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.

Elasticity of Solids with a Large Concentration of Point Defects II. The Chemical Strain Effect in Ce0.8Gd0.2O1.9

“…[2] Let us consider a solid with large concentrations of two types of point defects, A and B, capable of interacting with each other via an association/dissociation reaction:…”

“…The ionic conductivity in these materials originates in the large concentration (> 10 21 cm -3 ) of mobile point defects. [1] We have recently suggested (Part I, [2] ) that if, in addition to being highly mobile, the point defects can interact with each other, for instance form complexes or clusters, with associated volume change, then such materials may exhibit stress relaxation [3] via reversible defect association or dissociation. We have called this the chemical strain effect.…”

“…The magnitude of this volume change is estimated to be b > 15 Å 3 . [2] Therefore, Ce 0.8 Gd 0.2 O 1.9 ceramics satisfy both requirements for potentially exhibiting the chemical strain effect: [2] they contain a large concentration of highly mobile point defects and the point defects interact causing significant volume change. Here we report that, indeed, self-supported nanocrystalline films of Ce 0.8 Gd 0.2 O 1.9 experience a fully reversible change of linear dimensions in response to variation of external mechanical constraints.…”

Interactions Between Non‐Stoichiometric Stresses and Defect Transport in a Tubular Electrolyte

“…In addition to being detrimental to mechanical reliability, mechanical stresses can also alter the ionic transport in the electrolyte, thus affecting the electrochemical performance of the SOFC [19]. For example, it was shown [20] that defect association and dissociation may take place in 20 GDC through stress relaxation mechanisms owing to the coupling between mechanical stresses and electrochemical reactions. An uphill transport of oxygen ions in solid electrolytes was demonstrated [21] by measuring the polarization voltage across the faces of doped zirconia beam subject to bending.…”

Micro-solid oxide fuel cells: status, challenges, and chances

“…Microstructural features, such as the small grain size, texture, varying degrees of crystallinity, residual amorphous phases, and microstrains, form the nanoimpact on thermal and electric properties of electrolyte thin films. It was seen that nanocrystalline materials show unusual electrical conductivities [39][40][41][42] and thermal stabilities [43][44][45], because of the large amount of grain boundaries these materials contain in relation to the grain volume. In the case of nanocrystalline thin films, stresses within the films, which result from thermal expansion mismatch between the substrate and the thin films, can affect the electrical properties and must be taken into consideration for their application in SOFCs [46].…”