Abstract
This paper reports an analysis of the systematics of cohesive properties and equation-of-state parameters for a large number of stable, metastable and hypothetical binary MeaXb type phases formed by Me = Cu, Ni with X = In, Sn. To this aim, an ab initio database previously developed by the authors using spin polarized density-functional-theory calculations, using the VASP code, is adopted. The work involves the volume (V 0), Wigner–Seitz radius, bulk modulus (B 0) and cohesive energy (E coh) of the phases. At the outset of the paper it is shown that these properties can be studied as functions of the average group number (AGN), i.e., the weighted average of the number of valence electrons involved in the VASP calculations. Moreover, the cohesive energy density (CED), defined as E coh/V 0, is shown to correlate very well with the AGN variable and with B 0. These striking regularities are given two complementary interpretations. First, a general microscopic picture of the variations of cohesion is developed by studying the evolution of the contributions of the d- and p-electrons to their electronic density of states. In this way the effects of the hybridization of d- and p-electrons, and the filling up of bonding and anti-bonding states is highlighted. Next, a thermodynamic analysis based on the classical approach developed by Rose, Ferrante, Smith and collaborators is performed. It is concluded that the correlation involving CED and B 0 is a manifestation of a significant degree of “universality” in the variation of the cohesive properties with the Wigner–Seitz radius of these compounds.
Similar content being viewed by others
References
M. Hillert, The Compound Energy Formalism, J. Alloys Compd., 2001, 320, p 161-176
R. Hiren, P.D. Howes, and S.E. Hamman, A Review: On the Development of Low Melting Temperature Pb-free Solders, Microelectron. Reliab., 2014, 54, p 1253-1273
J.L. Freer and J.W. Morris, Microstructure and Creep of Eutectic Indium/Tin on Copper and Nickel Substrates, J. Electron. Mater., 1992, 21(6), p 647-652
K.N. Tu and K. Zeng, Tin–Lead (SnPb) Solder Reaction in Flip Chip Technology, Mater. Sci. Eng., 2001, R34, p 1-58
T.H. Chuang, C.L. Yu, S.Y. Chang, and S.S. Wang, Phase Identification and Growth Kinetics of the Intermetallic Compounds Formed During In–49Sn/Cu Soldering Reactions, J. Electron. Mater., 2002, 31(6), p 640-645
Dae-Gon Kim and Seung-Boo Jung, Interfacial Reactions and Growth Kinetics for Intermetallic Compound Layer Between In–48Sn Solder and Bare Cu Substrate, J. Alloys Compd., 2005, 386, p 151-156
S. Sommadossi and A. Fernández, Guillermet, Interface Reaction Systematics in the Cu/In–48Sn/Cu System Bonded by Diffusion Soldering, Intermetallics, 2007, 15, p 912-917
C.-Y. Huang and S.-W. Chen, Interfacial Reactions in In–Sn/Ni Couples and Phase Equilibria of the In–Sn–Ni System, J. Electron. Mater., 2002, 31, p 152-160
S.-W. Chen, C.-H. Wang, and S.-K. Lin, Phase Diagrams of Pb-Free Solders and Their Related Materials Systems, Lead-Free Electronic Solders, A Special Issue of the Journal of Materials Science: Materials in Electronics, K.N. Subramanian, Ed., Springer, Berlin, 2006, p 152-160
S. Ramos de Debiaggi, C. Deluque Toro, G.F. Cabeza, and A. Fernández Guillermet, Ab Initio Comparative Study of the Cu–In and Cu–Sn Intermetallic Phases in Cu–In–Sn Alloys, J. Alloys Compd., 2012, 542, p 280-292
S. Ramos de Debiaggi, C. Deluque Toro, G.F. Cabeza, and A. Fernández Guillermet, Ab Initio Study of the Cohesive Properties, Electronic Structure and Thermodynamic Stability of the Ni–In and Ni–Sn Intermetallics, J. Alloys Compd., 2013, 576, p 302-316
S. Ramos de Debiaggi, N.V. González Lemus, C. Deluque Toro, and A. Fernández Guillermet, Ab Initio Study of the Compound-Energy Modeling of Multisublattice Structures: The (hP6) Ni2In-Type Intermetallics of the Ni–In–Sn System, J. Alloys Compd., 2015, 619, p 464-473
S. Ramos de Debiaggi, N.V. González Lemus, G.F. Cabeza, and A. Fernández Guillermet, Cohesive Properties of (Cu, Ni)–(In, Sn) Intermetallics: Database, Electron–Density Correlations and Interpretation of Bonding Trends, J. Phys. Chem. Solids, 2016, 93, p 40-51
A. Fernández Guillermet and G. Grimvall, Cohesive Properties and Vibrational Entropy of 3d-Transition Metal Compounds: MX (NaCl) Compounds (X = C, N, O, S), Complex Carbides and Nitrides, Phys. Rev. B, 1989, 40, p 10582-10593
A. Fernández Guillermet and G. Grimvall, Bonding Properties and Vibrational Entropy of Transition Metal MeB2 (AlB2) Diborides, J. Less Common Met., 1991, 169, p 257-281
J. Häglund, G. Grimvall, T. Jarlborg, and A. Fernández Guillermet, Band Structure and Cohesive Properties of 3d-Transition-Metal Carbides and Nitrides with the NaCl-Type Structure, Phys. Rev. B, 1991, 43, p 14400-14408
A. Fernández Guillermet and G. Grimvall, Cohesive Properties and Vibrational Entropy of 3d-Transition Metal Carbides, J. Phys. Chem. Solids, 1992, 53, p 105-125
A. Fernández Guillermet, J. Häglund, and G. Grimvall, Cohesive Properties of 4d-Transition Metal Carbides and Nitrides with the NaCl-Type Structure, Phys. Rev. B, 1992, 45, p 11557-11567
A. Fernández Guillermet, J. Häglund, and G. Grimvall, Cohesive Properties and Electronic Structure of 5d-Transition Metal Carbides and Nitrides with the NaCl-Type Structure, Phys. Rev. B, 1993, 48, p 11673-11684
J. Häglund, A. Fernández Guillermet, G. Grimvall, and M. Körling, Theory of Bonding in Transition Metal Carbides and Nitrides, Phys. Rev. B, 1993, 48, p 11685-11691
K.A. Gschneidner, Physical Properties and Interrelationships of Metallic and Semimetallic Elements, Solid State Phys., 1964, 16, p 275-426
S. Wacke, T. Górecki, Cz Górecki, and K. Książek, Relations Between the Cohesive Energy, Atomic Volume, Bulk Modulus and Sound Velocity in Metals, J. Phys. Conf. Ser., 2011, 289(1), p 012020
J.H. Rose, J.R. Smith, F. Guinea, and J. Ferrante, Universal Features of the Equation of State of Metals, Phys. Rev. B, 1984, 29(6), p 2963-2969
P. Vinet, J.R. Smith, J. Ferrante, and J.H. Rose, Temperature Effects on the Universal Equation of State of Solids, Phys. Rev. B, 1987, 35(4), p 1945-1953
C.D. Gelatt, A.R. Williams, and V.L. Moruzzi, Theory of Bonding of Transition Metals–Nontransition Metals, Phys. Rev. B, 1983, 27(4), p 2005-2013
R.E. Watson and L.H. Bennett, Optimized Prediction for Heats of Formation of Transition Metal Alloys, Calphad, 1981, 5(1), p 25-40
C. Colinet, A. Pasturel, and P. Hicter, Trends in Cohesive Energy of Transition Metal Alloys, Calphad, 1985, 9(1), p 71-99
C. Colinet and A. Pasturel, Trends in Cohesive Energy Transition Rare-Earth Metal Alloys, Calphad, 1987, 11(4), p 335-348
R.E. Watson, M. Weinert, J.W. Davenport, and G.W. Fernando, The Energetics of Transition Metal Alloy Formation: Theory Versus Experiment, Scr. Metall., 1988, 22, p 1285-1289
J. Friedel, Transitions Metals, Electronic Structure of the d-Band. Its Role in the Crystalline and Magnetic Structures, The Physics of Metals-1 Electrons, J.M. Ziman, Ed., Cambridge University Press, Cambridge, 1969, p 340-403
J.C. Fuggle, F.U. Hillebrecht, R. Zeller, Z. Zolnierek, and P.A. Bennett, Electronic Structure of Ni and Pd Alloys. I. X-Ray Photoelectron Spectroscopy of the Valence Bands, Phys. Rev. B, 1982, 27(4), p 2145-2178
P.E. Blöchl, Projector Augmented-Wave Method, Phys. Rev. B, 1994, B50, p 17953-17979
G. Kresse and J. Joubert, From Ultrasoft Pseudopotentials to the Projector Augmented-Wave Method, Phys. Rev. B, 1999, B59, p 1758-1775
G. Kresse and J. Furthmüller, Efficiency of Ab-Initio Total Energy Calculations for Metals and Semiconductors Using a Plane-Wave Basis Set, Comput. Mater. Sci., 1996, 6, p 15-50
J.P. Perdew and Y. Wang, Accurate and Simple Analytic Representation of the Electron–Gas Correlation Energy, Phys. Rev. B, 1992, 45(23), p 13244-13249
H.J. Monkhorst and J.D. Pack, Special Points for Brillouin-Zones Integrations, Phys. Rev. B, 1976, 13, p 5188-5192
M. Methfessel and A.T. Paxton, High-Precision Sampling for Brillouin-Zone Integration in Metals, Phys. Rev. B, 1986, 40, p 3616-3621
G. Ghosh, Elastic Properties, Hardness, and Indentation Fracture Toughness of Intermetallics Relevant to Electronic Packaging, J. Mater. Res., 2004, 19, p 1439-1454
A.S. Mikhaylushkin, T. Sato, S. Carlson, S.I. Simak, and U. Häussermann, High-Pressure Structural Behavior of Large-Void CoSn-type Intermetallics: Experiments and First-Principles Calculations, Phys. Rev. B, 2008, 77, p 014102(8)
D.S. Bertoldi, S.B. Ramos, and A. Fernández Guillermet, Interrelations Between EOS Parameters and Cohesive Energy of Transition Metals: Thermostatistical Approach, Ab Initio Calculations and Analysis of “Universality” Features, J. Phys. Chem. Sol., 2016 (under review)
J.A. Garcés and A. Fernández Guillermet, Equation of State Parameters for Stable and Non-stable Transition Metal Phases from Universal Binding Energy Relation, Calphad, 1998, 22, p 469-493
Acknowledgments
This work was supported by Project PIP 112-20110100814 from CONICET and Project I197 from Universidad Nacional del Comahue.
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
Cite this article
Bertoldi, D.S., Ramos, S.B., González Lemus, N.V. et al. Cohesive Properties of Cu-X and Ni-X (In, Sn) Intermetallics: Ab Initio Systematics, Correlations and “Universality” Features. J. Phase Equilib. Diffus. 38, 257–267 (2017). https://doi.org/10.1007/s11669-017-0536-9
Received:
Revised:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s11669-017-0536-9