Li ⁺ diffusivity in 5 mol% MgO-doped LiNbO ₃ crystal and Li-poor vapor transport equilibration effect on its surface composition

Diffusivity of Li ⁺ in 5 mol% (in growth melt) MgO-doped LiNbO ₃ crystal has been studied as a function of Li ₂O-content ranging from 43.4 to 44.4 mol% under different temperatures. First, diffusion-limited Li ₂O-content depth profiles were produced by carrying out Li-poor vapour transport equilibration (VTE) treatments on two 0.5-mm-thick MgO-doped LiNbO ₃ plates at 1100 and 1130 °C for 40 h. Second, the profiles were obtained by alternatively doing the optical polish to one crystal surface and the Li ₂O-content characterization on the polished surface through the measurement of birefringence. Third, Boltzmann-Matano method was applied to the profile to derive the Li ⁺ diffusivity as a function of Li ₂O-content. The results show that the diffusivity decreases with the reduced Li ₂O-content by at least two orders of magnitude as the Li ₂O-content reduces by 1 mol% from the as-grown state. In the Li ₂O-content range studied, the diffusivity at 1130 °C is at least two times larger than that at 1100 °C. In addition, we also studied the time dependence of the Li-poor-VTE-induced reduction of Li ₂O-content on surface of the same MgO-doped crystal. The results show that the surface Li ₂O-content reduction induced has a square-root dependence on the VTE duration. Based upon this dependence, the mathematical solution to the Li ⁺ diffusion equation, an integral of error function complement, is obtained and verified by the experimental result. It is concluded that the MgO doping has less effect on both the Li ⁺ diffusivity and the dependence of surface Li ₂O-content reduction on the VTE duration.