Thermodynamically consistent variational principles for charged interfaces

A generalized framework that naturally incorporates the free energy contributions of thermochemical, structural, mechanical, and electrical fields is presented to describe Space Charge Layer (SCL) their effect on transport properties ionic ceramics. The theory recovers existing analytical, ideal solution models, such as Debye-Hückel (DH), Mott-Schottky(MS), Symmetric Gouy-Chapman (SGC), Asymmetric (AGC). Strong Mebane-De Souza (MDS) Vikrant-Chueh-García (VCG) are discussed. DH, SGC, AGC models SCL for intrinsic systems, while MS has capability capture substitutional systems with an immobile charged dopant. In general, fall short in capturing physical effects associated a highly doped system, even though millivolt adjustments interfacial voltage decreases cumulative error experimental conductivity values. contrast, MDS VCG very well concentration-dependent contribute smaller error, compared models. Even provides fits uncertainties lower than 0.549%, defect profiles show sharp, unphysically large concentration gradients, order few Angstroms. captures description thick SCL, up 20 nm, due locally induced chemomechanical stresses, by using quantities, delivering 1.79% total conductivity. comprehensive herein sets stage model microstructural evolution materials properties, enables design underlying microstructure under different external temperature, stress, electrical, magnetic, chemical stimuli.