A framework for solving atomistic phonon-structure scattering problems in the frequency domain using perfectly matched layer boundaries
A framework for solving atomistic phonon-structure scattering problems in the frequency domain using perfectly matched layer boundaries
复制标题
使用完美匹配的层边界解决频域中的原子声子结构散射问题的框架
DOI：
10.1063/1.4929780
复制
发表时间：
2015
影响因子：
3.2
通讯作者：
J. Feser
中科院分区：
文献类型：
--
作者：
R. Kakodkar;J. Feser
基于原子运动方程的频域分解和完全匹配层(PML)边界的使用，我们提出了一种求解弹性声子界面和声子纳米结构散射问题的数值方法。与分子动态波包分析不同，目前的方法提供了模拟单个声子模式的散射的能力，包括高度色散区域中的波矢。像原子格林函数方法一样，该技术通过一个稀疏的、紧密带状的矩阵将散射问题归结为一个线性代数方程组，而不管其维度如何。然而，PML边界的使用使得能够在边界处快速吸收散射波能量，并为根据PML中的能量耗散率计算的散射声子能流提供了一种简单且廉价的解释。在已知解析解的连通单原子链上证明了该方法的准确性。发现定义PML的参数对性能有影响，并给出了选择最优参数的指导原则。用该方法研究了连通双原子链在所有可用波矢上对光学声子和纵向声子的能量传输系数，发现当子晶格之间存在不连续时，即使是等效声阻抗的连通链在短波长时也有接近于零的传输系数。在较宽的频率范围内，计算了内嵌纳米柱体的声子散射截面，证明了该方法可以扩展到高维。这些计算与长波声子和大圆柱体半径的连续介质理论相吻合，但在其他方面显示了与晶格离散性相关的复杂物理。例如，当入射声子频率超过嵌入的纳米柱体中的最大可用频率时，Mie振荡终止，以及在布里渊区边缘附近的散射效率大于2。
We present a numerical approach to the solution of elastic phonon-interface and phonon-nanostructure scattering problems based on a frequency-domain decomposition of the atomistic equations of motion and the use of perfectly matched layer (PML) boundaries. Unlike molecular dynamic wavepacket analysis, the current approach provides the ability to simulate scattering from individual phonon modes, including wavevectors in highly dispersive regimes. Like the atomistic Green's function method, the technique reduces scattering problems to a system of linear algebraic equations via a sparse, tightly banded matrix regardless of dimensionality. However, the use of PML boundaries enables rapid absorption of scattered wave energies at the boundaries and provides a simple and inexpensive interpretation of the scattered phonon energy flux calculated from the energy dissipation rate in the PML. The accuracy of the method is demonstrated on connected monoatomic chains, for which an analytic solution is known. The parameters defining the PML are found to affect the performance and guidelines for selecting optimal parameters are given. The method is used to study the energy transmission coefficient for connected diatomic chains over all available wavevectors for both optical and longitudinal phonons; it is found that when there is discontinuity between sublattices, even connected chains of equivalent acoustic impedance have near-zero transmission coefficient for short wavelengths. The phonon scattering cross section of an embedded nanocylinder is calculated in 2D for a wide range of frequencies to demonstrate the extension of the method to high dimensions. The calculations match continuum theory for long-wavelength phonons and large cylinder radii, but otherwise show complex physics associated with discreteness of the lattice. Examples include Mie oscillations which terminate when incident phonon frequencies exceed the maximum available frequency in the embedded nanocylinder, and scattering efficiencies larger than two near the Brillouin zone edge.