Modeling of Surface Diffusion in hcp Zr and Ti

The statics and dynamics of vacancies and adatoms on different surface orientations in two hcp materials are studied by using static relaxation techniques and many-body potentials. Formation and migration energies and entropies as well as attempt frequencies are evaluated and used in the random walk approach to obtain correlation factors and diffusivities. It is found that the main features of surface diffusion are dominated by jumps on and between a few atomic layers, so that a consistent comparison between the two mechanisms is feasible. The activation energies and the diffusivities for different environments, namely, bulk Q_b, D_b, symmetric grain boundaries Q_gb, D_gb, and surfaces, Q_s, D_s, calculated using the same simulation technique and interatomic potentials, fulfil the expected relationships Q_s < Q_gb < Q_b and D_s > D_gb > D_b. It is also found that generally adatoms are faster surface diffusers than vacancies.