Size-dependent phase change in energy storage materials: Comparing the impact of solid-state wetting and of coherency stress

Coherent phase transformations in interstitial solid solutions or intercalation compounds with a miscibility gap are of practical relevance for energy storage materials and specifically for metal hydride or lithium-ion compound nanoparticles. Different conclusions on the size-dependence of the transformation conditions are reached by modeling or theory focusing on the impact of either one (internal, solid-state-) critical-point wetting of the nanoparticle surface or coherency constraints from solute-saturated surface layers. We report a hybrid numerical approach, combining atomistic grand canonical Monte Carlo simulation with a continuum mechanics analysis of coherency stress and modeling simultaneously wetting and mechanical constraints. When the ratio between chemical and misfit-strain-related contributions to the solute-solute interaction energy takes values realistic for interstitial solutions-which are typical for energy storage materials-we find that the impact of solid-state wetting is weak and that of coherency stress is dominant. Specifically, mechanical interaction can act to reduce the phase transformation hysteresis at small system size, and it can make the solid more binding for solute, thereby reducing the "plateau" chemical potential at phase coexistence. We present equations for the impact of coherency stress on the size-dependence of upper consolute temperature, plateau chemical potential, and charging/discharging hysteresis.