[Paper Review] A relaxation time model for efficient and accurate prediction of lattice thermal conductivity

Han Xie, Xiaokun Gu+1 more|arXiv (Cornell University)|Nov 25, 2018

Thermal properties of materials47 references4 citations

TL;DR

This paper proposes a quasi-harmonic approximation-based relaxation time model for efficient and accurate prediction of lattice thermal conductivity, leveraging phonon dispersion and three-phonon scattering strength approximations. It achieves superior accuracy over existing models—especially at low temperatures—while maintaining low computational cost and enabling extraction of phonon relaxation times with physical consistency.

ABSTRACT

Prediction of lattice thermal conductivity is important to many applications and technologies, especially for high-throughput materials screening. However, the state-of-the-art method based on three-phonon scattering process is bound with high computational cost while semi-empirical models such as the Slack equation are less accurate. In this work, we examined the theoretical background of the commonly-used computational models for high-throughput thermal conductivity prediction and proposed an efficient and accurate method based on an approximation for three-phonon scattering strength. This quasi-harmonic approximation has comparable computational cost with many widely-used thermal conductivity models but had the best performance in regard to quantitative accuracy. As compared to many models that can only predict lattice thermal conductivity values, this model also allows to include Normal processes and obtain the phonon relaxation time.

Motivation & Objective

• Address the challenge of balancing computational efficiency and quantitative accuracy in high-throughput lattice thermal conductivity prediction.
• Overcome the high computational cost of first-principles Boltzmann transport equation (BTE) methods based on anharmonic interatomic force constants.
• Improve upon semi-empirical models like the Slack equation and Debye-Grüneisen model by incorporating physical scattering phase space information.
• Enable inclusion of Normal processes in thermal conductivity modeling, particularly enhancing low-temperature performance.
• Provide a method that yields not only thermal conductivity but also physically meaningful phonon relaxation times for deeper material insight.

Proposed method

• Develops a relaxation time model based on a quasi-harmonic approximation (QHA) that approximates three-phonon scattering strength using harmonic interatomic force constants.
• Uses full phonon dispersion curves computed from harmonic IFCs as input, preserving detailed phonon band structure information.
• Incorporates scattering phase space information through a physically motivated approximation, improving accuracy over purely empirical models.
• Derives relaxation times from the model, enabling comparison with full SMRTA (self-consistent phonon relaxation time approximation) calculations.
• Avoids the need for computationally expensive anharmonic IFCs, reducing cost while retaining predictive power.
• Validates the model against full iterative BTE solutions and other widely used models across 37 materials.

Experimental results

Research questions

• RQ1 Can a relaxation time model based on QHA achieve both high accuracy and low computational cost for lattice thermal conductivity prediction?
• RQ2 How does the inclusion of Normal processes and scattering phase space affect low-temperature thermal conductivity predictions?
• RQ3 To what extent does the proposed model outperform established models like the Slack equation and Leibfried-Schlömann model in quantitative accuracy?
• RQ4 Can the model reliably predict phonon relaxation times that match results from full SMRTA calculations?
• RQ5 Does the model maintain accuracy across diverse crystal structures, including anisotropic and half-Heusler materials?

Key findings

• The proposed model achieves a mean absolute fractional deviation (AFD) of 1.730 at 100 K, significantly outperforming other models that show degraded performance at low temperatures.
• The model exhibits strong correlation (R² > 0.9) with full iterative BTE calculations across 37 materials, demonstrating high quantitative accuracy.
• At 300 K, the model’s AFD is 1.420, comparable to the best-performing existing models, but it shows markedly better low-temperature performance.
• The model predicts phonon relaxation times with better agreement to full SMRTA results than Slack’s relaxation time model, especially at 100 K.
• The inclusion of Normal processes and phase space information enables the model to capture the correct temperature dependence of relaxation times.
• The model maintains low computational cost—comparable to semi-empirical models—while providing physically consistent relaxation times and superior accuracy.