Anomalous energy pathway of vacancy migration and self-diffusion in hcp Ti

Abstract

An anomalous energy pathway with energetically-equivalent double saddle points for vacancy mediated self-diffusion within an hcp-Ti basal plane is unveiled by density functional theory.Examination of migration pathway and phonon force constants suggests that the migrating atom tries to follow the bcc-hcp phase transition via the Burgers shear deformation. We propose that the formed energy local minimum with a bcc-like atomic environment between the two saddle points originates from the existence of high-temperature bcc phase and is a feature of Group IV hcp metals with bcc-hcp phase transition. Computed diffusion coefficients are in favorable accord with experiments for hcp Ti. PACS numbers: 66.30.Fq, 63.20.dk, 82.20.Db 2

First principles study of normal and fast diffusing metallic impurities in hcp titanium

“…We also ignore differences in the migration energies of the vacancy, self interstitial, and impurity interstitials, as well as the X iÀs exchange barrier E b iÀsX . This is probably a more severe approximation, since unlike the prefactors the migration energies enter the rate expressions exponentially, and since interstitial migration is believed to have a lower energy than vacancy migration [22,23]. However, as we show below the scale of all of the migration energies, 6 0:5 eV, is significantly less than the variation among the relevant formation energies, and we therefore expect the neglected variation in migration energies to have no qualitative effect on our results.…”

“…The desire for chemically specific predictive information about different impurity elements requires the use of first principles electronic structure methods, such as density functional theory (DFT), which, unlike interatomic potentials, do not have to be parameterized for each combination of interacting species, but the large unit cells required make such calculations challenging. Most published simulations on Ti have considered only intrinsic defects [17][18][19][20][21][22][23], non-metallic impurities [21], or the interaction between substitutional impurities and vacancies [24]. There have also been some DFT simulations comparing the structure and migration of interstitial Fe and C in the related hcp material Zr [25,26], but none comparing different metal impurities.…”

Diffusion anisotropy of poor metal solute atoms in hcp-Ti

“…19,[21][22][23][24] The binding energies of vacancysolute pairs for Al, Si, Ga, Ge, In, and Sn in hcp-Ti are shown in Fig. 2.…”

“…The present DFT calculation of self-diffusivity of hcpTi is compared to the first-principles calculations of Shang et al 22 and experimental survey of Köppers et al 1 in Fig. 3.…”

Interstitial diffusion of O, N, and C in α-Ti from first-principles: Analytical model and kinetic Monte Carlo simulations

“…In the last few decades, there has been an increasing utilisation of first-principles calculations on the study of vacancy-mediated diffusion, [7][8][9][10] as well as interstitial diffusion 11,12 in hcp crystals. In Wu and Trinkle's and O'Hara's articles, 11,12 ab initio calculations were used to provide data for an analytical approach called the Multi-State Diffusion (MSD) method, developed by Landman and Shlesinger, 13,14 in order to evaluate the diffusivity of interstitial elements.…”