Hostname: page-component-cd9895bd7-7cvxr Total loading time: 0 Render date: 2025-01-01T08:14:42.943Z Has data issue: false hasContentIssue false
  • English
  • Français

Phase stability and cohesive properties of Au–Sn intermetallics: A first-principles study

Published online by Cambridge University Press:  31 January 2011

G. Ghosh
G. Ghosh*
Affiliation:
Department of Materials Science and Engineering, Robert R. McCormick School of Engineering and Applied Science, Northwestern University, Evanston, Illinois 60208-3108
*
a)Address all correspondence to this author. e-mail: g-ghosh@northwestern.edu
Get access

Abstract

The total energies and cohesive properties of 29 Au–Sn intermetallics (stable, metastable, and virtual) are calculated from first-principles density-functional theory (DFT) employing ultrasoft pseudopotentials (USPP) and both local-density approximation (LDA) and generalized gradient approximation (GGA) for the exchange-correlation functional. Among the intermetallics considered, the ground-state structures are found to be AuSn, AuSn2, and AuSn4. Another phase Au5Sn, though present in the equilibrium diagram, lies slightly above the ground state convex hull. The formation energies of stable phases calculated using USPP–LDA and USPP–GGA are nearly the same. Except for AuSn, calorimetric data for enthalpies of formation show a good agreement with the calculated formation energies. Based on our first-principles results, it is argued that the structures of two metastable phases are cP52-type γ brass (isotypic with Al4Cu9) at Au–20.5 at.% Sn and hP1-type γ (isotypic with HgSn6–10) at Sn–8 at.% Au. For the intermetallics considered in this study, we provide optimized values of lattice parameters and Wyckoff positions. The experimental lattice parameters show a better agreement with those calculated using USPP–LDA than with USPP–GGA. The results presented here form the basis for creating a reliable thermodynamic database to facilitate calculations of stable and metastable phase diagrams of binary and multicomponent systems containing Au and Sn, relevant to electronic packaging and many other joining applications.

Keywords

Elastic propertiesElectronic structurePhase equilibria
Type
Articles
Information
Journal of Materials Research , Volume 23 , Issue 5 , May 2008 , pp. 1398 - 1416
Copyright
Copyright © Materials Research Society 2008

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

REFERENCES

1Abtew, M.Selvaduray, G.: Lead-free solders in microelectronic. Mater. Sci. Eng., R 27, 95 2000Google Scholar
2Tu, K.N.Zeng, K.: Tin–lead (SnPb) solder reaction in flip chip technology. Mater. Sci. Eng., R 34, 1 2001Google Scholar
3Zeng, K.Tu, K.N.: Six cases of reliability study of Pb-free solder joints in electronic packaging technology. Mater. Sci. Eng., R 38, 55 2002Google Scholar
4Tu, K.N., Gusak, A.M.Li, M.: Physics and materials challenges for lead-free solders. J. Appl. Phys. 93, 1335 2003CrossRefGoogle Scholar
5Laurila, T., Vuorinen, V.Kivilahti, J.K.: Interfacial reactions between lead-free solders and common base materials. Mater. Sci. Eng., R 49, 1 2005CrossRefGoogle Scholar
6McNeil, M.B.: The properties of the intermetallic phases in the system Au-Sn. J. Electrochem. Soc. 110, 1169 1963Google Scholar
7Yost, F.G., Karnowsky, M.M., Drotning, W.D.Gieske, J.H.: Thermal expansion and elastic properties of high gold–tin alloys. Metall. Trans. A 21, 1885 1990Google Scholar
8Jiang, N., Clum, J.A., Chromik, R.R.Cotts, E.J.: Thermal expansion of several Sn-based intermetallic compounds. Scripta Mater. 37, 1851 1997Google Scholar
9Chromik, R.R., Vinci, R.P., Allen, S.L.Notis, M.R.: Nanoindentation measurements on Cu–Sn and Ag–Sn intermetallics formed in Pb-free solder joints. J. Mater. Res. 18, 2251 2003CrossRefGoogle Scholar
10Lucas, J.P., Rhee, H., Guo, F.Subramanian, K.N.: Mechanical properties of intermetallic compounds associated with Pb-free solder joints using nanoindentation. J. Electron. Mater. 32, 1375 2003Google Scholar
11Deng, X., Chawla, N., Chawla, K.K.Koopman, M.: Deformation behavior of (Cu, Ag)–Sn intermetallics by nanoindentation. Acta Mater. 52, 4291 2004CrossRefGoogle Scholar
12Ghosh, G.: Elastic properties, hardness, and indentation fracture toughness of intermetallics relevant to electronic packaging. J. Mater. Res. 19, 1439 2004Google Scholar
13Jang, G-Y., Lee, J-W.Duh, J-G.: The nanoindentation characteristics of Cu6Sn5, Cu3Sn, and Ni3Sn4 intermetallic compounds in the solder bump. J. Electron. Mater. 33, 1103 2004Google Scholar
14Pitely, S., Zavalij, L., Zarembo, S.Cotts, E.J.: Linear coefficients of thermal expansion of Au0.5Ni0.5Sn4, Au0.75Ni0.25Sn4, and AuSn4. Scripta Mater. 51, 745 2004CrossRefGoogle Scholar
15Chromik, R.R., Wang, D.N., Shugar, A., Limata, L., Notis, M.R.Vinci, R.P.: Mechanical properties of intermetallic compounds in the Au-Sn system. J. Mater. Res. 20, 2161 2004Google Scholar
16Chen, Z., He, M., Balakrisnan, B.Chum, C.C.: Elasticity modulus, hardness and fracture toughness of Ni3Sn4 intermetallic thin films. Mater. Sci. Eng., A 423, 107 2006Google Scholar
17Tsai, I., Wu, E., Yen, S.F.Chuang, T.H.: Mechanical properties of intermetallic compounds on lead-free solder by Moiré techniques. J. Electron. Mater. 35, 1059 2006Google Scholar
18Ghosh, G.Asta, M.: Phase stability, phase transformations, and elastic properties of Cu6Sn5: Ab initio calculations and experimental results. J. Mater. Res. 20, 3102 2005CrossRefGoogle Scholar
19Lee, N.T.S., Tan, V.B.C.Lim, K.M.: First-principles calculations of structural and mechanical properties of Cu6Sn5. Appl. Phys. Lett. 88, 031913 2006CrossRefGoogle Scholar
20Lee, N.T.S., Tan, V.B.C.Lim, K.M.: Structural and mechanical properties of Sn-based intermetallics from ab initio calculations. Appl. Phys. Lett. 88, 141908 2006Google Scholar
21Matijasevic, G.S., Lee, C.C.Wang, C.Y.: Controlling the microstructures from the gold–tin reaction. Thin Solid Films 223, 276 1993CrossRefGoogle Scholar
22Tsai, J.Y., Chang, C.W., Shieh, Y.C., Hu, Y.C.Kao, C.R.: Controlling the microstructures from the gold–tin reaction. J. Electron. Mater. 34, 182 2005Google Scholar
23Okamoto, H.Massalski, T.B.: The Au–Sn (Gold–Tin). Bull. Alloy Phase Diagrams 5, 492 1984Google Scholar
24Okamoto, H.: Au–Sn (Gold–Tin). J. Phase Equilib. 14, 765 1993Google Scholar
25Sundman, B.Ågren, J.: A regular solution model for phases with several components and sub-lattices, suitable for computer-applications. J. Phys. Chem. Solids 42, 297 1981Google Scholar
26Schubert, K., Breimer, H.Gohle, R.: The structures of the systems gold–indium, gold–tin, gold–indium–tin and gold– tin–antimony. Z. Metallkd. 50, 146 1959Google Scholar
27Ciulik, J.Notis, M.R.: The Au–Sn phase diagram. J. Alloys Compd. 191, 71 1993Google Scholar
28Hamilton, D.C., Raub, Ch.J., Matthias, B.T., Corenzwit, E., Hull, G.W. Jr.: Some new superconducting compounds. J. Phys. Chem. Solids 26, 665 1965Google Scholar
29Osada, K., Yamaguchi, S.Hirabayashi, M.: An ordered structure of Au5Sn. Trans. Jpn. Inst. Met. 15, 256 1974Google Scholar
30Vogel, R.: Gold-tin alloys. Z. Anorg. Chem. 46, 60 1905CrossRefGoogle Scholar
31Puschin, N.A.: Potential and nature of metallic alloys. Zh. Fiz. Khim. 39, 353 1906Google Scholar
32Preston, G.D.Owen, E.A.: The atomic structure of AuSn. Philos. Mag. 4, 133 1927CrossRefGoogle Scholar
33Steibeck, S.Westgren, A.: X-ray analysis of gold–tin alloys. Z. Phys. Chem. B14, 91 1931Google Scholar
34Jaeger, F.M.Bottema, J.A.: Exact determination of specific heats at high temperature. Recl. Trav. Chim. Pays-Bas 52, 89 1933Google Scholar
35Jan, J-P., Pearson, W.B., Kjekshus, A.Woods, S.B.: On the structural, thermal, electrical, and magnetic properties of AuSn. Can. J. Phys. 41, 2252 1963Google Scholar
36Charlton, J.S., Cordey-Hayes, M.Harris, I.R.: A study of the 119Sn Mössbauer isomer shifts in some platinum–tin and gold– tin alloys. J. Less-Common Met. 20, 105 1970Google Scholar
37Psarev, V., Kirly, V.G., Kuznetsov, A.V., Psareva, I.V.Ivanova, A.L.: Investigation of the crystallization of alloys in systems containing peritectic transformations. Russ. Met. 2, 175 1982Google Scholar
38Schubert, K., Rössler, U., Kluga, M., Anderko, K.Harle, L.: Crystallographic results on phases with penetration bands. Naturwissenschaften 40, 437 1953Google Scholar
39Schubert, K., Breimer, H., Gohle, R., Lukas, H.L., Meissner, H.G.Stolz, E.: Some structural results on metallic phases. Naturwissenschaften 45, 360 1958CrossRefGoogle Scholar
40Rodewald, U.C., Hoffmann, R.D., Wu, Z.Y.Pöttgen, R.: Structure refinement of AuSn2. Z. Naturforsch. [B] 61, 108 2006Google Scholar
41Tammann, G.Rocha, H.J.: The diffusion of two metals into one another with formation of intermetallic compounds. Z. Anorg. Chem. 199, 289 1931Google Scholar
42Schubert, K.Rösler, U.: The structure of PtSn4. Z. Metallkd. 41, 298 1950Google Scholar
43Schubert, K.Rösler, U.: The structure of PtSn4. Z. Naturforsch. 5, 127 1950Google Scholar
44Kubiak, R.: The influence of temperature on the crystal structure of AuSn4. J. Less-Common Met. 80, P53 1981Google Scholar
45Kubiak, R.Wolcyrz, M.: Refinement of the crystal structures of AuSn4 and PdSn4. J. Less-Common Met. 97, 265 1984Google Scholar
46Kubiak, R.Wolcyrz, M.: X-ray investigations of crystallization and thermal expansion of AuSn4, PdSn4 and PtSn4. J. Less-Common Met. 109, 339 1985CrossRefGoogle Scholar
47Kane, R.H., Giessen, B.C.Grant, N.J.: New metastable phases in binary tin systems. Acta Metall. 14, 605 1966Google Scholar
48Giessen, B.C.: A metastable γ-brass phase in the gold–tin system and a note on non-equilibrium Hume–Rothery phases. Z. Metallkd. 59, 805 1968Google Scholar
49Dufner, D.C.Eyring, L.: High-resolution electron microscopy and x-ray microanalysis of chemical reactions in the gold–tin thin-film system. J. Solid State Chem. 62, 112 1986CrossRefGoogle Scholar
50Ishihara, K.N., Gohchi, H.Shingu, P.H.: A metastable eutectic reaction in the Au–Sn system in Undercooled Alloy Phases, edited by E.W. Collings and K.C. Koch TMS-AIME Warrendale, PA 1987 49–57Google Scholar
51Midgley, P.A., Sleight, M.E.Vincent, R.: The structure of a metastable Au–Sn phase determined by convergent beam electron diffraction. J. Solid State Chem. 124, 132 1996Google Scholar
52Villars, P.Calvert, L.D.Pearson’s Handbook of Crystallographic Data for Intermetallic Phases, Vol. 1, ASM International Materials Park, OH 1991 1339Google Scholar
53Biltz, W., Rohlffs, G.von Vogel, H.U.: Systematic doctrine of affinity. LXI - Construction and use of a high-temperature calorimeter with a closed reaction chamber. Z. Anorg. Allgem. Chem. 220, 113 1934Google Scholar
54Kleppa, O.J.: Heats of formation of some solid and liquid binary alloys of gold with cadmium, indium, tin and antimony. J. Phys. Chem. 60, 858 1956Google Scholar
55Misra, S., Howlett, B.W.Bever, M.B.: On the thermodynamic properties of the intermediate phases in the system Au–Sn. Trans. AIME 233, 749 1965Google Scholar
56Jena, A.K.Bever, M.B.: On the thermodynamic properties of the phases zeta and AuSn in the system Au–Sn. Metall. Trans. B 10, 545 1979Google Scholar
57Hultgren, R., Desai, P., Hawkins, P., Gleiser, M.Kelley, K.K.: Selected Values of the Thermodynamic Properties of Binary Alloys ASM International Materials Park, OH 1973 320–328Google Scholar
58Chevalier, P-Y.: A thermodynamic evaluation of the Au–Sn system. Thermochim. Acta 130, 1 1988Google Scholar
59Liu, H.S., Liu, C.L., Ishida, K.Jin, Z.P.: Thermodynamic modeling of the Au–In–Sn system. J. Electron. Mater. 32, 1290 2003Google Scholar
60Grolier, V.Schmid-Fetzer, R.: Thermodynamic evaluation of the Au–Sn system. Int. J. Mater. Res. 98, 797 2007Google Scholar
61Kresse, G.Hafner, J.: Ab-initio molecular-dynamics simulation of the liquid-metal amorphous-semiconductor transition in germanium. Phys. Rev. B 49, 4251 1994Google Scholar
62Kresse, G.Furthmüller, J.: Efficient iterative schemes of ab initio total-energy calculations using a plane-wave basis set. Phys. Rev. B 54, 11169 1996Google Scholar
63Kresse, G.Furthmüller, J.: Efficiency of ab-initio total energy calculations for metals and semi-conductors using a plane-wave basis set. Comput. Mater. Sci. 6, 15 1996CrossRefGoogle Scholar
64Vanderbilt, D.: Soft self-consistent pseudo potential in a generalized eigenvalue formalism. Phys. Rev. B 41, 7892 1990CrossRefGoogle Scholar
65Kresse, G.Hafner, J.: Norm-conserving and ultrasoft pseudopotentials for first-row and transition-elements. J. Phys. Condens. Matter 6, 8245 1994CrossRefGoogle Scholar
66Ceperley, D.M.Alder, B.J.: Ground-state of the electron-gas by a stochastic method. Phys. Rev. Lett. 45, 566 1980Google Scholar
67Perdew, J.P.Zunger, A.: Self-interaction correction to density functional approximation for many-electron systems. Phys. Rev. B 23, 5048 1981Google Scholar
68Perdew, J.P.Wang, Y.: Accurate and simple analytic representation of the electron-gas correlation-energy. Phys. Rev. B 45, 13244 1992Google Scholar
69Monkhorst, H.J.Pack, J.D.: Special points for Brillouin-zone integrations. Phys. Rev. B 13, 5188 1976CrossRefGoogle Scholar
70Methfessel, M.Paxton, A.T.: High-precision sampling for Brillouin-zone integration in metals. Phys. Rev. B 40, 3616 1989Google Scholar
71Vinet, P., Rose, J.H., Ferrante, J.Smith, J.R.: Universal feature of the equation of state solids. J. Phys. Condens. Matter 1, 1941 1989Google Scholar
72Ashcroft, N.W.Mermin, N.D.: Solid State Physics Reinhart and Winston New York 1976Google Scholar
73Mehl, M.J., Klein, B.M.Papaconstatopolous, K.: Intermetallic Compounds, Principles and Practice Vol. 1 edited by J.H. Westbrook and R.L. Fleischer John Wiley & Sons New York 1994 195Google Scholar
74Ravindran, P., Fast, L., Korzhavyi, P.A., Johansson, B., Wills, J.Eriksson, O.: Density-functional theory for calculation of elastic properties of orthorhombic crystals: Application to TiSn2. J. Appl. Phys. 84, 4891 1998Google Scholar
75Mattesini, M.Matar, S.F.: Density-functional theory for the calculation of elastic properties of nanostructured superhard TiN/Si to TiSn2. Phys. Rev. B 65, 075110 2002Google Scholar
76Wang, S., Gudipati, R., Rao, A.S., Bostelmann, T.J.Shen, Y.G.: First-principles calculations for the elastic properties of nanostructured superhard TiN/SixNy superlattices. Appl. Phys. Lett. 91, 081916 2007Google Scholar
77Massalski, T.B., editor Binary Alloy Phase Diagrams, Vol. 1, ASM International Materials Park, OH 1990 350–351, 381–383Google Scholar
78Kaufman, L.Bernstein, H.: Computer Calculation of Phase Diagram Academic Press Inc. New York 1970Google Scholar
79Lukas, H.L., Fries, S.G.Sundman, B.: Computational Thermodynamics. The Calphad Method Cambridge University Press Cambridge, UK 2007Google Scholar
80Straumanis, M.E.: Redetermination of lattice parameters, densities and thermal expansion coefficients of silver and gold, and the perfection of their structures. Monatsh. Chem. 102, 1377 1971Google Scholar
81Godwal, B.K.Jeanloz, R.: First-principles equation of state of gold. Phys. Rev. B 40, 7501 1989Google Scholar
82Khein, A., Singh, D.J.Umrigar, C.J.: All-electron study of gradient corrections to the local-density functional in metallic systems. Phys. Rev. B 51, 4105 1995Google Scholar
83Korhonen, T., Puska, M.J.Nieminen, R.M.: Vacancy-formation energies for fcc and bcc transition-metals. Phys. Rev. B 51, 9526 1995Google Scholar
84Mehl, M.J.Papaconstantopoulos, D.A.: Applications of a tight-binding total-energy method for transition and noble metals: Elastic constants, vacancies, and surfaces of monatomic metals. Phys. Rev. B 54, 4519 1996Google Scholar
85Suzuki, S.Nakao, K.: A fully relativistic full-potential LCAO method for solids. J. Phys. Soc. Jpn. 68, 1982 1999CrossRefGoogle Scholar
86Ahuja, R., Rekhi, S.Johansson, B.: Theoretical prediction of a phase transition in gold. Phys. Rev. B 63, 212101 2001CrossRefGoogle Scholar
87Tsuchiya, T.Kawamura, K.: Ab initio study of pressure effect on elastic properties of crystalline Au. J. Chem. Phys. 116, 2121 2002CrossRefGoogle Scholar
88Boettger, J.C.: Theoretical extension of the gold pressure calibration standard beyond 3 Mbars. Phys. Rev. B 67, 174107 2003Google Scholar
89Greeff, C.W.Graf, M.J.: Lattice dynamics and the high-pressure equation of state of Au. Phys. Rev. B 69, 054107 2004CrossRefGoogle Scholar
90Bercegeay, C.Bernard, S.: First-principles equations of state and elastic properties of seven metals. Phys. Rev. B 72, 214101 2005CrossRefGoogle Scholar
91Daniels, W.B.Smith, C.S.: Pressure derivatives of elastic constants of copper, solver, and gold to 10,000 bars. Phys. Rev. 111, 713 1958Google Scholar
92Hiki, Y.Granato, A.V.: Anharmonicity in noble metals: Higher order elastic constants. Phys. Rev. 144, 411 1966Google Scholar
93Golding, B., Moss, S.C.Averbach, B.L.: Composition and pressure dependence of the elastic constants of gold-nickel alloys. Phys. Rev. 158, 637 1967Google Scholar
94Biswas, S.N., Klooster, P. Van’tTrappeniers, N.J.: Effect of pressure on the elastic-constants of noble-metals from −196 °C to +25 °C and up to 2500 bar. 2. Silver and gold. Phys. B+C (Amsterdam) 103, 235 1981Google Scholar
95Heinz, D.L.Jeanloz, R.: The equation of state of the gold calibration standard. J. Appl. Phys. 55, 885 1984Google Scholar
96Dewaele, A., Loubeyre, P.Mezouar, M.: Equations of state of six metals above 94 GPa. Phys. Rev. B 70, 094112 2004Google Scholar
97Neighbours, J.R.Alers, G.A.: Elastic constants of silver and gold. Phys. Rev. 111, 707 1958Google Scholar
98Chang, Y.A.Himmel, L.: Temperature dependence of elastic constants of Cu, Ag and Au above room temperature. J. Appl. Phys. 37, 3567 1966Google Scholar
99Wallace, D.C.: Thermodynamics of Crystals Wiley New York 1972Google Scholar
100Rayne, J.A.Chandrasekhar, B.S.: Elastic constants of beta-tin from 4.2 K to 300 K. Phys. Rev. 120, 1658 1960Google Scholar
101Akdim, B., Papaconstantopoulos, D.A.Mehl, M.J.: Tight-binding description of the electronic structure and total energy of tin. Philos. Mag. B 82, 47 2002Google Scholar
102Dinsdale, A.: SGTE data for pure elements. Calphad 15, 317 1991Google Scholar
103Andersson, J.O., Helander, T., Höglund, L., Shi, P.F.Sundman, B.: Thermo-Calc and DICTRA. Computational tools for materials science. Calphad 26, 273 2002Google Scholar
104Wang, Y., Curtarolo, S., Jiang, C., Arroyave, R., Wang, T., Ceder, G., Chen, L-Q.Liu, Z-K.: Ab initio lattice stability in comparison with CALPHAD lattice stability. Calphad 28, 79 2004Google Scholar
105Hirabayashi, M., Yamaguchi, S., Hiraga, K.Ino, N.: A new type of long period superlattice with hexagonal symmetry in Au–Cd alloys. J. Phys. Chem. Solids 31, 77 1970Google Scholar
106Yamaguchi, S.Hirabayashi, M.: Long period superstructures with hexagonal symmetry in the Cu–Sb alloys near 20 at.% Sb. J. Phys. Soc. Jpn. 33, 708 1972Google Scholar
107Massalski, T.B.King, H.W.: Lattice spacing relationships and the electronic band structure of close-packed α and ζ phases of gold-based alloys. Acta Metall. 8, 684 1960CrossRefGoogle Scholar
108Hume-Rothery, W.Raynor, G.V.: The Structure of Metals and Alloys The Institute of Metals London, UK 1962Google Scholar
109Khmelevska, T., Khmelevskyi, S., Ruban, A.V.Mohn, P.: Magnetism and origin of non-monotonous concentration dependence of the bulk modulus in Fe-rich alloys with Si, Ge and Sn: A first-principles study. J. Phys.: Cond. Matter. 18, 6677 2006Google Scholar