This work determines the phase stabilities and point defect energetics of TiSi₂ and TiGe₂ allotropes using density functional theory. The primary focus is on the C49 and C54 allotropes, which compete during TiSi₂ phase formation. It is found that the ground state structure for TiGe₂ is the C54 allotrope, desirable for its low sheet resistance, while the less desirable, higher resistance C49 allotrope forms the ground state structure of TiSi₂. A first attempt to understand the Ge atom's role in lowering the enthalpy of formation for the C54 structure is made from the perspective of the extended Born model. Charge density differences, the density of states, and Bader charge analysis show that these systems are predominantly ionically bonded, with the Ge atoms introducing additional covalent bond stability for the C54 allotrope. It is known that higher temperatures favor C54 formation in TiSi₂. Helmholtz free energy calculations for TiSi₂ suggest that the vibrational free energy does not drive the system to the C54 phase. The formation energies of certain point defects within the C49 structure of TiSi₂ are less than 1 eV, which is consistent with experiments that show high defect concentrations. Thus, the driving force for C54 formation at higher temperatures may be related to the high defect concentration in the C49 allotrope.

中文翻译：

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从第一性原理计算TiSi2和TiGe2取向索的晶格稳定性和点缺陷能

这项工作使用密度泛函理论确定了TiSi ₂和TiGe ₂同素异形体的相稳定性和点缺陷能。主要关注于C49和C54同素异形体，它们在TiSi ₂相形成过程中相互竞争。已经发现，TiGe ₂的基态结构是C54同素异形体，因为它具有较低的薄层电阻，而不太理想的，较高电阻的C49同素异形体形成了TiSi ₂。从扩展的Born模型的角度出发，首次尝试了解Ge原子在降低C54结构的形成焓中的作用。电荷密度差异，状态密度和Bader电荷分析表明，这些系统主要是离子键合的，Ge原子为C54同素异形体引入了额外的共价键稳定性。众所周知，较高的温度有利于在TiSi _2中形成C54 。TiSi _2的亥姆霍兹自由能计算表明，振动自由能不会将系统驱动到C54相。TiSi ₂的C49结构内某些点缺陷的形成能小于1 eV，这与显示高缺陷浓度的实验一致。因此，在较高温度下形成C54的驱动力可能与C49同素异形体中的高缺陷浓度有关。