Microstructure evolution and kinetics of B-site nanoparticle exsolution from an A-site-deficient perovskite surface: A phase-field modeling and simulation study

Segregation-exsolution of B-site catalytic dopants as nanoparticles from A-site-deficient perovskite (A_1-xBO_3-δ) surfaces has been actively used in recent years to promote the activity and durability of perovskite oxides towards efficient fuel oxidation and water splitting. The mechanistic understandings are currently gained from equilibrium thermodynamics, such as atomic scale density functional theory calculations, in terms of segregation energy, interaction energy and elastic energy. Herein, we have developed a micro-scale phase-field model framework that describes the kinetics and microstructure evolutions of the B-site segregation and nanoparticle exsolution from the A_1-xBO_3-δ surface. The model was derived in a thermodynamically consistent manner by employing a ternary regular-solution free-energy functional and Cahn-Hilliard kinetic equations. The key hypothesis is that the B-site nanoparticle is exsolved by a spinodal decomposition once the surface region of A_1-xBO_3-δ is driven to the spinodal region of the free-energy functional via B-site segregation to the surface and/or via expansion of the chemical spinodal region. The effects of oxygen partial pressure (or electric polarization), B-site supersaturation (or A-site deficiency), and segregation energy have been explicitly investigated, and the results obtained agree qualitatively with the experimental observations. The proposed model can serve as a multi-scale bridge that ties the atomic-scale understandings to the micro-scale observations and has the potential to be used for the design and optimization of nano-architectures of A_1-xBO_3-δ materials.