Li-rich/Li-poor vapor transport equilibration time dependence of surface composition of congruent LiNbO ₃ crystal

The influence of Li-rich/Li-poor vapor transport equilibration (VTE) at 1100°C on surface Li ₂O-content of 1 mm thick, congruent X- and Z-cut LiNbO ₃ crystal plates was studied against VTE duration. The VTE-induced surface Li ₂O-content alteration was determined from measured birefringence. The results show that the induced surface Li ₂O-content alteration has a square root dependence on the VTE duration for both cases of Li-rich and Li-poor VTE. The dependence shows a slight effect of cut of plate and is stronger for the Z-cut plate. The Li-rich VTE duration required for surface composition reaching the stoichiometric boundary is similar to 20.0/15.6 h for the X-/Z-cut plate. In contrast, the Li-poor VTE is a much slower process than the Li-rich VTE. The Li-poor duration required to reach the Li-deficient boundary is 400/323 h for the X-/Z-cut plate. Based upon the known VTE duration dependence of surface Li ₂O- content, a mathematical model is established and the solution to the diffusion equation, an integral of error function complement, is obtained and verified by previously reported experimental results on Li-poor VTE.