Determine whether the chemical-pressure model disagrees with standard Larché–Cahn theory

Determine whether the first-order corrections to the elastic moduli and the deviations from the transferability rule predicted by the chemical-pressure coupling model constitute a disagreement with standard Larché–Cahn theory.

Background

The paper proposes a chemical-pressure mechanism for coupling vacancy composition to strain in one-component crystals and compares its predictions with standard Larché–Cahn composition-strain theory. For systems deformed by surface tractions, the calculated stress and strain fields agree qualitatively with Larché–Cahn results after introducing modified elastic moduli. However, the chemical-pressure formulation predicts that closed-system elastic moduli receive corrections at first order in the coupling strength, and the system deformed by gravity does not follow the same transferability rule as the surface-traction examples.

The authors emphasize that a direct comparison is complicated by differing treatments of Cauchy stress: in the chemical-pressure model, the Cauchy stress is the sum of elastic and chemical stresses, whereas this distinction is not explicitly made in standard Larché–Cahn theory. Consequently, whether the reported differences represent a genuine theoretical inconsistency or arise from differing stress definitions remains unresolved.