On the Bi–Ni system. Ab initio calculations and thermodynamic remodeling
Introduction
The phase diagrams play important role in materials science and engineering as “road maps” for technological processes. The crucial information, such as phase equilibria, phase stability, or phase transformation can be read from equilibrium diagrams [1]. The traditional phase diagram determination involves a quite big number of experiments, which are cost and time consuming. Nowadays phase diagrams are calculated from so-called thermodynamic databases that include Gibbs energies of all phases involved in a given system. Therefore, it is obvious that a correct description of binary systems is crucial for further modeling of multi-components ones.
The binary Bi–Ni system is important for lead-free soldering technology. Nickel is often used as an under-bump metallurgy (UBM) layer on a substrate before soldering in microelectronic packages [2]. On other hand, bismuth is a common part of lead-free solders, such as Bi–Cu – Sn, Bi–Sn, or Ag–Bi – Sn [3]. Consequently, a knowledge on thermodynamic equilibrium between these systems and Ni substrate seems to be essential for understanding and steering soldering processes. As it was mentioned before, to model a multi-component system, the thermodynamic description of constituent binary systems is necessary, so it is obvious that thermodynamic description of binary Bi–Ni system is required for discussion on reaction between solder containing Bi and Ni substrate. A newly published information on mixing enthalpy of liquid Bi–Ni alloys [4] allows to determine a new set of optimized thermodynamic parameters. Moreover, application of ab-initio calculation adds supporting thermodynamic information allowing for more precise modeling.
Section snippets
Literature review
The binary Bi–Ni phase diagram includes five phases: liquid, Rhombohedral_A7 (Bi), Bi3Ni, BiNi, and FCC_A1 (Ni) as well as two peritectic reactions: (Ni)+L = BiNi and BiNi + L=Bi3Ni and one eutectic reaction: Bi3Ni+(Bi) = L.
The liquidus line and the transition temperatures was for the first time determined by Portevin [5] and Voss [6] by the differential thermal analysis (DTA). The data of liquidus presented by both authors match each other except the alloy of Ni composition equal 0.5 mol
Ab-initio calculations
The stabilities of BiNi and Bi3Ni were calculated by aid of the ab-initio method within the Density Functional Theory (DFT) that was implemented in Quantum Espresso package [21,22]. The calculation was used General Gradient Approximation (GGA) pseudopotential functional parametrized by Padrew, Burke, and Emzerhof revised for solids (PBEsol) approach [23]. For all the calculation the cut-off energy and the k-point distance were set to 50 eV and 0.15 1/Å, respectively. Before performing the final
Thermodynamic modeling
The thermodynamic model includes 5 phases: liquid, liquid, Rhombohedral_A7 (Bi), Bi3Ni, BiNi, and FCC_A1 (Ni).
The Gibbs free energies of pure elements with respect to temperature are as follows:
are represented by Eq. (2)
The data are referred to the constant enthalpy value of the standard element reference at 298.15 K and 1 bar as recommended by Scientific Group Thermodata Europe (SGTE) [26]. The reference states are:
Results and discussion
The first principle calculation results gave formation energies of BiNi as well as Bi3Ni phase. The obtained results were −0.03839 and −0.05231 eV/atom for BiNi and Bi3Ni, respectively. The obtained values formation energies are displayed in Fig. 1 and Table 2 together with formations energies of the same intermetallic compounds provided by ab-inito on-line databases: Materials Project, OQMD [28], and AFLOW [29]. The results provided in online databases were obtained by using VASP [30] code and
Summary
Combination of ab-initio calculation and CALPHAD approach was used for preparation of the thermodynamic database of binary Bi–Ni system that is important for lead-free soldering technology. A good agreement between calculation and experiment was found and the proposed thermodynamic description can be applied as a part of thermodynamic database of multi-component system.
Declaration of competing interest
The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.
Acknowledgment
The work was supported by Ministry of Science and Education (Taiwan) under a grant 107-2221-E-259 -011.
This research was supported in part by PLGrid Infrastructure.
Two of the authors (J.L. and V.L.) are thankful for a financial support provided by Taiwan government under TEEP Asia-Plus action.
The raw data required to reproduce these findings are available to download from.
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