agcu_microsegregation.ipynb

{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "\"\"\"\n",
    "Chris Hareland, Northwestern University.\n",
    "\n",
    "Perform the calculations for the Ag-Cu system with thermodynamic data from Murray (1984). \n",
    "\n",
    "Written with:\n",
    "    python 3.8.3\n",
    "    matplotlib 3.2.2\n",
    "    numpy 1.18.5\n",
    "    scipy 1.5.0\n",
    "\n",
    "References:\n",
    "    - Murray (1984) \"Calculations of Stable and Metastable Equilibrium Diagrams of the Ag-Cu and Cd-Zn Systems\", Metallurgical Transactions A 15(2), 261-268.\n",
    "    - Tong & Beckermann (1998) \"A diffusion boundary layer model of microsegregation\", Journal of Crystal Growth 187, 289-302.\n",
    "    - Maguin et al. (2019) \"Finite diffusion microsegregation model applied to multicomponent alloys\", IOP Conference Series: Materials Science and Engineering 529, 012029.\n",
    "    - Martin et al. (2024) \"Kinetic effects during the plane-front and dendritic solidification of multicomponent alloys\", Acta Materialia 263, 119473.\n",
    "\"\"\"\n",
    "\n",
    "import numpy as np\n",
    "from scipy.integrate import solve_ivp\n",
    "from scipy.optimize import fsolve\n",
    "import matplotlib.pyplot as plt\n",
    "from matplotlib.patches import Rectangle\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [],
   "source": [
    "def tong_and_beckermann_ode(solid_fraction, solid_composition, liquid_modified_fourier_number, alloy_composition, partition_coefficient):\n",
    "    \"\"\"Tong & Beckermann Eqs. 13 and 14.\"\"\"\n",
    "    F1 = 2*liquid_modified_fourier_number*solid_fraction/partition_coefficient * (1-np.exp(-(1-solid_fraction)/(2*liquid_modified_fourier_number*solid_fraction)))\n",
    "    F2 = (alloy_composition-solid_composition) + (solid_composition/partition_coefficient-alloy_composition) * (np.exp(-(1-solid_fraction)/(2*liquid_modified_fourier_number*solid_fraction))/solid_fraction - 2*liquid_modified_fourier_number*(1-np.exp(-(1-solid_fraction)/(2*liquid_modified_fourier_number*solid_fraction))))\n",
    "    return F2/F1\n",
    "\n",
    "TB_solution = solve_ivp(tong_and_beckermann_ode, (2.5e-5, 0.99), np.asarray([0.144]), args=(0.196,0.15,0.588), method='RK45', t_eval=np.linspace(2.5e-5,0.99,1000))\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [],
   "source": [
    "class AgCu_Murray1984:\n",
    "    \"\"\"Thermodynamic parameters for the Ag-Cu system from Murray.\"\"\"\n",
    "    def __init__(self, T, xb, phase):\n",
    "        self.R = 8.314\n",
    "        self.T = T\n",
    "        self.xb = xb\n",
    "\n",
    "        if phase=='solid':\n",
    "            self.G_Ag_o = -11945 + 9.67*self.T\n",
    "            self.G_Cu_o = -13054 + 9.62*self.T\n",
    "            self.f = 34532 - 9.178*self.T\n",
    "            self.f2 = -5996 + 1.725*self.T\n",
    "        elif phase=='liquid':\n",
    "            self.G_Ag_o = 0\n",
    "            self.G_Cu_o = 0\n",
    "            self.f = 15171 - 2.537*self.T\n",
    "            self.f2 = -2425 + 0.946*self.T\n",
    "        else:\n",
    "            raise ValueError('\"phase\" must be either \"solid\" or \"liquid\"')\n",
    "\n",
    "    def G(self):\n",
    "        \"\"\"Return the Gibbs energy [J/mol]\"\"\"\n",
    "        F_t1 = self.G_Ag_o*(1-self.xb) + self.G_Cu_o*self.xb\n",
    "        F_t2 = self.R*self.T * (self.xb*np.log(self.xb) + (1-self.xb)*np.log(1-self.xb))\n",
    "        F_t3 = self.f*self.xb*(1-self.xb)\n",
    "        F_t4 = self.f2*self.xb*(1-self.xb)*(1-2*self.xb)\n",
    "        return(F_t1 + F_t2 + F_t3 + F_t4)\n",
    "\n",
    "    def mu_a(self): \n",
    "        \"\"\"Return the chemical potential of Ag (component a)\"\"\"\n",
    "        t1 = self.G()\n",
    "        t2 = self.G_Cu_o - self.G_Ag_o\n",
    "        t3 = self.R*self.T*np.log(self.xb/(1-self.xb))\n",
    "        t4 = self.f * (1-2*self.xb)\n",
    "        t5 = self.f2 * (6*self.xb**2 - 6*self.xb + 1)\n",
    "        return(t1 - self.xb*(t2+t3+t4+t5))\n",
    "\n",
    "    def mu_b(self): \n",
    "        \"\"\"Return the chemical potential of Cu (component b)\"\"\"\n",
    "        t1 = self.G()\n",
    "        t2 = self.G_Cu_o - self.G_Ag_o\n",
    "        t3 = self.R*self.T*np.log(self.xb/(1-self.xb))\n",
    "        t4 = self.f * (1-2*self.xb)\n",
    "        t5 = self.f2 * (6*self.xb**2 - 6*self.xb + 1)\n",
    "        return(t1 + (1-self.xb)*(t2+t3+t4+t5))\n",
    "\n",
    "    def d2G_dx2(self):\n",
    "        \"\"\"Return the second derivative of G w.r.t. xb\"\"\"\n",
    "        t2 = self.R*self.T/(self.xb-self.xb**2)\n",
    "        t3 = -2*self.f\n",
    "        t4 = 6*self.f2*(2*self.xb-1)\n",
    "        return (t2 + t3 + t4)\n",
    "    \n",
    "\n",
    "def functions_for_equilibrium_liquidus(variables, liquid_composition):\n",
    "    \"\"\"Return the system of equations to calculate the equilibrium liquidus tie-line at a given liquid composition.\"\"\"\n",
    "\n",
    "    solid_composition, temperature = variables \n",
    "    solid = AgCu_Murray1984(temperature, solid_composition, 'solid')\n",
    "    liquid = AgCu_Murray1984(temperature, liquid_composition, 'liquid')\n",
    "    f1 = liquid.mu_a() - solid.mu_a()\n",
    "    f2 = liquid.mu_b() - solid.mu_b()\n",
    "    \n",
    "    return(f1,f2)\n",
    "\n",
    "\n",
    "def functions_for_nonequilibrium_liquidus(variables, liquid_composition, velocity, kinetic_parameters):\n",
    "    \"\"\"Return the system of equations to calculate the non-equilibrium liquidus tie-line at a given liquid composition.\"\"\"\n",
    "\n",
    "    solute_drag_parameter, maximum_crystallization_speed, trans_interface_diffusive_speed = kinetic_parameters\n",
    "    solid_composition, temperature = variables \n",
    "    solid = AgCu_Murray1984(temperature, solid_composition, 'solid')\n",
    "    liquid = AgCu_Murray1984(temperature, liquid_composition, 'liquid')\n",
    "    f1 = liquid.mu_a() - solid.mu_a()\n",
    "    f2 = liquid.mu_b() - solid.mu_b()\n",
    "\n",
    "    # Interface response functions (Martin et al., Eqs. A.1 and A.8)\n",
    "    effective_composition = solute_drag_parameter*liquid_composition + (1-solute_drag_parameter)*solid_composition\n",
    "    velocity_response_function = velocity - maximum_crystallization_speed/(8.314*temperature) * (effective_composition * f2 + (1-effective_composition)*f1)\n",
    "    concentration_response_function = velocity/trans_interface_diffusive_speed * (effective_composition-solid_composition) - effective_composition*(velocity/maximum_crystallization_speed - f2/(8.314*temperature)) \n",
    "    \n",
    "    return(velocity_response_function, concentration_response_function)\n",
    "\n",
    "\n",
    "def maguin_etal_odes(solid_fraction, liquid_composition, solid_composition, solid_fourier_numbers, liquid_modified_fourier_numbers):\n",
    "    \"\"\"Maguin et al., Eqs. 9-10 (present work Eqs. 19-21).\"\"\"\n",
    "    \n",
    "    ODEs = []\n",
    "    for i, xl in enumerate(liquid_composition):\n",
    "        Fi = np.exp(-(1-solid_fraction)/(2*liquid_modified_fourier_numbers[i]*solid_fraction))\n",
    "        G1 = 2*liquid_modified_fourier_numbers[i]*solid_fraction*(1-Fi)\n",
    "        G2 = (1+6*solid_fourier_numbers[i])*(0.23-solid_composition[i]) + (xl-0.23)*(Fi/solid_fraction - 2*liquid_modified_fourier_numbers[i]*(1+6*solid_fourier_numbers[i])*(1-Fi))\n",
    "        ODEs.append(G2/G1)\n",
    "    \n",
    "    return ODEs\n",
    "\n",
    "\n",
    "def step_ODE(step_size, solid_fourier_numbers, modified_liquid_fourier_numbers, kinetics=False, kinetic_parameters=[]):\n",
    "    \"\"\"Numerically integrate the ODE(s) in time.\"\"\"\n",
    "\n",
    "    # Initialize quantities and structures\n",
    "    solid_fraction = 1e-6\n",
    "    alloy_composition = 0.23\n",
    "    solid_fractions=[]\n",
    "    liquid_compositions=[alloy_composition]\n",
    "    temperatures=[]\n",
    "    solid_compositions=[]\n",
    "    counter = 0\n",
    "    \n",
    "    while solid_fraction < 0.99:\n",
    "        counter += 1\n",
    "        solid_fraction += step_size\n",
    "\n",
    "        # Obtain the tie-line at the current liquid composition\n",
    "        if kinetics == True:\n",
    "            if counter < 2: # use the melting point as the intial guess\n",
    "                roots  = fsolve(functions_for_nonequilibrium_liquidus, [alloy_composition*0.5, 1118.25], args=(alloy_composition, 0.12, kinetic_parameters)) \n",
    "            else: # use old solution as initial guess\n",
    "                roots  = fsolve(functions_for_nonequilibrium_liquidus, roots, args=(liquid_compositions[-1], 0.12, kinetic_parameters)) \n",
    "        elif kinetics == False:\n",
    "            if counter < 2: # use the melting point as the intial guess\n",
    "                roots  = fsolve(functions_for_equilibrium_liquidus, [alloy_composition*0.5, 1118.25], args=(alloy_composition)) \n",
    "            else: # use old solution as initial guess\n",
    "                roots  = fsolve(functions_for_equilibrium_liquidus, roots, args=(liquid_compositions[-1])) \n",
    "\n",
    "        solid_composition, temperature = roots\n",
    "        solid_compositions.append(solid_composition)\n",
    "        temperatures.append(temperature)\n",
    "        solid_fractions.append(solid_fraction)\n",
    "\n",
    "        # Step ODE\n",
    "        solution = solve_ivp(maguin_etal_odes, (solid_fraction-step_size, solid_fraction), [liquid_compositions[-1]], args=([solid_composition], solid_fourier_numbers, modified_liquid_fourier_numbers), method='RK45')\n",
    "        xl = []     \n",
    "        for item in solution.y:\n",
    "            xl.append(item[-1])\n",
    "        liquid_compositions.append(xl[0])\n",
    "\n",
    "    return solid_fractions, temperatures, liquid_compositions, solid_compositions\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [],
   "source": [
    "def to_mass_fraction_cu(mole_fraction):\n",
    "    \"\"\"Return the mass fraction of Cu in the Ag-Cu system given the mole fraction of Cu.\"\"\"\n",
    "    mass_fraction = [(x*63.546) / ((x*63.546) + (1-x)*107.868) for x in mole_fraction]\n",
    "    return mass_fraction"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "<ipython-input-3-50b0343cc843>:24: RuntimeWarning: invalid value encountered in log\n",
      "  F_t2 = self.R*self.T * (self.xb*np.log(self.xb) + (1-self.xb)*np.log(1-self.xb))\n",
      "<ipython-input-3-50b0343cc843>:33: RuntimeWarning: invalid value encountered in log\n",
      "  t3 = self.R*self.T*np.log(self.xb/(1-self.xb))\n",
      "<ipython-input-3-50b0343cc843>:42: RuntimeWarning: invalid value encountered in log\n",
      "  t3 = self.R*self.T*np.log(self.xb/(1-self.xb))\n",
      "/opt/anaconda3/lib/python3.8/site-packages/scipy/optimize/minpack.py:175: RuntimeWarning: The iteration is not making good progress, as measured by the \n",
      "  improvement from the last ten iterations.\n",
      "  warnings.warn(msg, RuntimeWarning)\n"
     ]
    },
    {
     "data": {
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",
      "text/plain": [
       "<Figure size 510.236x198.425 with 2 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig = plt.figure(figsize=(18/2.54, 7/2.54))\n",
    "ax1 = fig.add_subplot(121)\n",
    "ax2 = fig.add_subplot(122)\n",
    "\n",
    "# Calculate and plot the finite-diffusion model (without kinetics) using various modified liquid fourier numbers\n",
    "for Fo in [0.2,0.35,0.5]:\n",
    "    solid_fractions, temperatures, liquid_compositions, solid_compositions = step_ODE(1e-4, [0], [Fo], False)\n",
    "    ax1.plot(solid_fractions, temperatures)\n",
    "    ax2.plot(solid_fractions, to_mass_fraction_cu(solid_compositions), label='$\\widetilde{Fo}^l = %0.2f$' % Fo)\n",
    "    \n",
    "# Calculate and plot the Gulliver-Scheil limit (using the equilibrium phase diagram)\n",
    "solid_fractions_gs, temperatures_gs, liquid_compositions_gs, solid_compositions_gs = step_ODE(1e-4, [0], [1e3], False)\n",
    "ax1.plot(solid_fractions_gs, temperatures_gs)\n",
    "ax2.plot(solid_fractions_gs, to_mass_fraction_cu(solid_compositions_gs), label='GS limit')\n",
    "\n",
    "# Calculate and plot the lever-rule limit (using the equilibrium phase diagram)\n",
    "solid_fractions_lr, temperatures_lr, liquid_compositions_lr, solid_compositions_lr = step_ODE(1e-4, [1e3], [1e3], False)\n",
    "ax1.plot(solid_fractions_lr, temperatures_lr)\n",
    "ax2.plot(solid_fractions_lr, to_mass_fraction_cu(solid_compositions_lr),label='LR limit')\n",
    "\n",
    "# Add experimental range from Boettinger et al.\n",
    "ax2.add_patch(Rectangle((0,.1121),0.8685,.0222, facecolor='black', alpha=0.1,zorder=-1))\n",
    "ax2.add_patch(Rectangle((0.9766,.1597),1-0.9766,.0425, facecolor='black', alpha=0.1,zorder=-1))\n",
    "ax2.scatter([],[], s=50, marker='s', edgecolor='none', facecolor='black', alpha=0.1, label='Boettinger et al.')\n",
    "\n",
    "# Format plot\n",
    "ax1.set_xlim([0,1])\n",
    "ax1.set_ylim([975,1125])\n",
    "ax2.set_xlim([0,1])\n",
    "ax2.set_ylim([0.05,0.25])\n",
    "ax1.set_xlabel('solid fraction, $f_s$')\n",
    "ax1.set_ylabel('interface temperature, $T$ [K]')\n",
    "ax2.set_xlabel('solid fraction, $f_s$')\n",
    "ax2.set_ylabel('solid composition, $x_{Cu}^{sl}$ [wt. frac.]')\n",
    "ax2.legend(loc='center left',bbox_to_anchor=(1,0.5))\n",
    "plt.tight_layout()\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "/opt/anaconda3/lib/python3.8/site-packages/scipy/optimize/minpack.py:175: RuntimeWarning: The iteration is not making good progress, as measured by the \n",
      "  improvement from the last five Jacobian evaluations.\n",
      "  warnings.warn(msg, RuntimeWarning)\n",
      "<ipython-input-3-50b0343cc843>:24: RuntimeWarning: invalid value encountered in log\n",
      "  F_t2 = self.R*self.T * (self.xb*np.log(self.xb) + (1-self.xb)*np.log(1-self.xb))\n",
      "<ipython-input-3-50b0343cc843>:33: RuntimeWarning: invalid value encountered in log\n",
      "  t3 = self.R*self.T*np.log(self.xb/(1-self.xb))\n",
      "<ipython-input-3-50b0343cc843>:42: RuntimeWarning: invalid value encountered in log\n",
      "  t3 = self.R*self.T*np.log(self.xb/(1-self.xb))\n"
     ]
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 510.236x198.425 with 2 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig = plt.figure(figsize=(18/2.54,7/2.54))\n",
    "ax1 = fig.add_subplot(121)\n",
    "ax2 = fig.add_subplot(122)\n",
    "\n",
    "# Calculate and plot the finite-diffusion model (with kinetics) using various trans-interface diffusive speeds\n",
    "for vd in [0.1,0.2,0.4]:\n",
    "    solid_fractions, temperatures, liquid_compositions, solid_compositions = step_ODE(1e-4, [0], [0.2], True,[0.3,850,vd])\n",
    "    ax1.plot(solid_fractions, temperatures)\n",
    "    ax2.plot(solid_fractions, to_mass_fraction_cu(solid_compositions), label='$v^D = %0.1f$' % vd)\n",
    "    \n",
    "# Calculate and plot the Gulliver-Scheil limit (using the equilibrium phase diagram)\n",
    "solid_fractions_gs, temperatures_gs, liquid_compositions_gs, solid_compositions_gs = step_ODE(1e-4, [0], [1e3], False)\n",
    "ax1.plot(solid_fractions_gs, temperatures_gs)\n",
    "ax2.plot(solid_fractions_gs, to_mass_fraction_cu(solid_compositions_gs), label='GS limit')\n",
    "\n",
    "# Calculate and plot the Gulliver-Scheil limit (using the non-equilibrium phase diagram)\n",
    "solid_fractions_gs2, temperatures_gs2, liquid_compositions_gs2, solid_compositions_gs2 = step_ODE(1e-4, [0], [1e3], True, [0.3,850,0.1])\n",
    "ax1.plot(solid_fractions_gs2, temperatures_gs2)\n",
    "ax2.plot(solid_fractions_gs2, to_mass_fraction_cu(solid_compositions_gs2), label='GS limit, $v^D=0.1$ m/s')\n",
    "\n",
    "# Plot the Tong and Beckermann solution\n",
    "ax1.plot(TB_solution.t, 1118.25-800*TB_solution.y[0], '-.k', zorder=5, label='Tong & Beckermann')\n",
    "ax2.plot(TB_solution.t, TB_solution.y[0], '-.k', zorder=5, label='Tong & Beckermann')\n",
    "\n",
    "# Add experimental range from Boettinger et al.\n",
    "ax2.add_patch(Rectangle((0,.1121),0.8685,.0222, facecolor='black', alpha=0.1,zorder=-1))\n",
    "ax2.add_patch(Rectangle((0.9766,.1597),1-0.9766,.0425, facecolor='black', alpha=0.1,zorder=-1))\n",
    "ax2.scatter([],[], s=50, marker='s', edgecolor='none', facecolor='black', alpha=0.1, label='Boettinger et al.')\n",
    "\n",
    "# Format plot\n",
    "ax1.set_xlim([0,1])\n",
    "ax1.set_ylim([975,1125])\n",
    "ax2.set_xlim([0,1])\n",
    "ax2.set_ylim([0.05,0.25])\n",
    "ax1.set_xlabel('solid fraction, $f_s$')\n",
    "ax1.set_ylabel('interface temperature, $T$ [K]')\n",
    "ax2.set_xlabel('solid fraction, $f_s$')\n",
    "ax2.set_ylabel('solid composition, $x_{Cu}^{sl}$ [wt. frac.]')\n",
    "ax2.legend(loc='center left',bbox_to_anchor=(1,0.5))\n",
    "plt.tight_layout()\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [],
   "source": [
    "def functions_for_spinodal(temperature, composition):\n",
    "    \"\"\"Defines the function needed to calculate the spinodal temperature.\"\"\"\n",
    "    solid = AgCu_Murray1984(temperature, composition, 'solid')\n",
    "    return solid.d2G_dx2()\n",
    "\n",
    "\n",
    "def calculate_phase_boundaries(liquid_compositions, kinetics=False, kinetic_parameters=[]):\n",
    "    \"\"\"Calculate the tie-line and spinodal temperature for specified liquid compositions.\"\"\"\n",
    "    solid_compositions = []\n",
    "    temperatures = []\n",
    "    spinodal_temperatures = []\n",
    "    \n",
    "    for i, xl in enumerate(liquid_compositions):\n",
    "            \n",
    "        # Obtain the tie-line and spinodal temperature at the current liquid composition\n",
    "        if kinetics == True:\n",
    "            if i == 0: # use the melting point as the intial guess\n",
    "                roots  = fsolve(functions_for_nonequilibrium_liquidus, [liquid_compositions[0], 1235], args=(xl, True, kinetic_parameters)) \n",
    "                spinodal_roots = fsolve(functions_for_spinodal, x0=100, args=(xl))\n",
    "            else: # use old solution as initial guess\n",
    "                roots  = fsolve(functions_for_nonequilibrium_liquidus, roots, args=(xl, 0.12, kinetic_parameters)) \n",
    "                spinodal_roots = fsolve(functions_for_spinodal, spinodal_roots, args=(xl))\n",
    "        elif kinetics == False:\n",
    "            if i == 0: # use the melting point as the intial guess\n",
    "                roots  = fsolve(functions_for_equilibrium_liquidus, [liquid_compositions[0], 1235], args=(xl)) \n",
    "                spinodal_roots = fsolve(functions_for_spinodal, x0=100, args=(xl))\n",
    "            else: # use old solution as initial guess\n",
    "                roots  = fsolve(functions_for_equilibrium_liquidus, roots, args=(xl)) \n",
    "                spinodal_roots = fsolve(functions_for_spinodal, spinodal_roots, args=(xl))\n",
    "\n",
    "        solid_compositions.append(roots[0])\n",
    "        temperatures.append(roots[1])\n",
    "        spinodal_temperatures.append(spinodal_roots)\n",
    "\n",
    "    return np.asarray(solid_compositions), liquid_compositions, np.asarray(temperatures), np.asarray(spinodal_temperatures)\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "/opt/anaconda3/lib/python3.8/site-packages/scipy/optimize/minpack.py:175: RuntimeWarning: The iteration is not making good progress, as measured by the \n",
      "  improvement from the last ten iterations.\n",
      "  warnings.warn(msg, RuntimeWarning)\n",
      "<ipython-input-3-50b0343cc843>:24: RuntimeWarning: invalid value encountered in log\n",
      "  F_t2 = self.R*self.T * (self.xb*np.log(self.xb) + (1-self.xb)*np.log(1-self.xb))\n",
      "<ipython-input-3-50b0343cc843>:33: RuntimeWarning: invalid value encountered in log\n",
      "  t3 = self.R*self.T*np.log(self.xb/(1-self.xb))\n",
      "<ipython-input-3-50b0343cc843>:42: RuntimeWarning: invalid value encountered in log\n",
      "  t3 = self.R*self.T*np.log(self.xb/(1-self.xb))\n",
      "/opt/anaconda3/lib/python3.8/site-packages/scipy/optimize/minpack.py:175: RuntimeWarning: The iteration is not making good progress, as measured by the \n",
      "  improvement from the last ten iterations.\n",
      "  warnings.warn(msg, RuntimeWarning)\n",
      "<ipython-input-3-50b0343cc843>:24: RuntimeWarning: invalid value encountered in log\n",
      "  F_t2 = self.R*self.T * (self.xb*np.log(self.xb) + (1-self.xb)*np.log(1-self.xb))\n",
      "<ipython-input-3-50b0343cc843>:33: RuntimeWarning: invalid value encountered in log\n",
      "  t3 = self.R*self.T*np.log(self.xb/(1-self.xb))\n",
      "<ipython-input-3-50b0343cc843>:42: RuntimeWarning: invalid value encountered in log\n",
      "  t3 = self.R*self.T*np.log(self.xb/(1-self.xb))\n"
     ]
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 368.504x198.425 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig = plt.figure(figsize=(13/2.54,7/2.54))\n",
    "ax = fig.add_subplot(111)\n",
    "colors = ['#1f77b4','#ff7f0e','#2ca02c']\n",
    "\n",
    "# Calculate the kinetic phase boundaries for different trans-interface diffusive speeds\n",
    "for i,vd in enumerate([0.4,0.2,0.1]):\n",
    "    xs, xl, T, __ = calculate_phase_boundaries(np.linspace(0.001,0.8,250), True, [0.3, 850, vd])\n",
    "    ax.plot(to_mass_fraction_cu(xs), T, color=colors[i],label='$v^D = %0.1f$ m $\\cdot$ s$^{-1}$' % vd)\n",
    "    ax.plot(to_mass_fraction_cu(xl), T, color=colors[i])\n",
    "\n",
    "# Calculate the Tong and Beckermann phase boundaries\n",
    "ax.plot(xl, 1235-800*xl, '-', color='tab:red', label='Tong and Beckermann')\n",
    "ax.plot(xl*0.588, 1235-800*xl, '-', color='tab:red')\n",
    "\n",
    "# Calculate the equilibrium phase boundaries and spinodal\n",
    "xs_eq, xl_eq, T_eq, T_spin = calculate_phase_boundaries(np.linspace(0.001,0.8,250))\n",
    "ax.plot(to_mass_fraction_cu(xs_eq),T_eq, '-k',label='equilibrium')\n",
    "ax.plot(to_mass_fraction_cu(xl_eq),T_eq, '-k')\n",
    "ax.plot(to_mass_fraction_cu(xl_eq),T_spin, ':k',label='spinodal')\n",
    "\n",
    "# Format plot\n",
    "ax.set_xlim([0,0.25])\n",
    "ax.set_ylim([950,1250])\n",
    "ax.set_xlabel('composition, $x_{Cu}^{sl}$ [wt.%]')\n",
    "ax.set_ylabel('temperature, $T$ [K]')\n",
    "ax.legend(frameon=False,loc='center left',bbox_to_anchor=(1,0.5))\n",
    "plt.tight_layout()\n",
    "\n"
   ]
  }
 ],
 "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": "3.8.3"
  },
  "orig_nbformat": 4
 },
 "nbformat": 4,
 "nbformat_minor": 2
}