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

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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.

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References

  1. M. Abtew G. Selvaduray: Lead-free solders in microelectronic. Mater. Sci. Eng., R 27, 95 2000

    Article  Google Scholar 

  2. K.N. Tu K. Zeng: Tin–lead (SnPb) solder reaction in flip chip technology. Mater. Sci. Eng., R 34, 1 2001

    Article  Google Scholar 

  3. K. Zeng K.N. Tu: Six cases of reliability study of Pb-free solder joints in electronic packaging technology. Mater. Sci. Eng., R 38, 55 2002

    Article  Google Scholar 

  4. K.N. Tu, A.M. Gusak M. Li: Physics and materials challenges for lead-free solders. J. Appl. Phys. 93, 1335 2003

    Article  CAS  Google Scholar 

  5. T. Laurila, V. Vuorinen J.K. Kivilahti: Interfacial reactions between lead-free solders and common base materials. Mater. Sci. Eng., R 49, 1 2005

    Article  CAS  Google Scholar 

  6. M.B. McNeil: The properties of the intermetallic phases in the system Au-Sn. J. Electrochem. Soc. 110, 1169 1963

    Article  CAS  Google Scholar 

  7. F.G. Yost, M.M. Karnowsky, W.D. Drotning J.H. Gieske: Thermal expansion and elastic properties of high gold–tin alloys. Metall. Trans. A 21, 1885 1990

    Article  Google Scholar 

  8. N. Jiang, J.A. Clum, R.R. Chromik E.J. Cotts: Thermal expansion of several Sn-based intermetallic compounds. Scripta Mater. 37, 1851 1997

    Article  CAS  Google Scholar 

  9. R.R. Chromik, R.P. Vinci, S.L. Allen M.R. Notis: Nanoindentation measurements on Cu–Sn and Ag–Sn intermetallics formed in Pb-free solder joints. J. Mater. Res. 18, 2251 2003

    Article  CAS  Google Scholar 

  10. J.P. Lucas, H. Rhee, F. Guo K.N. Subramanian: Mechanical properties of intermetallic compounds associated with Pb-free solder joints using nanoindentation. J. Electron. Mater. 32, 1375 2003

    Article  CAS  Google Scholar 

  11. X. Deng, N. Chawla, K.K. Chawla M. Koopman: Deformation behavior of (Cu, Ag)–Sn intermetallics by nanoindentation. Acta Mater. 52, 4291 2004

    Article  CAS  Google Scholar 

  12. G. Ghosh: Elastic properties, hardness, and indentation fracture toughness of intermetallics relevant to electronic packaging. J. Mater. Res. 19, 1439 2004

    Article  CAS  Google Scholar 

  13. G-Y. Jang, J-W. Lee J-G. Duh: The nanoindentation characteristics of Cu6Sn5, Cu3Sn, and Ni3Sn4 intermetallic compounds in the solder bump. J. Electron. Mater. 33, 1103 2004

    Article  CAS  Google Scholar 

  14. S. Pitely, L. Zavalij, S. Zarembo E.J. Cotts: Linear coefficients of thermal expansion of Au0.5Ni0.5Sn4, Au0.75Ni0.25Sn4, and AuSn4. Scripta Mater. 51, 745 2004

    Article  CAS  Google Scholar 

  15. R.R. Chromik, D.N. Wang, A. Shugar, L. Limata, M.R. Notis R.P. Vinci: Mechanical properties of intermetallic compounds in the Au-Sn system. J. Mater. Res. 20, 2161 2004

    Article  CAS  Google Scholar 

  16. Z. Chen, M. He, B. Balakrisnan C.C. Chum: Elasticity modulus, hardness and fracture toughness of Ni3Sn4 intermetallic thin films. Mater. Sci. Eng., A 423, 107 2006

    Article  CAS  Google Scholar 

  17. I. Tsai, E. Wu, S.F. Yen T.H. Chuang: Mechanical properties of intermetallic compounds on lead-free solder by Moiré techniques. J. Electron. Mater. 35, 1059 2006

    Article  CAS  Google Scholar 

  18. G. Ghosh M. Asta: Phase stability, phase transformations, and elastic properties of Cu6Sn5: Ab initio calculations and experimental results. J. Mater. Res. 20, 3102 2005

    Article  CAS  Google Scholar 

  19. N.T.S. Lee, V.B.C. Tan K.M. Lim: First-principles calculations of structural and mechanical properties of Cu6Sn5. Appl. Phys. Lett. 88, 031913 2006

    Article  CAS  Google Scholar 

  20. N.T.S. Lee, V.B.C. Tan K.M. Lim: Structural and mechanical properties of Sn-based intermetallics from ab initio calculations. Appl. Phys. Lett. 88, 141908 2006

    Article  CAS  Google Scholar 

  21. G.S. Matijasevic, C.C. Lee C.Y. Wang: Controlling the microstructures from the gold–tin reaction. Thin Solid Films 223, 276 1993

    Article  CAS  Google Scholar 

  22. J.Y. Tsai, C.W. Chang, Y.C. Shieh, Y.C. Hu C.R. Kao: Controlling the microstructures from the gold–tin reaction. J. Electron. Mater. 34, 182 2005

    Article  CAS  Google Scholar 

  23. H. Okamoto T.B. Massalski: The Au–Sn (Gold–Tin). Bull. Alloy Phase Diagrams 5, 492 1984

    Article  Google Scholar 

  24. H. Okamoto: Au–Sn (Gold–Tin). J. Phase Equilib. 14, 765 1993

    Article  Google Scholar 

  25. B. Sundman J. Ågren: A regular solution model for phases with several components and sub-lattices, suitable for computer-applications. J. Phys. Chem. Solids 42, 297 1981

    Article  CAS  Google Scholar 

  26. K. Schubert, H. Breimer R. Gohle: The structures of the systems gold–indium, gold–tin, gold–indium–tin and gold–tin–antimony. Z. Metallkd. 50, 146 1959

    CAS  Google Scholar 

  27. J. Ciulik M.R. Notis: The Au–Sn phase diagram. J. Alloys Compd. 191, 71 1993

    Article  CAS  Google Scholar 

  28. D.C. Hamilton, Ch.J. Raub, B.T. Matthias, E. Corenzwit, G.W. Hull Jr.: Some new superconducting compounds. J. Phys. Chem. Solids 26, 665 1965

    Article  CAS  Google Scholar 

  29. K. Osada, S. Yamaguchi M. Hirabayashi: An ordered structure of Au5Sn. Trans. Jpn. Inst. Met. 15, 256 1974

    Article  CAS  Google Scholar 

  30. R. Vogel: Gold-tin alloys. Z. Anorg. Chem. 46, 60 1905

    Article  Google Scholar 

  31. N.A. Puschin: Potential and nature of metallic alloys. Zh. Fiz. Khim. 39, 353 1906

    Google Scholar 

  32. G.D. Preston E.A. Owen: The atomic structure of AuSn. Philos. Mag. 4, 133 1927

    Article  CAS  Google Scholar 

  33. S. Steibeck A. Westgren: X-ray analysis of gold–tin alloys. Z. Phys. Chem. B14, 91 1931

    Google Scholar 

  34. F.M. Jaeger J.A. Bottema: Exact determination of specific heats at high temperature. Recl. Trav. Chim. Pays-Bas 52, 89 1933

    Article  CAS  Google Scholar 

  35. J-P. Jan, W.B. Pearson, A. Kjekshus S.B. Woods: On the structural, thermal, electrical, and magnetic properties of AuSn. Can. J. Phys. 41, 2252 1963

    Article  CAS  Google Scholar 

  36. J.S. Charlton, M. Cordey-Hayes I.R. Harris: A study of the 119Sn Mössbauer isomer shifts in some platinum–tin and gold–tin alloys. J. Less-Common Met. 20, 105 1970

    Article  CAS  Google Scholar 

  37. V. Psarev, V.G. Kirly, A.V. Kuznetsov, I.V. Psareva A.L. Ivanova: Investigation of the crystallization of alloys in systems containing peritectic transformations. Russ. Met. 2, 175 1982

    Google Scholar 

  38. K. Schubert, U. Rössler, M. Kluga, K. Anderko L. Harle: Crystallographic results on phases with penetration bands. Naturwissenschaften 40, 437 1953

    Google Scholar 

  39. K. Schubert, H. Breimer, R. Gohle, H.L. Lukas, H.G. Meissner E. Stolz: Some structural results on metallic phases. Naturwissenschaften 45, 360 1958

    Article  CAS  Google Scholar 

  40. U.C. Rodewald, R.D. Hoffmann, Z.Y. Wu R. Pöttgen: Structure refinement of AuSn2. Z. Naturforsch. [B] 61, 108 2006

    Article  CAS  Google Scholar 

  41. G. Tammann H.J. Rocha: The diffusion of two metals into one another with formation of intermetallic compounds. Z. Anorg. Chem. 199, 289 1931

    Article  CAS  Google Scholar 

  42. K. Schubert U. Rösler: The structure of PtSn4. Z. Metallkd. 41, 298 1950

    CAS  Google Scholar 

  43. K. Schubert U. Rösler: The structure of PtSn4. Z. Naturforsch. 5, 127 1950

    Article  Google Scholar 

  44. R. Kubiak: The influence of temperature on the crystal structure of AuSn4. J. Less-Common Met. 80, P53 1981

    Article  CAS  Google Scholar 

  45. R. Kubiak M. Wolcyrz: Refinement of the crystal structures of AuSn4 and PdSn4. J. Less-Common Met. 97, 265 1984

    Article  CAS  Google Scholar 

  46. R. Kubiak M. Wolcyrz: X-ray investigations of crystallization and thermal expansion of AuSn4, PdSn4 and PtSn4. J. Less-Common Met. 109, 339 1985

    Article  CAS  Google Scholar 

  47. R.H. Kane, B.C. Giessen N.J. Grant: New metastable phases in binary tin systems. Acta Metall. 14, 605 1966

    Article  CAS  Google Scholar 

  48. B.C. Giessen: A metastable γ-brass phase in the gold–tin system and a note on non-equilibrium Hume–Rothery phases. Z. Metallkd. 59, 805 1968

    CAS  Google Scholar 

  49. D.C. Dufner L. Eyring: High-resolution electron microscopy and x-ray microanalysis of chemical reactions in the gold–tin thin-film system. J. Solid State Chem. 62, 112 1986

    Article  CAS  Google Scholar 

  50. K.N. Ishihara, H. Gohchi P.H. Shingu: 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 49–57

    Google Scholar 

  51. P.A. Midgley, M.E. Sleight R. Vincent: The structure of a metastable Au–Sn phase determined by convergent beam electron diffraction. J. Solid State Chem. 124, 132 1996

    Article  CAS  Google Scholar 

  52. P. Villars L.D. Calvert Pearson’s Handbook of Crystallographic Data for Intermetallic Phases, Vol. 1, ASM International Materials Park, OH 1991 1339

    Google Scholar 

  53. W. Biltz, G. Rohlffs H.U. von Vogel: Systematic doctrine of affinity. LXI - Construction and use of a high-temperature calorimeter with a closed reaction chamber. Z. Anorg. Allgem. Chem. 220, 113 1934

    Article  CAS  Google Scholar 

  54. O.J. Kleppa: Heats of formation of some solid and liquid binary alloys of gold with cadmium, indium, tin and antimony. J. Phys. Chem. 60, 858 1956

    Article  CAS  Google Scholar 

  55. S. Misra, B.W. Howlett M.B. Bever: On the thermodynamic properties of the intermediate phases in the system Au–Sn. Trans. AIME 233, 749 1965

    CAS  Google Scholar 

  56. A.K. Jena M.B. Bever: On the thermodynamic properties of the phases zeta and AuSn in the system Au–Sn. Metall. Trans. B 10, 545 1979

    Article  Google Scholar 

  57. R. Hultgren, P. Desai, P. Hawkins, M. Gleiser K.K. Kelley: Selected Values of the Thermodynamic Properties of Binary Alloys ASM International Materials Park, OH 1973 320–328

    Google Scholar 

  58. P-Y. Chevalier: A thermodynamic evaluation of the Au–Sn system. Thermochim. Acta 130, 1 1988

    Article  CAS  Google Scholar 

  59. H.S. Liu, C.L. Liu, K. Ishida Z.P. Jin: Thermodynamic modeling of the Au–In–Sn system. J. Electron. Mater. 32, 1290 2003

    Article  CAS  Google Scholar 

  60. V. Grolier R. Schmid-Fetzer: Thermodynamic evaluation of the Au–Sn system. Int. J. Mater. Res. 98, 797 2007

    Article  CAS  Google Scholar 

  61. G. Kresse J. Hafner: Ab-initio molecular-dynamics simulation of the liquid-metal amorphous-semiconductor transition in germanium. Phys. Rev. B 49, 4251 1994

    Article  Google Scholar 

  62. G. Kresse J. Furthmüller: Efficient iterative schemes of ab initio total-energy calculations using a plane-wave basis set. Phys. Rev. B 54, 11169 1996

    Article  CAS  Google Scholar 

  63. G. Kresse J. Furthmüller: Efficiency of ab-initio total energy calculations for metals and semi-conductors using a plane-wave basis set. Comput. Mater. Sci. 6, 15 1996

    Article  CAS  Google Scholar 

  64. D. Vanderbilt: Soft self-consistent pseudo potential in a generalized eigenvalue formalism. Phys. Rev. B 41, 7892 1990

    Article  CAS  Google Scholar 

  65. G. Kresse J. Hafner: Norm-conserving and ultrasoft pseudopotentials for first-row and transition-elements. J. Phys. Condens. Matter 6, 8245 1994

    Article  CAS  Google Scholar 

  66. D.M. Ceperley B.J. Alder: Ground-state of the electron-gas by a stochastic method. Phys. Rev. Lett. 45, 566 1980

    Article  CAS  Google Scholar 

  67. J.P. Perdew A. Zunger: Self-interaction correction to density functional approximation for many-electron systems. Phys. Rev. B 23, 5048 1981

    Article  CAS  Google Scholar 

  68. J.P. Perdew Y. Wang: Accurate and simple analytic representation of the electron-gas correlation-energy. Phys. Rev. B 45, 13244 1992

    Article  CAS  Google Scholar 

  69. H.J. Monkhorst J.D. Pack: Special points for Brillouin-zone integrations. Phys. Rev. B 13, 5188 1976

    Article  Google Scholar 

  70. M. Methfessel A.T. Paxton: High-precision sampling for Brillouin-zone integration in metals. Phys. Rev. B 40, 3616 1989

    Article  CAS  Google Scholar 

  71. P. Vinet, J.H. Rose, J. Ferrante J.R. Smith: Universal feature of the equation of state solids. J. Phys. Condens. Matter 1, 1941 1989

    Article  CAS  Google Scholar 

  72. N.W. Ashcroft N.D. Mermin: Solid State Physics Reinhart and Winston New York 1976

    Google Scholar 

  73. M.J. Mehl, B.M. Klein K. Papaconstatopolous: Intermetallic Compounds, Principles and Practice Vol. 1 edited by J.H. Westbrook and R.L. Fleischer John Wiley & Sons New York 1994 195

    Google Scholar 

  74. P. Ravindran, L. Fast, P.A. Korzhavyi, B. Johansson, J. Wills O. Eriksson: Density-functional theory for calculation of elastic properties of orthorhombic crystals: Application to TiSn2. J. Appl. Phys. 84, 4891 1998

    Article  CAS  Google Scholar 

  75. M. Mattesini S.F. Matar: Density-functional theory for the calculation of elastic properties of nanostructured superhard TiN/Si to TiSn2. Phys. Rev. B 65, 075110 2002

    Article  CAS  Google Scholar 

  76. S. Wang, R. Gudipati, A.S. Rao, T.J. Bostelmann Y.G. Shen: First-principles calculations for the elastic properties of nanostructured superhard TiN/SixNy superlattices. Appl. Phys. Lett. 91, 081916 2007

    Article  CAS  Google Scholar 

  77. T.B. Massalski, editor Binary Alloy Phase Diagrams, Vol. 1, ASM International Materials Park, OH 1990 350–351, 381–383

    Google Scholar 

  78. L. Kaufman H. Bernstein: Computer Calculation of Phase Diagram Academic Press Inc. New York 1970

    Google Scholar 

  79. H.L. Lukas, S.G. Fries B. Sundman: Computational Thermodynamics. The Calphad Method Cambridge University Press Cambridge, UK 2007

    Book  Google Scholar 

  80. M.E. Straumanis: Redetermination of lattice parameters, densities and thermal expansion coefficients of silver and gold, and the perfection of their structures. Monatsh. Chem. 102, 1377 1971

    Article  CAS  Google Scholar 

  81. B.K. Godwal R. Jeanloz: First-principles equation of state of gold. Phys. Rev. B 40, 7501 1989

    Article  CAS  Google Scholar 

  82. A. Khein, D.J. Singh C.J. Umrigar: All-electron study of gradient corrections to the local-density functional in metallic systems. Phys. Rev. B 51, 4105 1995

    Article  CAS  Google Scholar 

  83. T. Korhonen, M.J. Puska R.M. Nieminen: Vacancy-formation energies for fcc and bcc transition-metals. Phys. Rev. B 51, 9526 1995

    Article  CAS  Google Scholar 

  84. M.J. Mehl D.A. Papaconstantopoulos: 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 1996

    Article  CAS  Google Scholar 

  85. S. Suzuki K. Nakao: A fully relativistic full-potential LCAO method for solids. J. Phys. Soc. Jpn. 68, 1982 1999

    Article  CAS  Google Scholar 

  86. R. Ahuja, S. Rekhi B. Johansson: Theoretical prediction of a phase transition in gold. Phys. Rev. B 63, 212101 2001

    Article  CAS  Google Scholar 

  87. T. Tsuchiya K. Kawamura: Ab initio study of pressure effect on elastic properties of crystalline Au. J. Chem. Phys. 116, 2121 2002

    Article  CAS  Google Scholar 

  88. J.C. Boettger: Theoretical extension of the gold pressure calibration standard beyond 3 Mbars. Phys. Rev. B 67, 174107 2003

    Article  CAS  Google Scholar 

  89. C.W. Greeff M.J. Graf: Lattice dynamics and the high-pressure equation of state of Au. Phys. Rev. B 69, 054107 2004

    Article  CAS  Google Scholar 

  90. C. Bercegeay S. Bernard: First-principles equations of state and elastic properties of seven metals. Phys. Rev. B 72, 214101 2005

    Article  CAS  Google Scholar 

  91. W.B. Daniels C.S. Smith: Pressure derivatives of elastic constants of copper, solver, and gold to 10,000 bars. Phys. Rev. 111, 713 1958

    Article  CAS  Google Scholar 

  92. Y. Hiki A.V. Granato: Anharmonicity in noble metals: Higher order elastic constants. Phys. Rev. 144, 411 1966

    Article  CAS  Google Scholar 

  93. B. Golding, S.C. Moss B.L. Averbach: Composition and pressure dependence of the elastic constants of gold-nickel alloys. Phys. Rev. 158, 637 1967

    Article  CAS  Google Scholar 

  94. S.N. Biswas, P. Van’t Klooster N.J. Trappeniers: 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 1981

    Article  CAS  Google Scholar 

  95. D.L. Heinz R. Jeanloz: The equation of state of the gold calibration standard. J. Appl. Phys. 55, 885 1984

    Article  CAS  Google Scholar 

  96. A. Dewaele, P. Loubeyre M. Mezouar: Equations of state of six metals above 94 GPa. Phys. Rev. B 70, 094112 2004

    Article  CAS  Google Scholar 

  97. J.R. Neighbours G.A. Alers: Elastic constants of silver and gold. Phys. Rev. 111, 707 1958

    Article  CAS  Google Scholar 

  98. Y.A. Chang L. Himmel: Temperature dependence of elastic constants of Cu, Ag and Au above room temperature. J. Appl. Phys. 37, 3567 1966

    Article  CAS  Google Scholar 

  99. D.C. Wallace: Thermodynamics of Crystals Wiley New York 1972

    Book  Google Scholar 

  100. J.A. Rayne B.S. Chandrasekhar: Elastic constants of beta-tin from 4.2 K to 300 K. Phys. Rev. 120, 1658 1960

    Article  CAS  Google Scholar 

  101. B. Akdim, D.A. Papaconstantopoulos M.J. Mehl: Tight-binding description of the electronic structure and total energy of tin. Philos. Mag. B 82, 47 2002

    Article  CAS  Google Scholar 

  102. A. Dinsdale: SGTE data for pure elements. Calphad 15, 317 1991

    Article  CAS  Google Scholar 

  103. J.O. Andersson, T. Helander, L. Höglund, P.F. Shi B. Sundman: Thermo-Calc and DICTRA. Computational tools for materials science. Calphad 26, 273 2002

    Article  CAS  Google Scholar 

  104. Y. Wang, S. Curtarolo, C. Jiang, R. Arroyave, T. Wang, G. Ceder, L-Q. Chen Z-K. Liu: Ab initio lattice stability in comparison with CALPHAD lattice stability. Calphad 28, 79 2004

    Article  CAS  Google Scholar 

  105. M. Hirabayashi, S. Yamaguchi, K. Hiraga N. Ino: A new type of long period superlattice with hexagonal symmetry in Au–Cd alloys. J. Phys. Chem. Solids 31, 77 1970

    Article  CAS  Google Scholar 

  106. S. Yamaguchi M. Hirabayashi: Long period superstructures with hexagonal symmetry in the Cu–Sb alloys near 20 at.% Sb. J. Phys. Soc. Jpn. 33, 708 1972

    Article  CAS  Google Scholar 

  107. T.B. Massalski H.W. King: Lattice spacing relationships and the electronic band structure of close-packed α and ζ phases of gold-based alloys. Acta Metall. 8, 684 1960

    Article  CAS  Google Scholar 

  108. W. Hume-Rothery G.V. Raynor: The Structure of Metals and Alloys The Institute of Metals London, UK 1962

    Google Scholar 

  109. T. Khmelevska, S. Khmelevskyi, A.V. Ruban P. Mohn: 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 2006

    CAS  Google Scholar 

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Acknowledgments

This research was supported by the Semiconductor Research Corporation (Contract No. 2006-KJ-1393). In addition, this material is based on work supported by the National Science Foundation under the following NSF programs: Partnerships for Advanced Computational Infrastructure, Distributed Terascale Facility (DTF), and Terascale Extensions: Enhancements to the Extensible Terascale Facility. Specific to the NSF programs, this study utilizes Itanium clusters as a part of TeraGrid sites at the University of Illinois at Urbana-Champaign and at San Diego Supercomputing Center.

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    G. Ghosh

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Ghosh, G. Phase stability and cohesive properties of Au–Sn intermetallics: A first-principles study. Journal of Materials Research 23, 1398–1416 (2008). https://doi.org/10.1557/JMR.2008.0175

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