Scholar
[42] J.R.MacEwan, J.U.MacEwan, L.Yaffe: Can. J. Chem.37 (1959) 1629.10.1139/v59-237Suche in Google Scholar
[43] A.Messner, R.Benson, J.E.Dorn: Trans. ASM53 (1961) 227.Suche in Google Scholar
[44] K.-I.Hirano, M.Cohen, B.L.Averbach: Trans. ASM53 (1961) 910.Suche in Google Scholar
[45] K.-I.Hirano, R.P.Agarwala, B.L.Averbach, M.Cohen: J. Appl. Phys.33 (1962) 3049.10.1063/1.1728564Suche in Google Scholar
[46] A.Y.Shinyaev: Fiz. Metal. Metalloved.15 (1963) 100.10.2307/2710278Suche in Google Scholar
[47] A.R.Wazzan, J.E.Dorn: J. Appl. Phys.36 (1965) 222.10.1063/1.1713880Suche in Google Scholar
[48] A.R.Wazzan, J.E.Dorn: J. Appl. Phys.36 (1965) 3596.10.1063/1.1703047Suche in Google Scholar
[49] I.G.Ivantsov: Fiz. Metal. Metalloved.22 (1966) 725.10.1016/0030-4220(66)90361-6Suche in Google Scholar
[50] D.F.Kalinovich, I.I.Kovenskii, M.D.Smolin: Ukrain Fiz. Zhur. Mar.13 (1968) 515.Suche in Google Scholar
[51] H.Bakker: Phys. Stat. Sol.28 (1968) 569.10.1002/pssb.19680280214Suche in Google Scholar
[52] V.M.Amonenko, I.G.Ivantsov, A.M.Blinkin: Fiz. Metal. Metalloved.27 (1969) 466.Suche in Google Scholar
[53] B.Million, J.Kucera: Czech J. Phys. B21 (1971) 161.Suche in Google Scholar
[54] M.B.Bronfin, G.S.Bulatov, I.A.Drugova: Fiz. Metal. Metalloved.40 (1975) 363.Suche in Google Scholar
[55] K.Maier, H.Mehrer, E.Lessmann, W.Schüle: Phys. Stat. Sol. B78 (1976) 689.10.1002/pssb.2220780230Suche in Google Scholar
[56] M.Fellerkniepmeier, M.Gründler, H.Helfmeier: Z. Metallkd.67 (1976) 533.Suche in Google Scholar
[57] R.A.Swalin, A.Martin: J. Metals8 (1956) 567.Suche in Google Scholar
[58] H.W.Allison, H.Samelson: J. Appl. Phys.30 (1959) 1419.10.1063/1.1735346Suche in Google Scholar
[59] W.Gust, M.B.Hintz, A.Lodding, H.Odelius, B.Predel: Phys. Stat. Sol. A64 (1981) 187.10.1002/pssa.2210640120Suche in Google Scholar
[60] K.-I.Hirano, R.P.Agarwala, M.Cohen: Acta Metall.10 (1962) 857.10.1016/0001-6160(62)90100-1Suche in Google Scholar
[61] G.Erdélyi, D.L.Beke, F.J.Kedves, I.Gödény: Philos. Mag. B38 (1978) 445.10.1080/13642817808246394Suche in Google Scholar
[62] J.D.Whittenberger: Metall. Trans.3 (1972) 2010.10.1007/BF02642597Suche in Google Scholar
[63] M.M.P.Janssen: Metall. Trans.4 (1973) 1623.10.1007/BF02668017Suche in Google Scholar
[64] T.Yamamoto, T.Takashima, K.Nishida: Trans. Jpn. Inst. Metals21 (1980) 601.Suche in Google Scholar
[65] A.Green, N.Swindells: Mater. Sci. Technol.1 (1985) 101.Suche in Google Scholar
[66] M.Watanabe, Z.Horita, T.Fujinami, T.Sano, M.Nemoto: Defect Diffus. Forum95-98 (1993) 579.Suche in Google Scholar
[67] M.Watanabe, Z.Horita, D.J.Smith, M.R.McCartney, T.Sano, M.Nemoto: Defect Diffus. Forum95-98 (1993) 587.Suche in Google Scholar
[68] M.Watanabe, Z.Horita, D.J.Smith, M.R.McCartney, T.Sano, M.Nemoto: Acta Metall. Mater.42 (1994) 3381.10.1016/0956-7151(94)90470-7Suche in Google Scholar
[69] M.Watanabe, Z.Horita, T.Sano, M.Nemoto: Acta Metall. Mater.42 (1994) 3389.10.1016/0956-7151(94)90471-5Suche in Google Scholar
[70] M.Watanabe, Z.Horita, M.Nemoto: Interface Sci.4 (1997) 229.10.1007/BF00240244Suche in Google Scholar
[71] M.Watanabe, Z.Horita, M.Nemoto: Defect Diffus. Forum143-147 (1997) 345.Suche in Google Scholar
[72] D.F.Susan, A.R.Marder: Acta Mater.49 (2001) 1153.10.1016/S1359-6454(01)00022-2Suche in Google Scholar
[73] Y.Du, Y.A.Chang, B.Y.Huang, W.P.Gong, Z.P.Jin, H.H.Xu, Z.H.Yuan, Y.Liu, Y.H.He, F.-Y.Xie: Mater. Sci. Eng. A363 (2003) 140.10.1016/S0921-5093(03)00624-5Suche in Google Scholar
[74] L.N.Larikov, V.V.Geichenko, V.M.Fal'schenko: Diffusion process in ordered alloys, Naukova Dumka, Kiev (1975).Suche in Google Scholar
[75] Y.Shi, G.Frohberg, H.Wever: Phys. Stat. Sol. A152 (1995) 361.10.1002/pssa.2211520205Suche in Google Scholar
[76] K.Nonaka, T.Arayashiki, H.Nakajima, A.Almazouzi, K.Tanaka, T.Ikeda, H.Numakur, M.Koiwa: Defect Diffus. Froum143-147 (1997) 269.10.4028/www.scientific.net/DDF.143-147.269Suche in Google Scholar
[77] S.Frank, U.Södervall, Chr.Herzig: Defect Diffus. Forum143-147 (1997) 245.10.4028/www.scientific.net/DDF.143-147.245Suche in Google Scholar
[78] S.V.Divinski, St.Frank, U.Södervall, Chr. Herzig: Acta Mater.46 (1998) 4369.Suche in Google Scholar
[79] T.Ikeda, A.Almazouzi, H.Numakura, M.Koiwa, W.Sprengel, H.Nakajima: Acta Mater.46 (1998) 5369.10.1016/S1359-6454(98)00209-2Suche in Google Scholar
[80] K.Fujiwara, Z.Horita: Defect Diffus. Forum194–199 (2001) 565.Suche in Google Scholar
[81] K.Fujiwara, Z.Horita: Acta Mater.50 (2002) 1571.10.1016/S1359-6454(02)00018-6Suche in Google Scholar
[82] C.Cserháti, A.Paul, A.A.Kodentsov, M.J.H.van Dal, F.J.J.van Loo: Intermetallics11 (2003) 291.10.1016/S0966-9795(02)00235-2Suche in Google Scholar
[83] J.Cermak, V.Rothova: Acta Mater.51 (2003) 4411.10.1016/S1359-6454(03)00276-3Suche in Google Scholar
[84] V.Rothova, J.Cermak: Intermetallics13 (2005) 113.10.1016/j.intermet.2004.06.006Suche in Google Scholar
[85] G.F.Hancock: Phys. Stat. Sol. A7 (1971) 535.10.1002/pssa.2210070228Suche in Google Scholar
[86] M.B.Bronfin, G.S.Bulatov, I.A.Drugova: Fiz. Metal. Metalloved.40 (1975) 363.Suche in Google Scholar
[87] K.Hoshino, S.J.Rothman, R.S.Averback: Acta Metall.36 (1988) 1271.10.1016/0001-6160(88)90279-9Suche in Google Scholar
[88] S.Frank, U.Södervall, Chr.Herzig: Phys. Stat. Sol. B191 (1995) 45.10.1002/pssb.2221910105Suche in Google Scholar
[89] C.Cserháti, I.A.Szabó, Z.S.Márton, G.Erdélyi: Intermetallics10 (2002) 887.10.1016/S0966-9795(02)00089-4Suche in Google Scholar
[90] S.Shankar, L.L.Seigle: Metall. Trans. A9 (1978) 1467.10.1007/BF02661819Suche in Google Scholar
[91] T.Ikeda, A.Almazouzi, H.Numakura, M.Koiwa, W.Sprengel, H.Nakajima: Defect Diffus. Froum143-147 (1997) 275.10.4028/www.scientific.net/DDF.143-147.275Suche in Google Scholar
[92] A.Lutze-Birk, H.Jacobi: Scripta Metall.9 (1975) 761.10.1016/0036-9748(75)90236-7Suche in Google Scholar
[93] Y.Minamino, Y.Koizumi, Y.Inui: Defect Diffus. Forum194–199 (2001) 517.Suche in Google Scholar
[94] A.Paul, A.A.Kodentsov, F.J.J.van Loo: J. Alloys Compd.403 (2005) 147.10.1016/j.jallcom.2005.04.194Suche in Google Scholar
[95] G.F.Hancock, B.R.McDonnell: Phys. Stat. Sol. A4 (1971) 143.10.1002/pssa.2210040115Suche in Google Scholar
[96] St.FrankS.V.Divinski, U.Södervall, Chr.Herzig: Acta Mater.49 (2001) 1399.Suche in Google Scholar
[97] R.Nakamura, K.Fujita, Y.Iijima, M.Okada: Acta Mater.51 (2003) 3861.10.1016/S1359-6454(03)00210-6Suche in Google Scholar
[98] A.J.Hickl, R.W.Heckel: Metall. Trans. A6 (1975) 431.10.1007/BF02658400Suche in Google Scholar
[99] M.Kato, H.Sasano, K.Honma, T.Suzuki: J. Japan Inst. Metals62 (1998) 761.Suche in Google Scholar
[100] S.Kim, Y.A.Chang: Metall. Mater. Trans. A31 (2000) 1519.10.1007/s11661-000-0162-7Suche in Google Scholar
[101] R.Nakamura, K.Takasawa, Y.Yamazaki, Y.Iijima: Intermetallics10 (2002) 195.10.1016/S0966-9795(01)00125-XSuche in Google Scholar
[102] H.Wei, X.F.Sun, Q.Zheng, G.C.Hou, H.R.Guan, Z.Q.Hu: Acta Metall. Sin.40 (2004) 51.Suche in Google Scholar
[103] H.Wei, X.F.Sun, Q.Zheng, G.C.Hou, H.R.Guan, Z.Q.Hu: Acta Mater.52 (2004) 2645.10.1016/j.actamat.2004.02.012Suche in Google Scholar
[104] A.Paul, A.A.Kodentsov, F.J.J.van Loo: Acta Mater.52 (2004) 4041.10.1016/j.actamat.2004.05.028Suche in Google Scholar
[105] B.Sundman, B.Jönsson, J.-O.Andersson: CALPHAD9 (1985) 153.10.1016/0364-5916(85)90021-5Suche in Google Scholar
[106] M.Mantina, Y.Wang, R.Arroyave, L.Q.Chen, Z.K.Liu: Phys. Rev. Lett.100 (2008) 215901.10.1103/PhysRevLett.100.215901Suche in Google Scholar PubMed
[107] M.Mantina: Ph. D Thesis, Pennsylvania State University, USA (2008).Suche in Google Scholar
[108] D.Liu, L.Zhang, Y.Du, H.Xu, S.Liu, L.Liu: CALPHAD33 (2009) 761.10.1016/j.calphad.2009.10.004Suche in Google Scholar
[109] W.Gong, L.Zhang, D.Yao, C.Zhou: Scr. Mater.61 (2009) 100.10.1016/j.scriptamat.2009.03.010Suche in Google Scholar
[110] W.R.Upthegrove, M.J.Sinnott: Trans. ASM50 (1958) 1031.Suche in Google Scholar
[111] G.B.Fedorov, E.A.Smirnov, F.I.Zhomov: Met. i Metalloved. Chistykh Metal. Sb. Nauch. Rabot.4 (1963) 110.Suche in Google Scholar
[112] K.Monma, H.Suto, H.Oikawa: J. Japan Inst. Metals28 (1964) 188.Suche in Google Scholar
[113] A.Hässner, W.Lange: Phys. Stat. Sol.8 (1965) 77.10.1002/pssb.19650080108Suche in Google Scholar
[114] M.Wanin, A.Kohn: C.R. Acad. Sci. Ser. C267 (1968) 1558.Suche in Google Scholar
[115] A.B.Vladimirov, V.N.Kaigorodov, S.M.Klotsman, I.S.Trachtenberg: Fiz. Met. Metalloved.46 (1978) 1232.Suche in Google Scholar
[116] B.Million, J.Ru°žičková, J.Velíšek, J.Vrešt'ál: Mater. Sci. Eng.50 (1981) 43.10.1016/0025-5416(81)90084-7Suche in Google Scholar
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Artikel in diesem Heft
- Basic
- High-temperature in-situ microscopy during stress-induced phase transformations in Co49Ni21Ga30 shape memory alloy single crystals
- Contents
- contents
- Editorial
- Editorial December 2010
- Basic
- Atomic mobilities and diffusivities in the fcc, L12 and B2 phases of the Ni-Al system
- Experimental investigation of the Zn–Fe–V system at 450°C
- Time resolved X-ray imaging of eutectic cellular patterns evolving during solidification of ternary Al–Cu–Ag alloys
- Reassessment of the Mg–Ge binary system using CALPHAD supported by first-principles calculation
- A quantitative modeling of the unloading behavior of metals during a tensile test
- A technique for diameter enlargement in SiC crystal growth
- Applied
- Thermal and chemical stability of Cr2AlC in contact with α-Al2O3 and NiAl
- Microstructure and mechanical properties of Zn25Al3Cu based composites with large Al2O3 particles at room and elevated temperatures
- An investigation on Incoloy800-SS304 clad plate by explosive welding
- Effect of grain boundary precipitates on vibration damping of FeüCrüMgüAl/Si alloy
- Adsorption of metal ions on magnetic carbon nanomaterials bearing chitosan-functionalized silica
- Tensile and in-vitro degradation study of electro spun fibrous mat produced from eri silk fibroin
- Study of the influence of UV-irradiation on the photodegradation of plasticized poly(para-tert-butylstyrene) films
- Enhanced photocatalytic activity of beryllium doped titania in visible light on the degradation of methyl orange dye
- Progress in chemistry modelling for vapour and aerosol transport analyses
- DGM News
- Personal
Artikel in diesem Heft
- Basic
- High-temperature in-situ microscopy during stress-induced phase transformations in Co49Ni21Ga30 shape memory alloy single crystals
- Contents
- contents
- Editorial
- Editorial December 2010
- Basic
- Atomic mobilities and diffusivities in the fcc, L12 and B2 phases of the Ni-Al system
- Experimental investigation of the Zn–Fe–V system at 450°C
- Time resolved X-ray imaging of eutectic cellular patterns evolving during solidification of ternary Al–Cu–Ag alloys
- Reassessment of the Mg–Ge binary system using CALPHAD supported by first-principles calculation
- A quantitative modeling of the unloading behavior of metals during a tensile test
- A technique for diameter enlargement in SiC crystal growth
- Applied
- Thermal and chemical stability of Cr2AlC in contact with α-Al2O3 and NiAl
- Microstructure and mechanical properties of Zn25Al3Cu based composites with large Al2O3 particles at room and elevated temperatures
- An investigation on Incoloy800-SS304 clad plate by explosive welding
- Effect of grain boundary precipitates on vibration damping of FeüCrüMgüAl/Si alloy
- Adsorption of metal ions on magnetic carbon nanomaterials bearing chitosan-functionalized silica
- Tensile and in-vitro degradation study of electro spun fibrous mat produced from eri silk fibroin
- Study of the influence of UV-irradiation on the photodegradation of plasticized poly(para-tert-butylstyrene) films
- Enhanced photocatalytic activity of beryllium doped titania in visible light on the degradation of methyl orange dye
- Progress in chemistry modelling for vapour and aerosol transport analyses
- DGM News
- Personal