Nucleation

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A material's properties can be effected greatly by the method of synthesis of the material. The first step in the synthesis of any material is the nucleation of the material's phase. Nucleation and crystal growth are understood to be activated processes involving the crossing of free-energy barriers. Attempts to capture the entire crystallization process over long timescales with molecular dynamic simulations have met major obstacles because of the temporal constraints of molecular dynamics. Herein, we circumvent this temporal limitation by using an improved metadynamics method based on the adaptive basin-climbing algorithm to directly sample the potential-energy landscape of a monotonic, model-liquid Argon system. The algorithm biases the system to evolve from a liquid-like structure towards an FCC crystal structure through inherent structures. Compared to other computational techniques, our method requires no assumptions about the shape, size, or thermodynamics properties of the critical crystal nucleus, and does not require a nucleation seed to simulate the growth process. Consequently, the sampled timescale is macroscopically long, magnitudes longer than molecular dynamics simulations. Thus, we observe that the formation of a crystal involves two processes, each with a unique temperature-dependent energy barrier. One barrier corresponds to the creation of a crystal nucleation site; the other barrier corresponds to the crystal growth. We find the two processes dominate in different temperature regimes. Further, we provide empirical evidence for the non-monotonic temperature dependence of the nucleation energy barrier and the nucleation rate. Then, we also use metadynamics on a fragile glass forming system, and compare the landscape and timescale of the fragile glass former to the good crystal former. The stark difference in landscapes provides an energy landscape explanation for the nucleation process. The success of this method on a model liquid system is encouraging for elucidating the crystallization of more complex systems.

A movie of the real space and energy space perspective can be viewed below. The movies show that the system evolves from a high energy amorphous liquid to a perfect crystal while traversing the energy landscape. This movie is show as a function of metadynamics step not time, macroscopically this movie is actually occurring over very long time scales.

• Relevant Rescource: Masters Thesis

• Relevant Publication: Homogenous Nucleation and Crystal Growth in a Model Liquid from a Direct Energy Landscape Sampling Simulation, To be submitted

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Metadynamics

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Traditionally to study material behavior from an atomistic scale, researchers use molecular dynamics and Monte Carlo simulations to computationally explore the structure and dynamics of materials. However, molecular dynamics, which numerically integrates Newton's equation of motion, is limited in temporal scale to microseconds. Similarly, Monte Carlo, which randomly samples system configurations, lacks dynamical information. To overcome the limitations of molecular dynamics and Monte Carlo, metadynamics has been recently proposed and used to perform advanced sampling simulations for various applications. Metadynamics applies potential energy penalty functions to bias systems to overcome large energy barriers inhibiting dynamical behavior. Typically, at low temperatures, these large energy barriers are only overcome during macroscopically long time behavior, orders of magnitude larger in scale than accessible by molecular dynamics. By utilizing metadynamics, we are able to simulate long time dynamics and transient events. We have thus used metadynamics to study the long time dynamics of glassy systems experiencing dynamical arrest, the kinetic behavior of crystal nucleation, and look to extend our studies to surface behavior and protein folding. Other interesting work with metadynamics has used the method to study dislocation diffusion, Arrhenius nature of supercooled liquids, etc. A descriptive schematic movie of the method and a movie of the simulation from the real space and energy space perspective can be found below

We have implemented the metadynamics method into GROMACS , an open source molecular dynamics package. The code has been fully parallelized for efficiency, and has been benchmarked with the Kob-Andersen model liquid and the monoatomic Lennard-Jones model Argon. For information about the code or to request access to the code, please contact me.

• Relevant Rescource: Wikipedia Metadynamics

• Relevant Publication: Metadynamics Technique Implemented into GROMACS, To be submitted

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LiquidLib

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Neutron scattering is a highly successful experimental technique for studying structure and dynamics of materials. Often to understand the results of such experiments, computer simulations, including classical and ab initio molecular dynamics, are used to compare to neutron scattering experiments. LiquidLib is a post-processing package for analyzing trajectory data of computer simulations of liquids with application to neutron scattering experiments. LiquidLib allows computation of various statistical quantities including

New quantities to compute can easily be integrated into to the library in the future. LiquidLib can read molecular dynamics trajectories from the open source packages LAMMPS and GROMACS and the commercial package VASP . LiquidLib also offers an easy platform to extend the program to be able to read simulation trajectories organized in other file formats not included or from other packages. Incorporation of materials' neutron scattering lengths to weight the quantities' computations provides results comparable to neutron scattering measurements. Lastly, LiquidLib is dimensionally independent, which allows for trajectories in higher dimensions to be analyzed.

LiquidLib was a collaborative development effort by the Zhang Research Group . The package is open source and licensed under the MIT license. It was written in C++. The package is parallelized with OpenMP to increase speed of computation. The package was developed with intent to be used on UNIX/LINUX like systems (including clusters) but can also run on a Windows machine, however, a make file is not provided for windows users.

• Relevant Rescource: LiquidLib Registration

• Relevant Publication: LiquidLib: A comprehensive tool for post processing of molecular dynamic simulations of liquids with application to neutron scattering experiments, To be submitted

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Water

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We have implemented the ST2 water model into GROMACS , an open source molecular dynamics package. The code has been fully parallelized for efficiency, and has been benchmarked with the original work by Stillinger on ST2 . For information about the ST2 code or to request access to the ST2 code, please contact me.

• Relevant Rescource: Water Models for Simulation

• Relevant Publication: Validity boundary of the Stokes-Einstein relation in water, To be submitted

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Plasticity

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We explore, for the first time, the use of an analytical solution for associative flow, von Mises plasticity with rate hardening in a hydrocode, in particular an arbitrary Lagrangian-Eulerian (ALE) hydrocode. The analytical solution explored is of particular relevance for hydrocodes because high-speed deformation causes rate hardening to play a more important role. Its importance stands in contrast to other analytical solutions that are for lower speed flows and that do not accommodate rate hardening. Also in this article, using a previously published approach as an example, the analytical solution for the rate hardening solution is recast into a method wherein deviatoric stress is algebraically related to the current total and plastic strain, i.e., it is not dependent on the previous time step’s value for deviatoric stress. That recasting allows for strain to become the primary advection variable as opposed to stress, which is the traditional variable but for which there is no conservation law. Various aspects of the analytical solution’s value is explored, including how it mitigates issues with the underlying flow stress model, its sensitivity to ALE mesh relaxation, and the impact of artificial viscosity.

We performed this exploration with the Los Alamos production code FLAG. FLAG is a large scale program for studying material deformation on a continuum scale. The code set is written in a mixture of AJAX and FORTRAN77. We extended the program to be able to solve the constituent equations for plasticity with our new analytical solution.

• Relevant Rescource: Strain Space Hyperplasticity

• Relevant Publication: Extending a Strain Space Formulation for Plasticity to Rate-Hardening Materials and Finite Rotations, Submitted to Mathematics and Computers in Simulation

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Side Projects

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• Relevant Publication:

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