A comparison of chain-of-states based methods for finding minimum energy pathways (MEPs) is presented. In each method, a set of images along an initial pathway between two local minima is relaxed to find a MEP. We compare the nudged elastic band (NEB), doubly nudged elastic band, string, and simplified string methods, each with a set of commonly used optimizers. Our results show that the NEB and string methods are essentially equivalent and the most efficient methods for finding MEPs when coupled with a suitable optimizer. The most efficient optimizer was found to be a form of the limited-memory Broyden-Fletcher-Goldfarb-Shanno method in which the approximate inverse Hessian is constructed globally for all images along the path. The use of a climbing-image allows for finding the saddle point while representing the MEP with as few images as possible. If a highly accurate MEP is desired, it is found to be more efficient to descend from the saddle to the minima than to use a chain-of-states method with many images. Our results are based on a pairwise Morse potential to model rearrangements of a heptamer island on Pt(111), and plane-wave based density functional theory to model a rollover diffusion mechanism of a Pd tetramer on MgO(100) and dissociative adsorption and diffusion of oxygen on Au(111).

The EON software is designed for simulations of the state-to-state evolution of atomic scale systems over timescales greatly exceeding that of direct classical dynamics. States are defined as collections of atomic configurations from which a minimization of the potential energy gives the same inherent structure. The time evolution is assumed to be governed by rare events, where transitions between states are uncorrelated and infrequent compared with the timescale of atomic vibrations. Several methods for calculating the state-to-state evolution have been implemented in EON, including parallel replica dynamics, hyperdynamics and adaptive kinetic Monte Carlo. Global optimization methods, including simulated annealing, basin hopping and minima hopping are also implemented. The software has a client/server architecture where the computationally intensive evaluations of the interatomic interactions are calculated on the client-side and the state-to-state evolution is managed by the server. The client supports optimization for different computer architectures to maximize computational efficiency. The server is written in Python so that developers have access to the high-level functionality without delving into the computationally intensive components. Communication between the server and clients is abstracted so that calculations can be deployed on a single machine, clusters using a queuing system, large parallel computers using a message passing interface, or within a distributed computing environment. A generic interface to the evaluation of the interatomic interactions is defined so that empirical potentials, such as in LAMMPS, and density functional theory as implemented in VASP and GPAW can be used interchangeably. Examples are given to demonstrate the range of systems that can be modeled, including

Kinetic Monte Carlo is a method used to model the state-to-state kinetics of atomic systems when all reaction mechanisms and rates are known a priori. Adaptive versions of this algorithm use saddle searches from each visited state so that unexpected and complex reaction mechanisms can also be included. Here, we describe how calculated reaction mechanisms can be stored concisely in a kinetic database and subsequently reused to reduce the computational cost of such simulations. As all accessible reaction mechanisms available in a system are contained in the database, the cost of the adaptive algorithm is reduced towards that of standard kinetic Monte Carlo.

The A15 to bcc phase transition is simulated at the atomic scale based on an interatomic potential for molybdenum. The migration of the phase boundary proceeds via long-range collective displacements of entire groups of atoms across the interface. To capture the kinetics of these complex atomic rearrangements over extended time scales we use the adaptive kinetic Monte Carlo approach. An effective barrier of 0.5 eV is determined for the formation of each new bcc layer. This barrier is not associated with any particular atomistic process that governs the dynamics of the phase boundary migration. Instead, the effective layer transformation barrier represents a collective property of the complex potential energy surface. DOI: 10.1103/PhysRevLett.116.035701 Many properties of bulk materials are determined by internal interfaces. As only small amounts of interface active elements are required to modify the stability and mobility of interfaces, interface properties are a focus in alloy design. In Ni-based superalloys [1], for example, refractory elements such as Re, Mo, or W are added to suppress creep. These elements can induce the formation of topologically close-packed (TCP) phases [2] that are not coherent with the cubic and single-crystalline superalloy material. The TCP phases are detrimental to the mechanical properties of the alloys and thus their formation needs to be avoided or retarded. In addition to a detailed knowledge of the structure and stability of the interfaces between TCP phases and the host material it is key to obtain insight into the kinetics of the migration of the phase boundaries.Simulating the kinetics of complex phase boundaries in solid-solid phase transformations up to experimental time scales remains one of the great challenges in the atomistic modeling of materials. Molecular dynamics (MD) simulations are limited to time scales that are orders of magnitude shorter than experimental ones. To observe phase boundary migration on such short time scales unrealistically high driving forces are required that can alter the underlying atomistic mechanisms. Another challenge is presented by the collective atomic displacements at the interface that are too complex to use a lattice based kinetic Monte Carlo [3,4] approach to follow the dynamics over extended time scales. To capture the kinetics of complex phase boundaries we have to go beyond standard atomistic simulation techniques. One possibility is to use accelerated MD [5] if a suitable bias potential can be defined (hyperdynamics), very large computational resources are available (parallel replica dynamics), or the important reaction rates can be assumed to follow an Arrhenius form to a high temperature where they can be observed directly with MD (temperature accelerated dynamics).In this study we present the application of adaptive kinetic Monte Carlo (AKMC) [6] to interface migration between different phases. The AKMC approach allows for simulations of atomic systems over long time scales by focusing on the dynamics of rare events. The m...