{
 "cells": [
  {
   "cell_type": "markdown",
   "id": "9bc9d4ef-037d-45e3-a463-7ff60f16743b",
   "metadata": {},
   "source": [
    "# Basics"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "42ed4513-fb55-4858-80c1-4e55e209b9d3",
   "metadata": {},
   "source": [
    "## Prelude"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "id": "65814604-e0c7-47a5-bb22-60dd61647122",
   "metadata": {},
   "outputs": [],
   "source": [
    "import landau.phases as ldp\n",
    "import landau.interpolate as ldi\n",
    "import landau.calculate as ldc\n",
    "import landau.plot as lpl"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "id": "68191338-56a3-4ede-9924-1e331b28ba83",
   "metadata": {},
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "import pandas as pd\n",
    "import seaborn as sns"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "cc19299a-81c8-4c54-bab6-7637b90f96df",
   "metadata": {},
   "source": [
    "## Temperature Transitions"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "ad24e0fb-c960-4e4f-be41-ff84c350137f",
   "metadata": {},
   "source": [
    "### Set up basic phases"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "id": "d55f326c-8da6-4134-bcca-bc688e3fe080",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "\u001b[31mInit signature:\u001b[39m\n",
       "ldp.LinePhase(\n",
       "    name: str,\n",
       "    fixed_concentration: float,\n",
       "    line_energy: float,\n",
       "    line_entropy: float = \u001b[32m0\u001b[39m,\n",
       ") -> \u001b[38;5;28;01mNone\u001b[39;00m\n",
       "\u001b[31mDocstring:\u001b[39m      Simple phase with a fixed concentration and temperature independent entropy.\n",
       "\u001b[31mFile:\u001b[39m           ~/science/phd/dev/landau/landau/phases.py\n",
       "\u001b[31mType:\u001b[39m           ABCMeta\n",
       "\u001b[31mSubclasses:\u001b[39m     "
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "ldp.LinePhase?"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "id": "6115f999-1dae-4b1b-a8e3-4e8aab00cf18",
   "metadata": {},
   "outputs": [],
   "source": [
    "fcca = ldp.LinePhase(\"fccA\", fixed_concentration=0, line_energy=-3, line_entropy=1*ldp.kB)\n",
    "hcpa = ldp.LinePhase(\"hcp\", fixed_concentration=0, line_energy=-2.975, line_entropy=1.8*ldp.kB)\n",
    "lqda = ldp.LinePhase(\"liquidA\", fixed_concentration=0, line_energy=-2.75, line_entropy=5*ldp.kB)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "ffc050f3-4197-4178-af67-626ba9f8cfcc",
   "metadata": {},
   "source": [
    "Landau does not know about units, but energies should be \"per atom\" or at least consistent among phases."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "771a8cf0-50a7-43a6-bb6b-94d14dea154f",
   "metadata": {},
   "source": [
    "### Just Plot Around"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "44080b5e-1f21-4411-9b78-6a775a98730c",
   "metadata": {},
   "source": [
    "`semigrand_potential` is the main method.  For `dmu=0` it is the same as the free energy, otherwise\n",
    "\n",
    "$$\n",
    "\\phi(\\Delta\\mu, T) = \\min_c f(c, T) - c \\Delta\\mu\n",
    "$$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "id": "d5a9dbfa-48cc-46ec-acdb-fa93f1db1ceb",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "\u001b[31mSignature:\u001b[39m fcca.semigrand_potential(T, dmu)\n",
       "\u001b[31mDocstring:\u001b[39m Calculate the semigrand potential of the phase.\n",
       "\u001b[31mFile:\u001b[39m      ~/science/phd/dev/landau/landau/phases.py\n",
       "\u001b[31mType:\u001b[39m      method"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "fcca.semigrand_potential?"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "id": "63a00b09-519d-4803-9227-427026de33a6",
   "metadata": {},
   "outputs": [],
   "source": [
    "Ts = np.linspace(0, 1000)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "id": "a6abe7af-ed52-48b3-b3c4-11eb5dbfdd6e",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Text(0, 0.5, '$f$/$\\\\phi$ [eV/atom]')"
      ]
     },
     "execution_count": 7,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.plot(Ts, fcca.semigrand_potential(Ts, 0))\n",
    "plt.plot(Ts, hcpa.semigrand_potential(Ts, 0))\n",
    "plt.plot(Ts, lqda.semigrand_potential(Ts, 0))\n",
    "plt.xlabel(\"$T$ [K]\")\n",
    "plt.ylabel(r\"$f$/$\\phi$ [eV/atom]\")"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "15b450ba-6101-4ab4-90db-d7c5970849a9",
   "metadata": {},
   "source": [
    "Crossing points are phase transitions.  How to find them?"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "id": "e2599bac-faf2-412e-a257-4464d5838dfb",
   "metadata": {},
   "outputs": [],
   "source": [
    "Ts = np.linspace(0, 1000, 10)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "c4a97296-ff94-40c6-8077-1280482df7ce",
   "metadata": {},
   "source": [
    "Simple call to just find stable phases at sample points."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "id": "0062f5c1-74e4-4d83-9801-9781c786e141",
   "metadata": {},
   "outputs": [],
   "source": [
    "df = ldc.calc_phase_diagram([fcca, hcpa, lqda], Ts, mu=0.0, refine=False)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "92c1e7b9-01d2-445a-8251-6cb1d2f0e6fa",
   "metadata": {},
   "source": [
    "Columns:\n",
    "- `phi` semigrand potential\n",
    "- `mu` chemical potential difference between both species\n",
    "- `stable` True if a stable phase point\n",
    "- `f` free energy corresponding to `phi`\n",
    "- `f_excess` excess of the free energy wrt the stable phases"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "id": "d1269556-b86d-4aac-804b-9b07c91917d7",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
       "        vertical-align: middle;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>T</th>\n",
       "      <th>phase</th>\n",
       "      <th>phi</th>\n",
       "      <th>mu</th>\n",
       "      <th>c</th>\n",
       "      <th>stable</th>\n",
       "      <th>f</th>\n",
       "      <th>f_excess</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>0.000000</td>\n",
       "      <td>fccA</td>\n",
       "      <td>-3.000000</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0</td>\n",
       "      <td>True</td>\n",
       "      <td>-3.000000</td>\n",
       "      <td>0.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>111.111111</td>\n",
       "      <td>fccA</td>\n",
       "      <td>-3.009575</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0</td>\n",
       "      <td>True</td>\n",
       "      <td>-3.009575</td>\n",
       "      <td>0.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>222.222222</td>\n",
       "      <td>fccA</td>\n",
       "      <td>-3.019150</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0</td>\n",
       "      <td>True</td>\n",
       "      <td>-3.019150</td>\n",
       "      <td>0.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>333.333333</td>\n",
       "      <td>fccA</td>\n",
       "      <td>-3.028724</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0</td>\n",
       "      <td>True</td>\n",
       "      <td>-3.028724</td>\n",
       "      <td>0.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>14</th>\n",
       "      <td>444.444444</td>\n",
       "      <td>hcp</td>\n",
       "      <td>-3.043939</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0</td>\n",
       "      <td>True</td>\n",
       "      <td>-3.043939</td>\n",
       "      <td>0.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>15</th>\n",
       "      <td>555.555556</td>\n",
       "      <td>hcp</td>\n",
       "      <td>-3.061173</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0</td>\n",
       "      <td>True</td>\n",
       "      <td>-3.061173</td>\n",
       "      <td>0.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>16</th>\n",
       "      <td>666.666667</td>\n",
       "      <td>hcp</td>\n",
       "      <td>-3.078408</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0</td>\n",
       "      <td>True</td>\n",
       "      <td>-3.078408</td>\n",
       "      <td>0.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>17</th>\n",
       "      <td>777.777778</td>\n",
       "      <td>hcp</td>\n",
       "      <td>-3.095643</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0</td>\n",
       "      <td>True</td>\n",
       "      <td>-3.095643</td>\n",
       "      <td>0.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>28</th>\n",
       "      <td>888.888889</td>\n",
       "      <td>liquidA</td>\n",
       "      <td>-3.132993</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0</td>\n",
       "      <td>True</td>\n",
       "      <td>-3.132993</td>\n",
       "      <td>0.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>29</th>\n",
       "      <td>1000.000000</td>\n",
       "      <td>liquidA</td>\n",
       "      <td>-3.180867</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0</td>\n",
       "      <td>True</td>\n",
       "      <td>-3.180867</td>\n",
       "      <td>0.0</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "              T    phase       phi   mu  c  stable         f  f_excess\n",
       "0      0.000000     fccA -3.000000  0.0  0    True -3.000000       0.0\n",
       "1    111.111111     fccA -3.009575  0.0  0    True -3.009575       0.0\n",
       "2    222.222222     fccA -3.019150  0.0  0    True -3.019150       0.0\n",
       "3    333.333333     fccA -3.028724  0.0  0    True -3.028724       0.0\n",
       "14   444.444444      hcp -3.043939  0.0  0    True -3.043939       0.0\n",
       "15   555.555556      hcp -3.061173  0.0  0    True -3.061173       0.0\n",
       "16   666.666667      hcp -3.078408  0.0  0    True -3.078408       0.0\n",
       "17   777.777778      hcp -3.095643  0.0  0    True -3.095643       0.0\n",
       "28   888.888889  liquidA -3.132993  0.0  0    True -3.132993       0.0\n",
       "29  1000.000000  liquidA -3.180867  0.0  0    True -3.180867       0.0"
      ]
     },
     "execution_count": 10,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "df"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "ec037d03-413c-4217-adeb-96c2965f7fe2",
   "metadata": {},
   "source": [
    "Additionally refine the phase boundaries.  Adds additional columns `border` and `refined`.\n",
    "`border` is `True` if the point is a phase transition.\n",
    "`refined` is a string telling how the point was added."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "id": "759eab29-0010-40fa-ae60-8768de6ca073",
   "metadata": {},
   "outputs": [],
   "source": [
    "df = ldc.calc_phase_diagram([fcca, hcpa, lqda], Ts, mu=0.0, refine=True)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "id": "c174aaa7-ec29-4f13-ab08-d4f843f3b3c9",
   "metadata": {},
   "outputs": [
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       "      <th>4</th>\n",
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       "    <tr>\n",
       "      <th>6</th>\n",
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       "      <td>-3.078408</td>\n",
       "      <td>0.0</td>\n",
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       "      <th>7</th>\n",
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       "    <tr>\n",
       "      <th>30</th>\n",
       "      <td>362.641191</td>\n",
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       "      <td>0.0</td>\n",
       "      <td>0</td>\n",
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       "    <tr>\n",
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       "      <td>362.641191</td>\n",
       "      <td>hcp</td>\n",
       "      <td>-3.031250</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0</td>\n",
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       "    <tr>\n",
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       "      <td>815.942680</td>\n",
       "      <td>hcp</td>\n",
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      ],
      "text/plain": [
       "              T    phase       phi   mu  c  stable  border refined         f  \\\n",
       "0      0.000000     fccA -3.000000  0.0  0    True   False      no -3.000000   \n",
       "1    111.111111     fccA -3.009575  0.0  0    True   False      no -3.009575   \n",
       "2    222.222222     fccA -3.019150  0.0  0    True   False      no -3.019150   \n",
       "3    333.333333     fccA -3.028724  0.0  0    True   False      no -3.028724   \n",
       "4    444.444444      hcp -3.043939  0.0  0    True   False      no -3.043939   \n",
       "5    555.555556      hcp -3.061173  0.0  0    True   False      no -3.061173   \n",
       "6    666.666667      hcp -3.078408  0.0  0    True   False      no -3.078408   \n",
       "7    777.777778      hcp -3.095643  0.0  0    True   False      no -3.095643   \n",
       "8    888.888889  liquidA -3.132993  0.0  0    True   False      no -3.132993   \n",
       "9   1000.000000  liquidA -3.180867  0.0  0    True   False      no -3.180867   \n",
       "30   362.641191     fccA -3.031250  0.0  0    True    True       T -3.031250   \n",
       "31   362.641191      hcp -3.031250  0.0  0    True    True       T -3.031250   \n",
       "32   815.942680      hcp -3.101562  0.0  0    True    True       T -3.101562   \n",
       "33   815.942680  liquidA -3.101563  0.0  0    True    True       T -3.101563   \n",
       "\n",
       "        f_excess  \n",
       "0   0.000000e+00  \n",
       "1   0.000000e+00  \n",
       "2   0.000000e+00  \n",
       "3   0.000000e+00  \n",
       "4   0.000000e+00  \n",
       "5   0.000000e+00  \n",
       "6   0.000000e+00  \n",
       "7   0.000000e+00  \n",
       "8   0.000000e+00  \n",
       "9   0.000000e+00  \n",
       "30  0.000000e+00  \n",
       "31  0.000000e+00  \n",
       "32  4.440892e-16  \n",
       "33  0.000000e+00  "
      ]
     },
     "execution_count": 12,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "df"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "9f8641c7-9ace-4874-9a16-3cf42a431ab2",
   "metadata": {},
   "source": [
    "`keep_unstable` can be passed to also retain samples of the unstable phases."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "id": "7f2d4565-3869-4ee7-8114-3ecec2dfe704",
   "metadata": {},
   "outputs": [],
   "source": [
    "df = ldc.calc_phase_diagram([fcca, hcpa, lqda], Ts, mu=0.0, refine=True, keep_unstable=True)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "id": "28d5bdd8-ea1d-4cf4-abd0-2d2f8fd2660a",
   "metadata": {},
   "outputs": [
    {
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       "    </tr>\n",
       "    <tr>\n",
       "      <th>5</th>\n",
       "      <td>555.555556</td>\n",
       "      <td>hcp</td>\n",
       "      <td>-3.061173</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0</td>\n",
       "      <td>True</td>\n",
       "      <td>False</td>\n",
       "      <td>no</td>\n",
       "      <td>-3.061173</td>\n",
       "      <td>0.000000e+00</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>6</th>\n",
       "      <td>666.666667</td>\n",
       "      <td>hcp</td>\n",
       "      <td>-3.078408</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0</td>\n",
       "      <td>True</td>\n",
       "      <td>False</td>\n",
       "      <td>no</td>\n",
       "      <td>-3.078408</td>\n",
       "      <td>0.000000e+00</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>7</th>\n",
       "      <td>777.777778</td>\n",
       "      <td>hcp</td>\n",
       "      <td>-3.095643</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0</td>\n",
       "      <td>True</td>\n",
       "      <td>False</td>\n",
       "      <td>no</td>\n",
       "      <td>-3.095643</td>\n",
       "      <td>0.000000e+00</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>8</th>\n",
       "      <td>888.888889</td>\n",
       "      <td>liquidA</td>\n",
       "      <td>-3.132993</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0</td>\n",
       "      <td>True</td>\n",
       "      <td>False</td>\n",
       "      <td>no</td>\n",
       "      <td>-3.132993</td>\n",
       "      <td>0.000000e+00</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>9</th>\n",
       "      <td>1000.000000</td>\n",
       "      <td>liquidA</td>\n",
       "      <td>-3.180867</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0</td>\n",
       "      <td>True</td>\n",
       "      <td>False</td>\n",
       "      <td>no</td>\n",
       "      <td>-3.180867</td>\n",
       "      <td>0.000000e+00</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>10</th>\n",
       "      <td>444.444444</td>\n",
       "      <td>fccA</td>\n",
       "      <td>-3.038299</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0</td>\n",
       "      <td>False</td>\n",
       "      <td>False</td>\n",
       "      <td>NaN</td>\n",
       "      <td>-3.038299</td>\n",
       "      <td>5.639407e-03</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>11</th>\n",
       "      <td>555.555556</td>\n",
       "      <td>fccA</td>\n",
       "      <td>-3.047874</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0</td>\n",
       "      <td>False</td>\n",
       "      <td>False</td>\n",
       "      <td>NaN</td>\n",
       "      <td>-3.047874</td>\n",
       "      <td>1.329926e-02</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>12</th>\n",
       "      <td>666.666667</td>\n",
       "      <td>fccA</td>\n",
       "      <td>-3.057449</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0</td>\n",
       "      <td>False</td>\n",
       "      <td>False</td>\n",
       "      <td>NaN</td>\n",
       "      <td>-3.057449</td>\n",
       "      <td>2.095911e-02</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>13</th>\n",
       "      <td>777.777778</td>\n",
       "      <td>fccA</td>\n",
       "      <td>-3.067024</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0</td>\n",
       "      <td>False</td>\n",
       "      <td>False</td>\n",
       "      <td>NaN</td>\n",
       "      <td>-3.067024</td>\n",
       "      <td>2.861896e-02</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>14</th>\n",
       "      <td>888.888889</td>\n",
       "      <td>fccA</td>\n",
       "      <td>-3.076599</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0</td>\n",
       "      <td>False</td>\n",
       "      <td>False</td>\n",
       "      <td>NaN</td>\n",
       "      <td>-3.076599</td>\n",
       "      <td>5.639407e-02</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>15</th>\n",
       "      <td>1000.000000</td>\n",
       "      <td>fccA</td>\n",
       "      <td>-3.086173</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0</td>\n",
       "      <td>False</td>\n",
       "      <td>False</td>\n",
       "      <td>NaN</td>\n",
       "      <td>-3.086173</td>\n",
       "      <td>9.469333e-02</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>16</th>\n",
       "      <td>0.000000</td>\n",
       "      <td>hcp</td>\n",
       "      <td>-2.975000</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0</td>\n",
       "      <td>False</td>\n",
       "      <td>False</td>\n",
       "      <td>NaN</td>\n",
       "      <td>-2.975000</td>\n",
       "      <td>2.500000e-02</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>17</th>\n",
       "      <td>111.111111</td>\n",
       "      <td>hcp</td>\n",
       "      <td>-2.992235</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0</td>\n",
       "      <td>False</td>\n",
       "      <td>False</td>\n",
       "      <td>NaN</td>\n",
       "      <td>-2.992235</td>\n",
       "      <td>1.734015e-02</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>18</th>\n",
       "      <td>222.222222</td>\n",
       "      <td>hcp</td>\n",
       "      <td>-3.009469</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0</td>\n",
       "      <td>False</td>\n",
       "      <td>False</td>\n",
       "      <td>NaN</td>\n",
       "      <td>-3.009469</td>\n",
       "      <td>9.680296e-03</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>19</th>\n",
       "      <td>333.333333</td>\n",
       "      <td>hcp</td>\n",
       "      <td>-3.026704</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0</td>\n",
       "      <td>False</td>\n",
       "      <td>False</td>\n",
       "      <td>NaN</td>\n",
       "      <td>-3.026704</td>\n",
       "      <td>2.020445e-03</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>20</th>\n",
       "      <td>888.888889</td>\n",
       "      <td>hcp</td>\n",
       "      <td>-3.112877</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0</td>\n",
       "      <td>False</td>\n",
       "      <td>False</td>\n",
       "      <td>NaN</td>\n",
       "      <td>-3.112877</td>\n",
       "      <td>2.011526e-02</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>21</th>\n",
       "      <td>1000.000000</td>\n",
       "      <td>hcp</td>\n",
       "      <td>-3.130112</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0</td>\n",
       "      <td>False</td>\n",
       "      <td>False</td>\n",
       "      <td>NaN</td>\n",
       "      <td>-3.130112</td>\n",
       "      <td>5.075466e-02</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>22</th>\n",
       "      <td>0.000000</td>\n",
       "      <td>liquidA</td>\n",
       "      <td>-2.750000</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0</td>\n",
       "      <td>False</td>\n",
       "      <td>False</td>\n",
       "      <td>NaN</td>\n",
       "      <td>-2.750000</td>\n",
       "      <td>2.500000e-01</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>23</th>\n",
       "      <td>111.111111</td>\n",
       "      <td>liquidA</td>\n",
       "      <td>-2.797874</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0</td>\n",
       "      <td>False</td>\n",
       "      <td>False</td>\n",
       "      <td>NaN</td>\n",
       "      <td>-2.797874</td>\n",
       "      <td>2.117007e-01</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>24</th>\n",
       "      <td>222.222222</td>\n",
       "      <td>liquidA</td>\n",
       "      <td>-2.845748</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0</td>\n",
       "      <td>False</td>\n",
       "      <td>False</td>\n",
       "      <td>NaN</td>\n",
       "      <td>-2.845748</td>\n",
       "      <td>1.734015e-01</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>25</th>\n",
       "      <td>333.333333</td>\n",
       "      <td>liquidA</td>\n",
       "      <td>-2.893622</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0</td>\n",
       "      <td>False</td>\n",
       "      <td>False</td>\n",
       "      <td>NaN</td>\n",
       "      <td>-2.893622</td>\n",
       "      <td>1.351022e-01</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>26</th>\n",
       "      <td>444.444444</td>\n",
       "      <td>liquidA</td>\n",
       "      <td>-2.941496</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0</td>\n",
       "      <td>False</td>\n",
       "      <td>False</td>\n",
       "      <td>NaN</td>\n",
       "      <td>-2.941496</td>\n",
       "      <td>1.024424e-01</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>27</th>\n",
       "      <td>555.555556</td>\n",
       "      <td>liquidA</td>\n",
       "      <td>-2.989370</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0</td>\n",
       "      <td>False</td>\n",
       "      <td>False</td>\n",
       "      <td>NaN</td>\n",
       "      <td>-2.989370</td>\n",
       "      <td>7.180296e-02</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>28</th>\n",
       "      <td>666.666667</td>\n",
       "      <td>liquidA</td>\n",
       "      <td>-3.037244</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0</td>\n",
       "      <td>False</td>\n",
       "      <td>False</td>\n",
       "      <td>NaN</td>\n",
       "      <td>-3.037244</td>\n",
       "      <td>4.116356e-02</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>29</th>\n",
       "      <td>777.777778</td>\n",
       "      <td>liquidA</td>\n",
       "      <td>-3.085119</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0</td>\n",
       "      <td>False</td>\n",
       "      <td>False</td>\n",
       "      <td>NaN</td>\n",
       "      <td>-3.085119</td>\n",
       "      <td>1.052415e-02</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>30</th>\n",
       "      <td>362.641191</td>\n",
       "      <td>fccA</td>\n",
       "      <td>-3.031250</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0</td>\n",
       "      <td>True</td>\n",
       "      <td>True</td>\n",
       "      <td>T</td>\n",
       "      <td>-3.031250</td>\n",
       "      <td>0.000000e+00</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>31</th>\n",
       "      <td>362.641191</td>\n",
       "      <td>hcp</td>\n",
       "      <td>-3.031250</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0</td>\n",
       "      <td>True</td>\n",
       "      <td>True</td>\n",
       "      <td>T</td>\n",
       "      <td>-3.031250</td>\n",
       "      <td>0.000000e+00</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>32</th>\n",
       "      <td>815.942680</td>\n",
       "      <td>hcp</td>\n",
       "      <td>-3.101562</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0</td>\n",
       "      <td>True</td>\n",
       "      <td>True</td>\n",
       "      <td>T</td>\n",
       "      <td>-3.101562</td>\n",
       "      <td>4.440892e-16</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>33</th>\n",
       "      <td>815.942680</td>\n",
       "      <td>liquidA</td>\n",
       "      <td>-3.101563</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0</td>\n",
       "      <td>True</td>\n",
       "      <td>True</td>\n",
       "      <td>T</td>\n",
       "      <td>-3.101563</td>\n",
       "      <td>0.000000e+00</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "              T    phase       phi   mu  c  stable  border refined         f  \\\n",
       "0      0.000000     fccA -3.000000  0.0  0    True   False      no -3.000000   \n",
       "1    111.111111     fccA -3.009575  0.0  0    True   False      no -3.009575   \n",
       "2    222.222222     fccA -3.019150  0.0  0    True   False      no -3.019150   \n",
       "3    333.333333     fccA -3.028724  0.0  0    True   False      no -3.028724   \n",
       "4    444.444444      hcp -3.043939  0.0  0    True   False      no -3.043939   \n",
       "5    555.555556      hcp -3.061173  0.0  0    True   False      no -3.061173   \n",
       "6    666.666667      hcp -3.078408  0.0  0    True   False      no -3.078408   \n",
       "7    777.777778      hcp -3.095643  0.0  0    True   False      no -3.095643   \n",
       "8    888.888889  liquidA -3.132993  0.0  0    True   False      no -3.132993   \n",
       "9   1000.000000  liquidA -3.180867  0.0  0    True   False      no -3.180867   \n",
       "10   444.444444     fccA -3.038299  0.0  0   False   False     NaN -3.038299   \n",
       "11   555.555556     fccA -3.047874  0.0  0   False   False     NaN -3.047874   \n",
       "12   666.666667     fccA -3.057449  0.0  0   False   False     NaN -3.057449   \n",
       "13   777.777778     fccA -3.067024  0.0  0   False   False     NaN -3.067024   \n",
       "14   888.888889     fccA -3.076599  0.0  0   False   False     NaN -3.076599   \n",
       "15  1000.000000     fccA -3.086173  0.0  0   False   False     NaN -3.086173   \n",
       "16     0.000000      hcp -2.975000  0.0  0   False   False     NaN -2.975000   \n",
       "17   111.111111      hcp -2.992235  0.0  0   False   False     NaN -2.992235   \n",
       "18   222.222222      hcp -3.009469  0.0  0   False   False     NaN -3.009469   \n",
       "19   333.333333      hcp -3.026704  0.0  0   False   False     NaN -3.026704   \n",
       "20   888.888889      hcp -3.112877  0.0  0   False   False     NaN -3.112877   \n",
       "21  1000.000000      hcp -3.130112  0.0  0   False   False     NaN -3.130112   \n",
       "22     0.000000  liquidA -2.750000  0.0  0   False   False     NaN -2.750000   \n",
       "23   111.111111  liquidA -2.797874  0.0  0   False   False     NaN -2.797874   \n",
       "24   222.222222  liquidA -2.845748  0.0  0   False   False     NaN -2.845748   \n",
       "25   333.333333  liquidA -2.893622  0.0  0   False   False     NaN -2.893622   \n",
       "26   444.444444  liquidA -2.941496  0.0  0   False   False     NaN -2.941496   \n",
       "27   555.555556  liquidA -2.989370  0.0  0   False   False     NaN -2.989370   \n",
       "28   666.666667  liquidA -3.037244  0.0  0   False   False     NaN -3.037244   \n",
       "29   777.777778  liquidA -3.085119  0.0  0   False   False     NaN -3.085119   \n",
       "30   362.641191     fccA -3.031250  0.0  0    True    True       T -3.031250   \n",
       "31   362.641191      hcp -3.031250  0.0  0    True    True       T -3.031250   \n",
       "32   815.942680      hcp -3.101562  0.0  0    True    True       T -3.101562   \n",
       "33   815.942680  liquidA -3.101563  0.0  0    True    True       T -3.101563   \n",
       "\n",
       "        f_excess  \n",
       "0   0.000000e+00  \n",
       "1   0.000000e+00  \n",
       "2   0.000000e+00  \n",
       "3   0.000000e+00  \n",
       "4   0.000000e+00  \n",
       "5   0.000000e+00  \n",
       "6   0.000000e+00  \n",
       "7   0.000000e+00  \n",
       "8   0.000000e+00  \n",
       "9   0.000000e+00  \n",
       "10  5.639407e-03  \n",
       "11  1.329926e-02  \n",
       "12  2.095911e-02  \n",
       "13  2.861896e-02  \n",
       "14  5.639407e-02  \n",
       "15  9.469333e-02  \n",
       "16  2.500000e-02  \n",
       "17  1.734015e-02  \n",
       "18  9.680296e-03  \n",
       "19  2.020445e-03  \n",
       "20  2.011526e-02  \n",
       "21  5.075466e-02  \n",
       "22  2.500000e-01  \n",
       "23  2.117007e-01  \n",
       "24  1.734015e-01  \n",
       "25  1.351022e-01  \n",
       "26  1.024424e-01  \n",
       "27  7.180296e-02  \n",
       "28  4.116356e-02  \n",
       "29  1.052415e-02  \n",
       "30  0.000000e+00  \n",
       "31  0.000000e+00  \n",
       "32  4.440892e-16  \n",
       "33  0.000000e+00  "
      ]
     },
     "execution_count": 14,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "df"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "7c052abe-6f22-4154-bab8-ba8eeeda896f",
   "metadata": {},
   "source": [
    "A simple plot with `seaborn`."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "id": "3466e243-98af-413c-841c-18c9c909a4c1",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<Axes: xlabel='T', ylabel='f'>"
      ]
     },
     "execution_count": 15,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "sns.lineplot(\n",
    "    data=df,\n",
    "    x='T', y='f',\n",
    "    hue='phase',\n",
    "    style='stable', style_order=[True, False],\n",
    ")"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "e34e5b08-452b-4c45-953d-4dc7ad7bce7b",
   "metadata": {},
   "source": [
    "Or using landau"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "id": "dcb6ec7d-68e7-4cc0-bc0b-414097a879a8",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/plain": [
       "<Axes: xlabel='Temperature [K]', ylabel='Semi-grandcanonical potential [eV/atom]'>"
      ]
     },
     "execution_count": 16,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "lpl.plot_1d_T_phase_diagram(df)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "36483f1c-309c-4ab6-b424-695080183df6",
   "metadata": {},
   "source": [
    "## Including Concentration\n",
    "\n",
    "landau implicitly assumes there is only two species and that all `phase` objects agree on which is the 'first' and which is the 'second'.\n",
    "\n",
    "Phase objects with variable concentration are most easily assembled from objects of fixed concentration, because this is how e.g. `calphy` presents them."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "id": "119f66c7-d64c-43f3-afee-f42bac1d04df",
   "metadata": {},
   "outputs": [],
   "source": [
    "fccb = ldp.LinePhase(\"fccB\", fixed_concentration=1, line_energy=-2, line_entropy=1.1*ldp.kB)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "id": "65c1e652-ef55-4038-936c-8037f7335d9a",
   "metadata": {},
   "outputs": [],
   "source": [
    "hcpb = ldp.LinePhase(\"hcpB\", fixed_concentration=1, line_energy=-1.95, line_entropy=1.1*ldp.kB)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "id": "bd48b65c-bb1d-4805-8cd0-7846ad6086b3",
   "metadata": {},
   "outputs": [],
   "source": [
    "fcc = ldp.IdealSolution('fcc', fcca, fccb)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "id": "17b085e2-ec04-4ec0-8894-8bb47cd9cbd0",
   "metadata": {},
   "outputs": [],
   "source": [
    "hcp = ldp.IdealSolution('hcp', hcpa, hcpb)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "51f9bc3d-714f-4e5c-9ef0-bef6679dd663",
   "metadata": {},
   "source": [
    "All phases present the same interface to calculate the semi-grandcanonical potential."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "id": "c164e502-68c3-4816-bde4-e7f49821493d",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "\u001b[31mSignature:\u001b[39m fcc.semigrand_potential(T, dmu)\n",
       "\u001b[31mDocstring:\u001b[39m Calculate the semigrand potential of the phase.\n",
       "\u001b[31mFile:\u001b[39m      ~/science/phd/dev/landau/landau/phases.py\n",
       "\u001b[31mType:\u001b[39m      method"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "fcc.semigrand_potential?"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "id": "2ff3510b-c216-4ec6-81e4-12d6bcfb77c9",
   "metadata": {},
   "outputs": [],
   "source": [
    "mus = np.linspace(0, 2)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "id": "d85c951b-96c8-4881-a627-02b5bb8f9e5d",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.legend.Legend at 0x7fd7c26c1b90>"
      ]
     },
     "execution_count": 23,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.plot(mus, fcc.semigrand_potential(   0, mus), label='0K')\n",
    "plt.plot(mus, fcc.semigrand_potential(1000, mus), label='1000K')\n",
    "plt.xlabel(\"Chemical potential difference [eV]\")\n",
    "plt.ylabel(\"Semi-grandcanonical potential [eV/atom]\")\n",
    "plt.legend()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "362ec107-091c-4dcc-b0f3-1cd80bc00f4f",
   "metadata": {},
   "source": [
    "Chemical potential range can also be guessed."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "id": "77b6d017-a701-4abf-aa48-d321794975da",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(array([0.20348167, 0.59702767, 0.65649822, 0.69224108, 0.71784655,\n",
       "        0.73785687, 0.75505521, 0.76873383, 0.7816471 , 0.79224485,\n",
       "        0.8028426 , 0.81167202, 0.82000879, 0.82834556, 0.83561447,\n",
       "        0.84230052, 0.84898658, 0.85567263, 0.86147831, 0.86697089,\n",
       "        0.87246348, 0.87795607, 0.88344865, 0.88811217, 0.89275789,\n",
       "        0.89740361, 0.90204934, 0.90669506, 0.91113655, 0.9152035 ,\n",
       "        0.91927046, 0.92333741, 0.92740436, 0.93147132, 0.93553827,\n",
       "        0.93926782, 0.94297044, 0.94667306, 0.95037569, 0.95407831,\n",
       "        0.95778093, 0.96148355, 0.96502695, 0.9685459 , 0.97206486,\n",
       "        0.97558381, 0.97910276, 0.98262172, 0.98614067, 0.98965083,\n",
       "        0.99314975, 0.99664867, 1.0001476 , 1.00364652, 1.00714544,\n",
       "        1.01064436, 1.01414329, 1.01777959, 1.02142026, 1.02506093,\n",
       "        1.0287016 , 1.03234227, 1.03598294, 1.03962362, 1.04351443,\n",
       "        1.04747176, 1.0514291 , 1.05538644, 1.05934378, 1.06330112,\n",
       "        1.06735489, 1.07183317, 1.07631146, 1.08078974, 1.08526802,\n",
       "        1.0897463 , 1.09449426, 1.09974606, 1.10499786, 1.11024966,\n",
       "        1.11550146, 1.12116141, 1.127511  , 1.1338606 , 1.14021019,\n",
       "        1.14694898, 1.15482242, 1.16269587, 1.17056931, 1.18039948,\n",
       "        1.1903641 , 1.20122061, 1.21403758, 1.22791481, 1.24460976,\n",
       "        1.26503001, 1.29068089, 1.32576234, 1.38630569, 1.78603808]),\n",
       " np.float64(0.00010701744583500724),\n",
       " np.float64(0.9998999870320691))"
      ]
     },
     "execution_count": 24,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "ldc.guess_mu_range([fcc], T=1000, samples=100)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 25,
   "id": "dd68a04e-fd9f-43ad-9c79-dec14d21e0d7",
   "metadata": {},
   "outputs": [],
   "source": [
    "mus, *_ = ldc.guess_mu_range([fcc], T=1000, samples=100)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "2495c2c7-b0c7-407b-bba0-89e1f78d168b",
   "metadata": {},
   "source": [
    "Isothermals are available via the `concentration` method."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 26,
   "id": "33966aa3-c3db-401a-a792-1fea9627c08e",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "\u001b[31mSignature:\u001b[39m fcc.concentration(T, dmu)\n",
       "\u001b[31mDocstring:\u001b[39m Concentration of the phase at the given state.\n",
       "\u001b[31mFile:\u001b[39m      ~/science/phd/dev/landau/landau/phases.py\n",
       "\u001b[31mType:\u001b[39m      method"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "fcc.concentration?"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 27,
   "id": "07789622-9807-45d1-9f76-a6ec1ce50ad4",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.legend.Legend at 0x7fd7c25525d0>"
      ]
     },
     "execution_count": 27,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.plot(mus, fcc.concentration(   0, mus), label='0K')\n",
    "plt.plot(mus, fcc.concentration(1000, mus), label='1000K')\n",
    "plt.xlabel(\"Chemical potential difference [eV]\")\n",
    "plt.ylabel(\"Semi-grandcanonical potential [eV/atom]\")\n",
    "plt.legend()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "65e0df55-8fa0-41d9-ab76-0103b0188be6",
   "metadata": {},
   "source": [
    "Again, phase transitions are determined by the intersection points."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 28,
   "id": "4f2602f0-d70c-446a-a42f-ef8f9fc6dc56",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.legend.Legend at 0x7fd7ba12be90>"
      ]
     },
     "execution_count": 28,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.plot(mus, hcp.semigrand_potential(1000, mus), label='hcp')\n",
    "plt.plot(mus, fcc.semigrand_potential(1000, mus), label='fcc')\n",
    "plt.xlabel(\"Chemical potential difference [eV]\")\n",
    "plt.ylabel(\"Semi-grandcanonical potential [eV/atom]\")\n",
    "plt.legend()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 29,
   "id": "a9c2650a-aa90-4b8a-81c9-f84cf9f38388",
   "metadata": {},
   "outputs": [],
   "source": [
    "df = ldc.calc_phase_diagram([hcp, fcc], Ts=1000, mu=100, keep_unstable=True)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 30,
   "id": "3ec064f7-8478-4a39-aa34-9418020b9933",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "lpl.plot_1d_mu_phase_diagram(df)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "50a4984b-7fb2-40f3-8350-215d5c7e8f18",
   "metadata": {},
   "source": [
    "Adding a liquid phase as well and finally plotting the full diagram."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 31,
   "id": "0266e5fb-5c58-44d1-aac9-37c3fd5e9ce5",
   "metadata": {},
   "outputs": [],
   "source": [
    "lqdb = ldp.LinePhase(\"liquidB\", fixed_concentration=1, line_energy=-1.75, line_entropy=4.4*ldp.kB)\n",
    "lqd = ldp.IdealSolution('liquid', lqda, lqdb)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 32,
   "id": "8a2c49e1-f68d-415d-92a1-ab27b862a694",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "CPU times: user 1.32 s, sys: 5.93 ms, total: 1.33 s\n",
      "Wall time: 1.33 s\n"
     ]
    }
   ],
   "source": [
    "%%time\n",
    "Ts = np.linspace(200, 1000)\n",
    "df = ldc.calc_phase_diagram([hcp, fcc, lqd], Ts, mu=100)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 33,
   "id": "43b50988-ed0e-44fd-bbbc-ed00778baf94",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
       "        vertical-align: middle;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>T</th>\n",
       "      <th>phase</th>\n",
       "      <th>phi</th>\n",
       "      <th>mu</th>\n",
       "      <th>c</th>\n",
       "      <th>stable</th>\n",
       "      <th>border</th>\n",
       "      <th>refined</th>\n",
       "      <th>f</th>\n",
       "      <th>f_excess</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>363.265306</td>\n",
       "      <td>hcp</td>\n",
       "      <td>-3.031347</td>\n",
       "      <td>0.053318</td>\n",
       "      <td>1.641792e-14</td>\n",
       "      <td>True</td>\n",
       "      <td>False</td>\n",
       "      <td>no</td>\n",
       "      <td>-3.031347</td>\n",
       "      <td>-1.643130e-14</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>363.265306</td>\n",
       "      <td>hcp</td>\n",
       "      <td>-3.031347</td>\n",
       "      <td>0.645306</td>\n",
       "      <td>2.680972e-06</td>\n",
       "      <td>True</td>\n",
       "      <td>False</td>\n",
       "      <td>no</td>\n",
       "      <td>-3.031345</td>\n",
       "      <td>-1.026572e-06</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>363.265306</td>\n",
       "      <td>hcp</td>\n",
       "      <td>-3.031347</td>\n",
       "      <td>0.706245</td>\n",
       "      <td>1.878120e-05</td>\n",
       "      <td>True</td>\n",
       "      <td>False</td>\n",
       "      <td>no</td>\n",
       "      <td>-3.031334</td>\n",
       "      <td>-6.047016e-06</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>363.265306</td>\n",
       "      <td>hcp</td>\n",
       "      <td>-3.031349</td>\n",
       "      <td>0.742431</td>\n",
       "      <td>5.966762e-05</td>\n",
       "      <td>True</td>\n",
       "      <td>False</td>\n",
       "      <td>no</td>\n",
       "      <td>-3.031304</td>\n",
       "      <td>-1.705217e-05</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>363.265306</td>\n",
       "      <td>hcp</td>\n",
       "      <td>-3.031351</td>\n",
       "      <td>0.768429</td>\n",
       "      <td>1.368946e-04</td>\n",
       "      <td>True</td>\n",
       "      <td>False</td>\n",
       "      <td>no</td>\n",
       "      <td>-3.031246</td>\n",
       "      <td>-3.556378e-05</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>...</th>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>15708</th>\n",
       "      <td>798.894454</td>\n",
       "      <td>liquid</td>\n",
       "      <td>-3.107717</td>\n",
       "      <td>0.936009</td>\n",
       "      <td>1.780641e-01</td>\n",
       "      <td>True</td>\n",
       "      <td>True</td>\n",
       "      <td>delaunay</td>\n",
       "      <td>-2.941047</td>\n",
       "      <td>4.468980e-02</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>15709</th>\n",
       "      <td>798.894454</td>\n",
       "      <td>hcp</td>\n",
       "      <td>-3.107717</td>\n",
       "      <td>0.936009</td>\n",
       "      <td>1.199755e-01</td>\n",
       "      <td>True</td>\n",
       "      <td>True</td>\n",
       "      <td>delaunay</td>\n",
       "      <td>-2.995419</td>\n",
       "      <td>-6.523235e-03</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>15710</th>\n",
       "      <td>782.832625</td>\n",
       "      <td>fcc</td>\n",
       "      <td>-3.115044</td>\n",
       "      <td>0.994895</td>\n",
       "      <td>5.060824e-01</td>\n",
       "      <td>True</td>\n",
       "      <td>True</td>\n",
       "      <td>delaunay-triple</td>\n",
       "      <td>-2.611545</td>\n",
       "      <td>1.301759e-01</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>15711</th>\n",
       "      <td>782.832625</td>\n",
       "      <td>liquid</td>\n",
       "      <td>-3.115044</td>\n",
       "      <td>0.994895</td>\n",
       "      <td>3.372285e-01</td>\n",
       "      <td>True</td>\n",
       "      <td>True</td>\n",
       "      <td>delaunay-triple</td>\n",
       "      <td>-2.779537</td>\n",
       "      <td>6.686710e-03</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>15712</th>\n",
       "      <td>782.832625</td>\n",
       "      <td>hcp</td>\n",
       "      <td>-3.115044</td>\n",
       "      <td>0.994895</td>\n",
       "      <td>2.411723e-01</td>\n",
       "      <td>True</td>\n",
       "      <td>True</td>\n",
       "      <td>delaunay-triple</td>\n",
       "      <td>-2.875103</td>\n",
       "      <td>-6.356284e-02</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "<p>5713 rows × 10 columns</p>\n",
       "</div>"
      ],
      "text/plain": [
       "                T   phase       phi        mu             c  stable  border  \\\n",
       "0      363.265306     hcp -3.031347  0.053318  1.641792e-14    True   False   \n",
       "1      363.265306     hcp -3.031347  0.645306  2.680972e-06    True   False   \n",
       "2      363.265306     hcp -3.031347  0.706245  1.878120e-05    True   False   \n",
       "3      363.265306     hcp -3.031349  0.742431  5.966762e-05    True   False   \n",
       "4      363.265306     hcp -3.031351  0.768429  1.368946e-04    True   False   \n",
       "...           ...     ...       ...       ...           ...     ...     ...   \n",
       "15708  798.894454  liquid -3.107717  0.936009  1.780641e-01    True    True   \n",
       "15709  798.894454     hcp -3.107717  0.936009  1.199755e-01    True    True   \n",
       "15710  782.832625     fcc -3.115044  0.994895  5.060824e-01    True    True   \n",
       "15711  782.832625  liquid -3.115044  0.994895  3.372285e-01    True    True   \n",
       "15712  782.832625     hcp -3.115044  0.994895  2.411723e-01    True    True   \n",
       "\n",
       "               refined         f      f_excess  \n",
       "0                   no -3.031347 -1.643130e-14  \n",
       "1                   no -3.031345 -1.026572e-06  \n",
       "2                   no -3.031334 -6.047016e-06  \n",
       "3                   no -3.031304 -1.705217e-05  \n",
       "4                   no -3.031246 -3.556378e-05  \n",
       "...                ...       ...           ...  \n",
       "15708         delaunay -2.941047  4.468980e-02  \n",
       "15709         delaunay -2.995419 -6.523235e-03  \n",
       "15710  delaunay-triple -2.611545  1.301759e-01  \n",
       "15711  delaunay-triple -2.779537  6.686710e-03  \n",
       "15712  delaunay-triple -2.875103 -6.356284e-02  \n",
       "\n",
       "[5713 rows x 10 columns]"
      ]
     },
     "execution_count": 33,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "df"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 34,
   "id": "8020bd1e-f16f-49d6-a755-a6cee8de41be",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "lpl.plot_phase_diagram(df, tielines=True, poly_method='fasttsp')"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "379f68cc-6268-4d54-9167-b16d4b8dfce5",
   "metadata": {},
   "source": [
    "Can also plot in mu/T space."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 35,
   "id": "04641ce3-8077-450e-b4fb-76f789c03316",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "CPU times: user 3.8 s, sys: 29 ms, total: 3.83 s\n",
      "Wall time: 3.85 s\n"
     ]
    }
   ],
   "source": [
    "%%time\n",
    "Ts = np.linspace(200, 1000, 200)\n",
    "mus = np.linspace(0.5, 1.5, 200)\n",
    "df = ldc.calc_phase_diagram([hcp, fcc, lqd], Ts, mu=mus)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 36,
   "id": "188655bd-c37f-4b62-92c6-343eec97f336",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "CPU times: user 15.1 s, sys: 26.6 ms, total: 15.1 s\n",
      "Wall time: 12.1 s\n"
     ]
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "%%time\n",
    "lpl.plot_mu_phase_diagram(df)"
   ]
  }
 ],
 "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": "3.13.0"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 5
}