{ "cells": [ { "cell_type": "markdown", "metadata": {}, "source": [ "# Centrosymmetry parameter\n" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Centrosymmetry parameter (CSP) was introduced by [*Kelchner et al.*](https://journals.aps.org/prb/abstract/10.1103/PhysRevB.58.11085) to identify defects in crystals. The parameter measures the loss of local symmetry. For an atom with $N$ nearest neighbors, the parameter is given by,\n", "\n", "$$\n", "\\mathrm{CSP} = \\sum_{i=1}^{N/2} \\big | \\textbf{r}_i + \\textbf{r}_{i+N/2} \\big |^2\n", "$$\n", "\n", "$\\textbf{r}_i$ and $\\textbf{r}_{i+N/2}$ are vectors from the central atom to two opposite pairs of neighbors. There are two main methods to identify the opposite pairs of neighbors as described in [this publication](https://arxiv.org/abs/2003.08879). Pyscal uses the first approach called [*Greedy Edge Selection*](https://iopscience.iop.org/article/10.1088/0965-0393/20/4/045021/meta)(GES) and is implemented in [LAMMPS](https://lammps.sandia.gov/) and [Ovito](https://www.ovito.org/). GES algorithm calculates a weight $w_{ij} = |\\textbf{r}_i + \\textbf{r}_j|$ for all combinations of neighbors around an atom and calculates CSP over the smallest $N/2$ weights. \n", "\n", "A centrosymmetry parameter calculation using GES algorithm can be carried out as follows. First we can try a perfect crystal.\n" ] }, { "cell_type": "code", "execution_count": 4, "metadata": {}, "outputs": [], "source": [ "import pyscal as pc\n", "import pyscal.crystal_structures as pcs\n", "\n", "import matplotlib.pyplot as plt" ] }, { "cell_type": "code", "execution_count": 5, "metadata": {}, "outputs": [], "source": [ "atoms, box = pcs.make_crystal(structure='fcc', lattice_constant=4.0, repetitions=(3,3,3))" ] }, { "cell_type": "code", "execution_count": 6, "metadata": {}, "outputs": [], "source": [ "sys = pc.System()\n", "sys.box = box\n", "sys.atoms = atoms\n", "csm = sys.calculate_centrosymmetry(nmax = 12)" ] }, { "cell_type": "code", "execution_count": 8, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "[]" ] }, "execution_count": 8, "metadata": {}, "output_type": "execute_result" }, { "data": { "image/png": "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\n", "text/plain": [ "
" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "plt.plot(csm, 'o')" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "You can see all values are zero, as expected. Now lets add some noise to the structure and see how the centrosymmetry parameter changes." ] }, { "cell_type": "code", "execution_count": 9, "metadata": {}, "outputs": [], "source": [ "atoms, box = pcs.make_crystal(structure='fcc', lattice_constant=4.0, repetitions=(3,3,3), noise=0.1)" ] }, { "cell_type": "code", "execution_count": 10, "metadata": {}, "outputs": [], "source": [ "sys = pc.System()\n", "sys.box = box\n", "sys.atoms = atoms\n", "csm = sys.calculate_centrosymmetry(nmax = 12)" ] }, { "cell_type": "code", "execution_count": 11, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "[]" ] }, "execution_count": 11, "metadata": {}, "output_type": "execute_result" }, { "data": { "image/png": "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\n", "text/plain": [ "
" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "plt.plot(csm, 'o')" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "The centrosymmetry parameter shows a distribution, owing to the thermal vibrations." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "`nmax` parameter specifies the number of nearest neighbors to be considered for the calculation of CSP. If bcc structure is used, this should be changed to either 8 or 14." ] } ], "metadata": { "kernelspec": { "display_name": "pyscal-test", "language": "python", "name": "pyscal-test" }, "language_info": { "codemirror_mode": { "name": "ipython", "version": 3 }, "file_extension": ".py", "mimetype": "text/x-python", "name": "python", "nbconvert_exporter": "python", "pygments_lexer": "ipython3", "version": "3.9.7" } }, "nbformat": 4, "nbformat_minor": 4 }