Institut für Festkörperphysik, Universität Bremen, Otto-Hahn-Allee 1, Bremen 28359, Germany.
Institut für Festkörperphysik, Universität Bremen, Otto-Hahn-Allee 1, Bremen 28359, Germany; Institute for Solar Energy Research Hamelin, Am Ohrberg 1, Emmerthal 31860, Germany.
Ultramicroscopy. 2018 Jun;189:124-135. doi: 10.1016/j.ultramic.2018.03.025. Epub 2018 Mar 30.
For simulation of transmission electron microscopic images and diffraction patterns, the accurate inclusion of thermal diffuse scattering by phonons is important. In the frozen phonon multislice algorithm, this is possible, if thermal displacements according to the realistic, quantum mechanical distribution can be generated. For pure crystals, quantum mechanical calculations based on DFT yield those displacements. But for alloys one is usually restricted to the Einstein approximation, where correlations between atoms are neglected. In this article, molecular dynamics simulations are discussed and used as an alternative method for displacement calculation. Employing an empirical Stillinger-Weber type potential, classical motion is used as an approximation for the quantum mechanical dynamics. Thereby, correlations and possible static atomic displacements are inherently included. An appropriate potential is devised for AlGaN by fitting to force constant matrices determined from DFT and elastic constants of AlN and GaN. A comparison shows that the empiric potential reproduces phonon dispersions and displacement expectations from DFT references. The validity for alloys is successfully demonstrated by comparison to DFT calculations in special quasirandom structures. Subsequently, molecular dynamics were used in multislice simulations of both conventional and scanning TEM images. The resulting images are in very good agreement with DFT based calculations, while a slight yet significant deviation from Einstein approximation results can be seen, which can be attributed to the neglect of correlations in the latter. The presented potential hence proves to be a useful tool for accurate TEM simulations of AlGaN alloys.
为了模拟透射电子显微镜图像和衍射图案，准确包含声子的热扩散散射非常重要。在冻结声子多片层算法中，如果可以根据实际的量子力学分布生成热位移，则可以实现这一点。对于纯晶体，基于 DFT 的量子力学计算可以得出这些位移。但是对于合金，通常只能限制在爱因斯坦近似中，忽略原子之间的相关性。本文讨论了分子动力学模拟，并将其用作位移计算的替代方法。采用经验 Stillinger-Weber 类型势能，将经典运动用作量子力学动力学的近似。因此，相关性和可能的静态原子位移被固有地包含在内。通过拟合由 DFT 确定的力常数矩阵和 AlN 和 GaN 的弹性常数，为 AlGaN 设计了一个合适的势能。比较表明，经验势能再现了来自 DFT 参考的声子色散和位移预期。通过与特殊准随机结构中的 DFT 计算进行比较，成功证明了该经验势在合金中的有效性。随后，分子动力学被用于常规和扫描 TEM 图像的多片层模拟。得到的图像与基于 DFT 的计算非常吻合，而与爱因斯坦近似结果相比，可以看到略微但显著的偏差，这可以归因于后者忽略了相关性。因此，所提出的势能被证明是准确模拟 AlGaN 合金的 TEM 的有用工具。
