Zero point corrections and entropy effect on ab-initio equation-of-state: A case study on bulk titanium

From a practical point of view, titanium is one of the most used metals for aerospace and industrial processing. The reasons behind this are fundamental issues such as its high resistance to corrosion and the α→β martensitic transformation. Thus titanium appears to be an attractive element for the scientific community, especially as its mechanical and elastic properties are concerned. In this paper, we report on a basic approach of taking into consideration the zero point energies of phonons and electrons on the computed bulk modulus by ab-initio density functional theory method. The zero point energy of electrons is considerably greater than the zero point energy of phonons, but their effects on the bulk modulus are almost the same. In addition, starting from a thermodynamic description, the question of the entropy contribution to the bulk modulus is addressed. We show that for titanium, the entropy effect is significant only for temperatures above 600 K. The temperature dependence of the Anderson–Grüneisen parameter for titanium is shown to be δT=a+bT−1−cT−2, with a=0.94, b=1.9×103K and c=1.9×105K2. To the best of our knowledge, this is the first numerical work reported until now on the temperature dependence of this parameter for titanium. Other thermoelastic parameters such as the Grüneisen parameter γ, the volume and linear thermal coefficients, αV and αl, are obtained with good accuracy.