{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Pourbaix Diagram for Aluminium"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "import pyPourbaix as pb"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We now have all the basics to get cracking with some more compilcated diagrams. In this tuturial, we will generate that for the element aluminium. To start off, lets copy over the previously defined list of species needed to plot the hydrogen evolution reaction (HER) and oxygen evolution reaction (OER)."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [],
   "source": [
    "species = ('H|+1|,      state=aq,   dGf=0,              dHf=0,              Sm=0',\n",
    "           'H2,         state=g,    dGf=0,              dHf=0,              Sm=0',\n",
    "           'e|-1|,      state=e,    dGf=0,              dHf=0,              Sm=0',\n",
    "           'H2O,        state=l,    dGf=-2.37140E+05,   dHf=-2.85830E+05,   Sm=69.95',\n",
    "           'O2,         state=g,    dGf=0,              dHf=0,              Sm=205.137'\n",
    "           )"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The Pourbaix diagram for Aluminium commonly features two solid phases, crystalline $\\text{Al}^{0}(\\text{s})$ and aluminum oxide $\\text{Al}_2\\text{O}_3(\\text{s})$. They are added to the list of species below:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [],
   "source": [
    "species = ('H|+1|,      state=aq,   dGf=0,              dHf=0,              Sm=0',\n",
    "           'H2,         state=g,    dGf=0,              dHf=0,              Sm=0',\n",
    "           'e|-1|,      state=e,    dGf=0,              dHf=0,              Sm=0',\n",
    "           'H2O,        state=l,    dGf=-2.37140E+05,   dHf=-2.85830E+05,   Sm=69.95',\n",
    "           'O2,         state=g,    dGf=0,              dHf=0,              Sm=205.137',\n",
    "           'Al|0|,      state=s,    dGf=0,              dHf=0,              Sm=28.3',\n",
    "           'Al2O3|0|,   state=s,    dGf=-1608.9E+03,    dHf=0,              Sm=0'\n",
    "           )\n",
    "\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "In addition, two aquous species, $\\text{Al}^{3+}$ and $\\text{AlO}_2^{-}$ are considered."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [],
   "source": [
    "species = ('H|+1|,      state=aq,   dGf=0,              dHf=0,              Sm=0',\n",
    "           'H2,         state=g,    dGf=0,              dHf=0,              Sm=0',\n",
    "           'e|-1|,      state=e,    dGf=0,              dHf=0,              Sm=0',\n",
    "           'H2O,        state=l,    dGf=-2.37140E+05,   dHf=-2.85830E+05,   Sm=69.95',\n",
    "           'O2,         state=g,    dGf=0,              dHf=0,              Sm=205.137',\n",
    "           'Al|0|,      state=s,    dGf=0,              dHf=0,              Sm=28.3',\n",
    "           'Al2O3|0|,   state=s,    dGf=-1608.9E+03,    dHf=0,              Sm=0',\n",
    "           'Al|+3|,     state=aq,   dGf=-483708,        dHf=-530630,        Sm=-325.097',\n",
    "           'AlO2|-1|,   state=aq,   dGf=-827479,        dHf=-925571,        Sm=-30.209'\n",
    "           )\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "As previous, we can deposit all input species in a database:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [],
   "source": [
    "db = pb.Database.from_default(species)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Just like before, we can now proceed to define reactions from the species we have just created. Let's first implement various $\\text{Al}^{0}(\\text{s})$ oxidation reactions to form $\\text{Al}^{3+}$ ad acidic, $\\text{Al}_2\\text{O}_3(\\text{s})$ mildly acidic to mildly alkaline and $\\text{AlO}_2^{-}$ at alkaline $\\text{pH}$. All of these transitions involve the exchange of electrons and will thus appear as horizontal or tilted lines on the Pourbaix diagram."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [],
   "source": [
    "reactions = ('2H|+1| + 2e|-1| -> H2',\n",
    "             'O2 + 4H|+1| + 4e|-1| -> 2H2O',\n",
    "             'Al|+3| + 3e|-1| -> Al|0|',\n",
    "             'Al2O3|0| + 6H|+1| + 6e|-1| -> 2Al|0| + 3H2O',\n",
    "             'AlO2|-1| + 4H|+1| + 3e|-1| -> Al|0| + 2H2O'\n",
    "             )"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The oxidised $\\text{Al}(\\text{III})$ species can furthermore transform into one another through two pH-independent reactions that will appear as vertical lines on the Pourbaix diagram:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [],
   "source": [
    "reactions = ('2H|+1| + 2e|-1| -> H2',\n",
    "            'O2 + 4H|+1| + 4e|-1| -> 2H2O',\n",
    "            'Al|0| -> Al|+3| + 3e|-1|',\n",
    "            '2Al|0| + 3H2O -> Al2O3|0| + 6H|+1| + 6e|-1|',\n",
    "            'Al|0| + 2H2O -> AlO2|-1| + 5H|+1| + 3e|-1|',\n",
    "            'Al2O3|0| + H2O -> AlO2|-1| + 2H|+1|',\n",
    "            '2Al|+3| + 3H2O -> Al2O3|0| + 6H|+1|'\n",
    "            )\n",
    "\n",
    "\n",
    "reactions = ('2H|+1| + 2e|-1| -> H2',\n",
    "             'O2 + 4H|+1| + 4e|-1| -> 2H2O',\n",
    "             'Al|+3| + 3e|-1| -> Al|0|',\n",
    "             'Al2O3|0| + 6H|+1| + 6e|-1| -> 2Al|0| + 3H2O',\n",
    "             'AlO2|-1| + 4H|+1| + 3e|-1| -> Al|0| + 2H2O',\n",
    "             '2AlO2|-1| + 2H|+1| -> Al2O3|0| + H2O',\n",
    "             'Al2O3|0| + 6H|+1| -> 2Al|+3| + 3H2O'\n",
    "             )\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We will now create a new system called <code>Al_system</code>, featuring all required reactions and physiochemical parameters.\n",
    "Since we want to draw the diagram at the default temperature of $\\text{T} = 298.15 \\ \\text{K}$ and pressure of $\\text{P} = 1.00$ bar, we will skip modifying both parameters. Instead, we set the pH limits to the interval $[0, \\ 13]$, define the <code>SHE</code> as our reference electrode and set the system database to the databse of species previously created:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {},
   "outputs": [],
   "source": [
    "Al_system = pb.System()\n",
    "Al_system.set_database(db)\n",
    "Al_system.pHs = (0, 13)\n",
    "Al_system.reference_electrode = (\"SHE\",0.00)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "As the oxidation of $\\text{Al}^{0}(\\text{s})$ proceeds at comparatively low potentials, we will choose a slightly larger potential interval of $[-2.50, \\ 2.00]$:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {},
   "outputs": [],
   "source": [
    "Al_system.electrode_potentials = (-2.5, 2)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Before resuming to generate the diagram, we first have to add the elements we would like to include in the Pourbaix diagram. This is done via the function <code>.add_elemends()</code>."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {},
   "outputs": [],
   "source": [
    "Al_system.add_elements([\"O\",\"H\",\"Al\"])"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The diagram now features aqueous species, whose activity is, for the first time, not implicitly changed by changing the pH. Let's quickly modify the activity of both $\\text{Al}^{3+}$ and $\\text{AlO}_2^{-}$ to $\\{\\text{Al}\\}_{\\text{aq}} = 1\\times10^{-5}$ by modifying the aquous activity of all species of the element $\\text{Al}$ in the system with the command <code>.set_aqueous_activity</code>."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {},
   "outputs": [],
   "source": [
    "Al_system.set_aqueous_activity(\"Al\",1e-5)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "All that is left to do now is to add above reactions to the existing <code>Al_system</code>, create a diagram and plot it. As illustrated previously, we will include plots of the HER and OER by specifying the appropriate keyword arguments in the <code>PourbaixDiagram</code> as <code>True</code>."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {},
   "outputs": [
    {
     "data": {
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",
      "text/plain": [
       "<Figure size 800x800 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "Al_system.add_reactions(reactions)\n",
    "Al_diagram = pb.PourbaixDiagram(Al_system,HER=True,OER=True)\n",
    "Al_diagram.solve()\n",
    "Al_diagram.show(backend='matplotlib',plot_regions=True)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "As we can see, all species added to the chemical system appear at their designated positions in the potential-pH diagram, where the 3 oxidised forms of $\\text{Al}$, i.e. $\\text{Al}^{3+}$, $\\text{Al}_2\\text{O}_3(s)$ and $\\text{AlO}_2^-$ are separated by vertical, pH-independent lines. In the next tutorial, we will generate the Pourbaix diagram for copper."
   ]
  }
 ],
 "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": "3.10.12"
  },
  "widgets": {
   "application/vnd.jupyter.widget-state+json": {
    "state": {},
    "version_major": 2,
    "version_minor": 0
   }
  }
 },
 "nbformat": 4,
 "nbformat_minor": 4
}