Multiple phase transition path and saddle point search in computer aided nano design

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He, Lijuan
Wang, Yan
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Functional materials with controllable phase transitions have been widely used in devices for information storage (e.g. hard-disk, CD-ROM, memory) and energy storage (e.g. battery, shape memory alloy). One of the important issues to design such materials is to realize the desirable phase transition processes, in which atomistic simulation can be used for the prediction of materials properties. The accuracy of the prediction is largely dependent on searching the true value of the transition rate, which is determined by the minimum energy barrier between stable states, i.e. the saddle point on a potential energy surface (PES). Although a number of methods that search for saddle points on a PES have been developed, they intend to locate only one saddle point with the maximum energy along the transition path at a time. In addition, they do not consider the input uncertainty associated with the calculation of potential energy. To overcome the limitations, in this dissertation, new saddle point search methods are developed to provide a global view of energy landscape with improved efficiency and robustness. First, a concurrent search algorithm for multiple phase transition pathways is developed. The algorithm is able to search multiple local minima and saddle points simultaneously without prior knowledge of initial and final stable configurations. A new representation of transition paths based on parametric Bézier curves is introduced. A curve subdivision scheme is developed to dynamically locate all the intermediate local minima and saddle points along the transition path. Second, a curve swarm search algorithm is developed to exhaustively locate the local minima and saddle points within a region concurrently. The algorithm is based on the flocking of multiple groups of curves. A collective potential model is built to simulate the communication activities among curves. Third, a hybrid saddle-point search method using stochastic kriging models is developed to improve the efficiency of the search algorithm as well as to incorporate model-form uncertainty and numerical errors associated with density functional theory calculation. These algorithms are demonstrated by predicting the hydrogen diffusion process in FeTiH and body-centered iron Fe8H systems.
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