On the Nature of Transport Phenomena during Proton Exchange Technological Process

Extremely complex transfer processes characterize the technology of waveguides production by proton exchange method in the lithium niobate single crystal. The melt of benzoic acid C6H5COOH, which acts as a source of protons, is used most often as a working fluid. Proton exchange occurs because of dissociative absorption of protons into the crystal, accompanied by the extrusion of lithium ions back into the working fluid. Electrokinetic transport phenomena in the melt of benzoic acid are fundamentally different from diffusion processes in the crystal, however, these processes are interrelated. However, the dynamics of crystal protonation is of greatest interest to technologists, which is why, historically, the first calculations were made for proton exchange process, as a result of which optical waveguides are formed in it. Experimental data reliably show that the concentration front of protons in the volume of the crystal moves in dependence on time according to the approximately square root law and has a sharp, practically stepped profile. It is even more surprising that the so-called nonlinear diffusion equation is the most efficient for describing the penetration of protons deep into the crystal. It is obtained from a more general quasi-linear second order diffusion equation in the consequence of assumption about a power dependence of the diffusion coefficient on the concentration. The difference from classical diffusion is expressed by the stepped nature of the profile and means the finite speed of disturbance propagation in the system.