熱導(dǎo)率（κ）與輻射特性（ε）是評(píng)估材料在熱電和光學(xué)應(yīng)用性能的核心指標(biāo)，它們與聲子間相互作用的散射過(guò)程緊密相關(guān)。近期研究揭示，除了常規(guī)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(jì)算這些散射過(guò)程需要巨大的計(jì)算資源，挑戰(zhàn)了材料科學(xué)的研究邊界。因此，開(kāi)發(fā)新的計(jì)算方法以降低計(jì)算成本，對(duì)于高性能材料的發(fā)展至關(guān)重要。

美國(guó)普渡大學(xué)機(jī)械工程系的Guang Lin（林光）教授和Xiulin Ruan（阮修林）教授領(lǐng)導(dǎo)的團(tuán)隊(duì)，提出了一種基于采樣技術(shù)與最大似然估計(jì)（MLE）的方法，顯著降低了聲子散射計(jì)算的復(fù)雜性，并加速了熱導(dǎo)率（κ）與輻射特性（ε）的預(yù)測(cè)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(shí)間近似（RTA）條件下，該采樣技術(shù)旨在通過(guò)所有聲子散射過(guò)程中的部分樣本來(lái)估計(jì)每種聲子模式λ的三聲子（3ph）和四聲子（4ph）散射率。

這個(gè)概念很簡(jiǎn)單，但實(shí)施起來(lái)效果卻出奇的好。在獲得散射率數(shù)據(jù)后，研究團(tuán)隊(duì)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(dǎo)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(jì)算成本低，而且能在大幅度縮減計(jì)算時(shí)間的同時(shí)，保持高精度的預(yù)測(cè)結(jié)果。這使得作者能夠以前所未有密集的32×32×32的精細(xì)倒空間網(wǎng)格劃分來(lái)精確計(jì)算硅的四聲子散射，并獲得了一個(gè)收斂的熱導(dǎo)率數(shù)值，與實(shí)驗(yàn)數(shù)據(jù)的吻合度大幅提升。

該方法的準(zhǔn)確性和高效性使其成為熱學(xué)和光學(xué)應(yīng)用材料高通量篩選的理想選擇。該文近期發(fā)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(yù)測(cè)聲子散射率以獲得收斂的熱導(dǎo)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(dǎo)率和輻射特性的準(zhǔn)確預(yù)測(cè)對(duì)科學(xué)研究至關(guān)重要。然而，計(jì)算聲子散射，尤其是涉及復(fù)雜的四聲子散射，不僅成本高昂，而且現(xiàn)有文獻(xiàn)中對(duì)硅的熱導(dǎo)率進(jìn)行的預(yù)測(cè)，考慮到四聲子散射后，結(jié)果往往低于實(shí)際值且數(shù)值并未達(dá)到理論上的收斂狀態(tài)。在這里，我們提出了一種方法，該方法只需對(duì)少量散射過(guò)程樣本進(jìn)行分析，就能夠利用最大似然估計(jì)技術(shù)來(lái)估算散射率。通過(guò)這種策略，我們顯著加快了散射率及其相關(guān)的熱導(dǎo)率和輻射特性的計(jì)算速度，達(dá)到了比傳統(tǒng)方法快上三到四個(gè)數(shù)量級(jí)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(xì)倒空間網(wǎng)格劃分來(lái)精確計(jì)算硅的四聲子散射，并獲得了一個(gè)收斂的熱導(dǎo)率數(shù)值，與實(shí)驗(yàn)數(shù)據(jù)的吻合度大幅提升。我們方法的高準(zhǔn)確性和高效率使其成為熱學(xué)和光學(xué)應(yīng)用材料篩選領(lǐng)域的理想工具，尤其適合進(jìn)行大規(guī)模的高通量材料篩查。