Atomistic Simulations of Activated Processes in Materials

Abstract

Activated processes in materials are important for many of the properties that make them function. Batteries and catalysts are examples for which understanding how the component materials function on a timescale of milliseconds to seconds is critical to making improvements in a rational way. Modeling materials over these long timescales, relative to the timescale of atomic vibrations, is one of the grand challenges of the field. Transition state theory is central to bridging this timescale gap, and in the materials community, the harmonic approximation and the determination of saddle points to quantify reaction rates are ubiquitous. In this review, single-and doubleended methods for saddle point finding are discussed, as well as how finding saddle points can be used in the adaptive kinetic Monte Carlo method to model materials properties on the timescale of activated processes. Applications of surface diffusion and chemistry, phase boundary migration, and solid-solid phase transitions are presented.

Surface‐supported cluster catalysis: Ensembles of metastable states run the show

“…In this section, we discuss the methods and models that are mainly being used in the nanocluster catalysis community, and emphasize why we need to be careful when using some of these models to describe the catalytic properties when the catalytic interface is so dynamic. It is clear that finding the correlation between catalyst morphology and catalytic performance is essential to designing new catalysts with enhanced efficiency . Hence, a major tool is global optimization, already discussed above, to be used for the finding of both the global and the accessible local minima of cluster catalysts.…”

Discovering minimum energy pathways via distortion symmetry groups

“…It should be noted that there are additional methods commonly employed to try and obtain MEPs that are not of the chain-of-states type mentioned. In general, these can be categorized into two types: those involving potential energy "surface-walking" 21,22,28 , and others involving Monte Carlo sampling [29][30][31][32][33] . In walking algorithms, such as those based on restricted-step Newton Raphson methods [34][35][36] , saddle points are searched for by starting with a reference structure which sits in a local minima, and then moving it within the potential energy landscape according to a system dependent reaction coordinate.…”

Unsupervised Calculation of Free Energy Barriers in Large Crystalline Systems

“…As is well known, the free energy barrier ΔF ≡ max½F ðξÞ − min½F ðξÞ is widely used in the transition state theory [6] rate k ¼ ω 0 expð−βΔF Þ, while the total free energy difference F ð1Þ − F ð0Þ gives the ratio of equilibrium populations n 1 =n 0 ¼ expf−β½F ð1Þ − F ð0Þg. Both quantities require accurate calculation of F ðξÞ and are of critical importance to materials simulation [4,7,8]. However, materials science applications are typically forced to use approximate harmonic methods in the absence of any systematic tool to probe anharmonicity, an issue which this Letter aims to address.…”

“…However, the application of these methods to materials science problems such as dislocation migration [1] or point defect cluster transformations [19] is hindered by the general inability to define a suitable set of collective variable functions outside of a few simple cases [20]. This is well recognized as a critical problem for the implementation of free energy methods to go beyond harmonic approximation in automated, unsupervised, simulation schemes such as adaptive kinetic Monte Carlo calculations [8,[21][22][23], accelerated molecular dynamics [24,25], and a rapidly growing number of statistical learning approaches [26][27][28] that represent an active forefront of materials simulation.…”

“…The initial reaction pathway X 0 ðξÞ is produced by a spline interpolation of images from a NEB calculation. An ensemble of typically 100-1000 independent trajectories are generated in parallel according to (9) independent simulations typically gave an acceptable sampling error in (8). Application to interstitial cluster transformation α iron.-The first application is a complex transformation pathway in α iron that links disjoint basins of C15 clusters [41] and traditional clusters of h110i dumbbells [42].…”