{ "cells": [ { "cell_type": "markdown", "metadata": {}, "source": [ "# Calculate constituent strain parameters\n", "This notebook demonstrates how to calculate the constituent strain in a fashion suitable for subsequent fitting of cluster expansions and Monte Carlo simulations. The result will be a file with Redlich-Kister parameters that can be used to quickly evaluate the strain energy for a superlattice with a particular concentration and interface orientation.\n", "\n", "Here, the Ag-Cu system will be used as example. This is a cubic system, and the below code relies on cubic symmetry; for non-cubic symmetries, siginificant changes need to be made. For simplicity, we will use ASE's EMT calculator to calculate energy. This should typically be replaced with DFT calculations. The algorithm used here is based on the one outlined by [Ozoliņš et al. (doi: 10.1103/PhysRevB.57.4816)](https://doi.org/10.1103/PhysRevB.57.4816), which in turn was based on [Laks et al. (doi: 10.1103/PhysRevB.46.12587](https://doi.org/10.1103/PhysRevB.46.12587)." ] }, { "cell_type": "code", "execution_count": 1, "metadata": {}, "outputs": [], "source": [ "from icet.tools.constituent_strain_helper_functions import redlich_kister, redlich_kister_vector\n", "from scipy.optimize import minimize, curve_fit\n", "from ase.build import bulk\n", "from ase.calculators.emt import EMT\n", "import matplotlib.pyplot as plt\n", "import numpy as np" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Extract cohesive energy and equilibrium lattice parameter" ] }, { "cell_type": "code", "execution_count": 2, "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", "text/plain": [ "
" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "fig, axes = plt.subplots(ncols=2, figsize=(10, 4))\n", "\n", "elements = ('Ag', 'Cu')\n", "a_guess = {'Ag': 4.064, 'Cu': 3.59} # We can refine these guesses if they are wrong\n", "a_calculated = {} # Will hold the calculated equilibrium lattice parameter\n", "E_coh = {} # Will hold cohesive energies\n", "calc = EMT()\n", "\n", "npoints = 11\n", "scales = np.linspace(0.999, 1.001, npoints)\n", "for element_i, element in enumerate(elements):\n", " \n", " # Calculate energy for cells with increasing size\n", " energies = []\n", " for scale in scales:\n", " a = a_guess[element] * scale\n", " structure = bulk(element, a=a, crystalstructure='fcc')\n", " structure.set_calculator(calc)\n", " energy = structure.get_potential_energy()\n", " energies.append(energy)\n", " \n", " # Find minimum.\n", " # Can obviously be done in many ways; here we fit a polynomial\n", " pfit = np.polyfit(a_guess[element] * scales, energies, deg=3)\n", " res = minimize(np.poly1d(pfit), x0=a_guess[element],\n", " bounds=[(a_guess[element] * scales[0], a_guess[element] * scales[-1])])\n", " a_calculated[element] = res.x[0]\n", " E_coh[element] = res.fun[0]\n", " \n", " ax = axes[element_i]\n", " ax.set_title(element)\n", " ax.plot(a_guess[element] * scales, energies, '-o')\n", " ax.set_xlabel('Lattice parameter (Angstrom)')\n", " \n", " ax.plot([a_calculated[element]], [E_coh[element]], 'x')\n", "\n", "axes[0].set_ylabel('Cohesive energy (eV)') \n", "plt.tight_layout()\n", "plt.show()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Fit energy as a function of epitaxial strain for different interface orientiations\n", "This part may take a few minutes to run." ] }, { "cell_type": "code", "execution_count": 3, "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", 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" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "def get_scaled_atoms(structure, G, scale_parallel, scale_perpendicular):\n", " \"\"\"\n", " Prepare structure that is scaled along G,\n", " as well as perpendicular to G. This function assumes\n", " an initially cubic symmetry, so we do not need to make a distinction\n", " between real and reciprocal space for the definition of G.\n", " \"\"\"\n", " # Choose direction G (cubic, so no need to distinguish\n", " # reciprocal and real lattice vectors)\n", " G = [float(i) for i in G]\n", " G = np.array(G)\n", " G /= np.linalg.norm(G)\n", "\n", " # Find two vectors that are perpendicular to that direction\n", " Gp1 = np.array([9., 8., 0.])\n", " Gp1[2] = - np.dot(Gp1, G) / G[2]\n", " Gp1 = Gp1 / np.linalg.norm(Gp1)\n", " assert abs(np.dot(Gp1, G) < 1e-6)\n", " Gp2 = np.cross(G, Gp1)\n", "\n", " # Now scale the cell such that the G vectors get the desired length\n", " C = structure.cell.T\n", " X = np.array([G, Gp1, Gp2]).T\n", " Xp = np.array([scale_parallel * G,\n", " scale_perpendicular * Gp1,\n", " scale_perpendicular * Gp2]).T\n", "\n", " Cp = np.dot(np.dot(Xp, np.linalg.inv(X)), C)\n", "\n", " structure_new = structure.copy()\n", " structure_new.set_cell(Cp.T, scale_atoms=True)\n", " return structure_new\n", "\n", "fig, axes = plt.subplots(ncols=2, figsize=(10, 4))\n", "colors = [i['color'] for i in plt.rcParams['axes.prop_cycle']]\n", "\n", "# We will scale the cell perpendicular to the interface normal G\n", "npoints = 11\n", "scale_perps = {'Ag': np.linspace(a_calculated['Cu'] / a_calculated['Ag'], 1.01, npoints),\n", " 'Cu': np.linspace(0.99, a_calculated['Ag'] / a_calculated['Cu'], npoints)}\n", "\n", "# We will eventually save polynomial fits with\n", "# energy as a function of epitaxial strain perpendicular to\n", "# the following G vectors\n", "Gs = [(0, 0, 1), (1, 1, 1), (0, 1, 1), (2, 0, 1), (2, 2, 1), (3, 1, 1)]\n", "epitaxial_fits = {G: {el: [] for el in elements} for G in Gs}\n", "\n", "for element_i, element in enumerate(elements):\n", " ax = axes[element_i]\n", " a0 = a_calculated[element]\n", " \n", " for G_i, G in enumerate(Gs):\n", " a_epi = []\n", " E_epi = []\n", " for scale_perp in scale_perps[element]:\n", " # For each \"perpendicular straining\", we want to find the\n", " # equilibrium in terms of straining in the direction parallel\n", " # to the interface normal.\n", " # These limits are arbitrary but turned out to work OK.\n", " scale_pars = np.linspace(1 / scale_perp**0.8 - 0.12,\n", " 1 / scale_perp**0.8 + 0.12,\n", " npoints)\n", " energies = []\n", " for scale_par in scale_pars:\n", " structure = bulk(element, a=a0, crystalstructure='fcc')\n", " structure_scaled = get_scaled_atoms(structure, G=G,\n", " scale_parallel=scale_par,\n", " scale_perpendicular=scale_perp)\n", " structure_scaled.set_calculator(calc)\n", " energy = structure_scaled.get_potential_energy()\n", " energies.append(energy)\n", " pfit = np.polyfit(a0 * scale_pars, energies, deg=3)\n", " res = minimize(np.poly1d(pfit), x0=a0,\n", " bounds=[(a0 * scale_pars[0], a0 * scale_pars[-1])])\n", " a_epi.append(scale_perp * a0)\n", " E_epi.append(res.fun[0])\n", " \n", " # Now fit energy as a function of perpendicular strain\n", " pfit = np.polyfit(a_epi, E_epi, deg=5)\n", " \n", " # Ensure that the excess is 0 at equilibrium lattice parameter\n", " bounds = (min(a_epi), max(a_epi))\n", " res = minimize(np.poly1d(pfit), x0=np.average(bounds), bounds=[bounds])\n", " pfit[-1] = pfit[-1] - res.fun[0]\n", "\n", " epitaxial_fits[G][element] = pfit\n", " \n", " # Plot it\n", " scale_plot = np.linspace(0.99*min(scale_perps[element]), 1.01 * max(scale_perps[element]))\n", " ax.plot(a0 * scale_plot, np.poly1d(pfit)(a0 * scale_plot), label=G, color=colors[G_i])\n", " ax.plot(a_epi, np.array(E_epi) - res.fun[0], 'o', color=colors[G_i])\n", "\n", " ax.set_title(element)\n", " ax.set_xlabel('Perpendicular lattice parameter')\n", " ax.set_ylim([-0.003, 0.15])\n", " ax.legend()\n", "\n", "axes[0].set_ylabel('Excess energy (eV)')\n", "plt.tight_layout()\n", "plt.show()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Fit energy as a function of concentration using Redlich-Kister polynomials" ] }, { "cell_type": "code", "execution_count": 4, "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", 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" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "def E_CS(a, x, epitaxials):\n", " \"\"\"\n", " Returns energy of linear combination of phases\n", " epitaxially strained to lattice constant a.\n", " \"\"\"\n", " return (1 - x) * np.poly1d(epitaxials['Ag'])(a) + x * np.poly1d(epitaxials['Cu'])(a)\n", "\n", "fig, ax = plt.subplots()\n", "\n", "# Prepare a file to store R-K coefficents in\n", "f = open('constituent-strain-RK-parameters.data', 'w')\n", "f.write('# Col 1-3: G vector\\n')\n", "f.write('# Col 4-: Redlich-Kister coefficients\\n')\n", "\n", "concentrations = np.linspace(0, 1, 51)\n", "\n", "for G_i, G in enumerate(epitaxial_fits):\n", " E_CS_eq = []\n", " for c in concentrations:\n", " # For each G and concentration, find the minimum energy by\n", " # minimizing over perpendicular lattice constant\n", " guess = c * a_calculated['Cu'] + (1 - c) * a_calculated['Ag']\n", " res = minimize(E_CS, x0=guess, args=(c, epitaxial_fits[G]),\n", " bounds=[(a_calculated['Cu'], a_calculated['Ag'])])\n", " E_CS_eq.append(res.fun[0])\n", "\n", " # Fit Redlich-Kister polynomial to the resulting minimizing energies\n", " L, _ = curve_fit(redlich_kister_vector, np.array(concentrations),\n", " np.array(E_CS_eq).ravel(), p0=[1.0] * 5)\n", " \n", " # Write results for this G to file\n", " f.write('{:2d} {:2d} {:2d} '.format(*G))\n", " for l in L:\n", " f.write(' {:15.9f}'.format(l))\n", " f.write('\\n')\n", " \n", " # Plot\n", " ax.plot(concentrations, E_CS_eq, label=G, color=colors[G_i])\n", " ax.plot(concentrations, redlich_kister_vector(concentrations, *L), ':', color=colors[G_i])\n", "\n", "f.close()\n", " \n", "ax.legend()\n", "ax.set_xlabel('Cu concentration')\n", "ax.set_ylabel('Constituent strain energy (eV/atom)')\n", "plt.tight_layout()\n", "plt.show()" ] }, { "cell_type": "code", "execution_count": 5, "metadata": {}, "outputs": [], "source": [ "def _fit_cs_functions(cs_functions):\n", " \"\"\"\n", " Make a polynomial fit of Redlich-Kister parameters on\n", " the stereographic projection of the 1BZ of FCC.\n", " \"\"\"\n", " A = []\n", " y = []\n", " for orientation, parameters in cs_functions.items():\n", " projection = _get_projection(orientation)\n", " A.append(_get_xy_vector(*projection))\n", " y.append(parameters)\n", "\n", " rk_fit, _, _, _ = np.linalg.lstsq(A, y, rcond=None)\n", " return rk_fit\n", "\n", "\n", "def _get_projection(orientation):\n", " \"\"\"\n", " Stereographic projection of the orientation of an interface.\n", " Assumes cubic symmetry.\n", " \"\"\"\n", " orientation = np.array(sorted(np.abs(orientation)))\n", " orientation = orientation / np.linalg.norm(orientation)\n", " return orientation[:2]\n", "\n", "\n", "def _get_xy_vector(x, y, deg=2):\n", " \"\"\"\n", " 2D polynomial of degree `deg`\n", " \"\"\"\n", " vector = []\n", " for i, j in itertools.product(range(deg + 1), repeat=2):\n", " if i + j > deg:\n", " continue\n", " vector.append(x**i * y**j)\n", " return vector\n", "\n", "\n", "def k_to_parameter_function(k, cs_fitted_rk_parameters):\n", " \"\"\"\n", " Calculate strain energy at a specific concentration and k point\n", " using constitutent_strain_functions as fitted with\n", " _fit_cs_parameters.\n", " \"\"\"\n", " projection = _get_projection(k)\n", " vector = _get_xy_vector(*projection)\n", " parameters = np.dot(vector, cs_fitted_rk_parameters)\n", " return parameters\n", "\n", "# Define functions for converting k point and concentration to strain\n", "def my_k_to_parameter_function(k): return k_to_parameter_function(k, cs_fitted_rk_parameters)\n", "def my_strain_energy_function(parameters, c): return redlich_kister(c, *parameters)\n", "\n" ] } ], "metadata": { "kernelspec": { "display_name": "Python 3 (ipykernel)", "language": "python", "name": "python3" }, "language_info": { "codemirror_mode": { "name": "ipython", "version": 3 }, "file_extension": ".py", "mimetype": "text/x-python", "name": "python", "nbconvert_exporter": "python", "pygments_lexer": "ipython3", "version": "3.8.10" } }, "nbformat": 4, "nbformat_minor": 2 }