{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Fe-C diffusion and elastodiffusivity\n",
    "Taking data from R.G.A. Veiga, M. Perez, C. Becquart, E. Clouet and C. Domain, Acta mater. **59** (2011) p. 6963 [doi:10.1016/j.actamat.2011.07.048](http://dx.doi.org/10.1016/j.actamat.2011.07.048)\n",
    "\n",
    "Fe in the body-centered cubic phase, $a_0 = 0.28553\\text{ nm}$; C sit at octahedral sites, where the transition states between octahedral sites are represented by tetrahedral sites. The data is obtained from an EAM potential, where $C_{11} = 243\\text{ GPa}$, $C_{12}=145\\text{ GPa}$, and $C_{44} = 116\\text{ GPa}$. The tetrahedral transition state is 0.816 eV above the octahedral site, and the attempt frequency is taken as 10 THz ($10^{13}\\text{ Hz}$).\n",
    "\n",
    "The dipole tensors can be separated into *parallel* and *perpendicular* components; the parallel direction points towards the closest Fe atoms for the C, while the perpendicular components lie in the interstitial plane. For the octahedral, the parallel component is 8.03 eV, and the perpendicular is 3.40 eV; for the tetrahedral transition state, the parallel component is 4.87 eV, and the perpendicular is 6.66 eV."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "import sys\n",
    "sys.path.extend(['../'])\n",
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "plt.style.use('seaborn-whitegrid')\n",
    "%matplotlib inline\n",
    "import onsager.crystal as crystal\n",
    "import onsager.OnsagerCalc as onsager\n",
    "from scipy.constants import physical_constants\n",
    "kB = physical_constants['Boltzmann constant in eV/K'][0]"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Create BCC lattice (lattice constant in nm)."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "#Lattice:\n",
      "  a1 = [-0.142765  0.142765  0.142765]\n",
      "  a2 = [ 0.142765 -0.142765  0.142765]\n",
      "  a3 = [ 0.142765  0.142765 -0.142765]\n",
      "#Basis:\n",
      "  (Fe) 0.0 = [ 0.  0.  0.]\n"
     ]
    }
   ],
   "source": [
    "a0 = 0.28553\n",
    "Fe = crystal.Crystal.BCC(a0, \"Fe\")\n",
    "print(Fe)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Elastic constants converted from GPa ($10^9$ J/m$^3$) to eV/(atomic volume)."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "S11 = 0.1023 S12 = -0.0382 S44 = 0.1187\n"
     ]
    }
   ],
   "source": [
    "stressconv = 1e9*1e-27*Fe.volume/physical_constants['electron volt'][0]\n",
    "c11, c12, c44 = 243*stressconv, 145*stressconv, 116*stressconv\n",
    "s11, s12, s44 = (c11+c12)/((c11-c12)*(c11+2*c12)), -c12/((c11-c12)*(c11+2*c12)), 1/c44\n",
    "print('S11 = {:.4f} S12 = {:.4f} S44 = {:.4f}'.format(s11, s12, s44))\n",
    "stensor = np.zeros((3,3,3,3))\n",
    "for a in range(3):\n",
    "    for b in range(3):\n",
    "        for c in range(3):\n",
    "            for d in range(3):\n",
    "                if a==b and b==c and c==d: stensor[a,b,c,d] = s11\n",
    "                elif a==b and c==d: stensor[a,b,c,d] = s12\n",
    "                elif (a==d and b==c) or (a==c and b==d): stensor[a,b,c,d] = s44/4"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Add carbon interstitial sites at octahedral sites in the lattice. This code (1) gets the set of symmetric Wyckoff positions corresponding to the single site $[00\\frac12]$ (first translated into unit cell coordinates), and then adds that new basis to our Fe crystal to generate a *new* crystal structure, that we name \"FeC\"."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "#Lattice:\n",
      "  a1 = [-0.142765  0.142765  0.142765]\n",
      "  a2 = [ 0.142765 -0.142765  0.142765]\n",
      "  a3 = [ 0.142765  0.142765 -0.142765]\n",
      "#Basis:\n",
      "  (Fe) 0.0 = [ 0.  0.  0.]\n",
      "  (C) 1.0 = [ 0.5  0.   0.5]\n",
      "  (C) 1.1 = [ 0.5  0.5  0. ]\n",
      "  (C) 1.2 = [ 0.   0.5  0.5]\n"
     ]
    }
   ],
   "source": [
    "uoct = np.dot(Fe.invlatt, np.array([0, 0, 0.5*a0]))\n",
    "FeC = Fe.addbasis(Fe.Wyckoffpos(uoct), [\"C\"])\n",
    "print(FeC)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Next, we construct a *diffuser* based on our interstitial. We need to create a `sitelist` (which will be the Wyckoff positions) and a `jumpnetwork` for the transitions between the sites. There are tags that correspond to the unique states and transitions in the diffuser. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Diffuser for atom 1 (C)\n",
      "#Lattice:\n",
      "  a1 = [-0.142765  0.142765  0.142765]\n",
      "  a2 = [ 0.142765 -0.142765  0.142765]\n",
      "  a3 = [ 0.142765  0.142765 -0.142765]\n",
      "#Basis:\n",
      "  (Fe) 0.0 = [ 0.  0.  0.]\n",
      "  (C) 1.0 = [ 0.5  0.   0.5]\n",
      "  (C) 1.1 = [ 0.5  0.5  0. ]\n",
      "  (C) 1.2 = [ 0.   0.5  0.5]\n",
      "states:\n",
      "i:+0.500,+0.000,+0.500\n",
      "transitions:\n",
      "i:+0.500,+0.000,+0.500^i:+0.000,-0.500,+0.500\n",
      "\n"
     ]
    }
   ],
   "source": [
    "chem = 1  # 1 is the index corresponding to our C atom in the crystal\n",
    "sitelist = FeC.sitelist(chem)\n",
    "jumpnetwork = FeC.jumpnetwork(chem, 0.6*a0)  # 0.6*a0 is the cutoff distance for finding jumps\n",
    "FeCdiffuser = onsager.Interstitial(FeC, chem, sitelist, jumpnetwork)\n",
    "print(FeCdiffuser)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Next, we assemble our data: the energies, prefactors, and dipoles for the C atom in Fe, matched to the *representative* states: these are the first states in the lists, which are also identified by the tags above.\n",
    "\n",
    "*A note about units:* If $\\nu_0$ is in THz, and $a_0$ is in nm, then $a_0^2\\nu_0 = 10^{-2}\\text{ cm}^2/\\text{s}$. Thus, we multiply by `Dconv` = $10^{-2}$ so that our diffusivity is output in cm<sup>2</sup>/s."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "dipole: [[ 3.4   0.    0.  ]\n",
      " [ 0.    8.03  0.  ]\n",
      " [ 0.    0.    3.4 ]]\n",
      "pre: [ 1.]\n",
      "dipoleT: [[ 6.66  0.    0.  ]\n",
      " [ 0.    6.66  0.  ]\n",
      " [ 0.    0.    4.87]]\n",
      "ene: [ 0.]\n",
      "preT: [ 0.1]\n",
      "eneT: [ 0.816]\n"
     ]
    }
   ],
   "source": [
    "Dconv = 1e-2\n",
    "vu0 = 10*Dconv\n",
    "Etrans = 0.816\n",
    "dipoledict = {'Poctpara': 8.03, 'Poctperp': 3.40, \n",
    "              'Ptetpara': 4.87, 'Ptetperp': 6.66}\n",
    "FeCthermodict = {'pre': np.ones(len(sitelist)), 'ene': np.zeros(len(sitelist)),\n",
    "                 'preT': vu0*np.ones(len(jumpnetwork)), \n",
    "                 'eneT': Etrans*np.ones(len(jumpnetwork))}\n",
    "# now to construct the site and transition dipole tensors; we use a \"direction\"--either\n",
    "# the site position or the jump direction--to determine the parallel and perpendicular\n",
    "# directions.\n",
    "for dipname, Pname, direction in zip(('dipole', 'dipoleT'), ('Poct', 'Ptet'), \n",
    "                                     (np.dot(FeC.lattice, FeC.basis[chem][sitelist[0][0]]),\n",
    "                                      jumpnetwork[0][0][1])):\n",
    "    # identify the non-zero index in our direction:\n",
    "    paraindex = [n for n in range(3) if not np.isclose(direction[n], 0)][0]\n",
    "    Ppara, Pperp = dipoledict[Pname + 'para'], dipoledict[Pname + 'perp']\n",
    "    FeCthermodict[dipname] = np.diag([Ppara if i==paraindex else Pperp \n",
    "                                      for i in range(3)])\n",
    "for k,v in FeCthermodict.items():\n",
    "    print('{}: {}'.format(k, v))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We look at the diffusivity $D$, the elastodiffusivity $d$, and the activation volume tensor $V$ over a range of temperatures from 300K to 1200K.\n",
    "\n",
    "First, we calculate all of the pieces, including the diffusivity prefactor and activation barrier. As we only *have* one barrier, we compute the barrier at $k_\\text{B}T = 1$."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "D0: 1.3588e-03 cm^2/s\n",
      "Eact: 0.816 eV\n"
     ]
    }
   ],
   "source": [
    "Trange = np.linspace(300, 1200, 91)\n",
    "Tlabels = Trange[0::30]\n",
    "Dlist, dDlist, Vlist = [], [], []\n",
    "for T in Trange:\n",
    "    beta = 1./(kB*T)\n",
    "    D, dD = FeCdiffuser.elastodiffusion(FeCthermodict['pre'], \n",
    "                                        beta*FeCthermodict['ene'], \n",
    "                                        [beta*FeCthermodict['dipole']],\n",
    "                                        FeCthermodict['preT'], \n",
    "                                        beta*FeCthermodict['eneT'], \n",
    "                                        [beta*FeCthermodict['dipoleT']])\n",
    "    Dlist.append(D[0,0])\n",
    "    dDlist.append([dD[0,0,0,0], dD[0,0,1,1], dD[0,1,0,1]])\n",
    "    Vtensor = (kB*T/(D[0,0]))*np.tensordot(dD, stensor, axes=((2,3),(0,1)))\n",
    "    Vlist.append([np.trace(np.trace(Vtensor))/3, \n",
    "                  Vtensor[0,0,0,0], Vtensor[0,0,1,1], Vtensor[0,1,0,1]])\n",
    "D0 = FeCdiffuser.diffusivity(FeCthermodict['pre'], \n",
    "                             np.zeros_like(FeCthermodict['ene']), \n",
    "                             FeCthermodict['preT'], \n",
    "                             np.zeros_like(FeCthermodict['eneT']))\n",
    "D, dbeta = FeCdiffuser.diffusivity(FeCthermodict['pre'], \n",
    "                                   FeCthermodict['ene'], \n",
    "                                   FeCthermodict['preT'], \n",
    "                                   FeCthermodict['eneT'],\n",
    "                                   CalcDeriv=True)\n",
    "print('D0: {:.4e} cm^2/s\\nEact: {:.3f} eV'.format(D0[0,0], dbeta[0,0]/D[0,0]))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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ppQKBx4C1WuurziZzl7XWyWo052znvUhrHeyccLBUa73O+dwJoFBSu6nGioyM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\nSUhERHKjJCQiIrlREhIRkdz8HxTBeNyArqcBAAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x10a4072e8>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "D, dD = np.array(Dlist), np.array(dDlist)\n",
    "d11_T = np.vstack((Trange, dD[:,0])).T\n",
    "d11pos = np.array([(T,d) for T,d in d11_T if d>=0])\n",
    "d11neg = np.array([(T,d) for T,d in d11_T if d<0])\n",
    "fig, ax1 = plt.subplots()\n",
    "ax1.plot(1./Trange, D, 'k', label='$D$')\n",
    "# ax1.plot(1./Trange, dD[:,0], 'b', label='$d_{11}$')\n",
    "ax1.plot(1./d11pos[:,0], d11pos[:,1], 'b', label='$d_{11}$')\n",
    "ax1.plot(1./d11neg[:,0], -d11neg[:,1], 'b--')\n",
    "ax1.plot(1./Trange, dD[:,1], 'r', label='$d_{12}$')\n",
    "ax1.plot(1./Trange, dD[:,2], 'g-.', label='$d_{44} = D$')\n",
    "ax1.set_yscale('log')\n",
    "ax1.set_ylabel('$D$ [cm$^2$/s]', fontsize='x-large')\n",
    "ax1.set_xlabel('$T^{-1}$ [K$^{-1}$]', fontsize='x-large')\n",
    "ax1.legend(bbox_to_anchor=(0.15,0.15,0.2,0.4), ncol=1, \n",
    "           shadow=True, frameon=True, fontsize='x-large')\n",
    "ax2 = ax1.twiny()\n",
    "ax2.set_xlim(ax1.get_xlim())\n",
    "ax2.set_xticks([1./t for t in Tlabels])\n",
    "ax2.set_xticklabels([\"{:.0f}K\".format(t) for t in Tlabels])\n",
    "ax2.set_xlabel('$T$ [K]', fontsize='x-large')\n",
    "ax2.grid(False)\n",
    "ax2.tick_params(axis='x', top='on', direction='in', length=6)\n",
    "plt.show()\n",
    "# plt.savefig('Fe-C-diffusivity.pdf', transparent=True, format='pdf')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(430.0, 420.0)"
      ]
     },
     "execution_count": 9,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "d11pos[0,0], d11neg[-1,0]"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Activation volume. We plot the isotropic value (change in diffusivity with respect to pressure), but also the $V_{xxxx}$, $V_{xxyy}$, and $V_{xyxy}$ terms. Interestingly, the $V_{xxxx}$ term is negative---which indicates that diffusivity along the $[100]$ direction *increases* with compressive stress in the $[100]$ direction."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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KBKT4NDt/pOXs1NMzuN349uPzmeXOzqFluerEyzJp164Gqqtzl421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\nJEIBSEREEvH/AwS9lS+dZiSEAAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x10aad8a20>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "V = np.array(Vlist)\n",
    "fig, ax1 = plt.subplots()\n",
    "ax1.plot(1./Trange, V[:,0], 'k', label='$V_{\\\\rm{total}}$')\n",
    "ax1.plot(1./Trange, V[:,1], 'b', label='$V_{11}$')\n",
    "ax1.plot(1./Trange, V[:,2], 'r', label='$V_{12}$')\n",
    "ax1.plot(1./Trange, 2*V[:,3], 'g', label='$V_{44}$')\n",
    "ax1.set_yscale('linear')\n",
    "ax1.set_ylabel('$V$ [atomic volume]', fontsize='x-large')\n",
    "ax1.set_xlabel('$T^{-1}$ [K$^{-1}$]', fontsize='x-large')\n",
    "ax1.legend(bbox_to_anchor=(0.3,0.3,0.5,0.2), ncol=2, \n",
    "           shadow=True, frameon=True, fontsize='x-large')\n",
    "ax2 = ax1.twiny()\n",
    "ax2.set_xlim(ax1.get_xlim())\n",
    "ax2.set_xticks([1./t for t in Tlabels])\n",
    "ax2.set_xticklabels([\"{:.0f}K\".format(t) for t in Tlabels])\n",
    "ax2.set_xlabel('$T$ [K]', fontsize='x-large')\n",
    "ax2.grid(False)\n",
    "ax2.tick_params(axis='x', top='on', direction='in', length=6)\n",
    "plt.show()\n",
    "# plt.savefig('Fe-C-activation-volume.pdf', transparent=True, format='pdf')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Total volume: 0.0921, 1.0722A^3\n",
      "V_xxxx: -0.1175, -1.3681A^3\n",
      "V_xxyy: 0.1048, 1.2202A^3\n",
      "V_xyxy: 0.0061, 0.0714A^3\n"
     ]
    }
   ],
   "source": [
    "print('Total volume: {v[0]:.4f}, {V[0]:.4f}A^3\\nV_xxxx: {v[1]:.4f}, {V[1]:.4f}A^3\\nV_xxyy: {v[2]:.4f}, {V[2]:.4f}A^3\\nV_xyxy: {v[3]:.4f}, {V[3]:.4f}A^3'.format(v=V[-1,:], V=V[-1,:]*1e3*Fe.volume))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Spherical average uniaxial activation volume: -0.0237 -0.2757A^3\n"
     ]
    }
   ],
   "source": [
    "Vsph = 0.2*(3*V[-1,1] + 2*V[-1,2] + 4*V[-1,3])  # (3V11 + 2V12 + 2V44)/5\n",
    "print('Spherical average uniaxial activation volume: {:.4f} {:.4f}A^3'.format(Vsph, Vsph*1e3*Fe.volume))"
   ]
  }
 ],
 "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": "3.4.5"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 0
}