DOI: 10.5061/dryad.0k6djhb8v
title: Multiscale simulation data for demonstrating the analogy between grain boundaries and Brownian ratchets

description: We demonstrate that grain boundaries (GBs) behave as Brownian ratchets,
 exhibiting direction-dependent mobilities and unidirectional motion under
 oscillatory driving forces or cyclic thermal annealing. We observed these
 phenomena for nearly all non-symmetric GBs but not for symmetric ones. Our
 observations build upon molecular dynamics and phase-field crystal
 simulations for a wide range of GB types and driving forces in both
 bicrystal and polycrystalline microstructures. We corroborate these
 simulation results through in situ experimental observations. We analyze
 these results with a Markov chain model and explore the implications of GB
 ratchet behavior for materials processing and microstructure tailoring.
description: # Grain Boundaries are Brownian Ratchets
 [https://doi.org/10.5061/dryad.0k6djhb8v](https://doi.org/10.5061/dryad.0k6djhb8v) Here, we provide the input files and the data for plotting the figures in the Main Text. ## !Update of our database! Since the acceptance and publication of our paper, our friends and colleagues are all interested in whether larger acceleration in grain growth rate through cyclic annealing can be achieved. We update the dataset to a new version with an additional set of cyclic annealing simulations indicating more robust evidence of cyclic annealing-accelerating grain growth. The additional data can be found in the folder “New_PFC_Grain_Growth_Simulation_with_Larger_Acceleration” and the details and discussion can be found in the README file in the same folder.  ## Description of the data and file structure First of all, we provide the data in each folder to reproduce the plots in all the figures (in either xlsx or csv form). Furthermore, in the current database, we also provide the input files for the MD simulations, neb calculations and python codes for the Markov modellings.  To be more specifically, * In folder "Figure 1", we provide the LAMMPS input files for MD simulation cases shown in Figure 1 (i.e., Σ11, Σ27, Σ25, Σ99, Σ19) in the main text. - In folder "Figure 2", we provide the LAMMPS input files for MD simulation cases shown in Figure 2 (i.e., Σ39 STGB, ATGB, SMGB, AMGB and half-loops) in the main text. - In folder "Figure 3", we provide the LAMMPS input files for NEB calculations and python codes for the Markov chain analysis (one can directly run the python codes to reproduce the results) shown in Figure 3 in the main text. - In folder "Figure 4", we provide the LAMMPS input files for (i) MD simulation for bicrystals (i.e., Σ39 STGB, ATGB under oscillatory ψ, τ); (ii) MD simulation for general polycrystal under constant annealing and under oscillatory τ. One can run the MD simulation with those input files to reproduce the results in main text. We also provide the experimentally-measured results for the cyclic annealing of the bicrystal shown in Figure 4 in the main text and cyclic electron-beam irradiation of the bicrystal shown in the supplementary materials. We also provide the input file for the repetition of our simulation with different initial configuration (i.e., STGB2 and ATGB2 in Figs. S18A, B). - In folder "New_PFC_Grain_Growth_Simulation_with_Larger_Acceleration", we provide the evolutions of the mean grain sizes of the cases of the new PFC simulations including constant high temperature, low temperature and mean temperature (infinite temperature limit), average of the high and low temperature curve (zero-frequency limit) and cyclic annealing (finite frequency). It is clear that the grain growth rate under cyclic annealing with finite frequency is close to and even slightly larger than that under constant high temperature! The PFC codes and more details can be found on our gitlab page. For the PFC simulation codes, please see the following link to a gitlab page. ## Code/Software (i) Molecular dynamics simulations are implemented using the Large-scale Atomic/Molecular Massively Parallel Simulator (LAMMPS) package ([https://www.lammps.org/](https://www.lammps.org/)). (ii) Markov chain modelling is performed using Python codes (see the deposited codes). (iii) Phase field crystal simulations are conducted using matlab codes provided in [https://gitlab.com/3ms-group/directional-migration.git](https://gitlab.com/3ms-group/directional-migration.git)