Jutta Rogal

Multiple state transition path sampling

We developed a multiple state transition path sampling (TPS) approach in which it is possible to simultaneously sample pathways connecting a number of different stable states. Based on the original formulation of the TPS we have extended the path ensemble to include trajectories connecting not only two distinct stable states but any two states defined within a system. The multiple state TPS approach is useful in complex systems exhibiting a number of intermediate stable states that are interconnected in phase space. Combining this approach with transition interface sampling we can also directly obtain an expression for the rate constants of all possible transitions within the system.

Nonlinear reaction coordinate analysis in the reweighted path ensemble

We present a flexible nonlinear reaction coordinate analysis method for the transition path ensemble based on the likelihood maximization approach developed by Peters and Trout [J. Chem. Phys. 125, 054108 (2006)]. By parametrizing the reaction coordinate by a string of images in a collective variable space, we can optimize the likelihood that the string correctly models the committor data obtained from a path sampling simulation. The collective variable space with the maximum likelihood is considered to contain the best description of the reaction. The use of the reweighted path ensemble [J. Rogal et al., J. Chem. Phys. 133, 174109 (2010)] allows a complete reaction coordinate description from the initial to the final state. We illustrate the method on a z-shaped two-dimensional potential. While developed for use with path sampling, this analysis method can also be applied to regular molecular dynamics trajectories.

Diffusion of hydrogen within idealized grains of bcc Fe: A kinetic Monte Carlo study

Structural defects in materials such as vacancies, grain boundaries, and dislocations may trap hydrogen and a local accumulation of hydrogen at these defects can lead to the degradation of the materials properties. An important aspect in obtaining insight into hydrogen induced embrittlement on the atomistic level is to understand the diffusion of hydrogen in these materials. In our study we employ kinetic Monte Carlo (kMC) simulations to investigate hydrogen diffusion in bcc iron within different microstructures. All input data to the kMC model, such as available sites, solution energies, and diffusion barriers are obtained from first-principles calculations. We find that hydrogen mainly diffuses within the interface region with an overall diffusivity that is lower than in pure bcc-Fe bulk. The concentration dependence of the diffusion coefficient is strongly non-linear and the diffusion coefficient may even decrease with increasing hydrogen concentration. To describe the macroscopic diffusion coefficient we derive an analytic expression as a function of hydrogen concentration and temperature which is in excellent agreement with our numerical results for idealised microstructures.

The reweighted path ensemble

We introduce a reweighting scheme for the path ensembles in the transition interface sampling framework. The reweighting allows for the analysis of free energy landscapes and committor projections in any collective variable space. We illustrate the reweighting scheme on a two dimensional potential with a nonlinear reaction coordinate and on a more realistic simulation of the Trp-cage folding process. We suggest that the reweighted path ensemble can be used to optimize possible nonlinear reaction coordinates.

Analytic bond-order potentials for the bcc refractory metals Nb, Ta, Mo and W.

Bond-order potentials (BOPs) are based on the tight-binding approximation for determining the energy of a system of interacting atoms. The bond energy and forces are computed analytically within the formalism of the analytic BOPs. Here we present parametrizations of the analytic BOPs for the bcc refractory metals Nb, Ta, Mo and W. The parametrizations are optimized for the equilibrium bcc structure and tested for atomic environments far from equilibrium that had not been included in the fitting procedure. These tests include structural energy differences for competing crystal structures; tetragonal, trigonal, hexagonal and orthorhombic deformation paths; formation energies of point defects as well as phonon dispersion relations. Our tests show good agreement with available experimental and theoretical data. In practice, we obtain the energetic ordering of vacancy, [1 1 1], [1 1 0], and [1 0 0] self-interstitial atom in agreement with density functional theory calculations.

Solid-state dimer method for calculating solid-solid phase transitions

The dimer method is a minimum mode following algorithm for finding saddle points on a potential energy surface of atomic systems. Here, the dimer method is extended to include the cell degrees of freedom for periodic solid-state systems. Using this method, reaction pathways of solid-solid phase transitions can be determined without having to specify the final state structure or reaction mechanism. Example calculations include concerted phase transitions between CdSe polymorphs and a nucleation and growth mechanism for the A15 to BCC transition in Mo.

On the efficiency of biased sampling of the multiple state path ensemble

Developed for complex systems undergoing rare events involving many (meta)stable states, the multiple state transition path sampling aims to sample from an extended path ensemble including all possible trajectories between any pair of (meta)stable states. The key issue for an efficient sampling of the path space in this extended ensemble is sufficient switching between different types of trajectories. When some transitions are much more likely than others the collective sampling of the different path types can become difficult. Here we introduce a Wang-Landau based biasing approach to improve the sampling. We find that the biasing of the multiple state path ensemble does not influence the switching behavior, but does improve the sampling and thus the quality of the individual path ensembles.

Atomistic insight into the non-classical nucleation mechanism during solidification in Ni

Nucleation is a key step during crystallization, but a complete understanding of the fundamental atomistic processes remains elusive. We investigate the mechanism of nucleation during solidification in nickel for various undercoolings using transition path sampling simulations. The temperature dependence of the free energy barriers and rate constants that we obtain is consistent with the predictions of classical nucleation theory and experiments. However, our analysis of the transition path ensemble reveals a mechanism that deviates from the classical picture of nucleation: the growing solid clusters have predominantly non-spherical shapes and consist of face-centered-cubic and random hexagonal-close-packed coordinated atoms surrounded by a cloud of prestructured liquid. The nucleation initiates in regions of supercooled liquid that are characterized by a high orientational order with structural features that predetermine the polymorph selection. These results provide atomistic insight not only into the nucleation mechanism of nickel but also into the role of the preordered liquid regions as precursors for crystallization.

Maximum Likelihood Analysis of Reaction Coordinates during Solidification in Ni

Understanding the underlying mechanism of crystal nucleation is a fundamental aspect in the prediction and control of materials properties. Classical nucleation theory (CNT) assumes that homogeneous nucleation occurs via random fluctuations within the supercooled liquid, that the structure of the growing clusters resembles the most stable bulk phase, and that the nucleus size is the sole reaction coordinate (RC) of the process. Many materials are, however, known to exhibit multiple steps during crystallization, forming different polymorphs. As a consequence, more complex RCs are often required to capture all relevant information about the process. Here, we employ transition path sampling together with a maximum likelihood analysis of candidate order parameters to identify suitable RCs for the nucleation mechanism during solidification in Ni. In contrast to CNT, the analysis of the reweighted path ensemble shows that a prestructured liquid region that surrounds the crystal cluster is a relevant order parameter that enhances the RC and therefore plays a key role in the description of the nucleus and the interfacial free energy. We demonstrate that prestructured liquid clusters that emerge within the liquid act as precursors of the crystallization in a nonclassical two-step mechanism, which predetermines the coordination of the selected polymorphs.