Periodic Layer Formation during Multiphase Diffusion in Silicide Systems

Abstract:

Periodic layered morphology may occur during displacement solid-state reactions in ternary (and higher-order) silicide and other material systems. This periodic layered structure consists of regularly spaced layers (bands) of particles of one reaction product embedded in a matrix phase of another reaction product. The number of systems that is known to produce the periodic layered structure is rather small but increasing and includes metal/metal and metal/ceramic semi-infinite diffusion couples. The experimental results on different systems, where the periodic pattern formation has been observed are systematized and earlier explanations for this peculiar diffusion phenomenon are discussed. Formation of the reaction zone morphologies periodic in time and space can be considered as a manifestation of the Kirkendall effect accompanying interdiffusion in the solid state. The patterning during multiphase diffusion is attributed to diverging vacancy fluxes within the interaction zone. This can generate multiple Kirkendall planes, which by attracting in situ-formed inclusions of “secondary-formed phase” can result in a highly patterned microstructure.

• Periodical: Diffusion Foundations (Volume 21)
• Pages: 157-189
• DOI: https://doi.org/10.4028/www.scientific.net/DF.21.157
• Online since: March 2019
• Authors: Alexander Kodentsov, Joanna Wojewoda-Budka, Anna Wierzbicka-Miernik
• Keywords: Interfacial Reactions, Kirkendall Effect, Microstructure, Multiphase Diffusion, Periodic Pattern Formation, Silicide Systems

References

[1] J.B. Clark, F.N. Rhines, Diffusion layer formation in the ternary system aluminum-magnesium-zinc, Trans. ASM 51 (1959)199-221.

[2] J.S. Kirkaldy, L.C. Brown, Diffusion behaviour in ternary, multiphase systems, Can. Metall. Quat. 2 (1963) 89-117.

[3] J.B. Clark, Conventions for plotting the diffusion paths in multiphase ternary diffusion couple on the isothermal section of a ternary phase diagram, Trans. Met. Soc. AIME 227 (1963) 1250-1251.

[4] C. Wagner, Über den Mechanismus von doppelten Umsetzungen durch Reaktion im festen Zustand, Z. Anorg. Allgem. Chem. 236 (1938) 320-338 (in German).

DOI: 10.1002/zaac.19382360130

[5] C. Wagner, Oxidation of alloys involving noble metals, J. Electrochem. Soc. 103 (1956) 571-580.

DOI: 10.1149/1.2430159

[6] R.A. Rapp, A. Ezis, G.J. Yurek, Displacement reactions in the solid state, Metall. Trans. 4 (1973) 1283-1292.

DOI: 10.1007/bf02644523

[7] F.J.J. van Loo, J.A. van Beek, G.F. Bastin, R. Metselaar, The role of thermodynamics and kinetics in multiphase ternary diffusion, in: M.A. Dayananda, G.E. Murch (Eds.), Diffusion in Solids: Recent Developments, The Metallurgical Society, Inc., 1985, pp.231-259.

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

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

[9] F.N. Rhines, A metallographic study of internal oxidation in the alfa solid solution of copper, Trans. AIME 137 (1940) 246-290.

[10] J.L. Meijering, M.J. Druyvesteyn, Hardening of metals by internal oxidation, Part II, Philips Res. Rep. 2 (1947) 260-280.

[11] R.A. Bosch, F.V. Lenel, G.S. Ansell, The influence and rate of oxidation upon the properties of internally oxidized silver-magnesium alloys, Trans. ASM 57 (1964) 960-971.

[12] Y.S. Shen, E.J. Zdanuk, R.H. Krock, The influence of additives on the formation of periodic precipitation (Liesegang bands) in the Ag-Cd system, Met. Trans 2 (1971) 2839-2844.

DOI: 10.1007/bf02813261

[13] V.A. van Rooijen, E.W. van Royen, J. Vrijen, S. Radelaar, On Liesegang bands in internally oxidized AgCd-based ternary alloys, Acta Met. 23 (1975) 987-995.

DOI: 10.1016/0001-6160(75)90013-9

[14] D.L. Ricoult, H. Schmalzried, Periodic precipitation during internal oxidation of Iron-doped magnesium oxide crystals, Ber. Bunsenges. Phys. Chem. 9 (1986) 135-141.

DOI: 10.1002/bbpc.19860900209

[15] R. E. Liesegang, Ueber einige Eigenschaften von Gallerten, Naturwiss. Wochenschr. 11 (1896) 353-362 (in German).

[16] J.E. Gerrard, M. Hoch, F.R. Meeks, Counterdiffusion of aluminium and arsenic in copper, Acta Met. 10 (1962) 751-758.

DOI: 10.1016/0001-6160(62)90088-3

[17] R.L. Klueh, W.W. Mullins, Periodic precipitation (Liesegang phenomena) in solid silver-I. Experimental, Acta Met. 17 (1969) 59-67.

DOI: 10.1016/0001-6160(69)90163-1

[18] K. Osinski, A.W. Vriend, G.F. Bastin, F.J.J. van Loo, Periodic formation of FeSi bands in diffusion couples Fe(15wt%Si)-Zn, Z. Metallkd. 73 (1982) 258-261.

DOI: 10.1515/ijmr-1982-730412

[19] W. B. Pearson, The Physical Chemistry and Physics of Metals and Alloys, Wiley & Sons, Inc, (1972).

[20] M.R. Rijnders, A.A. Kodentsov, Cs. Cserháti, J. van den Akker, F.J.J. van Loo, Periodic layer formation during solid state reactions, Defect Diffusion Forum 129-130 (1996) 253-266.

DOI: 10.4028/www.scientific.net/ddf.129-130.253

[21] K. Osinski, The Influence of Aluminium and Silicon on the Reaction between Iron and Zinc, PhD thesis, Eindhoven, The Netherlands, (1983).

[22] M.R. Rijnders, F.J.J. van Loo, Aspects of periodic layer formation in Co2Si/Zn diffusion couples, Scripta Metall. Mater. 32 (1995)1931-1935.

DOI: 10.1016/0956-716x(95)00082-7

[23] M.R. Rijnders. Periodic Layer Formation during Solid State Reactions, PhD thesis, Eindhoven, The Netherlands, (1996).

[24] M.R. Rijnders, A.A. Kodentsov, J.A. van Beek, F.J.J. van Loo, Periodic layered morphologies resulting from solid state reactions, in: Proc. TMS Annual Meeting, Design Fundamentals of High-Temperature Composites, Intermetallics and Metal-Ceramics Systems, R.Y. Lin, Y. A. Chang R.G. Reddy, C.T. Liu (Eds.), The Minerals, Metals and Materials Society,1996, pp.153-167.

[25] A.A. Kodentsov, M.R. Rijnders, F.J.J. van Loo, Periodic pattern formation in solid state reactions related to the Kirkendall effect. Acta Mater. 46 (1998) 6521-6528.

DOI: 10.1016/s1359-6454(98)00309-7

[26] A.A. Kodentsov, M.J.H. van Dal, C. Cserháti, A.M. Gusak, F.J.J. van Loo, Patterning in reactive diffusion, Defect Diffusion Forum 194-199 (2001)1491-1502.

DOI: 10.4028/www.scientific.net/ddf.194-199.1491

[27] J. Bardeen, C. Herring, Diffusion in Alloys, in: Imperfections in Nearly Perfect Crystals, W. Shockley, J.H. Hollomon, R. Maurer, F. Seitz (Eds.), Wiley, Ney York, 1952, pp.261-288.

DOI: 10.1107/s0365110x52002677

[28] M. He, X. Su, F. Yin, J. Wang, Zh. Li, Periodic layered structure in Ni3Si/Zn diffusion couples, Scripta Mater. 59 (2008) 411-413.

DOI: 10.1016/j.scriptamat.2008.04.015

[29] X. Su, C. Liu, S. Yang, F. Yin, J. Wang, A general qualitative description for the initial stages of periodic pattern formation in Ni3Si/Zn diffusion couples, Scripta Mater. 62 (2010) 485-487.

DOI: 10.1016/j.scriptamat.2009.12.021

[30] Y.C. Chen, X.F. Zhang, Y.K. Ren, L. Han, D.Y. Lin, Q.P. Wang, Microstructure evolution of periodic layers formed during soli state reaction between Zn and Ni3Si, Intermetallics 36 (2013) 8-11.

DOI: 10.1016/j.intermet.2012.12.015

[31] P. Nash, Y.Y. Pan, Ni-Zn (Nickel-Zinc), in: P. Nash (Ed.), Phase Diagrams of Binary Nickel Alloys, ASM International, 1991, pp.382-390.

[32] H.H. Stadelmaier, J.M. Brett, G. Hofer, Das Dreistoffsystem Nickel-Zink-Silizium, Z. Metallkd. 59 (1968) 881-882 (in German).

DOI: 10.1515/ijmr-1968-591108

[33] H. Xu, B. Hu, W. Sun, P. Wang, Y. Du, X. Xiong, J.L. Liang, Zh. Jin, Phase equilibria in the Ni-Si-Zn system at 600 ºC, Intermetallics 19 (2011) 1089-1095.

DOI: 10.1016/j.intermet.2010.11.005

[34] Y.C. Chen, X.F. Zhang, L. Han, Z.W. Du, Periodic layer formation during solid state reaction between Zn and CuTi, Mater. Lett. 76 (2012) 151-154.

DOI: 10.1016/j.matlet.2012.02.063

[35] Th. B. Massalski, Binary Alloy Phase Diagrams, ASM, Metal Park, (1986).

[36] S.A. Zver'kov, S.F. Dunaev, E. M. Slusarenko, Interaction of magnesium with alloys of the Co-Ni system, Vestn. Mosk. Univ., Ser 2, Khim. 29 (1988) 182-184.

[37] S.F. Dunaev, S.A. Zver'kov, Influence of high pressure on the formation of periodic regular structures in multicomponent diffusion zones, J. Less-Comm. Met. 153 (1989) 143-150.

DOI: 10.1016/0022-5088(89)90540-7

[38] F. Mazaudier, C. Proye, F. Hodaj, Further insight into mechanisms of solid state interactions in UMo/Al system, J. Nucl. Mater. 377 (2008) 476-485.

DOI: 10.1016/j.jnucmat.2008.04.016

[39] I. Barin, O. Knacke, Thermochemical Properties of Inorganic Substances, Springer-Verlag, Berlin, (1973).

[40] Y.C. Chen, J. Xu, X.H. Fan, X.F. Zhang, L. Han, D.Y. Lin, Q.H. Li, C. Uher, The mechanism of periodic layer formation during solid-state reaction between Mg and SiO2, Intermetallics 17 (2009) 920-926.

DOI: 10.1016/j.intermet.2009.04.002

[41] I. Gutman, L. Klinger, I. Gotman, M. Shapiro, Experimental observation of periodic structure formation in SiO2-Mg system, Scripta Mater. 45 (2001) 363-367.

DOI: 10.1016/s1359-6462(01)01043-0

[42] I. Gutman, I. Gotman, M. Shapiro, Kinetics and mechanism of periodic structure formation at SiO2/Mg interface, Acta Mater. 54 (2006) 4677-4684.

DOI: 10.1016/j.actamat.2006.05.048

[43] L. Klinger, I. Gutman, I. Gotman, A switch-over model of periodic structure formation in ternary diffusion couples, Scripta Mater. 45 (2001) 1221-1226.

DOI: 10.1016/s1359-6462(01)01153-8

[44] I. Gutman, L. Klinger, I. Gotman, M. Shapiro, Model for evolution of periodic layered structure in the SiO2/Mg system, Solid State Ionics 180 (2009) 1350-1355.

DOI: 10.1016/j.ssi.2009.08.015

[45] L. Shi, P. Shen, E. Dong, Q. Jiang, Reactive wetting in liquid magnesium/silica and magnesium/silicon systems, Appl. Surf. Sci. 274 (2013) 124-130.

DOI: 10.1016/j.apsusc.2013.02.126

[46] D.W. Song, R. Subramanian, R. Dieckmann, Displacement reactions in the Ni-Al-O system resulting in periodic layer structures, Mat. Res. Soc. Symp. Proc. 365 (1995) 59-64.

DOI: 10.1557/proc-365-59

[47] M.M.P. Janssen, G.D. Rieck, Reaction diffusion and Kirkendall effect in the nickel-aluminium system, Trans. Met. Soc. AIME 239 (1967) 1372-1385.

[48] R.L. Mehan, R.B. Bolon, Interaction between silicon carbide and a nickel-based superalloy at elevated temperatures, J. Mater. Sci. 14 (1979) 2471-2481.

DOI: 10.1007/bf00737038

[49] M.R. Jackson, R.L. Mehan, A.M. Devis, E.L. Hall, Solid state SiC/Ni alloy reaction, Met. Trans. A 14A (1983) 355-364.

DOI: 10.1007/bf02644213

[50] R.C.J. Schiepers, F.J.J. van Loo, G. de With, Reactions between α-silicon carbide ceramic and nickel or iron, J. Amer. Ceram. Soc. 71 (1988) C284-C287.

[51] M. Backhaus-Ricoult, Solid state reactions between silicon carbide and various transition metals, Ber. Bunsenges. Phys. Chem. 93 (1989) 1277-1281.

DOI: 10.1002/bbpc.19890931127

[52] T.C. Chou, Anomalous solid state reaction between SiC and Pt, J. Mater. Res. 5 (1990) 601-608.

DOI: 10.1557/jmr.1990.0601

[53] T.C. Chou, High temperature reactions between SiC and platinum, J. Mater. Sci. 26 (1991) 1412-1420.

DOI: 10.1007/bf00544487

[54] T.C. Chou, A. Joshi, J. Wadsworth, Solid state reactions of SiC with Co, Ni and Pt, J. Mater. Res. 6 (1991) 796-809.

DOI: 10.1557/jmr.1991.0796

[55] R.C.J. Schiepers, J.A. van Beek, F.J.J. van Loo, G. de With, The interaction between SiC and Ni, Fe (Fe,Ni) and steel: Morphology and kinetics, J. Eur. Ceram. Soc. 9 (1993) 211-218.

DOI: 10.1016/0955-2219(93)90090-e

[56] C. Rado, S. Kalogeropoulou, N. Eustathopoulos, Surface and bulk interactions in M-SiC systems (M=Au, Cu, Ni), Mat. Res. Soc. Symp. Proc. 327 (1994) 319-324.

DOI: 10.1557/proc-327-319

[57] J.H. Gülpen, A.A. Kodentsov, F.J.J. van Loo, Growth of silicides in Ni-Si and Ni-SiC bulk diffusion couples, Z. Metallkd. 86 (1995) 530-539.

DOI: 10.1515/ijmr-1995-860803

[58] K. Bhanumurhy, R. Schmid-Fetzer, Experimental study of ternary Pd-Si-C phase equilibria and Pd/SiC interface reactions, Z. Metallkd. 87 (1996) 244-253.

DOI: 10.1515/ijmr-1996-870402

[59] A.A. Kodentsov, M.R. Rijnders, F.J.J. van Loo, Chemical aspects of metal-ceramic interactions, Mater. Sci. Forum 207-209 (1996) 69-78.

DOI: 10.4028/www.scientific.net/msf.207-209.69

[60] R. Metselaar, A. Kodentsov and F.J.J. van Loo, Microstructural evolution of SiC/metal interfaces at elevated temperatures, Key Eng. Mater. 132-136 (1997) 1758-1761.

DOI: 10.4028/www.scientific.net/kem.132-136.1758

[61] A.A. Kodentsov and F.J.J. van Loo, Metallization of SiC ceramics: Chemical aspects, in: High Temperature Materials Chemistry, K. E. Spear (Ed.), The Electrochemical Society, Inc., Pennington, New Jersey, Vol. 97-39, 1997, pp.468-471.

[62] M.R. Rijnders, A.A. Kodentsov, J.A. van Beek, J. van den Akker, F.J.J. van Loo, Pattern formation in Pt-SiC diffusion couples, Solid State Ionics 95 (1997) 51-59.

DOI: 10.1016/s0167-2738(96)00578-4

[63] A.A. Kodentsov, F.J.J. van Loo, Periodic pattern formation in metal-ceramic reactions, Adv. Sci. Tech. 46 (2006)136 -145.

[64] S.L. Markovski, M.J.H. van Dal, M.J.L. Verbeek, A.A. Kodentsov, F.J.J. van Loo, Microstructology of solid-state reactions, J. Phase Equilibria 20 (1999) 373–388.

DOI: 10.1361/105497199770340905

[65] C. Wagner, Mathematical analysis of the formation of periodic precipitation, J. Colloid. Sci. 5 (1950) 85-97.

[66] W. Ostwald, Lehrbuch der allgemeinen Chemie, An. Engelman Verlag, Leipzig, 1897 (in German).

[67] J.S. Kirkaldy, Spontaneous evolution of spatiotemporal patterns in materials, Rep. Prog. Phys. 55 (1992) 723-795.

DOI: 10.1088/0034-4885/55/6/002

[68] J.S. Kirkaldy, Spontaneous evolution of microstructure in materials, Met. Trans. A 24A (1993) 1689-1721.

[69] C.R. Kao, Y.A. Chang, A theoretical analysis for the formation of periodic layered structure in ternary diffusion couples involving a displacement type of reactions, Acta Metall. Mater. 41 (1993) 3463-3472.

DOI: 10.1016/0956-7151(93)90226-i

[70] F.-Y. Shiau, Y.A. Chen, Reactions between cobalt and gallium arsenide in bulk and thin-film, Mater. Chem. Phys. 32 (1992) 300-309.

[71] Y.C. Chen, Y.G. Zhang, C.Q. Chen, Quantitative description of periodic layer formation during solid-state reactions, Mater. Sci. Eng. A A362 (2003) 135-144.

[72] A.A. Kodentsov, A. Paul, F.J.J. van Loo, Bifurcation of the Kirkendall plane and patterning in reactive diffusion, Z. Metallkd. 95 (2004) 258-260.

DOI: 10.3139/146.017946

[73] M.J.H. van Dal, A.M. Gusak, C. 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

[74] A. Paul, A.A. Kodentsov, M.J.H. van Dal, F.J.J. van Loo, The Kirkendall effect in multiphase diffusion, Acta Mater. 52 (2004) 623-630.

DOI: 10.1016/j.actamat.2003.10.007

[75] 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) 210-233.

DOI: 10.1080/10408430802462958

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

[77] M.J.H. van Dal, M.C.L.P Pleumeekers, A.A. Kodentsov, F.J.J. van Loo, Intrinsic diffusion and Kirkendall effect in Ni-Pd and Fe-Pd solid solutions, Acta Mater. 48 (2000) 385-396.

DOI: 10.1016/s1359-6454(99)00375-4

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

DOI: 10.1002/andp.18942891315

[79] 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.

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

[81] M.J.H. van Dal, D.G.G.M. Huibers, A.A. Kodentsov, F.J.J. van Loo, Formation of Co–Si intermetallics in bulk diffusion couples, Part I. Growth kinetics and mobilities of species in the silicide phases, Intermetallics 9 (2001) 409- 421.

DOI: 10.1016/s0966-9795(01)00018-8

[82] P. Villars and L. Calvert, Pearson's Handbook of Crystallographic Data for Intermetallic Phases, ASM, (1985).

[83] M.J.H. van Dal, A.A. Kodentsov, F.J.J. van Loo, Formation of Co-Si intermetallics in bulk diffusion couples. Part II: Manifestations of the Kirkendall effect accompanying reactive diffusion, Intermetallics 9 (2001) 451-456.

DOI: 10.1016/s0966-9795(01)00019-x

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

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

[85] F.J.J. van Loo, B. Pieraggi, R.A. Rapp, Interface migration and the Kirkendall effect in diffusion-driven phase transformations, Acta Metall. Mater. 38 (1990) 1769-1779.

DOI: 10.1016/0956-7151(90)90019-d

[86] B. Pieraggi, R.A. Rapp, F.J.J. van Loo, J.P. Hirth, Interfacial dynamics in diffusion-driven phase transformations, Acta Metall. Mater. 38 (1990) 1781-1788.

DOI: 10.1016/0956-7151(90)90020-h

[87] F.J.J. van Loo, B. Pieraggi, Reaction and diffusion in multiphase systems: Phenomenology and frames, Mater. Sci. Forum 155-156 (1994) 307-316.

DOI: 10.4028/www.scientific.net/msf.155-156.307

[88] G.F. Bastin, G.D. Rieck, Diffusion in the titanium-nickel system: I. Occurrence and growth of the various intermetallic compounds, Met. Trans. 5 (1974) 1817-1826.

DOI: 10.1007/bf02644146

[89] 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

[90] M.J.H. van Dal, A.M. Gusak, Cs. Cserháti, A.A. Kodentsov, F.J.J. van Loo, Spatio-temporal instabilities of the Kirkendall-marker planes during interdiffusion in βʹ-AuZn, Phil. Mag. A 82 (2002) 943-954.

DOI: 10.1080/01418610208240011