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Accelerating first-principles estimation of thermal conductivity by machine-learning interatomic potentials: A MTP/ShengBTE solution
Bohayra Mortazavi, Evgeny P. Podryabinkin, Ivan S. Nvikovb, Timon Rabczuk, Xiaoying Zhuang, Alexander V. Shapeev
TL;DR
Accurate lattice thermal-conductivity calculations are limited by uncertain measurements and the high cost of DFT-based anharmonic force constants. This work trains MTPs on short AIMD trajectories and combines them with ShengBTE, obtaining close agreement with full-DFT results for bulk and two-dimensional materials while substantially reducing computational cost.
Problem
DFT combined with Boltzmann transport is trusted for thermal-conductivity estimation, but acquiring anharmonic interatomic force constants is computationally demanding.
Method
MTPs trained on short ab-initio molecular-dynamics trajectories are used to evaluate anharmonic force constants for the ShengBTE lattice-thermal-conductivity calculation.
Results
Comparisons for several bulk and two-dimensional structures confirm the remarkable accuracy of MTP-based BTE solutions against full-DFT counterparts.
Takeaways & Limitations
The MTP/ShengBTE approach is expected to serve as a convenient, efficient, and accurate tool for examining lattice thermal conductivity with reduced computational resources.
Abstract
from arXiv · showhide
Accurate evaluation of the thermal conductivity of a material can be a challenging task from both experimental and theoretical points of view. In particular for the nanostructured materials, the experimental measurement of thermal conductivity is associated with diverse sources of uncertainty. As a viable alternative to experiment, the combination of density functional theory (DFT) simulations and the solution of Boltzmann transport equation is currently considered as the most trusted approach to examine thermal conductivity. The main bottleneck of the aforementioned method is to acquire the anharmonic interatomic force constants using the computationally demanding DFT calculations. In this work we propose a substantially accelerated approach for the evaluation of anharmonic interatomic force constants via employing machine-learning interatomic potentials (MLIPs) trained over short ab-initio molecular dynamics trajectories. The remarkable accuracy of the proposed accelerated method is confirmed by comparing the estimated thermal conductivities of several bulk and two-dimensional materials with those computed by the full-DFT approach. The MLIP-based method proposed in this study can be employed as a standard tool, which would substantially accelerate and facilitate the estimation of lattice thermal conductivity in comparison with the commonly used full-DFT solution.
1. Introduction
Thermal conductivity is central to engineering design and thermal management, but accurate evaluation is especially challenging for nanostructured and two-dimensional materials. The proposed MTP/ShengBTE approach accelerates anharmonic force-constant evaluation while closely matching full-DFT thermal-conductivity results.
- Thermal conductivity informs engineering design, temperature evolution, heat dissipation, and avoidance of overheating.
- Accurate thermal-conductivity estimation is challenging because experimental measurements involve diverse uncertainties, particularly for nanostructured materials.
- The integrated MTP/ShengBTE method uses machine-learning interatomic potentials with ShengBTE to calculate lattice thermal conductivity.
- The approach substantially accelerates anharmonic interatomic force-constant evaluation relative to the DFT-based solution.
- Tests on bulk and two-dimensional materials show close agreement with literature results based on full-DFT calculations.
2. Computational methods
The method combines DFT, short AIMD trajectories, MTP fitting, and PHONOPY to obtain force constants and phonons more efficiently. MTPs represent local atomic environments through moment-tensor-based descriptors and are trained by weighted fitting of energies, forces, and stresses.
- DFT supplies phonon dispersions, second-order force constants, and training data for the MTPs.VASP with GGA functionals is used for the first-principles calculations.
- PHONOPY generates atomic-position sets and obtains phonon dispersions and second-order force constants from DFT or MTP forces.
- MTPs represent each central atom through its neighboring atoms within a cutoff radius, including interatomic vectors and atomic types.
- The MLIP energy contribution is expanded in basis functions with fitted parameters constructed from contractions of moment tensor descriptors.
- MTP parameters are fitted by minimizing weighted errors in AIMD total energies, atomic forces, and stresses.The optimization weights for energies, forces, and stresses are 1, 0.1, and 0.001, respectively.
- Anharmonic force constants are obtained from MTPs trained on AIMD runs at 50, 300, 500, and 700 K, each shorter than 1000 time steps.Training configurations are sampled every five time steps.
3. Results and discussions
The MTP-based BTE solution closely reproduces full-DFT and experimental thermal-conductivity results across bulk and two-dimensional materials. Its reduced computational cost enables larger supercells and offers a practical alternative for complex lattices.
- Validation against reference results: MTP-based calculations closely agree with experimental and full-DFT thermal conductivities for graphene and several bulk materials.For graphene, cumulative mean-free-path trends and acoustic-mode contributions also show close agreement with full-DFT results.
- Validation against reference results: The maximum discrepancy for the bulk-material comparison is approximately 12% for BAs.The discrepancy is partly associated with computational details in the compared studies.
- Bulk materials: The accelerated method is evaluated for bulk diamond, silicon, InAs, and BAs using comparisons with experimental and full-DFT counterparts.The bulk calculations use 5×5×5 supercells for anharmonic force constants and include interactions through fourth-nearest neighbors.
- Two-dimensional materials: For two-dimensional materials, MTP-based BTE conductivities are compared with full-DFT results despite substantial scattering among reported DFT-based values.The paper highlights increasing computational complexity as lattice symmetry decreases and primitive-cell size increases.
- Overall assessment: Across the considered bulk and 2D lattices, comparisons confirm the accelerated approach’s remarkable accuracy while substantially reducing computational costs.MTPs permit larger supercells and cutoff distances and avoid DFT convergence tests for k-point grids and plane-wave cutoff energies.