# What information about a crystalline solid material goes into calculating phase diagrams in Thermo-Calc, and how?

Gibbs free energy, $$G$$, for a crystalline solid material could be described as: $$\begin{equation} G\: =\: H_{T=0}\: +\: H_{T>0}\: +\: \text{ZPE}\: -\: T\cdot S, \end{equation}$$ Where $$H$$ is enthalpy, ZPE is the zero-point energy and S is entropy (all kinds).

Solids (condensed matter might be a better term) are highly incompressible, so their internal energy computed with either empirical potentials or otherwise can be considered equal to their enthalpy. That takes care of the $$H_{T=0}$$ term. What about the rest? Can each of them be included in a Thermocalc phase transition study?

I haven't explored Thermocalc enough (blame it on VASP!). As far as I know, we make Gibbs free energy equations for a material at various temperature ranges and dump those in a .tdb (database) file. If these other terms are accounted for, please help me understand how, code and theory-wise.

• It is unusual for a question on our site to have only one vote. Does anyone want to explain why I was the only one that voted?! – Nike Dattani Dec 7 '20 at 3:19

## 1 Answer

Enthalpy and entropy are the temperature dependent terms in free energy from which enthalpy is a dominant term mainly at lower temperature and entropy is dominant at higher temperature (because randomness is more at higher temperature). This temperature effect can be considered by utilizing the heat capacity at constant pressure (Cp). Phonopy code is there to evaluate Cp as a function of temperature (Quasi harmonic approximation).

Change in enthalpy and entropy terms are obtained by integrating Cp and Cp/T from 0 K to the desired temperature, respectively.

Other terms like magnetic ordering (if the system is magnetic), pressure effect (mostly in geology) can also be included. Another most important term is the excess free energy, which is due to the interaction between the different kinds of atoms. This is basically used while considering solid solutions.

• Thank you for your answer Niraja. What I understand is that we calculate these properties using whatever means we prefer, then we put them in some kind of database for the material in Thermocalc. Am I right to think that? – Hitanshu Sachania Dec 9 '20 at 19:33
• You are right Hitanshu. But we don't put those data directly in the database. We have to make a file (called POP file in the context of CALPHAD) containing the collected experimental data, ab initio data, relevant to the phase diagram. These data will be used optimize the redlich-kister coefficients (Redlich-Kister polynomial is used to express the excess free energy term) using the PARROT module in Thermo-Calc. Then only the database file (.TDB file) can be generated and used to plot the phase diagram. – Niraja moharana Dec 12 '20 at 13:44
• Understood. This sounds like a nice and neat workflow. – Hitanshu Sachania Dec 15 '20 at 10:12
• Thanks so much for this answer! There's a \$50 bounty on this thermo-calc question right now, do you know anything about that question's topic that could help the user in any way at all? mattermodeling.stackexchange.com/q/3785/5 – Nike Dattani Apr 20 at 22:22