Ab Initio Calculation of Phonon-phonon Interaction for High Thermal Conductivity

本研究的目的是建立声子-声子相互作用和相关宏观量如热导率的第一性原理计算方法，旨在寻找具有高热导率的材料，在研究期间（2000-2003），我在这一领域取得了一些进展。首先，编写了第一性原理声子计算程序。为了研究声子-声子相互作用的影响，开发了声子的压力依赖性、热膨胀等处理程序，建立了从这些声子-声子相互作用数据获得声子寿命的基本程序。但是，用第一性原理程序计算的可行性并不确定。在这项研究中，我们证明了这在对我们的程序代码进行一些修改的水平上确实是可能的。然而，明智地使用线性响应理论在这个问题上还没有得到充分利用。同时，本文还研究了另一种计算输运系数的方法，即利用分子动力学模拟得到的含时相关函数。基本策略已经在我们的代码中建立。然而，我们的计算能力仍然不足以解决细节的输运系数在时间尺度和空间尺度。在真实的材料，我已经检查了上述基本程序，并估计声子寿命。通过这样的估算，我已经表明了个别材料的物理机制，否则就无法澄清。

The purpose of this study is to establish first-principles calculation of phonon-phonon interactions and the related macroscopic quantities such as thermal conductivities, aimed at surveying materials possessing high thermal conductivity.During the period of study (2000-2003), I have made several pieces of progress in this field. First, a code of first-principles phonon calculation has been written. This code is written so as to match calculation of any crystals, and hence it was released to public as the name "Osaka2000".In order to see the effects of phonon-phonon interactions, the program code is developed to treat pressure dependence of phonons, thermal expansion, etc. The basic procedure to obtain phonon life-time from these data of phonon-phonon interactions had been established. But, the feasibility of calculation by first-principles code was not certain. In this study, we showed that this is indeed possible at a level of some modifications to our program code. However, judicious use of linear response theory in this subject is yet fully exploited. This issue is a remaining problem.Meanwhile, another approach of calculation of transport coefficients, though time-dependent correlation functions obtained by molecular dynamic simulations, has been examined. The basic strategy has been established in our code. However, the ability of our calculation is still not enough to resolve details of transport coefficients in terms of both the time scale and the space scale.In real materials, I have examined the above basic procedures, and estimated phonon life-times. By estimation in this way, I have shown physical mechanism of individual materials, which were otherwise not clarified.