The third generation Calphad description of Al–C including revisions of pure Al and C

New descriptions of pure Al and liquid C were developed and used to describe the Al–C system for the third generation of Calphad databases. The stable phases of the elements are described with a single expression for the entire temperature range. The expression is based on the Einstein model and an important parameter is therefore the Einstein temperature. For the metastable phases, the difference in entropy between stable and metastable phases is used to calculate the Einstein temperature for the metastable allotrope. In this way we avoid breaking the third law of thermodynamics, which would be the consequence if the SGTE lattice stabilities were used. The liquid-amorphous phase for the pure substances and for the binary is described with the two-state model. For the pure substances, we introduce a zero-point entropy that is related to the entropy of melting. The heat capacity of the liquid of the pure substances approaches 3R at high temperatures if the electronic contribution is subtracted. The Al–C system has one stable carbide, Al4C3, which is described with a model equivalent to that used for the solid unary phases but with two Einstein functions. In Al–C, the FCC phase is stable and its metastable end-member, Al1C1, is described with a new model, here called the hybrid model, as it combines the Einstein model (giving the harmonic contribution) and the Neumann–Kopp relationship (adding the additional contributions) to describe the heat capacity. Its Einstein temperature is estimated and its formation energy is obtained from DFT calculations. The total energy of the end-members of the metastable phases BCC(Al1C3) and HCP(Al1C0.5) is calculated with DFT and their Einstein temperatures are estimated using the mass-effect model. The Al–C system was chosen because it is a simple system without magnetism and the results show that the proposed models can reproduce experimental information well. When only one temperature range is used to describe the solid phases, they may be re-stabilized at high temperatures and the recently presented equal-entropy criterion (EEC) is used to exclude solid phases with higher entropy than the liquid.