Exploring energy landscapes of solid-state materials : from individual atoms to collective motions



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Chemical reactions can be understood as transitions from basin to basin on a high dimensional potential energy landscape. Varying temperature only changes the average kinetic energy of the system. While applying voltages or external pressures directly tilts the landscape and drives the reactions in desired directions. In solids at relatively low temperature, where the entropy term is approximately invariant, the reaction spontaneity is determined by the energy difference between the reactant and product basins and the reaction rate can be calculated from the barriers in between. To achieve sufficient accuracy to explain experimental observations we are interested in, density functional theory (DFT) is usually employed to calculate energies. There are two types of reactions I have studied: the first type of reaction only involves a few number of individual atoms, corresponding to traveling in a small volume in the high dimensional configuration space; the other type involves a large amount of atoms moving in a concerted pattern, and the distance traveled in the configuration space is significantly longer. The scopes of these two in the energy landscapes are in different scales and thus proper metrics for distance measurements are required. In the first case, I have mainly studied Li/Na behaviors in the cathode materials of secondary batteries. Here resolving the energy landscape step by step with detailed information is possible and useful. By analyzing the energy landscapes with DFT plus the Hubbard U correction, I have explained several phenomena related to the degradation of lithium-rich layered oxides, rate performance of surface modified LiFePO₄, and capacity of vanadium-based fluorophosphates. Predictions on both thermodynamic and kinetic properties of materials are also made based on the calculation results and some are confirmed by experiments. In the second case, my focus is on solid-solid phase transitions. With a tremendous long reaction pathway, examining every possible atomic step is too expensive. By adopting periodic boundary conditions, a small supercell can represent the main feature of the energy landscape in a coarse grained way, where the connection between phases is easier to explore. After the big picture of a phase transition mechanism learned from this simplified model, details along the reaction pathway, like new phase nucleation and growth, could be resolved by using a larger supercell. In the above treatment, two types of variables, the cell vectors and atomic positions, span a generalized configuration space. Special consideration is required to balance these two to keep consistency under different supercells and avoid biases. A solid-state NEB (SSNEB) and a solid-state dimer (SSD) method are then developed to locate saddle points in the generalized configuration space. With the methodology well justified, we are able to efficiently find possible nucleation mechanisms, for examples the CdSe rock salt to wurtzite and Mo A15 to BCC phase transitions. SSNEB is also applied in studying phases transitions under pressures, including the graphite to diamond, and CaIrO₃ perovskite to post-perovskite transitions. Combined with the adaptive kinetic Monte Carlo (AKMC) algorithm, SSD shows the ability to find new polymorphs of CdSe and the connecting barriers between them.