A Generalized Approach Obeying the Third Law of Thermodynamics for the Expression of Lattice Stability and Compound Energy: A Case Study of Unary Aluminum

Recently, Hillert and Selleby proposed a simple method for expression of the lattice stability or Gibbs energy of formation that does not violate the third law of thermodynamics. This method describes the derivation of the Gibbs energy function from high temperatures down to 0 K by interpolation, instead of extrapolation from room temperature to 0 K. In the present work, their original method is discussed in terms of determination of the characteristic parameter values. Keeping the essential interpolation character of their method, a generalized approach is presented for expressing the lattice stability through parameter optimizations. This approach retains the zero point entropy of substances and is in line with the development of the third generation CALPHAD databases. Using the Al unary system as a case study, the lattice stabilities of the hcp and bcc phases are investigated. The respective Einstein temperatures are also evaluated. At high temperatures, the present descriptions reproduce the lattice stabilities suggested by SGTE for the existing second generation of databases, with a reasonable accuracy. More importantly, information from ab initio calculations (total energy at 0 K) is also used for this optimization and the present method results in a physically sounder description of thermodynamic properties at lower temperatures down to 0 K. The present approach provides a simple and flexible way to estimate the lattice stabilities, with potential applicability for the Gibbs energy of formation of stoichiometric compounds and the excess energy of solution phases, in accordance with the third law of thermodynamics.