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The one dimensional model for the dynamic of hydrogen in lithium niobate isexplained by adopting Morse potential. The diffused hydrogen substitutesLithium and it makes bonding with one oxygen atom of a facet ofoxygen-triangle. The bonds will be stretched to set up anharmonic vibration.The damped anharmonic oscillation is derived to explain the dynamics ofhydrogen as an impurity. The thermal fluctuation is studied by Fokker Planckequation has an important role to determine the diffusion constant forsubstitutional hydrogen. The hydrogen diffusion constant and relaxation timeare calculated to support the proposed theory and existing experimentalresults. The concentration of substitutional hydrogens is studied with the helpof Boltzmann distribution.

The relaxation time of OH bond for hydrogen impurity in LiNbO3