TCHEA1: A Thermodynamic Database Not Limited for “High Entropy” Alloys

J. Phase Equilib. Diffus. (2017) 38:353–368 DOI 10.1007/s11669-017-0570-7 TCHEA1: A Thermodynamic Database Not Limited for ‘‘High Entropy’’ Alloys Huahai Mao1,2 • Hai-Lin Chen2 • Qing Chen2 Submitted: 24 April 2017 / in revised form: 1 June 2017 / Published online: 5 July 2017  The Author(s) 2017. This article is an open access publication Abstract In this paper we report a thermodynamic database which was developed by using the CALPHAD approach. The TCHEA1 database includes 15 chemical elements (Al, Co, Cr, Cu, Fe, Hf, Mn, Mo, Nb, Ni, Ta, Ti, V, W and Zr). It is suitable for the study of Bcc and Fcc HEA systems. The database is constructed based on the thermodynamic assessment of all binary systems and many key ternary systems where almost all possible metastable and stable phases are considered. It is extensively demonstrated in the present work that TCHEA1 gives satisfactory prediction on the phase equilibria in various HEA systems (quaternary to ennead) and wide temperature ranges (liquidus to subsolidus). Thermodynamic stability calculations of simple solid solutions (Bcc and Fcc) and intermetallics (sigma, Laves, l-phase etc.) are validated against the available experimental information in as-cast or as-annealed state. Such CALPHAD database focusing on the modelling of Gibbs energy rather than entropy makes reliable predictions of thermodynamic equilibrium and phase transformation, no matter whether the alloy/system has high entropy or not. Cases with miscibility gap in liquid and solid solutions and second-order phase transition at low temperatures are demonstrated. With the volume data included, TCHEA1 is capable to predict the density and thermal expansion coefficient of HEAs as well. This thermodynamic database is also & Huahai Mao 1 Materials Science and Engineering, KTH Royal Institute of Technology, Brinellvägen 23, 10044 Stockholm, Sweden 2 Thermo-Calc Software AB, Råsundavägen 18A, 16967 Solna, Sweden applicable in process simulations when used together with compatible kinetic databases. Keywords CALPHAD  computational thermodynamics  high-entropy alloys  phase diagram  solid solution 1 Introduction High entropy alloys (HEAs) have gained ever-increasing attention from academia and industries since the concept was firstly proposed in 2004.[1,2] The concept of HEA opens new areas in materials science and engineering. It stimulates the exploration of new alloy systems from the traditional small corner composition regions to the vast uncharted central fields in the multi-dimensional composition space. This paradigm shift provides us unlimited opportunities to design and develop new materials through various combinations of chemical elements. As the number of possible combinations is immense, even a small fraction of it is still unbelievably large. This tremendous potential has driven an explosive increase of interest in HEAs in recent years as reviewed in the recent publications.[3–5] Obviously the exploration of new HEAs in the multi-dimensional composition space cannot rely on Edisonian approach. It requires a more efficient and systematical strategy. To meet the challenges, computational methods are indispensable. Different computational approaches, ranging from empirical rules[6,7] to semi-empirical CALPHAD method,[8–12] and to theoretical first principles method,[13,14] have been applied for screening of HEAs. For example, many empirical rules in terms of mixing enthalpy, configurational entropy, atomic size mismatch, valence electron concentration and their various combinations, have been proposed and tested to explore potential 123 354 HEAs of simple solid solutions. This method works well in some particular HEA systems where intermetallics are unstable. Nevertheless, it is oversimplified to study the stability of some particular phases without considering the total Gibbs energy minimization of the whole system at various temperatures. On the other hand, the first principles calculations are too computationally expensive. It is not feasible to study the phase stability at finite temperatures of multi-component HEA systems. The semi-empirical CALPHAD approach is the optimal method for this purpose. The calculation of phase diagrams (CALPHAD) method has been widely and successfully employed in materials science and engineering for decades.[15,16] With the CALPHAD approach, the integral Gibbs energy, including enthalpy or entropy, of each phase is thermodynamically modeled and evaluated as a function of temperature, pressure, and composition in low-order systems. During the thermodynamic assessment the phase diagram and thermodynamic property information are coupled. Thermodynamic equilibria are determined by the Gibbs energy minimization of the whole system including all possible phases. By using a CALPHAD computational tool, for example Thermo-Calc,[17] together with a self-consistent thermodynamic database, both thermodynamic properties and phase equilibria in the binary and ternary as well as multicomponent systems can be calculated on the basis of Gibbsian thermodynamics. In this paper we report a special thermodynamic database, TCHEA1, for the application in HEA systems. The credibility of a CALPHAD calculation is solely dependent on the suitability and quality of the thermodynamic database used. For the study of conventional single principal element alloys it is good enough for a database if the thermodynamic descriptions mainly focus on the ternary systems containing the major component, and the thermodynamic descriptions may not be complete for a whole system but limited to the major component rich corner, and irrelevant phases to the targeted type of alloys are deliberately excluded. However, these databases for conventional alloys are apparently not adequate for making phase stability predictions for HEA systems where all ternary systems are in theory equally important. The new thermodynamic database TCHEA1 has been developed without the simplifications and omissions pertinent to conventional databases. In this database, all binary and many key ternary systems have been assessed. Since its debut about 2 years ago, TCHEA1 has been applied by many groups interested in HEAs to interpret the experimental phase formation and to explore new alloys and new compositions.[18–23] In this paper, an overview about this thermodynamic database is given firstly in section 2. Followed in section 3 where selected thermodynamic models applied for the 123 J. Phase Equilib. Diffus. (2017) 38:353–368 important phases namely Bcc, Fcc, sigma and Laves phases are illustrated. The main body of this paper is section 4, where extensive validation cases using TCHEA1 are demonstrated in various HEA systems over wide temperature ranges. Thereafter, some extended discussions on the application area of this database are given in section 5. In section 6 some concluding remarks and future works are highlighted finally. 2 Database Overview TCHEA1 is a (...truncated)