Ab initio comparative study of the Cu–In and Cu–Sn intermetallic phases in Cu–In–Sn alloys

Abstract

The present paper reports a comparative account of the structural, cohesive and thermodynamic stability properties of the binary intermetallic phases (IPs) occurring in the Cu–In and the Cu–Sn phase diagrams, both at low and at high temperatures, based upon systematic density-functional-theory (DFT) calculations. Using the projector augmented wave method and the exchange and correlation functions of Perdew and Wang in the generalized gradient approximation (GGA), as well as the local-density-approximation (LDA) with the Ceperley and Alder exchange and correlation potentials, we determine the lattice-parameters, molar volume, bulk modulus and its pressure derivative, the electronic density of states (DOS) and the energy of formation (EOF) from the elements of the δ-Cu7In3 (aP40), γ-Cu9In4 (cP52) and CuIn2 (tI12) compounds of the Cu–In system. Moreover, DFT–GGA calculations were performed for the compounds: γ-Cu4Sn (cF16), ξ-Cu10Sn3 (hP26), ε-Cu3Sn both in the (oP8) structure and the (oP80) superstructure, η′-Cu6Sn5 (mC44) and η-Cu5Sn4 both in the η1 (mP36) and η2 (mC54) structural forms. In addition, the hypothetical structures obtained by replacing In (or Sn) by Sn (or In) are studied, because of their relevance in the CALPHAD modeling of the Cu–In–Sn phase diagram. The work includes a discussion of the composition dependence of the structural and equation-of-state parameters, the electronic DOS, the EOF of the compounds and the differences between the results of the GGA or LDA calculations and the measured values. Besides, various quantities expressing the relative stability of the IPs are introduced and compared with experimental data and with indirect information obtained in a CALPHAD-type two-sublattice modeling of the Cu–In-Sn phase diagram.