Theoretical approach to study Li self-diffusivities dependence on composition in lithium niobate single crystals

Abstract

Abstract This study proposes an Arrhenius laws formula for lithium self-diffusion in lithium niobate single crystals ( <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:msub> <mml:mrow> <mml:mi mathvariant="normal">LiNbO</mml:mi> </mml:mrow> <mml:mrow> <mml:mn>3</mml:mn> </mml:mrow> </mml:msub> </mml:math> , LN) as a function of nonstoichiometry x , with general formula, <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:msub> <mml:mrow> <mml:mi mathvariant="normal">Li</mml:mi> </mml:mrow> <mml:mrow> <mml:mn>1</mml:mn> <mml:mo>−</mml:mo> <mml:mn>5</mml:mn> <mml:mi>x</mml:mi> </mml:mrow> </mml:msub> <mml:msub> <mml:mrow> <mml:mi mathvariant="normal">Nb</mml:mi> </mml:mrow> <mml:mrow> <mml:mn>1</mml:mn> <mml:mo>+</mml:mo> <mml:mi>x</mml:mi> </mml:mrow> </mml:msub> <mml:msub> <mml:mrow> <mml:mi mathvariant="normal">V</mml:mi> </mml:mrow> <mml:mrow> <mml:mn>4</mml:mn> <mml:mi>x</mml:mi> </mml:mrow> </mml:msub> <mml:msub> <mml:mrow> <mml:mi mathvariant="normal">O</mml:mi> </mml:mrow> <mml:mrow> <mml:mn>3</mml:mn> </mml:mrow> </mml:msub> </mml:math> , where V denotes a vacancy, based on the ferroelectric phase transition theory in lithium niobate. This approach demonstrates that the variation in Li self-diffusivities depends on factors such as mass, charge, defect structure, and, consequently, temperature. This theoretical investigation enables us to reproduce the measured data of Li diffusivities in LN single crystals of three different compositions with various ratios of Li/(Li+Nb) = 0.499, 0.494, 0.486 by a mixed vacancy model.