Coupling rate of ordering with degree of disorder: Developing a cation pair model for order-disorder in Li2Ti1-xZrxO3 solid solution

Abstract

The order-disorder phenomenon of the cation sub-lattice is of substantial interests recently. However, randomness of the disordered local atomic structures poses great challenges for the modeling of ordering at larger size/time scales. In this work, a cation-pair model is developed to simulate the order-disorder of layered Li2TiO3. The configurational order of the lattice is simplified by the number of cation pairs at ordered/disordered state. Simulated x-ray diffraction of lattice models is performed to allow comparison with experimental observations. The configuration dependent activation energy is obtained by the simulated evolution of order-disorder based on density functional total energies. The cation-pair simplification enables fast estimation of ordering by tracking the number of pairs with rate theory. The model successfully reproduces the inhibition of ordering from increasing Zr/Ti in the Li2Ti1-xZrxO3 solid solution. Different stages of order-disorder have distinct features of ordering rates, which is explained by the coupling between ordering rates and degree of disorder. In addition, the model predicts stage-specific equilibrium conditions at various Zr/Ti and temperatures.