A mathematical model for Ti diffusion in LiNbO3

Abstract
The diffusion of titanium in crystalline lithium niobate is studied within the framework of the Nernst-Planck theory for ionic diffusion. Under this conceptualization, a concentration-dependent diffusivity emerges naturally from the mathematical model as a direct consequence of the electric field induced by ion dislocation in the lattice. Numerical simulations of the one-dimensional case show strong evidence of enhanced diffusive transport of mass. This might explain the anomalous lateral penetration of Ti in LiNbO3 which has been observed in previous experiments.