  Strong coupling among external voltage, electrochemical potentials,
concentrations of electronic and ionic species, and strains is a ubiquitous
feature of solid state mixed ionic-electronic conductors (MIECs), the materials
of choice in devices ranging from electroresistive and memristive elements to
ion batteries and fuel cells. Here, we analyze in detail the electromechanical
coupling mechanisms and derive generalized bias-concentration-strain equations
for MIECs including effects of concentration-driven chemical expansion,
deformation potential, and flexoelectric effect contributions. This analysis is
extended towards the bias-induced strains in the uniform and scanning probe
microscopy-like geometries. Notably, the contribution of the electron-phonon
and flexoelectric coupling to the local surface displacement of the mixed
ionic-electronic conductor caused by the electric field scanning probe
microscope tip has not been considered previously. The developed thermodynamic
approach allows evolving theoretical description of mechanical phenomena
induced by the electric fields (electro-mechanical response) in solid state
ionics towards analytical theory and phase-field modeling of the MIECs in
different geometries and under varying electrical, chemical, and mechanical
boundary conditions.
