Screening and strain in superionic conductors

I calculate the screening length and its relation to elastic constants from mean-field models of superionic conductors. The Debye formula for a continuous fluid's screening length is replaced by one that accounts for the discrete nature of the lattice. Interactions alter the screening length and in some cases give oscillations in the charge structure. The screening lengths derived here are exact not only at low temperature where there are few defects, but also at high temperature where the effective interaction strength is small. The mean-field treatment correctly gives the decrease in an elastic constant observed at the superionic transition for a variety of crystals. This decrease is best explained by a change in the defect creation entropy with density. The effect of doping on the elastic constant also agrees well with experiment. The extension to the mean-field models given here provides a consistent picture of the response of a superionic crystal to electrical, mechanical and thermal stresses, as well as to doping.