ALATDYN: A set of Anharmonic LATtice DYNamics codes to compute thermodynamic and thermal transport properties of crystalline solids

Abstract

We introduce a lattice dynamics package which calculates elastic, thermodynamic and thermal transport properties of crystalline materials from data on their force and potential energy as a function of atomic positions. The data can come from density functional theory (DFT) calculations or classical molecular dynamics runs performed in a supercell. First, the model potential parameters, which are anharmonic force constants are extracted from the latter runs. Then, once the anharmonic model is defined, thermal conductivity and equilibrium properties at finite temperatures can be computed using lattice dynamics, Boltzmann transport theories, and a variational principle respectively. In addition, the software calculates the mechanical properties such as elastic tensor, Gruneisen parameters and the thermal expansion coefficient within the quasi-harmonic approximation (QHA). Phonons, elastic constants and thermodynamic properties results applied to the germanium crystal will be illustrated. Using the force constants as a force field, one may also perform molecular dynamics (MD) simulations in order to investigate the combined effects of anharmonicity and defect scattering beyond perturbation theory.

Program summary

Program Title: ALATDYN

CPC Library link to program files: https://doi.org/10.17632/4jm4fh2nk2.1

Developer's repository link: https://github.com/KeivanS/Anharmonic-lattice-dynamics/tree/main

Licensing provisions: GPLv3

Programming language: FORTRAN90

Nature of problem: The ALATDYN suite of codes develops a lattice dynamical model of a crystalline solid. The FOCEX code extracts the model parameters from supercell calculations data on forces versus position and calculates the phonon spectrum, elastic constants and thermodynamic properties within the quasi-harmonic approximation. The SCOP8 code goes beyond QHA and implements the self-consistent phonon theory to minimize the free energy with respect to the strain tensor, atomic positions and harmonic force constants, and thus obtains the state of equilibrium at the given temperature along with the effective phonon bands structure. The THERMACOND code uses the cubic force constants and the crystal symmetries to solve the phonon Boltzmann equation (PhBE) efficiently and deduce the thermal conductivity. Finally, ANFOMOD uses the extracted force constants to perform a molecular dynamics simulation in a supercell.

Solution method: Force constants are obtained from a singular value decomposition (or the ridge regression) method. PhBE is solved by first setting up the collision matrix and effectively inverting it using the conjugate-gradients method.

Additional comments including restrictions and unusual features: This code has the ability to extract force constants up to 8th order provided enough force-displacement data is provided. SCOP8 can thus use them to potentially predict phase changes. Coupling of phonons to magnetic or orbital degrees of freedom is an extension we plan to add to the FOCEX and SCOP8 codes in the future.