熱導率（κ）與輻射特性（ε）是評估材料在熱電和光學應用性能的核心指標，它們與聲子間相互作用的散射過程緊密相關。近期研究揭示，除了常規的三聲子散射，四聲子散射在高溫或特殊材料中也極其重要。

然而，精確計算這些散射過程需要巨大的計算資源，挑戰了材料科學的研究邊界。因此，開發新的計算方法以降低計算成本，對于高性能材料的發展至關重要。

美國普渡大學機械工程系的Guang Lin（林光）教授和Xiulin Ruan（阮修林）教授領導的團隊，提出了一種基于采樣技術與最大似然估計（MLE）的方法，顯著降低了聲子散射計算的復雜性，并加速了熱導率（κ）與輻射特性（ε）的預測速度。

Fig. 3 Average computational cost of estimating scattering rate with respect to sample sizes for Si. a τ-1λ3ph, b τ-1λ4ph.

在弛豫時間近似（RTA）條件下，該采樣技術旨在通過所有聲子散射過程中的部分樣本來估計每種聲子模式λ的三聲子（3ph）和四聲子（4ph）散射率。

這個概念很簡單，但實施起來效果卻出奇的好。在獲得散射率數據后，研究團隊利用所有聲子模式的散射率和僅使用紅外活躍聲子模式的散射率，分別確定了熱導率κ和輻射特性ε。

Fig. 5 Estimation of the anisotropic κ of LiCoO2 with the sampling method.

作者的方法不僅計算成本低，而且能在大幅度縮減計算時間的同時，保持高精度的預測結果。這使得作者能夠以前所未有密集的32×32×32的精細倒空間網格劃分來精確計算硅的四聲子散射，并獲得了一個收斂的熱導率數值，與實驗數據的吻合度大幅提升。

該方法的準確性和高效性使其成為熱學和光學應用材料高通量篩選的理想選擇。該文近期發表于npj Computational Materials 10: 31 (2024)。

Editorial Summary

Thermal conductivity (κ) and radiative properties (ε) are essential indicators for assessing material performance in thermoelectric and optical applications, closely related to the scattering processes of phonon interactions. Recent studies have revealed that, in addition to conventional three-phonon scattering, four-phonon scattering plays a vital role in materials at high temperatures or with special properties. However, accurately calculating these scattering processes requires substantial computational resources, challenging the frontiers of material science research. Therefore, developing new computational methods to reduce the cost of calculations is crucial for the advancement of high-performance materials.?

A team lead by Prof. Guang Lin and Prof. Xiulin Ruan from Department of Mechanical Engineering, Purdue University, USA, proposed an approach based on sampling and maximum likelihood estimation (MLE) to reduce the computational cost of phonon scattering calculations and accelerate the predictions of κ and ε. Under the relaxation time approximation (RTA), the sampling method aims to estimate the scattering rates of 3ph and 4ph scattering for each phonon mode λ (denoted as ?and , respectively) by sampling a subset from all phonon scattering processes. The concept is simple but works surprisingly well. After that, κ and ε are determined by using the scattering rate of all phonon modes and the IR-active phonon mode only, respectively. The authors demonstrate that the sampling method can significantly reduce the computational cost of the predictions of thermal conductivity and radiative properties. This allows the authors to revisit the thermal conductivity prediction of Si with an unprecedented q-mesh of 32×32?×32, resulting in a converged thermal conductivity value that closely aligns with experimental data. The accuracy and efficiency of the approach make it ideal for high-throughput screenings of materials for thermal and optical applications.?This article was recently published in npj Computational Materials 10: 31 (2024).

原文Abstract及其翻譯

Sampling-accelerated prediction of phonon scattering rates for converged thermal conductivity and radiative properties?（采樣加速預測聲子散射率以獲得收斂的熱導率和輻射特性）

Ziqi Guo, Zherui Han, Dudong Feng, Guang Lin & Xiulin Ruan

Abstract?The prediction of thermal conductivity and radiative properties is crucial. However, computing phonon scattering, especially for four-phonon scattering, could be prohibitively expensive, and the thermal conductivity for silicon after considering four-phonon scattering is significantly under-predicted and not converged in the literature. Here we propose a method to estimate scattering rates from a small sample of scattering processes using maximum likelihood estimation. The calculation of scattering rates and associated thermal conductivity and radiative properties are dramatically accelerated by three to four orders of magnitude. This allows us to use an unprecedented q-mesh (discretized grid in the reciprocal space) of 32?×?32?×?32 for calculating four-phonon scattering of silicon and achieve a converged thermal conductivity value that agrees much better with experiments. The accuracy and efficiency of our approach make it ideal for the high-throughput screening of materials for thermal and optical applications.

摘要 熱導率和輻射特性的準確預測對科學研究至關重要。然而，計算聲子散射，尤其是涉及復雜的四聲子散射，不僅成本高昂，而且現有文獻中對硅的熱導率進行的預測，考慮到四聲子散射后，結果往往低于實際值且數值并未達到理論上的收斂狀態。在這里，我們提出了一種方法，該方法只需對少量散射過程樣本進行分析，就能夠利用最大似然估計技術來估算散射率。通過這種策略，我們顯著加快了散射率及其相關的熱導率和輻射特性的計算速度，達到了比傳統方法快上三到四個數量級的效率。這使得我們能夠使用前所未有密集的32×32×32的精細倒空間網格劃分來精確計算硅的四聲子散射，并獲得了一個收斂的熱導率數值，與實驗數據的吻合度大幅提升。我們方法的高準確性和高效率使其成為熱學和光學應用材料篩選領域的理想工具，尤其適合進行大規模的高通量材料篩查。