Interdiffusion Studies in β- and γ′-Intermetallic Phases of the Binary Ni-Al System

Abstract:

A critical review of interdiffusion processes in the binary β-NiAl and γ'-Ni₃Al intermetallic compounds is presented. The molar volume changes associated with interdiffusion and partial molar volumes of the reacting species, required for the determination of the diffusion parameters, are found using lattice parameter data and, in the case of NiAl, the available information about vacancy concentration within homogeneity range of the β-phase. The presented treatment is purely phenomenological, and its use is convenient since no exlicit assumption of the underlying mechanisms required. A critical analysis of diffusion data for β-NiAl and γ'-Ni₃Al ordered phases is followed by discussion of error sources encountered in the interdiffusion experiments. From Kirkendall marker experiments with incremental diffusion couples, information about relative mobilities of species in the intermetallic phases can be obtained, and tracer diffusion coefficients can be deduced using pertinent thermodynamic data on the nickel aluminides. Contribution of the vacancy wind effect to the calculated tracer diffusivities can also be estimated. The Kirkendall plane bifurcation in the Ni_41.7Al_58.3/Ni_72.24Al_27.76 reaction couple, in which a single-phased layer of β-NiAl intermatallic is formed during interdiffusion from its adjacent phases, is directly related to the growth of grains of the reaction product at a location in between interfaces with starting materials. This diffusion phenomenon can be rationallised using a corresponding Kirkendall velocity diagram. Changes in magnitude and sign of the difference in intrinsic mobilities of the components inside the homogeneity range of the β-NiAl lead to a velocity curve that makes bifurcation of the Kirkendall marker plane possible.

• Periodical: Diffusion Foundations (Volume 13)
• Pages: 56-97
• DOI: https://doi.org/10.4028/www.scientific.net/DF.13.56
• Online since: November 2017
• Authors: Alexander Kodentsov*
• Keywords: Interdiffusion, Intrinsic Mobilities, Kirkendall Plane, Nickel Aluminides, Tracer Diffusivities

References

[1] P. Nash, M.F. Singleton, J.L. Murray, Al-Ni (Aluminum-Nickel), in: P. Nash (Ed. ), Phase Diagrams of Binary Nickel Alloys, ASM International, Materials Park, Ohio, 1991, pp.3-11.

[2] M.M.P. Janssen, Reactiediffusie in het systeem Nikkel-Aluminium, PhD thesis, Eindhoven, The Netherlands, 1966 (in Dutch).

[3] S. Divinski, Defects and Diffusion in Ordered Compounds, in: A. Paul, S. Divinski (Eds. ), Handbook of Solid State Diffusion-Diffusion Fundamentals and Techniques, Vol 1, Elsevier, 2017, pp.449-517.

DOI: 10.1016/b978-0-12-804287-8.00010-5

[4] J. Philbert, Atom Movements. Diffusion and Mass Transport in Solids, Les Éditions de Physique, Les Ulis, (1991).

[5] H. Mehrer, Diffusion in Solids, Springer-Verlag, Berlin, Heidelberg, (2007).

[6] A. Paul, T. Laurila, V. Vuorinen, S.V. Divinski, Thermodynamics, Diffusion and the Kirkendall Effect in Solids, Springer International Publishing, Switzerland, (2014).

DOI: 10.1007/978-3-319-07461-0

[7] L. Boltzmann, Zur Integration der Diffusionsgleichung bei Variabeln Diffusions-Coefficienten, Ann. Physik. 53 (1894) pp.959-964 (in German).

DOI: 10.1002/andp.18942891315

[8] C. Matano, On the relation between the diffusion-coefficients and concentrations of solid metals (The Nickel-Copper system), Jap. J. Phys. 8 (1933) 109-113.

[9] F. Sauer, V. Freise, Diffusion in Binären Gemischen mit Volumenänderung, Z. Electrochem. 66 (1962) 353-363 (in German).

[10] C. Wagner, The evaluation of data obtained with diffusion couples of binary single-phase and multiphase systems, Acta Metall. 17 (1969) 99-107.

DOI: 10.1016/0001-6160(69)90131-x

[11] F.J.A. den Broeder, A general simplification and improvement of the Matano-Boltzmann method in the determination of the interdiffusion coefficient in binary systems, Scripta Metall. 3 (1969) 321-326.

DOI: 10.1016/0036-9748(69)90296-8

[12] F.J.J. van Loo, On the determination of diffusion coefficients in a binary metal system, Acta Metall. 18 (1970) 1107-1111.

DOI: 10.1016/0001-6160(70)90009-x

[13] F.J.J. van Loo, Multiphase diffusion in binary and ternary solid-state systems, Prog. Solid St. Chem. 20 (1990) 47-99.

DOI: 10.1016/0079-6786(90)90007-3

[14] M.J.H. van Dal, A.M. Gusak, Cs. Cserháti, A.A. Kodentsov, F.J.J. van Loo, Microstructural stability of the Kirkendall plane in solid-state diffusion, Phys. Rev. Lett. 86 (2001) 3352-3355.

DOI: 10.1103/physrevlett.86.3352

[15] A.A. Kodentsov, A. Paul, M.J.H. van Dal, Cs. Cserháti, A.M. Gusak, F.J.J. van Loo, On the spatial stability and bifurcation of the Kirkendall plane during solid-state interdiffusion, Crit. Rev. Solid State Mater. Sci. 33 (2008) 210-232.

DOI: 10.1080/10408430802462958

[16] Th. Heumann, G. Walther, Der Kirklendall-Effekt in Silber-Gold-Legirungen im gesamtem Konzentrtionsbereich, Z. Metallkd. 48 (1957) 151-157 (in German).

DOI: 10.1515/ijmr-1957-480401

[17] L.S. Darken, Diffusion, mobility and their interrelation through free energy in binary metallic systems, Trans. AIME 175 (1948) 184-201.

DOI: 10.1007/s11661-010-0177-7

[18] J. R. Manning, Diffusion and the Kirkendall shift in binary alloys, Acta Metall. 15 (1967) 817-826.

DOI: 10.1016/0001-6160(67)90363-x

[19] M.M.P. Janssen, G.D. Rieck, Reaction diffusion and Kirkendall-effect in the Nickel-Aluminium system, Trans. TMS-AIME 239 (1967) 1372-1285.

[20] S. Shankar, L.L. Seigle, Interdiffusion and intrinsic diffusion in the NiAl (δ) phase of the Al-Ni system, Metall. Trans. A 9A (1978) 1467-1476.

DOI: 10.1007/bf02661819

[21] M. Watanabe, Z. Horita, M. Nemoto, Measurements of interdiffusion coefficient in Ni-Al system, Defect Diffusion Forum 143-147 (1997) 345-350.

DOI: 10.4028/www.scientific.net/ddf.143-147.345

[22] T. Helander, J. Ågren, A phenomenological treatment of diffusion in Al-Fe and Al-Ni alloys having B2-b. c. c. ordered structure, Acta Mater. 47 (1999) 1141-1152.

DOI: 10.1016/s1359-6454(99)00010-5

[23] S.P. Garg, G.B. Kale, R.V. Patil, T. Kundu, Thermodynamic interdiffusion coefficient in binary system with intermediate phases, Intermetallics 7 (1999) 901-908.

DOI: 10.1016/s0966-9795(98)00139-3

[24] S. Kim and Y.A. Chang, An interdiffusion study of a NiAl alloy using single-phase diffusion couple, Metall. Mater. Trans. A 31A (2000) 1519-1524.

DOI: 10.1007/s11661-000-0162-7

[25] R. Nakamura, K. Takasava, Y. Yamazaka, Y. Iijima, Single-phase interdiffusion in the B2 type intermetallic compounds NiAl, CoAl and FeAl, Intermetallics 10 (2002) 195-204.

DOI: 10.1016/s0966-9795(01)00125-x

[26] R. Nakamura, Y. Iijima, M. Okada, Diffusion mechanisms in B2 NiAl phase studied by experiments on Kirkendall effect and interdiffusion under high pressures, Acta Mater. 51 (2003) 3861-3870.

DOI: 10.1016/s1359-6454(03)00210-6

[27] H. Wei, X. Sun, Q. Zheng, H. Guan, Z. Hu, Estimation of interdiffusivity in the NiAl phase in Ni-Al binary system, Acta Mater. 52 (2004) 2645-2651.

DOI: 10.1016/j.actamat.2004.02.012

[28] A. Paul, A.A. Kodentsov, F.J.J. van Loo, Bifurcation of the Kirkendall plane during interdiffusion in the intermetallic compound β-NiAl, Acta Mater. 52 (2004) 4041-4048.

DOI: 10.1016/j.actamat.2004.05.028

[29] A. Paul, A.A. Kodentsov, F.J.J. van Loo, On diffusion in the β-NiAl phase, J. Alloy Comp. 403 (2005) 147-153.

[30] L. Zhang, Y. Du, Q. Chen, I. Steinbach, B. Huang, Atomic mobilities and diffusivities in the fcc, L12 and B2 phases of the Ni-Al system, Int. J. Mat. Res. 101 (2010) 1461-1475.

DOI: 10.3139/146.110428

[31] Q. Xu, A. van der Ven, The effect of large vacancy concentration on intrinsic and interdiffusion coefficient: A first-principle study of B2-NiAl, Acta Mater. 59 (2011) 1095-1104.

DOI: 10.1016/j.actamat.2010.10.040

[32] P. Georgopoulos, J.H. Cohen, The defect structure and Debye-Waller factors vs. composition in β Ni1±xAl1±x, Scripa Metall. 11 (1971) 147-150.

DOI: 10.1016/0036-9748(77)90295-2

[33] A. Taylor, N. J. Doyle, Further studies on the nickel–aluminum system. II. Vacancy filling in β and δ-phase alloys by compression at high temperatures, J. Appl. Cryst. 5 (1972) 210-215.

DOI: 10.1107/s0021889872009215

[34] H. Jacobi, H.J. Engell, Defect structure in non-stoichiometric β-(Ni, Cu)Al, Acta Metall. 19 (1971) 701-711.

DOI: 10.1016/0001-6160(71)90025-3

[35] A.J. Bradley, A. Taylor, An X-ray analysis of the Nickel-Aluminum system, Proc. Roy. Soc. (London) A159 (1937) 56-72.

[36] L.P. Zelenin, A.N. Bashkatov, F.A. Sidorenko, P.V. Gel'd, Fizika Metallov i Metallovedenie 30 (1970) 740-746.

[37] Y.A. Chang, J.P. Neumann, Thermodynamics and defect structure of intermetallic phases with the B2 (CsCl) structure, Prog. Solid St. Chem. 14 (1982) 221-301.

DOI: 10.1016/0079-6786(82)90004-8

[38] S. Kim and Y.A. Chang, Use of lattice mole fraction to analyze interdiffusion data in strongly ordered triple-defect B2 intermetallic phases, Scripta Mater. 40 (1999) 1277-1281.

DOI: 10.1016/s1359-6462(99)00114-1

[39] C.R. Kao, S. Kim, Y.A. Chang, Diffusional behavior in B2 intermetallic compounds, Mater. Sci. Eng. A 192/193 (1995) 965-979.

DOI: 10.1016/0921-5093(95)03344-0

[40] S.V. Divinski, Chr. Herzig, Ni tracer self-diffusion, interdiffusion, and diffusion mechanism in NiAl, Defect Diffusion Forum 203-205 (2002) 177-192.

DOI: 10.4028/www.scientific.net/ddf.203-205.177

[41] S.V. Divinski, St. Frank, U. Södervall, Chr. Herzig, Solute diffusion of Al-substituting elements in Ni3Al and the diffusion mechanism of the minority component, Acta Mater. 46 (1998) 4369-4380.

DOI: 10.1016/s1359-6454(98)00109-8

[42] .

[42] A. Steiner, K.L. Komarek, Thermodynamic activity of solid Nickel-Aluminum alloys, Trans. Met. Soc. AIME 230 (1964) 786-790.

[43] R.E. Hanneman, A.U. Seybolt, Nickel activity data in the Nickel-Aluminum system at 1000 ºC, Trans. Met. Soc. AIME 245 (1969) 434-435.

[44] D.R. Gaskell, Introduction to the Thermodynamics of Materials, Taylor & Francis, London, (1995).

[45] N.C. Oforka, Thermodynamics of Aluminum-Nickel alloys, Ind. J. Chem. 25A (1986) 1027-1031.

[46] J. Wang, H. -J. Engell, Investigation of the thermodynamic properties of Ni-Al intermetallic compounds by an EMF method, Steel Research 63 (1992) 320–323.

DOI: 10.1002/srin.199200527

[47] N.S. Jacobson, Double Knudsen cell for alloy activity measurements by mass spectrometry, in: P. Nash, B. Sundman (Eds. ), Application of Thermodynamics in the Synthesis and Processing of Materials, The Minerals, Metals & Materials Society, Pennsylvania, 1995, pp.319-329.

[48] K. Rzyman, Z. Moser, R. E. Watson, M. Weinert, Enthalpies of formation of AlNi: Experiment versus theory, J. Phase Equilibria 19 (1998) 106-112.

DOI: 10.1361/105497198770342562

[49] E. -Th. Henig, H.L. Lukas, Kalorimetrische Bestimmung der Bildungsenthalpie und die Beschreibung der Fehlordnung der georgneten β-Phase (Ni, Cu)1-xAlx, Z. Metallkd. 66 (1975) 98-106. (in German).

DOI: 10.1515/ijmr-1975-660207

[50] T. Ansara, N. Dupin. H.L. Lukas, B. Sundman, Thermodynamic assessment of the Al-Ni system, J. Alloy Comp. 247 (1997) 20-30.

DOI: 10.1016/s0925-8388(96)02652-7

[51] W. Huang, Y. A. Chang, A thermodynamic analysis of the Ni-Al system, Intermetallics 6 (1998) 487-498.

[52] L. Bencze, D.D. Raj, D. Kath, W.A. Oates, L. Singheiser, K. Hilpert, Thermodynamic properties and diffusion factor in B2-NiAl, Metall. Mater. Trans. B 35B (2004) 867-876.

DOI: 10.1007/s11663-004-0081-x

[53] I.V. Belova, G.E. Murch, The Manning relations for atomic diffusion in a binary ordered alloy, Phil. Mag. 75 (1997) 1715-1723.

DOI: 10.1080/01418619708223752

[54] T. Shimozaki, Y. Goda, Y. Wakamatsu, M. Onishi, Interdiffusion and the Kirkendall effect in Au-Zn ordered β¢ phase, Defect Diffusion Forum 95-98 (1993) 629-634.

DOI: 10.4028/www.scientific.net/ddf.95-98.629

[55] G.F. Hancock, B.R. McDonnell, Diffusion in the intermetallic compound NiAl, Phys. stat. sol. (a) 4 (1973) 143-150.

[56] St. Frank, S.V. Divinski, U. Södervall, Chr. Herzig, Ni tracer diffusion in the B2-compound NiAl: Influence of temperature and composition, Acta Mater. 49 (2001) 1399-1411.

DOI: 10.1016/s1359-6454(01)00037-4

[57] Y. Minamino, Y. Koizumi, Y. Inui, In diffusion in B2-type ordered NiAl intermetallic compound, Defect Diffusion Forum 194-199 (2001) 517-522.

DOI: 10.4028/www.scientific.net/ddf.194-199.517

[58] A. Lutze-Birk, H. Jacobi, Diffusion of 114mIn in NiAl, Scripta Metall. 9 (1975) 761-765.

DOI: 10.1016/0036-9748(75)90236-7

[59] C. Ghosh, A. Paul, A physico-chemical approach in binary solid-state diffusion, Acta Mater. 55 (2007) 1927-(1939).

DOI: 10.1016/j.actamat.2006.10.051

[60] C. Ghosh, A. Paul, Different phenomenological theories and their abilities to describe the interdiffusion process in a binary system during multiphase growth, Acta Mater. 57 (2009) 493-502.

DOI: 10.1016/j.actamat.2008.09.032

[61] M. Koiwa, H. Numakura, S. Ishioka, Diffusion in L12 type intermetallic compounds, Defect Diffusion Forum 143-147 (1997) 209-222.

DOI: 10.4028/www.scientific.net/ddf.143-147.209

[62] H. Numakura, T. Ikeda, M. Koiwa, A. Almazouzi, Self-diffusion mechanism in Ni-based L12 type intermetallic compounds, Phil. Mag. A 77 (1998) 887-909.

DOI: 10.1080/01418619808221218

[63] G.F. Hancock, Diffusion of Nickel in alloys based on the intermetallic compound Ni3Al ( γ'), Phys. stat. sol. (a) 7 (1971) 535-540.

DOI: 10.1002/pssa.2210070228

[64] M.B. Bronfin, G.S. Bulatov, I.A. Drugova, Self-diffusion of Ni in the intermetallic compound Ni3Al and pure Ni, Fizika Metallov i Metallovedenie 40 (1975) 363-366.

[65] K. Hishino, S.J. Rothman, R.S. Averback, Tracer diffusion in pure and Boron-doped Ni3Al, Acta Metall. 36 (1988) 1271-1279.

DOI: 10.1016/0001-6160(88)90279-9

[66] St. Frank, U. Södervall, Chr. Herzig, Self-diffusion of Ni in single and polycrystals of Ni3Al, Phys. stat. sol. (a) 191 (1971) 45-55.

DOI: 10.1002/pssb.2221910105

[67] Y. Shi, G. Frohberg, H. Wever, Diffusion of 63Ni and 114mIn in the g'-phase Ni3Al, Phys. stat. sol. (a) 152 (1995) 361-375.

DOI: 10.1002/pssa.2211520205

[68] C. Cserháti, I.A. Szabó, Zs. Márton, G. Erdélyi, Tracer diffusion of 63Ni in Ni3(Al, Ge) ternary intermetallic compound, Intermetallics 10 (2002) 887-892.

DOI: 10.1016/s0966-9795(02)00089-4

[69] L.N. Larikov, V.V. Geichenko, V.M. Fal'chenko, Diffusion Processes in Ordered Alloys, Oxonian Press Pvt. Ltd., New Delhi, (1981).

[70] M.M.P. Janssen, Diffusion in the Nickel-rich part of the Ni-Al system at 1000 º to 1300 ºC; Ni3Al layer growth, diffusion coefficients, and interface concentrations, Metall. Trans. 4 (1973) 1623-1633.

DOI: 10.1007/bf02668017

[71] M. Watanabe, Z. Horita, T. Fujinami, T. Sano, M. Nemoto, Measurements of interdiffusion coefficient in Ni-Al system, Defect Diffusion Forum 95-98 (1993) 579-586.

DOI: 10.4028/www.scientific.net/ddf.95-98.579

[72] M. Watanabe, Z. Horita, T. Sano, M. Nemoto, Electron microscopy study of Ni/Ni3Al diffusion-couple interface - II. Diffusivity measurements, Acta Metall. Mater. 42 (1994) 3389-3396.

DOI: 10.1016/0956-7151(94)90471-5

[73] M. Watanabe, Z. Horita, M. Nemoto, Analytical electron microscopy study of diffusion-bonded multiphase system, Interface Science 4 (1997) 229-241.

DOI: 10.1007/bf00240244

[74] T. Ikeda, A. Almazouzi, H. Namakura, M. Koiwa, W. Sprengel, H. Nakajima, Interdiffusion in Ni3Al, Defect Diffusion Forum 143-147 (1997) 275-278.

DOI: 10.4028/www.scientific.net/ddf.143-147.275

[75] T. Ikeda, A. Almazouzi, H. Namakura, M. Koiwa, W. Sprengel, H. Nakajima, Single-phase interdiffusion in Ni3Al, Acta Mater. 46 (1998) 5369-5376.

DOI: 10.1016/s1359-6454(98)00209-2

[76] K. Fujiwara, Z. Horita, Intrinsic diffusion in Ni3Al, Defect Diffusion Forum 194-199 (2001) 565-570.

DOI: 10.4028/www.scientific.net/ddf.194-199.565

[77] K. Fujiwara, Z. Horita, Measurement of intrinsic diffusion coefficients of Al and Ni in Ni3Al using Ni/NiAl diffusion couples, Acta Mater. 50 (2002) 1571-1579.

DOI: 10.1016/s1359-6454(02)00018-6

[78] K. Hilpert, M. Miller, H. Gerads, H. Nickel, Thermodynamic study of the liquid and solid alloys of the Nickel-rich part of the Al-Ni phase diagram including the AlNi3 phase, Ber. Bunsenges. Phys. Chem. 94 (1990) 40-47.

DOI: 10.1002/bbpc.19900940109

[79] M. Koiwa, S. Ishioka, Random walks and correlation factor in diffusion in a three-dimensional lattice with coordination number 8, Phil. Mag. A 48 (1983) 1-9.

DOI: 10.1080/01418618308234882

[80] I.V. Belova, G.E. Murch, Test of the validity of the Darken/Manning relation for diffusion in ordered alloys taking the L12 structure, Phil. Mag. A 78 (1998) 1085-1092.

DOI: 10.1080/01418619808239976

[81] C. Cserháti, A. Paul, A.A. Kodentsov, M.J.H. van Dal, F.J.J. van Loo, Intrinsic diffusion in Ni3Al, Intermetallics 11 (2003) 291-297.

DOI: 10.1016/s0966-9795(02)00235-2

[82] A. Paul, The Kirkendall Effect in Solid State Diffusion, PhD thesis, Eindhoven, The Netherlands, (2004).

[83] Z. Qin, G. E. Murch, Computer simulation of chemical diffusion in a binary alloy with an equilibrium concentration of vacancies, Phil. Mag. A 71 (1995) 323-332.

DOI: 10.1080/01418619508244359

[84] A.B. Lidiard, On thermodynamic factor in the theory of diffusion in alloys, Phil. Mag. Lett. 74 (1996) 43-49.