Ab initio investigation of the atomic volume, thermal expansion, and formation energy of WTi solid solutions

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 Gr\"uneisen 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-Gr\"uneisen model yields results for WTi comparable to the quasiharmonic approach at a fraction of the computational cost.