WTi is used as an adhesive layer in integrated circuit devices. The temperature dependent mechanical properties of WTi are still largely unexplored. In this paper we investigate WTi solid solutions with density functional theory calculations to determine the temperature and concentration dependent behavior of volume and coefficient of thermal expansion. The coefficient of thermal expansion is analyzed in terms of the bulk modulus, heat capacity, and Grüneisen parameter. Furthermore, we gain insight into the bonding of the system via investigation of the electronic structure, phonon density of states, and analysis of the formation energy. Low Ti concentrations lead to strong W-Ti bonding, as manifested in additional high frequency peaks in the phonon density of states. As a consequence, deviations from Vegard's law are found at low Ti concentrations, with a minimum of the lattice constant at about 15 at. % Ti. The CTE as a function of Ti concentration shows a negative trend at low temperatures and Ti concentrations, which is related to a strong decrease of heat capacity. Finally we show that the Debye-Grüneisen model yields results for WTi comparable to the quasiharmonic approach at a fraction of the computational cost.

中文翻译：

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从头开始研究WTi固溶体的原子量，热膨胀和形成能

WTi用作集成电路设备中的粘合层。WTi的温度相关的机械性能仍未开发。在本文中，我们使用密度泛函理论计算研究WTi固溶体，以确定温度和浓度相关的体积行为和热膨胀系数。根据体积模量，热容量和Grüneisen参数分析热膨胀系数。此外，我们通过研究电子结构，声子态密度和形成能分析，深入了解了系统的键合。低的Ti浓度会导致牢固的W-Ti键，这在声子密度的状态中出现了其他高频峰值。结果，偏离了Vegard' 在低Ti浓度下发现s律，晶格常数的最小值大约为15 at。钛％。CTE作为Ti浓度的函数在低温和Ti浓度下显示出负趋势，这与热容的大幅降低有关。最后，我们证明Debye-Grüneisen模型产生的WTi结果与准谐波方法相当，而计算成本却很小。