Change of electrochemical potential and entropy of Li around an edge dislocation in solid electrolytes

The equations of the electrochemical potential and entropy of Li atoms near an edge dislocation inside solid electrolytes are derived. Although a stress field becomes complex in the presence of many dislocations in polycrystalline materials, the equations are still valid and the qualitative conclusions are robust at least for lower dislocation density than about ${10}^{16}$ $m^{-2}$. As the modified electrochemical potential of ${\mathrm{Li}}^{+}$ ions in a stress field is spatially uniform at equilibrium in solid electrolytes due to the high mobility of ${\mathrm{Li}}^{+}$ ions, the spatial variations of the entropies associated with the stress and electric-potential field are obtained. From the increase in the local entropy by a positively charged dislocation, the concentration of Frenkel pairs of ${\mathrm{Li}}^{+}$ interstitials and vacancies is derived, which could be considerably higher near the dislocation. It could be the reason for higher ionic conductivity along a dislocation. It is suggested that a dislocation should be positively charged in an ionic conductor of positive ions in the absence of impurities. When the dilation due to ${\mathrm{Li}}^{+}$ interstitials is relatively large, reduction or oxidation of the solid electrolyte may possibly occur near a dislocation although considerable diffusion of atoms and electrons is necessary for it.