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, Al${}_4$C${}_3$, 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, Al${}_1$C${}_1$, 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(Al${}_1$C${}_3$) and HCP(Al${}_1$C_0.5) 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.

开发了对纯铝和液态碳的新描述，并将其用于描述第三代Calphad数据库的Al–C系统。在整个温度范围内用单个表达式描述了元素的稳定相。该表达式基于爱因斯坦模型，因此一个重要的参数是爱因斯坦温度。对于亚稳态相，稳定相和亚稳态相之间的熵差用于计算亚稳态同素异形体的爱因斯坦温度。这样，我们避免了违反热力学第三定律的情况，如果使用SGTE晶格稳定性，这将是后果。用两态模型描述了纯物质和二元化合物的液相-非晶相。对于纯物质，我们介绍了一个与融化熵有关的零点熵​​。纯物质液体的热容量接近$3\mathrm{[R}$在高温下，如果减去电子贡献。Al–C系统具有一种稳定的碳化物，即Al${}_4$C${}_3$，使用与固态一元相等效的模型进行描述，但具有两个爱因斯坦函数。在Al–C中，FCC相是稳定的，其亚稳定的末端成员Al${}_{\mathrm{1个}}$C${}_{\mathrm{1个}}$用一个称为混合模型的新模型进行描述，因为它结合了爱因斯坦模型（给出了谐波贡献）和诺伊曼-科普关系（添加了附加贡献）来描述热容量。估计其爱因斯坦温度，并通过DFT计算获得其形成能。亚稳态相BCC（Al${}_{\mathrm{1个}}$C${}_3$）和HCP（铝${}_{\mathrm{1个}}$使用DFT计算C _0.5），并使用质量效应模型估算其爱因斯坦温度。选择Al-C系统是因为它是一个没有磁性的简单系统，结果表明所提出的模型可以很好地再现实验信息。当仅使用一个温度范围来描述固相时，它们可以在高温下重新稳定，并且最近提出的等熵标准（EEC）用于排除具有比液体更高的熵的固相。