DOI: 10.5061/dryad.79cnp5j62
title: Data from: Ab initio grand canonical Monte Carlo calculation of grain boundary composition and structure

description: The prediction of grain boundary structure has gained great attention in
 materials science because grain boundaries have a significant effect on
 material properties. However, the prediction of grain boundaries by
 multi-elemental systems has been difficult so far because the number of
 atoms and compositions are determined by a delicate energy balance between
 elements, which requires high calculation accuracy. Here, we have
 developed the ab initio grand canonical Monte Carlo (ai-GCMC) theory to
 grain boundaries, combining density functional theory and grand canonical
 Monte Carlo to overcome this problem, and apply this methodology to
 predict Ti segregation patterns in Ti-doped Σ13[1210](1014) α-Al2O3 grain
 boundaries. That is, we generated tons of Ti-segregated Al2O3 grain
 boundaries with DFT accuracy by GCMC and compare their free energy to
 determine the thermodynamically stable structure. Our prediction
 successfully corresponds with the experimentally observed structure, while
 providing precise chemical compositions. This dataset includes those Al2O3
 grain boundaries generated by ab initio GCMC.
description: All energy evaluations of grain boundaries were conducted using
 VASP software.
description: # Data from: Ab initio grand canonical Monte Carlo calculation of grain
 boundary composition and structure
 [https://doi.org/10.5061/dryad.79cnp5j62](https://doi.org/10.5061/dryad.79cnp5j62) ## Description of the data and file structure Program codes and xsf files for Al2O3 grain boundary structures generated by ab initio grand canonical Monte Carlo simulations. Please see our manuscript for details. ### File: 2024\_08\_26\_aiGCMC\_Al2O3\_sigma13.zip #### **`2024_08_26_aiGCMC_Al2O3_sigma13_Al*_Ti*`** (ex. **_**Al2_Ti2 means the relative chemical potential of elements are -2 and -2 (eV/atom). Please see our publications for the details) ##### /temp_*  the trial of GCMC simulations.       **/temp_*/coord_accept.axsf** The structure evolution of grain boundaries with the XCrySDen format. #0 shows atoms are in the grain boundary regions, #1 and #2 shows atoms are in the grain regions, and #3 shows atoms are in the buffer regions.      **/temp_*/log.dat** Log file for GCMC simulations. New_en and free_en is an energy and free energy of a new structure (unit is eV). When a new structure is accepted, en_curr is updated. en_low is the lowest free energy in the simulation. Action is an attempted action. Time is computation time (unit is second). Natom is the number of atoms and their compositions. Others can be neglected.       **/temp_*/CHG, CHGCAR, CONTCAR, DOSCAR, EIGENVAL, IBZKPT, INCAR, KPOINTS, OSZICAR, OUTCAR, PCDAT, POSCAR, POTCAR, REPORT, vaspout.h5, vasprun.xml, WAVECAR, XDATCAR** VASP output files.       **/temp_*/Total_time.txt** Total computation time [second]       **/temp_*/monitor.sh** A shell file that make STOPCAR when DFT calculation by VASP fails. STOPCAR stops vasp calculation. This file is copied from template/monitor.sh       **/temp_*/condition.txt** Calculation conditions used for simulations. initial_xsf is a name for an initial structure file. T_move is temperature [K], move, swap, jump, add, remove, gmove, remove are GCMC actions allows in the simulation when they are set 1. mu_Al, mu_O, mu_Ti are absolute chemical potentials for Al, O, and Ti atoms [eV/atom]. ##### /main.py, /mc.py, /io\_lammps.py, bv.py         A main python code to run GCMC simulations. main.py is a main file. mc.py are bv.py a code for Monte Carlo simulations. io_lammps.py is a code for read and write files. ##### /el\_list.txt         The information of Al, O, and Ti atoms for GCMC simulations. mass is atomic mass. rmin and rmax are minimum and maxmum distance from nearby atoms when they are added [unit is Å]. prob-add is a probability to be chosen for an addiing atom. Others can be neglected. ##### /make\_grain\_boundary.py, /grain\_boundary\_modified.xsf         A code for making a xsf file for grain boundary models, and generated xsf file. ##### /summary         xsf files extracted by make_summary.py ##### /make\_summary.py         Extract a xsf file into /summary from axsf file in /temp_*. ##### /templates * INCAR, KPOINTS, OSZICAR, POTCAR: Input files for vasp calculations for grain boundary.  * make_potcar.sh: A shell file that make POTCAR file for vasp calculation. POTCAR is pseudopotential files. * monitor.sh: A shell file that make STOPCAR when DFT calculation by VASP fails. STOPCAR stops vasp calculation. ##### /shell.sh Shell file used for simulation (we used NERSC perlmutter hosted by the National Energy Research Scientific Computing Center of the United States Department of Energy). #### **calculate\_stable\_structures.ipynb** Calculate a phase diagram of grain boundaries. #### **stable\_structures, stable\_structures.csv** Stable structures and their xsf files by calculate_stable_structures.ipynb. The meaning of term in csv is the same as log.dat. ## Code/software Python version 3 and VASP6 are required to reproduce results. ## How to reuse 1\) Install packages pip install ase  pip install py4vasp module load vasp/6.4.2-cpu 2\) Run python main.py Then you get a temp folder that includes the results. 3\) Visualization axsf files includes the results of GCMC simulations and can visualized by OVITO software. Other outputs are opened by text editors you like. ## Access information Other publicly accessible locations of the data: * n/a Data was derived from the following sources: * n/a