Elasticity of Solids with a Large Concentration of Point Defects

Abstract

The elastic behavior of solids with a large concentration of interacting point defects has been analyzed. The analysis predicts that, in such solids, mechanical stress may be partially relieved by a shift in the association/dissociation equilibrium of the point defects. Association/dissociation of the point defects in response to an external stress will proceed until the decrease in elastic energy is balanced by the increased chemical energy of the defect distribution. The resulting change in the linear dimensions may be called "chemical strain", in analogy to the previously studied "chemical stress". A solid in which chemical strain may develop in response to external stress should exhibit two distinct Young's moduli: relaxed, on a time scale which allows the defects to reach equilibrium; and unrelaxed, on a time scale which is too short for the defect equilibrium to be established. Our analysis suggests that materials exhibiting the chemical-strain effect are capable of reversible adaptation to external mechanical constraints. Measurements on a self-supported film of Ce0.8Gd0.2O1.9 strongly support the theoretical predictions.