Crystal structure prediction codes like USPEX, use DFT calculated values of energy ($0$ K) to study the phase space (or potential energy surface or internal energy surface, I'm confused which is it). All of this is at $0$ K.

Lattice dynamics is the direction to take in studying finite temperature properties of materials, but these studies are costly, very costly. The evolutionary algorithm that USPEX employs is quite costly too. At the current state of commercial computing infrastructure, combining the two sounds like a recipe for trouble.

What ways can we think of, machine learning or otherwise, to make finite temperature crystal structure prediction possible today? (More interested in the "otherwise".)

Older post: HEAs or multiple atom alloys (MAAs) have become quite popular recently. The trend in modeling these materials is to represent them as random solid solutions. I use special quasirandom structures to model them. I wonder if this is appropriate. At each temperature, which configuration is the most stable is almost impossible to predict.

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    $\begingroup$ Are you specifically interested in crystal structures, or are you using crystal structures to determine if high entropy phases are present and stable at finite temperatures? $\endgroup$
    – Anyon
    Dec 9, 2020 at 22:05
  • $\begingroup$ @Anyon, specifically crystal structures. $\endgroup$ Dec 10, 2020 at 12:58
  • $\begingroup$ OK. Then the Monte Carlo approach described here is maybe not so useful to you. $\endgroup$
    – Anyon
    Dec 10, 2020 at 15:30
  • $\begingroup$ @Anyon, theirs is an interesting way to predict the feasibility of specific high entropy oxide phases. As you guessed, I was thinking of a more general prescription for finite temperature csp for any material. $\endgroup$ Dec 10, 2020 at 17:36

1 Answer 1


The static energy at 0K is usually the major component of the free energy (at least for crystalline substances at moderate temperatures). So I will proceed first a search based on static energy (using USPEX or otherwise) and, then, calculate free energies for the top candidates within QHA approximation and rank them again appropriately.


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