Contribution of the space charge to the grain boundary energy in yttria-stabilized zirconia

Abstract

A model based on the effect of a modest applied dc electric field on grain growth is proposed for the contribution of the space charge to the grain boundary (GB) energy in 3 mol % yttria-stabilized zirconia (3 YSZ). The model considers that the total GB energy $\gamma_{\text{b}}^0$ (the capillary driving force for grain growth) consists of three major components: (a) $\gamma_{\text{b}}^\varSigma$ due to the misorientation between neighboring grains, (b) $\gamma_{\text{b}}^{\text{s}}$ due to the size misfit between the segregated solute and the solvent cations, and (c) $\gamma_{\text{b}}^{\text{e}}$ the electrostatic (space charge) component, which results from the segregation of the aliovalent yttrium ions to the grain boundaries. The former two components combined comprise 40 % of the total GB energy in 3 YSZ and the electrostatic component 60 %. Based on the model, the calculated magnitudes of the three components were in qualitative accord with theoretical considerations and with values reported in the literature. A reduction in $\gamma_{\text{b}}^{\text{e}} ,$ and in turn in $\gamma_{\text{b}}^0 ,$ results from the bias exerted by the applied field on the space charge potential that occurs with the segregation of the yttrium ions to the grain boundaries. The observed reduction of grain growth in 3 YSZ by an applied electric field is attributed mainly to the reduction in $\gamma_{\text{b}}^{\text{e}}$ by the field.