Non-Equilibrium Thermodynamic Treatments of Lattice Diffusion Dynamics in Ceria-Zirconia and Related Redox-Active Oxides

Redox-active oxides function as mixed ionic-electronic conductors that store and release O atoms, rendering them effective as oxidation catalysts, O atom carriers in chemical looping, electrolytes in solid oxide fuel cells, separation membranes, and sensors for toxic and flammable molecules. In each case, their function requires chemical reactions at surfaces and transport of ions and electrons through bulk lattices. The diversity in their practical applications has led, in turn, to disparate treatments and nomenclature to describe their function. This study describes and implements a framework for analysis enabled by the lexicon and concepts of nonequilibrium thermodynamics to describe O atom diffusion in Ce0.5Zr0.5O2–x (CZO) solids, which are used as O-carriers in emissions control and chemical looping. The properties and driving forces are those of classical thermodynamics (chemical potential, activity coefficient, (excess) free energy), and the foundational constructs stem from transition state theory and scaling relations, which are prevalent in all aspects of chemistry and physics. These reaction-diffusion models accurately describe measured oxidation rates of CZO crystals with regressed parameters that account for how oxidation free energies, O anion (and vacancy) mobilities, and diffusion barriers change as intracrystal O contents evolve in time and space during transient oxidation reactions. The models show that free energy barriers for lattice diffusion increase as oxidation free energies increase with increasing O content, which implies that diffusion is limited not by the migration of O anions but instead by electron transfer between vicinal Ce(III) and Ce(IV) cations. Crystal size affects oxidation rates through its consequences to the diffusion path length and through the effects of size and crystal inhomogeneities on redox thermodynamics, because oxidation free energies become more positive and O anion mobilities decrease with increasing crystal size. These inferences are not all new; in fact, some confirm in general terms the effects of size and O content on electronic conduction and lattice diffusion reported from electrochemical data. They emerge, however, from straightforward measurements of oxidation rates and analysis methods that account for thermodynamic nonidealities by using chemical potentials as the correct diffusion driving force and treating lattice hops as exchange events with barriers connected to redox thermodynamics through scaling relations. The use of N2O as the oxidant and CZO as the host not only represents a convenient illustrative example to convey the lessons learned about lattice diffusion by using formalisms ubiquitous in chemistry, but also to show how the nonequilibrium thermodynamics canon is able to describe and predict chemical dynamics in thermodynamically nonideal complex systems.