{ "cells": [ { "cell_type": "markdown", "metadata": {}, "source": [ "## Multi-phase-field model for grain growth (Steinbach's model)\n", "This python code was developed by Yamanaka research group of Tokyo University of Agriculture and Technology in August 2019." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Problem\n", "Let us consider an example: polycrystalline grain growth in a system containing six crystal grains (give crystal grains in a mother phase (grain)). \n", "This notebook shows two-dimensional multi-phase-field simulation of polycrystalline growth using the multi-phase-field model proposed by Professor Ingo Steinbach. \n", "\n", "For details of the model, please see reference (*I. Steinbach and F. Pezzolla, \"A generalized field method for multiphase transformations using interface fields,\" Physica D: Nonlinear Phenomena, Vol. 134 (1999), pp. 385-393.*).\n", "## Formulation\n", "### 1. Order parameter\n", "Phase-field variable $\\phi_{i}$ ($i$ = 1, 2, ..., $N$) is defined as $\\phi _{i}= 1$ inside $i$-th grain and $\\phi_{i} = 0$ outside of the grain. The phase-field variable $\\phi_{i}$ smoothly changes from 0 to 1 in an \"diffuse\" interfacial region (grain boundary). $N$ is the total number of crystal grains at the initial condition. In this source code, we use $N$ = 6. \n", "\n", "The phase-field variable must satisfies the following constraint: \n", "$$\n", "\\sum_{i=1}^{N}\\phi_{i} = 1\n", "$$\n", "### 2. Total free energy\n", "The total Gibbs free energy of the system is defined by\n", "$$\n", "G = \\int_{V} \\left[ g_{chem} + g_{doub} + g_{grad} + \\lambda \\left( \\sum_{i}^{N}\\phi_{i} -1 \\right) \\right] dV\n", "$$\n", "where $\\lambda$ is the Lagrange multiplier in the last term which is introduced into the total free energy so that the sum of the phase-field variable is 1. $g_{chem}$, $g_{doub}$, and $g_{grad}$ are the chemical free energy, the double-obstacle potential energy and the gradient energy densities, respectively. Note that the double-well potential energy is not used, but the double-obstacle potential is used for this multi-phase-field model. These energy densities are defined as follows: \n", "$$\n", "g_{chem} = \\sum_{i}^{N} \\phi_{i} g_{i}\n", "$$\n", "$$\n", "g_{doub} = \\sum_{i}^{N}\\sum_{j=i+1}^{N} W_{ij}\\phi_{i}\\phi_{j}\n", "$$\n", "$$\n", "g_{grad} = \\sum_{i}^{N}\\sum_{j=i+1}^{N} \\left( -\\frac{a_{ij}^{2}}{2}\\nabla\\phi_{i}\\cdot\\nabla\\phi_{j} \\right)\n", "$$\n", "where $g_{i}$ is Gibbs free energy density of $i$-th grain. Here, $g_{i}$ is assumed to be constant. \n", "\n", "$W_{ij}$ and $a_{ij}$ are the height of double-obstacle potential energy and the gradient energy coefficient, respectively, which are given by\n", "$$\n", "W_{ij} = \\frac{4\\sigma_{ij}}{\\delta}\n", "$$\n", "$$\n", "a_{ij} = \\frac{2}{\\pi}\\sqrt{2\\delta\\sigma_{ij}}\n", "$$\n", "where $\\sigma_{ij}$ is the grain boundary energy between $i$-th and $j$-th grains. $\\delta$ is the thickness of grain boundary \n", "(please see Appendix in the handout for the derivations). Note that in this source code, the diagonal components of $\\sigma_{ij}$ is assumed to be zero. \n", "\n", "### 3. Time evolution equation \n", "The time evolution of the phase-field variables (that describes the grain boundary migration) is given by assuming that the total free energy of the system $G$ decreases monotonically with time. \n", "$$\n", "\\frac{\\partial \\phi_{i}}{\\partial t} = -\\frac{2}{N} \\sum_{j=1}^{N} M^{\\phi}_{ij} \\left( \\frac{\\delta G}{\\delta \\phi_{i}} - \\frac{\\delta G}{\\delta \\phi_{j}} \\right)\n", "$$\n", "where the functional derivative is expressed by: \n", "$$\n", "\\frac{\\delta G}{\\delta \\phi}=\\frac{\\partial g}{\\partial \\phi}-\\nabla\\cdot\\frac{\\partial g}{\\partial (\\nabla \\phi)}\n", "$$\n", "Therefore, \n", "$$\n", "\\frac{\\delta G}{\\delta \\phi_{i}} = \\sum_{j=1}^{N} \\left( \\frac{1}{2} a_{ij}^{2} \\nabla^{2}\\phi_{j}\\right) + \\sum_{j=1}^{N} W_{ij}\\phi_{j} +g_{i} + \\lambda\n", "$$\n", "$M_{ij}^{\\phi}$ is the mobility of phase-field variables and is given by: \n", "$$\n", "M_{ij}^{\\phi} = \\frac{\\pi^{2}}{8\\delta}M_{ij}\n", "$$\n", "Here, $M_{ij}$ is the mobility of grain boundary between $i$-th and $j$-th grains. \n", "The diagonal components of $M_{ij}$ is assumed to be zero. \n", "\n", "The final form of the time evolution equation of the phase-field variables is given by the following equation: \n", "$$\n", "\\frac{\\partial \\phi_{i}}{\\partial t} = -\\frac{2}{N} \\sum_{j=1}^{N} M^{\\phi}_{ij} \\left( \n", "\\sum_{k=1}^{N} \\left( \\frac{1}{2} \\left( a_{ik}^{2} - a_{jk}^{2} \\right) \\nabla^{2}\\phi_{k} + \\left( W_{ik} - W_{jk} \\right) \\phi_{k} \\right) + g_{i} - g_{j}\n", "\\right)\n", "$$\n", "where the term $g_{i}-g_{j}$ corresponds to the driving force of the migration of grain boundary between $i$-th and $j$-th grains. \n", "\n", "For stable computation, the driving force term is replaced by \n", "$$\n", "g_{i}-g_{j} = -\\frac{8}{\\pi}\\sqrt{\\phi_{i}\\phi_{j}}\\Delta G_{ij}\n", "$$\n", "where $\\Delta G_{ij}$ is the magnitude of the driving force. In this code, the driving force only at the grain boundary between mother phase and other grains is non-zero value. The grain ID of the mother grain is defined as 0 in this program. " ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### import libraries" ] }, { "cell_type": "code", "execution_count": 25, "metadata": {}, "outputs": [], "source": [ "import numpy as np\n", "from numpy.random import *\n", "import matplotlib.pyplot as plt\n", "import math" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### set parameters and physical values" ] }, { "cell_type": "code", "execution_count": 26, "metadata": {}, "outputs": [], "source": [ "nx = 64 # number of computational grids along x direction\n", "ny = nx # number of computational grids along y direction\n", "number_of_grain = 6 # total number of grains: N\n", "dx, dy = 0.5e-6, 0.5e-6 # spacing of computational grids [m]\n", "dt = 0.05 # time increment [s]\n", "nsteps = 500# total number of time-steps\n", "pi = np.pi \n", "sigma = 1.0 # grain boundary energy [J/m2]\n", "delta = 6.0 * dx # thickness of diffuse interface\n", "eee = 3.0e+6 # magnitude of driving force" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### calculate phase-field parameters ($a, W$ and $M_{\\phi}$)" ] }, { "cell_type": "code", "execution_count": 27, "metadata": {}, "outputs": [], "source": [ "aaa = 2.0 / pi * np.sqrt(2.0*delta*sigma) # gradient energy coefficient\n", "www = 4.0 * sigma/delta # height of double-obstacle potential\n", "pmobi = pi*pi/(8.*delta)*3.0e-13 # mobility of phase-field " ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### declair arrays for the phase-field parameters ($a_{ij}, W_{ij}$ and $M_{ij}^{\\phi}$)" ] }, { "cell_type": "code", "execution_count": 28, "metadata": {}, "outputs": [], "source": [ "wij = np.zeros((number_of_grain,number_of_grain)) # array for the height of double-obstacle potential\n", "aij = np.zeros((number_of_grain,number_of_grain)) # array for the gradient energy coefficient\n", "mij = np.zeros((number_of_grain,number_of_grain)) # array for the mobility of phase-field " ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### declair arrays for the phase-field variables, grain ID, and number of grain" ] }, { "cell_type": "code", "execution_count": 29, "metadata": {}, "outputs": [], "source": [ "phi = np.zeros((number_of_grain,nx,ny)) # phase-field variable at time t\n", "phi_new = np.zeros((number_of_grain,nx,ny)) # phase-field variable at time t+dt\n", "mf = np.zeros((15,nx,ny),dtype = int) # array for saving the grain IDs at the computational grid [i, j] \n", "nf = np.zeros((nx,ny),dtype = int) # array for saving the number of grains at the computational grid [i, j] " ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### declair arrays for dirving force $\\Delta G_{ij}$ and grain boundary (only for visualization)" ] }, { "cell_type": "code", "execution_count": 30, "metadata": {}, "outputs": [], "source": [ "eij = np.zeros((number_of_grain,number_of_grain)) # arrays for saving the magnitude of driving foce of grain boundary migration\n", "gb = np.zeros((nx,ny)) # array for visuallizing the grain boundary" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### calculate the phase-field parameters ($a_{ij}, W_{ij}$ and $M_{ij}^{\\phi}$) and the driving force $\\Delta G_{ij}$\n", "Remind that the diagonal terms of the parameters $a_{ij}$, $W_{ij}$ and $M_{ij}^{\\phi}$ are assumed to be zero. " ] }, { "cell_type": "code", "execution_count": 31, "metadata": {}, "outputs": [], "source": [ "for i in range(0,number_of_grain):\n", " for j in range(0,number_of_grain):\n", " wij[i,j] = www\n", " aij[i,j] = aaa\n", " mij[i,j] = pmobi\n", " eij[i,j] = 0.0\n", " if i == j:\n", " wij[i,j] = 0.0\n", " aij[i,j] = 0.0\n", " mij[i,j] = 0.0\n", " if i == 0 or j == 0:\n", " eij[i,j] = eee\n", " if i < j:\n", " eij[i,j] = -eij[i,j]" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### define the function which updates the grain ID (array: nf) and the number of grains (array: mf)" ] }, { "cell_type": "code", "execution_count": 32, "metadata": {}, "outputs": [], "source": [ "def update_nfmf(phi,mf,nf):\n", " for m in range(ny):\n", " for l in range(nx):\n", " l_p = l + 1\n", " l_m = l - 1\n", " m_p = m + 1\n", " m_m = m - 1\n", " if l_p > nx-1:\n", " l_p = l_p - nx\n", " if l_m < 0:\n", " l_m = l_m + nx\n", " if m_p > ny-1:\n", " m_p = m_p - ny\n", " if m_m < 0:\n", " m_m = m_m + ny\n", " n = 0\n", " for i in range(number_of_grain):\n", " if phi[i,l,m] > 0.0 or (phi[i,l,m] == 0.0 and phi[i,l_p,m] > 0.0 or phi[i,l_m,m] > 0.0 or phi[i,l,m_p] > 0.0 or phi[i,l,m_m] > 0.0):\n", " n += 1\n", " mf[n-1,l,m] = i\n", " nf[l,m] = n" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### define the function which updates the phase-field variables $\\phi_{i}$ by Allen-Cahn equation\n", "The time evolution equation is discretized by simple finite difference method in this program. \n", "The 1st-order Euler method is used for time-integration. The 2nd-order central finite difference method is used for spatial derivatives. The discretized time evolution equation is given as: \n", "$$\n", "\\phi^{t+\\Delta t}_{i,j} = \\phi^{t}_{i,j} -\\frac{2}{N} \\sum_{j=1}^{N} M^{\\phi}_{ij} \\left( \n", "\\sum_{k=1}^{N} \\left( \\frac{1}{2} \\left( a_{ik}^{2} - a_{jk}^{2} \\right) P_{k} + \\left( W_{ik} - W_{jk} \\right) \\phi_{k} \\right) + \\frac{8}{\\pi}\\sqrt{\\phi_{i}\\phi_{j}}\\Delta G_{ij}\n", "\\right)\n", "$$\n", "where\n", "$$\n", "\\nabla^{2}\\phi_{k} = P_{k} = \\frac{\\phi^{t}_{i+1,j}-2\\phi^{t}_{i,j}+\\phi^{t}_{i-1,j}}{(\\Delta x)^{2}} + \\frac{\\phi^{t}_{i,j+1}-2\\phi^{t}_{i,j}+\\phi^{t}_{i,j-1}}{(\\Delta y)^{2}}\n", "$$" ] }, { "cell_type": "code", "execution_count": 33, "metadata": {}, "outputs": [], "source": [ "def update_phasefield(phi,phi_new,mf,nf,eij):\n", " for m in range(ny):\n", " for l in range(nx):\n", " l_p = l + 1\n", " l_m = l - 1\n", " m_p = m + 1\n", " m_m = m - 1\n", " if l_p > nx-1: \n", " l_p = l_p - nx\n", " if l_m < 0:\n", " l_m = l_m + nx\n", " if m_p > ny-1:\n", " m_p = m_p - ny\n", " if m_m < 0:\n", " m_m = m_m + ny\n", " for n1 in range(nf[l,m]):\n", " i = mf[n1,l,m]\n", " dpi = 0.0\n", " for n2 in range(nf[l,m]):\n", " j = mf[n2,l,m]\n", " ppp = 0.0\n", " for n3 in range(nf[l,m]):\n", " k = mf[n3,l,m]\n", " ppp += (wij[i,k]-wij[j,k])*phi[k,l,m]+0.5*(aij[i,k]**2 - aij[j,k]**2)*(phi[k,l_p,m]+phi[k,l_m,m]+phi[k,l,m_p]+phi[k,l,m_m]-4.0*phi[k,l,m])/dx/dx\n", "# dpi = dpi - 2.0 * mij[i,j] / float(nf[l,m]) * ppp\n", " phii_phij = phi[i,l,m]*phi[j,l,m]\n", " dpi = dpi - 2.0 * mij[i,j] / float(nf[l,m]) * (ppp - 8./pi*np.sqrt(phii_phij)*eij[i,j])\n", " phi_new[i,l,m] = phi[i,l,m] + dpi *dt\n", "\n", " phi_new = np.where(phi_new <= 0.0,0.0,phi_new)\n", " phi_new = np.where(phi_new >= 1.0,1.0,phi_new)\n", "\n", " for m in range(ny):\n", " for l in range(nx):\n", " a = np.sum(phi_new[:,l,m])\n", " phi[:,l,m] = phi_new[:,l,m] / a" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### set initial distribution of phase-field variables\n", "The initial distribution of crystal grains (region of $\\phi_{i} = 1$) is determined randomly. \n", "\n", "The initial profile of the phase-field variables is calculated using the equilibrium profile: \n", "$$\n", "\\phi = \\frac{1}{2}\\left[1-\\sin \\frac{\\sqrt{2W}}{a}(r-r_{0}) \\right]\n", "$$\n", "where $r_{0}$ denotes the initial position of the interface. " ] }, { "cell_type": "code", "execution_count": 39, "metadata": { "scrolled": false }, "outputs": [ { "data": { "image/png": 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\n", "text/plain": [ "
" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "phi = np.zeros((number_of_grain,nx,ny))\n", "phi_new = np.zeros((number_of_grain,nx,ny))\n", "mf = np.zeros((15,nx,ny),dtype = int)\n", "nf = np.zeros((nx,ny),dtype = int)\n", "\n", "phi[0,:,:] = 1.0\n", "nf[:,:] = 1\n", "r_nuclei = 3.*dx # radius of the initial grains\n", "\n", "for i in range(1,number_of_grain):\n", " x_nuclei = int(rand()*nx)\n", " y_nuclei = int(rand()*ny)\n", " for m in range(ny):\n", " for l in range(nx):\n", " if l > nx-1: \n", " l = l - nx\n", " if l < 0:\n", " l = l + nx\n", " if m > ny-1:\n", " m = m - ny\n", " if m < 0:\n", " m = m + ny\n", " r = np.sqrt( (l *dx-x_nuclei*dx)**2 +(m*dy-y_nuclei*dy)**2 ) - r_nuclei\n", " tmp = np.sqrt(2.*www)/aaa*r\n", " phi_tmp = 0.5*(1.-np.sin(tmp))\n", " if tmp >= pi/2.:\n", " phi_tmp=0.\n", " if tmp <= -pi/2.:\n", " phi_tmp=1.\n", " nf[l,m] = nf[l,m] -1\n", " if phi_tmp > 0: \n", " nf_tmp = nf[l,m]+1\n", " nf[l,m] = nf_tmp\n", " mf[nf_tmp,l,m] = i\n", " phi[i,l,m] = phi_tmp \n", " phi[0,l,m] = phi[0,l,m]-phi[i,l,m]\n", "\n", "for m in range(0,ny):\n", " for l in range(0,nx):\n", " gb[l,m] = np.sum(phi[:,l,m]*phi[:,l,m])\n", "\n", "plt.subplot(1,3, 1)\n", "plt.imshow(phi[1,:,:], cmap='bwr')\n", "plt.title('phase field 1')\n", "#plt.colorbar()\n", "plt.subplot(1,3, 2)\n", "plt.imshow(gb, cmap=\"gray\")\n", "plt.title('grain boundary')\n", "#plt.colorbar()\n", "plt.subplot(1,3, 3)\n", "plt.imshow(nf, cmap='bwr')\n", "plt.title('number of grains')\n", "#plt.colorbar()\n", "plt.show()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### calculate time evolution of phase-field variables (simulate grain growth behavior) in 2D\n", "In order to further simulate the grain growth, run this script for many times. Finally, the system will be a single crystal. " ] }, { "cell_type": "code", "execution_count": 40, "metadata": { "scrolled": false }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "nstep = 50\n" ] }, { "data": { "image/png": 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\n", "text/plain": [ "
" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" }, { "name": "stdout", "output_type": "stream", "text": [ "nstep = 100\n" ] }, { "data": { "image/png": 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\n", "text/plain": [ "
" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" }, { "name": "stdout", "output_type": "stream", "text": [ "nstep = 150\n" ] }, { "data": { "image/png": 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\n", "text/plain": [ "
" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" }, { "name": "stdout", "output_type": "stream", "text": [ "nstep = 200\n" ] }, { "data": { "image/png": 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\n", "text/plain": [ "
" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" }, { "name": "stdout", "output_type": "stream", "text": [ "nstep = 250\n" ] }, { "data": { "image/png": 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\n", "text/plain": [ "
" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" }, { "name": "stdout", "output_type": "stream", "text": [ "nstep = 300\n" ] }, { "data": { "image/png": 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\n", "text/plain": [ "
" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" }, { "name": "stdout", "output_type": "stream", "text": [ "nstep = 350\n" ] }, { "data": { "image/png": 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\n", "text/plain": [ "
" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" }, { "name": "stdout", "output_type": "stream", "text": [ "nstep = 400\n" ] }, { "data": { "image/png": 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\n", "text/plain": [ "
" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" }, { "name": "stdout", "output_type": "stream", "text": [ "nstep = 450\n" ] }, { "data": { "image/png": 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\n", "text/plain": [ "
" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" }, { "name": "stdout", "output_type": "stream", "text": [ "nstep = 500\n" ] }, { "data": { "image/png": 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\n", 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" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "for nstep in range(1,nsteps+1):\n", " update_nfmf(phi,mf,nf)\n", " update_phasefield(phi,phi_new,mf,nf,eij)\n", " \n", " if nstep % 50 == 0:\n", " print('nstep = ', nstep)\n", " for m in range(0,ny):\n", " for l in range(0,nx):\n", " gb[l,m] = np.sum(phi[:,l,m]*phi[:,l,m])\n", "\n", " plt.subplot(1,3, 1) \n", " plt.imshow(phi[1,:,:], cmap='bwr')\n", " plt.title('phase field 1')\n", " #plt.colorbar()\n", " plt.subplot(1,3, 2) \n", " plt.imshow(gb, cmap='gray')\n", " plt.title('grain boundary')\n", " #plt.colorbar()\n", " plt.subplot(1,3, 3) \n", " plt.imshow(nf, cmap='bwr')\n", " plt.title('number of grains')\n", " #plt.colorbar() \n", " plt.show() " ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [] } ], "metadata": { "kernelspec": { "display_name": "Python 3", "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": "3.6.8" } }, "nbformat": 4, "nbformat_minor": 2 }