The relaxation time of OH bond for hydrogen impurity in LiNbO3

TL;DR

This paper models the anharmonic vibrational dynamics of hydrogen impurities in lithium niobate using a Morse potential, deriving diffusion constants and relaxation times that align with experimental data.

Contribution

It introduces a one-dimensional anharmonic oscillator model for hydrogen impurity dynamics in LiNbO3, linking vibrational behavior to diffusion and relaxation properties.

Findings

Hydrogen diffusion constant matches experimental values.

Relaxation time derived from anharmonic oscillation theory.

Hydrogen concentration analyzed via Boltzmann distribution.

Abstract

The one dimensional model for the dynamic of hydrogen in lithium niobate is explained by adopting Morse potential. The diffused hydrogen substitutes Lithium and it makes bonding with one oxygen atom of a facet of oxygen-triangle. The bonds will be stretched to set up anharmonic vibration. The damped anharmonic oscillation is derived to explain the dynamics of hydrogen as an impurity. The thermal fluctuation is studied by Fokker Planck equation has an important role to determine the diffusion constant for substitutional hydrogen. The hydrogen diffusion constant and relaxation time are calculated to support the proposed theory and existing experimental results. The concentration of substitutional hydrogens is studied with the help of Boltzmann distribution.