Influence of postgrowth Li-poor vapor-transport equilibration on the surface Li ₂O content of a congruent LiNbO ₃ crystal

The influence of Li-poor vapor-transport equilibration (VTE) on the surface Li ₂O content of initially congruent X- and Z-cut LiNbO ₃ crystal plates was studied against the VTE temperature and time. The VTE-induced surface-Li ₂O-content reduction was evaluated from the measured birefringence. The results show that the reduction and VTE temperature follow the traditional Arrhenius law with a surface-Li ₂O-content alteration constant of (1.0 ± 0.2) × 10 ⁸/(1.6 ± 0.2) × 10 ¹⁰ mol % and an activation energy (2.2 ± 0.2)/(2.8 ± 0.2) eV for the X/Z-cut plate, and the reduction has a square-root dependence on the VTE time, δC ^X = 0.15t ^0.5 for the X-cut plate and δC ^Z = 0.167t ^0.5 for the Z-cut plate. A generalized empirical expression that relates the reduction to both the VTE temperature and duration is presented. The expression is useful for producing an off-congruent, Li-deficient LiNbO ₃ plate with the desired surface Li ₂O content via adjustment of the VTE temperature and duration. On the basis of the known VTE time dependence on the surface-Li ₂O- content reduction, a solution to the Li ⁺ out-diffusion equation, an integral of the error function complement, is obtained and verified by previously reported experimental results. The results also show that the VTE displays slight anisotropy and is slightly faster along the optical axis direction of the crystal. The Li-poor VTE is a slow process. At 1100 °C, the Li-poor VTE time required for the surface Li ₂O content reaching the Li-deficient boundary is about 400/323 h for the X/Z-cut plate.