Matter Modeling Asked on November 18, 2021

To build a model using the CALPHAD approach, i.e. Gibbs free energy as a function of composition and temperature, typically taking the form of a Redlich-Kister polynomial, what kind of thermodynamic data needs to be collected from experiment (or from first principles calculations)?

As a retired professor in Computational Thermodynamics I am happy that young students try to use the Calphad methods to understand materials. However, to model a phase using Calphad there are some background needed. A Calphad database is built from a set of data for the pure elements in different phases describing how the Gibbs energy of the element vary with T from 300 K up to some higher T. Such data are obtained from experimental data for the stable state or estimated for metastable phases for the elements. It also include the heat capacity of the element. For solution phases one can introduce excess parameters which depend on the fraction of the elements and is normally constant or linearly T dependent. One does not use higher T terms (such as Tln(T)) unless one has experimental heat capacity for the solution. There are several models to select from which can describe LRO or SRO transitions in the phase which require more model parameters. Some of these can be determined by DFT calculations unless there are experimental data. In short, try to find some reference paper or book to read about Calphad, it is not just and an equation or a black box.

Answered by Bo Sundman on November 18, 2021

I concur with the answer by Alone programmer, but his answer only gives half the story. The coefficients or the model parameters come into the picture later and are actually obtained by optimization of both the experimentally obtained and theoretically calculated data. Here I will discuss the experimental data since the DFT part has already been discussed. The experimental data can be basically classified into three categories:

Structural (Crystallographic): this helps in selecting the Gibbs energy models

Constitutional: for example, tie-line, invariant points, special points, phase boundaries, phase amounts, etcetera. These can be obtained through suitable experiments.

Thermochemical: for example, enthalpy, activity, heat capacity, etcetera. This data actually serves as constraints during the optimization of the model parameters since using only the constitutional data will make the calculation of model parameters difficult as many solutions are possible without using constraints.

Hope this helps.

Answered by Achintya Patra on November 18, 2021

Basically you need to find $L_{ij}^{m}$ coefficients in the Redlich-Kister polynomials from DFT calculations, related to temperature as:

$$L_{ij}^{m} = a_{ij}^{m} + b_{ij}^{m} T + c_{ij}^{m} T ln(T) + d_{ij}^{m} T^{2} + e_{ij}^{m} T^{3} + frac{f_{ij}^{m}}{T}$$

Typically you need just the values for $m leq 2$. I think this is a good reference for the data infrastructure that is needed for CALPHAD simulations: https://link.springer.com/content/pdf/10.1186/2193-9772-3-12.pdf

Answered by Mithridates the Great on November 18, 2021

1 Asked on January 5, 2022 by quantumx

computational chemistry coupled cluster gaussian quantum chemistry

1 Asked on January 5, 2022

ab initio calculations density functional theory functional many body perturbation theory quantum chemistry

1 Asked on January 3, 2022

density functional theory mathematical modeling quantum chemistry spectroscopy td dft

3 Asked on January 1, 2022 by anyon

1 Asked on January 1, 2022 by bnd

1 Asked on December 22, 2021

lammps molecular dynamics molecular interactions molecular modeling software

2 Asked on December 22, 2021

1 Asked on December 20, 2021

electronic structure fcidump integrals one topic per answer software

1 Asked on December 20, 2021 by c-alexander

density functional theory from phys se quantum chemistry spectroscopy td dft

1 Asked on December 20, 2021

1 Asked on December 18, 2021 by kfc

1 Asked on December 16, 2021

density functional theory from phys se mathematical modeling statistical thermodynamics variational principle

1 Asked on December 16, 2021 by luphys

alloys density functional theory from phys se relativistic software

1 Asked on December 16, 2021

1 Asked on December 13, 2021 by roman-korol

atomic physics full configuration interaction high precision molecular modeling periodic system

1 Asked on December 13, 2021

band structure density functional theory from phys se quantum espresso

9 Asked on December 11, 2021

high performance computing matter modeling specific technology one topic per answer open source software

4 Asked on December 9, 2021 by georgios-karaiskakis

computational chemistry density functional theory functional history

2 Asked on December 9, 2021 by koroma

band structure lattice dynamics perovskites phonons symmetry

Get help from others!

Recent Questions

Recent Answers

- Lex on Does Google Analytics track 404 page responses as valid page views?
- haakon.io on Why fry rice before boiling?
- Peter Machado on Why fry rice before boiling?
- Jon Church on Why fry rice before boiling?
- Joshua Engel on Why fry rice before boiling?

© 2022 AnswerBun.com. All rights reserved. Sites we Love: PCI Database, MenuIva, UKBizDB, Menu Kuliner, Sharing RPP, SolveDir