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

这项研究的目的是建立声子-声子相互作用的第一性原理计算以及相关的宏观量，如热导率，旨在调查具有高热导率的材料。在研究期间(2000-2003年)，我在这方面取得了一些进展。首先，编写了第一原理声子计算程序。这个程序是为了与任何晶体的计算相匹配而编写的，因此它被命名为“Osaka2000”。为了了解声子-声子相互作用的影响，开发了处理声子压力依赖、热膨胀等问题的程序代码。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，用第一性原理程序进行计算的可行性尚不确定。在这项研究中，我们证明了这确实是可能的，只需对我们的程序代码进行一些修改。然而，线性反应理论在这门学科中的明智使用还没有得到充分的利用。同时，还研究了通过分子动力学模拟得到随时间变化的关联函数来计算输运系数的另一种方法。基本策略已在我们的代码中确立。然而，我们的计算能力仍然不足以从时间尺度和空间尺度来解析输运系数的细节。在实际材料中，我已经研究了上述基本程序，并估计了声子寿命。通过这样的估计，我已经展示了个别材料的物理机制，否则就没有弄清楚。

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.