Importance of coordination number and bond length in titanium revealed by electronic structure investigations

We study the influence of coordination number and bond length on the phase stability and orbital occupation in Ti using density functional theory. In particular, Ti under a wide range of conditions (equilibrium state, hydrostatic pressure, anisotropic strain, and phase transformations) is systematically investigated allowing us to derive generic energetic and electronic trends. Our analysis of the correlations between electronic structure and the atomic geometry reveals that the most suitable descriptors of the system are an effective coordination number and an effective bond length. Utilizing these descriptors, we show that (i) the phase stability of Ti increases with coordination number, because of the increased number of interatomic bonds; (ii) the occupation number of the d (s and p) orbital decreases (increases) with increasing the bond length, because of the localized (delocalized) character of the d (p and s) orbital. These dependencies are particularly evident after applying a simple harmonic strain correction to the energy and an electron-transfer correction within the ω phase. The physical picture derived from pure Ti is used to explain the phase stability and orbital occupation of Ti-Nb and Ti-Zr alloys, which reveals the underlying mechanisms for various experimental phenomena in Ti alloys. The lattice coordination number determines the bonding states and phase stability of Ti, which explains the energy-pressure and energy-strain relationships, energy variations in phase transformations, and phase stabilities of Ti-transition metal alloys. The bond length influences the occupation numbers of s, p, and d orbitals in pure Ti and Ti alloys by changing the effective pressures on their electron clouds.