The elastic properties, lattice wave propagation and phonon focusing of TiAl are studied in detail based on Bond matrices model and lattice-dynamical method. The results contain remarkably complex three-dimensional variations in the phonon flux with angular distribution. The feature of elastic waves and phonon distribution is affected by the elastic anisotropy of the lattice. The correspondence between these features and contours of Gaussian curvature on the slowness surface is explored and the phonon topology is discussed about the presence of caustics in the anistropic flux of phonons emanating from a localized phonon distribution. The topology slowness surface gives insights into the mixing of longitudinal and transverse modes and gives the origin of the phonon focusing. The elastic anisotropy not only affects lattice wave propagation but also influences phonon focusing.

基于Bond矩阵模型和晶格动力学方法，详细研究了TiAl的弹性，晶格波传播和声子聚焦。结果包含具有角分布的声子通量中非常复杂的三维变化。弹性波和声子分布的特征受晶格的弹性各向异性影响。探索了这些特征与慢速表面上高斯曲率轮廓之间的对应关系，并讨论了声子拓扑的声子拓扑，该声子拓扑是由局部声子分布产生的声子各向异性通量中的苛性碱的存在。拓扑慢度表面提供了对纵向和横向模式混合的见解，并给出了声子聚焦的起源。