Abstract
The minimum energy path (MEP) and transition state are two key parameters in the investigation of the mechanisms of chemical reactions and structural phase transformations. However, determination of transition paths in solids is challenging. Here, we present an evolutionary method to search for the lowest energy path and the transition state for pressure-induced structural transformations in solids without any user input or prior knowledge of possible paths. Instead, the initial paths are chosen stochastically by connecting randomly selected atoms from the initial to final structure. The MEP of these trials paths were computed and ranked in order of their energies. The matrix particle swarm optimization algorithm is then used to generate improved transition paths. The procedure is repeated until the lowest energy MEP is found. This method is validated by reproducing results of several known systems. The new method also successfully located the MEP for the direct low-temperature pressure induced transformation of face centered-cubic (FCC) silicon to the simple hexagonal(sh) phase and FCC lithium to a complex body centered-cubic cI16 high-pressure phase. The proposed method provides a convenient, robust, and reliable approach to identify the MEP of phase transformations. The method is general and applicable to a variety of problems requiring the location of the transition state.
Highlights
Phase transitions of solids are a critical part of nature
A new matrix particle swarm optimization (PSO) (MPSO) algorithm for discrete global optimization is proposed for the selection of an minimum energy path (MEP) from among a collection of candidate transition paths
A new method of searching for the MEP and transition state (TS) of solid–solid transformations based on the global MPSO scheme was presented
Summary
Phase transitions of solids are a critical part of nature. Identification of the atomistic mechanism of a solid–solid phase transition is critical to understanding the physical process, and is essential to the development of synthesis strategies for new materials[1,2]. The most notable approaches are the dimer method[11], transition path sampling[12], and stochastic surface walking (SSW)[13] The latter involves exploration of the entire PES using molecule dynamic (MD) simulations. Many successes have been achieved using these methods[24] They are often feasible for simple structures which is limited by either (i) the need to guess the initial transition paths[25] or (ii) the substantial computational cost of long MD simulations. A straightforward implementation of an exhaustive search strategy is impractical because of the astronomically large number of possible solutions To address this problem, a new method for identifying the MEP and the TS for solid–solid phase transitions is proposed here that do not require any prior knowledge of probable reaction paths. The method is applied to provide insight into the unknown transition mechanism of the recently observed, low-temperature, kinetically controlled transition of FCC silicon to an sh structure and the more challenging long-sought-after pathway and associated change in the electronic structure during the high-pressure transition from a simple FCC lithium to a complex cI16 structure
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