然而，這類計算，尤其是在復(fù)雜晶體中，往往涉及到尷尬的幾何形狀，其中 Wigner-Seitz 單元格和第一布里淵區(qū)在笛卡爾空間中具有不規(guī)則、非直觀的形狀。此外，目前仍不清楚如何利用對稱關(guān)系使晶格動力學(xué)計算在更大的單元格中更有效率。

來自美國橡樹嶺國家實(shí)驗(yàn)室的Xun Li等，提出了一種利用慣用晶胞內(nèi)原始平移對稱性（PTS）的高效動力學(xué)來研究晶格動力學(xué)和聲子輸運(yùn)的方法。基于PTS，他們將原始到慣用單元格的動態(tài)方法應(yīng)用于由非諧相互作用限制的熱傳輸計算中。在慣用幾何結(jié)構(gòu)中，這種PTS動力學(xué)方法通過在典型傳統(tǒng)動力學(xué)中隱藏的守恒規(guī)則，顯著減少準(zhǔn)粒子散射相空間，并減少散射矩陣元素計算中的求和次數(shù)，從而降低熱導(dǎo)率計算的計算成本。

作者通過計算三種不同空間群材料的聲子輸運(yùn)性質(zhì)，證明了這種PTS方法的便利性，這三種材料為空間群R3m的GeTe、空間群I2₁3的固體N₂和空間群R-3的鐵磁CrCl₃?。作者提出的動力學(xué)方法能夠準(zhǔn)確描述傳輸現(xiàn)象，并且比傳統(tǒng)動力學(xué)方法在計算上成本更低，這對于研究復(fù)雜材料系統(tǒng)中的準(zhǔn)粒子相互作用具有重要價值。該文近期發(fā)布于npj Computational Materials 9: 193 (2023)。

Fig. 4 Thermal conductivity of N2 (black curve, inset), GeTe (blue?curve), and CrCl3 (red curve) from PTS dynamics as a function of?temperature in bulk naturally occurring samples.

Editorial Summary

Calculations and simulations of crystalline material properties are typically based on periodically arranged unit cells that contain the smallest number of degrees of freedom, i.e., the primitive unit cell. The most widely used primitive cells are called Wigner-Seitz cells (WSC) and their corresponding first Brillouin zones (FBZ). These are typically used for calculations of lattice vibrational and transport properties because they have the cheapest computational cost. However, such calculations, particularly in complex crystals, often have awkward geometries with WSC and FBZ having irregular, non-intuitive shapes in Cartesian space. In addition, it is not well known how to use symmetry relations to make lattice dynamical calculations more efficient in larger unit cells.?

Xun Li et al. from Oak Ridge National Laboratory, explored the lattice dynamics and phonon transport using an efficient dynamic method that utilizes primitive translational symmetry (PTS) within conventional cells. Theyapplied this primitive to conventional cell dynamic method based on PTS to thermal transport calculations limited by anharmonic interactions. In conventional geometries, this PTS dynamic method significantly reduces the computational cost of thermal conductivity calculations by reducing the quasiparticle scattering phase space through a conservation rule that is hidden in typical conventional dynamics and reducing the number of summations in scattering matrix element calculations. They demonstrated the convenience of this PTS method by calculating phonon transport properties for three materials from different space groups: GeTe with space group R3m, solid N₂?with space group I2₁3, and ferromagnetic CrCl₃?with space group R-3. The proposed dynamics accurately describes transport phenomena and costs significantly less computationally compared to conventional dynamics, which is valuable for studying quasiparticle interactions in complex material systems. This article was recently published in npj Computational Materials 9: 193 (2023).

原文Abstract及其翻譯

Primitive to conventional geometry projection for efficient phonon transport calculations（有效計算聲子輸運(yùn)的原胞到晶胞幾何投影）

Xun Li,?Simon Thébaud?&?Lucas Lindsay?

Abstract

The primitive Wigner-Seitz cell and corresponding first Brillouin zone (FBZ) are typically used in calculations of lattice vibrational and transport properties as they contain the smallest number of degrees of freedom and thus have the cheapest computational cost. However, in complex materials, the FBZ can take on irregular shapes where lattice symmetries are not apparent. Thus, conventional cells (with more atoms and regular shapes) are often used to describe materials, though dynamical and transport calculations are more expensive. Here we discuss an efficient anharmonic lattice dynamic method that maps conventional cell dynamics to primitive cell dynamics based on translational symmetries. Such symmetries have not been utilized in typical lattice dynamical calculations. This leads to phase interference conditions that act like conserved quantum numbers and a conservation rule for phonon scattering that is hidden in conventional dynamics which significantly reduces the computational cost. We demonstrate this method for phonon transport in a variety of materials with inputs from first-principles calculations and attribute its efficiency to reduced scattering phase space and fewer summations in scattering matrix element calculations.

摘要?

Wigner-Seitz原胞和相應(yīng)的第一布里淵區(qū)（FBZ）通常用于計算晶格振動和輸運(yùn)性質(zhì)，因?yàn)樗鼈儼钚〉淖杂啥?，因此計算成本也最低。然而，在?fù)雜材料中，FBZ可能是不規(guī)則的形狀，晶格對稱不明顯。因此，盡管其動力學(xué)計算和輸運(yùn)計算更昂貴，慣用晶胞（具有更多的原子和規(guī)則的形狀）也經(jīng)常被用來描述材料。本文討論了一種有效的非諧晶格動力學(xué)方法，該方法利用平移對稱性將慣用晶胞動力學(xué)映射到原胞動力學(xué)上。這種對稱性還沒有被用于典型的晶格動力學(xué)計算。這導(dǎo)致了類似于守恒量子數(shù)的相位干涉條件，以及隱藏在傳統(tǒng)動力學(xué)中的聲子散射守恒規(guī)則，這大大降低了計算成本。我們利用第一性原理計算的輸入，演示了這種方法用于各種材料中的聲子輸運(yùn)的計算，并將其效率歸因于減少散射相空間和減少散射矩陣元計算中的求和。