{
 "cells": [
  {
   "cell_type": "markdown",
   "id": "46e6da05-a241-4176-aba6-18cc508a3e02",
   "metadata": {},
   "source": [
    "# Converting from fo2 to buffer position\n",
    "- You can download the spreadsheet here: https://github.com/PennyWieser/Thermobar/blob/main/docs/Examples/Other_features/Redox_Conversions.xlsx"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "id": "9ba780a7-dda6-4d50-803b-bff4d90ebd78",
   "metadata": {},
   "outputs": [],
   "source": [
    "# Loading various python things\n",
    "import numpy as np\n",
    "import pandas as pd\n",
    "import matplotlib.pyplot as plt\n",
    "import Thermobar as pt"
   ]
  },
  {
   "attachments": {
    "15f21235-dfec-488d-b966-33de11e40510.png": {
     "image/png": 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"
    }
   },
   "cell_type": "markdown",
   "id": "124ea656-9cef-4f60-a9b8-f7b9ffee102b",
   "metadata": {},
   "source": [
    "## Pichavent experimental data\n",
    "![image.png](attachment:15f21235-dfec-488d-b966-33de11e40510.png)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 52,
   "id": "a75c13c3-5ad9-423a-b8f6-afc734e57224",
   "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>deltaNNO_Frost1991</th>\n",
       "      <th>deltaQFM_Frost1991</th>\n",
       "      <th>QFM_equation_Choice</th>\n",
       "      <th>T_K</th>\n",
       "      <th>P_kbar</th>\n",
       "      <th>fo2</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>2.040004</td>\n",
       "      <td>2.68716</td>\n",
       "      <td>High T</td>\n",
       "      <td>1223.15</td>\n",
       "      <td>2.176</td>\n",
       "      <td>1.258925e-09</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "   deltaNNO_Frost1991  deltaQFM_Frost1991 QFM_equation_Choice      T_K  \\\n",
       "0            2.040004             2.68716              High T  1223.15   \n",
       "\n",
       "   P_kbar           fo2  \n",
       "0   2.176  1.258925e-09  "
      ]
     },
     "execution_count": 52,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Say its really in MPa\n",
    "logfo2_MPa=-9.9\n",
    "fo2_MPa=10**(logfo2_MPa)\n",
    "fo2_bar=10*fo2_MPa\n",
    "convert_fo2_to_buffer(fo2=fo2_bar, \n",
    "                      T_K=950+273.15, P_kbar=217.6/100)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 54,
   "id": "aa512342-bfe8-43ad-bc32-6b84df31d608",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
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       "\n",
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       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>deltaNNO_Frost1991</th>\n",
       "      <th>deltaQFM_Frost1991</th>\n",
       "      <th>QFM_equation_Choice</th>\n",
       "      <th>T_K</th>\n",
       "      <th>P_kbar</th>\n",
       "      <th>fo2</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>1.040004</td>\n",
       "      <td>1.68716</td>\n",
       "      <td>High T</td>\n",
       "      <td>1223.15</td>\n",
       "      <td>2.176</td>\n",
       "      <td>1.258925e-10</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "   deltaNNO_Frost1991  deltaQFM_Frost1991 QFM_equation_Choice      T_K  \\\n",
       "0            1.040004             1.68716              High T  1223.15   \n",
       "\n",
       "   P_kbar           fo2  \n",
       "0   2.176  1.258925e-10  "
      ]
     },
     "execution_count": 54,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Say its really in bars\n",
    "logfo2_MPa=-9.9\n",
    "fo2_MPa=10**(logfo2_MPa)\n",
    "fo2_bar=fo2_MPa\n",
    "convert_fo2_to_buffer(fo2=fo2_bar, \n",
    "                      T_K=950+273.15, P_kbar=217.6/100)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "da7ba1ae-0896-4529-b7ff-2fbfdebfd066",
   "metadata": {},
   "source": [
    "## Load in data\n",
    "- No suffix in file, so add here to say they are liquids"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "id": "f43a8682-3d9c-48b9-b7f7-06a7208eb27d",
   "metadata": {},
   "outputs": [
    {
     "data": {
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       "\n",
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       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>Experiment</th>\n",
       "      <th>Phase</th>\n",
       "      <th>SiO2_Liq</th>\n",
       "      <th>TiO2_Liq</th>\n",
       "      <th>Al2O3_Liq</th>\n",
       "      <th>FeOt_Liq</th>\n",
       "      <th>MgO_Liq</th>\n",
       "      <th>CaO_Liq</th>\n",
       "      <th>Na2O_Liq</th>\n",
       "      <th>K2O_Liq</th>\n",
       "      <th>Total</th>\n",
       "      <th>P_kbar</th>\n",
       "      <th>T_K</th>\n",
       "      <th>DeltaNNO</th>\n",
       "      <th>logfo2_MPa</th>\n",
       "      <th>fo2_Mpa</th>\n",
       "      <th>fo2_bars</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>SG13</td>\n",
       "      <td>Gl</td>\n",
       "      <td>72.6</td>\n",
       "      <td>0.28</td>\n",
       "      <td>14.7</td>\n",
       "      <td>2.89</td>\n",
       "      <td>0.89</td>\n",
       "      <td>3.99</td>\n",
       "      <td>2.79</td>\n",
       "      <td>1.85</td>\n",
       "      <td>92</td>\n",
       "      <td>2.04</td>\n",
       "      <td>1073.15</td>\n",
       "      <td>0.6</td>\n",
       "      <td>-13.8</td>\n",
       "      <td>1.584893e-14</td>\n",
       "      <td>1.584893e-13</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "  Experiment Phase  SiO2_Liq  TiO2_Liq  Al2O3_Liq  FeOt_Liq  MgO_Liq  CaO_Liq  \\\n",
       "0       SG13    Gl      72.6      0.28       14.7      2.89     0.89     3.99   \n",
       "\n",
       "   Na2O_Liq  K2O_Liq  Total  P_kbar      T_K  DeltaNNO  logfo2_MPa  \\\n",
       "0      2.79     1.85     92    2.04  1073.15       0.6       -13.8   \n",
       "\n",
       "        fo2_Mpa      fo2_bars  \n",
       "0  1.584893e-14  1.584893e-13  "
      ]
     },
     "execution_count": 16,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "load=pt.import_excel('Redox_Conversions.xlsx', sheet_name=\"Pichavent_2018\")\n",
    "Liqs=load['Liqs']\n",
    "myinput=load['my_input']\n",
    "myinput.head()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 36,
   "id": "e57bddbf-476c-4fba-8275-49492f90e241",
   "metadata": {},
   "outputs": [
    {
     "data": {
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       "    }\n",
       "\n",
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       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>deltaNNO_Frost1991</th>\n",
       "      <th>deltaQFM_Frost1991</th>\n",
       "      <th>QFM_equation_Choice</th>\n",
       "      <th>T_K</th>\n",
       "      <th>P_kbar</th>\n",
       "      <th>fo2</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>-0.016725</td>\n",
       "      <td>0.641639</td>\n",
       "      <td>High T</td>\n",
       "      <td>1073.15</td>\n",
       "      <td>2.04</td>\n",
       "      <td>1.584893e-14</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "   deltaNNO_Frost1991  deltaQFM_Frost1991 QFM_equation_Choice      T_K  \\\n",
       "0           -0.016725            0.641639              High T  1073.15   \n",
       "\n",
       "   P_kbar           fo2  \n",
       "0    2.04  1.584893e-14  "
      ]
     },
     "execution_count": 36,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "convert_fo2_to_buffer(fo2=myinput['fo2_Mpa'], \n",
    "                      T_K=myinput['T_K'], P_kbar=myinput['P_kbar'])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 33,
   "id": "5a00f79a-98f2-43dc-8701-926e7a6ab2c8",
   "metadata": {},
   "outputs": [
    {
     "data": {
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       "\n",
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       "\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>deltaNNO_Frost1991</th>\n",
       "      <th>deltaQFM_Frost1991</th>\n",
       "      <th>QFM_equation_Choice</th>\n",
       "      <th>T_K</th>\n",
       "      <th>P_kbar</th>\n",
       "      <th>fo2</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>0.983275</td>\n",
       "      <td>1.641639</td>\n",
       "      <td>High T</td>\n",
       "      <td>1073.15</td>\n",
       "      <td>2.04</td>\n",
       "      <td>1.584893e-13</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "   deltaNNO_Frost1991  deltaQFM_Frost1991 QFM_equation_Choice      T_K  \\\n",
       "0            0.983275            1.641639              High T  1073.15   \n",
       "\n",
       "   P_kbar           fo2  \n",
       "0    2.04  1.584893e-13  "
      ]
     },
     "execution_count": 33,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "\n",
    "convert_fo2_to_buffer(fo2=myinput['fo2_bars'], \n",
    "                      T_K=myinput['T_K'], P_kbar=myinput['P_kbar'])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 48,
   "id": "0aabe2e5-6874-48f7-9c4c-04fb86cc9b41",
   "metadata": {},
   "outputs": [],
   "source": [
    "def convert_fo2_to_buffer(fo2=None, T_K=None, P_kbar=None):\n",
    "    \n",
    "    \"\"\" Converts fo2 in bars to deltaNNO and delta QFM using Frost 1991 \n",
    "    based on user-entered T in Kelvin and P in kbar\n",
    "    \"\"\"\n",
    "    logfo2=np.log10(fo2)\n",
    "# NNO Buffer position from frost (1991)\n",
    "    logfo2_NNO=(-24930/T_K) + 9.36 + 0.046 * ((P_kbar*1000)-1)/T_K\n",
    "\n",
    "    fo2_NNO=10**logfo2\n",
    "    DeltaNNO=logfo2-logfo2_NNO\n",
    "    \n",
    "\n",
    "\n",
    "#  QFM Buffer position from frost (1991)\n",
    "\n",
    "    # Calculates cut off T for alpha-beta qtz transition that determins QFM\n",
    "    Cut_off_T=573+273.15+0.025*(P_kbar*1000)\n",
    "    \n",
    "    logfo2_QFM_highT=(-25096.3/T_K) + 8.735 + 0.11 * ((P_kbar*1000)-1)/T_K\n",
    "    T_Choice='HighT Beta Qtz'\n",
    "\n",
    "    logfo2_QFM_lowT=(-26455.3/T_K) +10.344 + 0.092 * ((P_kbar*1000)-1)/T_K\n",
    "    T_Choice='Low T alpha Qtz'\n",
    "\n",
    "        \n",
    "    fo2_QFM_highT=10**logfo2_QFM_highT\n",
    "    fo2_QFM_lowT=10**logfo2_QFM_lowT\n",
    "\n",
    "    Delta_QFM_highT=logfo2-logfo2_QFM_highT\n",
    "    Delta_QFM_lowT=logfo2-logfo2_QFM_highT   \n",
    "    if isinstance(fo2, float) or isinstance(fo2, int):\n",
    "        if T_K<Cut_off_T:\n",
    "            DeltaQFM=Delta_QFM_lowT\n",
    "        if T_K>=Cut_off_T:\n",
    "            DeltaQFM=Delta_QFM_highT\n",
    "        out=pd.DataFrame(data={'deltaNNO_Frost1991':  DeltaNNO,\n",
    "                               'deltaQFM_Frost1991':  DeltaQFM,\n",
    "                               'QFM_equation_Choice': 'High T',\n",
    "                               'T_K': T_K,\n",
    "                               'P_kbar': P_kbar,\n",
    "                               'fo2': fo2}, index=[0])\n",
    "    else:\n",
    "        out=pd.DataFrame(data={'deltaNNO_Frost1991':  DeltaNNO,\n",
    "                               'deltaQFM_Frost1991': Delta_QFM_highT,\n",
    "                               'QFM_equation_Choice': 'High T',\n",
    "                               'T_K': T_K,\n",
    "                               'P_kbar': P_kbar,\n",
    "                               'fo2': fo2}) \n",
    "        out.loc[(T_K<Cut_off_T), 'deltaQFM_Frost1991']=Delta_QFM_lowT\n",
    "        out.loc[(T_K<Cut_off_T), 'QFM_equation_Choice']='Low T'\n",
    "    \n",
    "    return out\n",
    "                           \n",
    "                           \n",
    "                           "
   ]
  },
  {
   "cell_type": "markdown",
   "id": "68d37e2b-147a-4545-bf08-d307e3755bef",
   "metadata": {},
   "source": [
    "## Example 1: Calculating Fe3Fet for a series of liquid compositions\n",
    "- Remember, Fe3Fet_Liq to buffer positions is very dependent on temperature, so first we need to choose a thermometer"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "id": "44ef4249-bd9e-4d60-92e3-ba5ceb3edd27",
   "metadata": {},
   "outputs": [],
   "source": [
    "# Calculate temperature\n",
    "T_HT87=pt.calculate_liq_only_temp(liq_comps=Liqs, equationT='T_Helz1987_MgO')"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "dbbbd147-3b52-4792-a90b-f36c3c0e681c",
   "metadata": {},
   "source": [
    "### 1a: Using a value for logfo2"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "id": "24ffb052-cbc6-455e-b5b6-fd5e971c0807",
   "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>SiO2_Liq</th>\n",
       "      <th>TiO2_Liq</th>\n",
       "      <th>Al2O3_Liq</th>\n",
       "      <th>Fe2O3_Liq</th>\n",
       "      <th>FeO_Liq</th>\n",
       "      <th>MnO_Liq</th>\n",
       "      <th>MgO_Liq</th>\n",
       "      <th>CaO_Liq</th>\n",
       "      <th>Na2O_Liq</th>\n",
       "      <th>K2O_Liq</th>\n",
       "      <th>P2O5_Liq</th>\n",
       "      <th>Fe3Fet_Liq</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>51.524017</td>\n",
       "      <td>2.605133</td>\n",
       "      <td>13.546977</td>\n",
       "      <td>3.774733</td>\n",
       "      <td>7.730924</td>\n",
       "      <td>0.186119</td>\n",
       "      <td>6.707341</td>\n",
       "      <td>10.989132</td>\n",
       "      <td>2.410111</td>\n",
       "      <td>0.484441</td>\n",
       "      <td>0.248864</td>\n",
       "      <td>0.305237</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>51.535177</td>\n",
       "      <td>2.645197</td>\n",
       "      <td>13.736989</td>\n",
       "      <td>3.780389</td>\n",
       "      <td>7.788015</td>\n",
       "      <td>0.189839</td>\n",
       "      <td>6.507155</td>\n",
       "      <td>10.829918</td>\n",
       "      <td>2.454594</td>\n",
       "      <td>0.494123</td>\n",
       "      <td>0.253838</td>\n",
       "      <td>0.303996</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>51.575604</td>\n",
       "      <td>2.775984</td>\n",
       "      <td>13.689274</td>\n",
       "      <td>3.864310</td>\n",
       "      <td>8.061706</td>\n",
       "      <td>0.200831</td>\n",
       "      <td>6.285636</td>\n",
       "      <td>10.477006</td>\n",
       "      <td>2.513328</td>\n",
       "      <td>0.521354</td>\n",
       "      <td>0.268537</td>\n",
       "      <td>0.301340</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>51.600593</td>\n",
       "      <td>2.878059</td>\n",
       "      <td>13.594286</td>\n",
       "      <td>3.933036</td>\n",
       "      <td>8.275994</td>\n",
       "      <td>0.209284</td>\n",
       "      <td>6.149388</td>\n",
       "      <td>10.236264</td>\n",
       "      <td>2.548374</td>\n",
       "      <td>0.542061</td>\n",
       "      <td>0.279838</td>\n",
       "      <td>0.299531</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>51.614175</td>\n",
       "      <td>3.065335</td>\n",
       "      <td>13.378208</td>\n",
       "      <td>4.052142</td>\n",
       "      <td>8.592254</td>\n",
       "      <td>0.224249</td>\n",
       "      <td>5.869192</td>\n",
       "      <td>9.998340</td>\n",
       "      <td>2.598055</td>\n",
       "      <td>0.578352</td>\n",
       "      <td>0.299848</td>\n",
       "      <td>0.297925</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "    SiO2_Liq  TiO2_Liq  Al2O3_Liq  Fe2O3_Liq   FeO_Liq   MnO_Liq   MgO_Liq  \\\n",
       "0  51.524017  2.605133  13.546977   3.774733  7.730924  0.186119  6.707341   \n",
       "1  51.535177  2.645197  13.736989   3.780389  7.788015  0.189839  6.507155   \n",
       "2  51.575604  2.775984  13.689274   3.864310  8.061706  0.200831  6.285636   \n",
       "3  51.600593  2.878059  13.594286   3.933036  8.275994  0.209284  6.149388   \n",
       "4  51.614175  3.065335  13.378208   4.052142  8.592254  0.224249  5.869192   \n",
       "\n",
       "     CaO_Liq  Na2O_Liq   K2O_Liq  P2O5_Liq  Fe3Fet_Liq  \n",
       "0  10.989132  2.410111  0.484441  0.248864    0.305237  \n",
       "1  10.829918  2.454594  0.494123  0.253838    0.303996  \n",
       "2  10.477006  2.513328  0.521354  0.268537    0.301340  \n",
       "3  10.236264  2.548374  0.542061  0.279838    0.299531  \n",
       "4   9.998340  2.598055  0.578352  0.299848    0.297925  "
      ]
     },
     "execution_count": 5,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "logfo2=-13.2\n",
    "\n",
    "# Calculate oxides using Kress 1991 and 3 kbar, and \n",
    "myLiquids_Fe3_Kress_norm=pt.convert_fo2_to_fe_partition(liq_comps=Liqs, T_K=800+273.15, \n",
    "                            P_kbar=3, fo2=10**logfo2, model=\"Kress1991\", renorm=True)\n",
    "myLiquids_Fe3_Kress_norm.head()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "id": "e7b39fbd-5e6a-4f20-b2ac-ed6981b23740",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Text(0, 0.5, 'Fe3Fet Liq')"
      ]
     },
     "execution_count": 19,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.plot(myLiquids_Fe3_Kress_norm['MgO_Liq'], myLiquids_Fe3_Kress_norm['Fe3Fet_Liq'], '-r')\n",
    "plt.xlabel('MgO Liq')\n",
    "plt.ylabel('Fe3Fet Liq')"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "f10c8a85-434c-4101-8be1-ea985857eace",
   "metadata": {},
   "source": [
    "### 1b: At a known buffer (here, QFM)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "id": "2dd4b3e4-d7b2-4dd9-8132-fbca9aa7b471",
   "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>SiO2_Liq</th>\n",
       "      <th>TiO2_Liq</th>\n",
       "      <th>Al2O3_Liq</th>\n",
       "      <th>Fe2O3_Liq</th>\n",
       "      <th>FeO_Liq</th>\n",
       "      <th>MnO_Liq</th>\n",
       "      <th>MgO_Liq</th>\n",
       "      <th>CaO_Liq</th>\n",
       "      <th>Na2O_Liq</th>\n",
       "      <th>K2O_Liq</th>\n",
       "      <th>P2O5_Liq</th>\n",
       "      <th>Fe3Fet_Liq</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>51.621424</td>\n",
       "      <td>2.610058</td>\n",
       "      <td>13.572588</td>\n",
       "      <td>1.881698</td>\n",
       "      <td>9.456264</td>\n",
       "      <td>0.186471</td>\n",
       "      <td>6.720022</td>\n",
       "      <td>11.009907</td>\n",
       "      <td>2.414668</td>\n",
       "      <td>0.485357</td>\n",
       "      <td>0.249335</td>\n",
       "      <td>0.151860</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>51.632661</td>\n",
       "      <td>2.650201</td>\n",
       "      <td>13.762974</td>\n",
       "      <td>1.886144</td>\n",
       "      <td>9.514574</td>\n",
       "      <td>0.190198</td>\n",
       "      <td>6.519464</td>\n",
       "      <td>10.850404</td>\n",
       "      <td>2.459237</td>\n",
       "      <td>0.495057</td>\n",
       "      <td>0.254318</td>\n",
       "      <td>0.151373</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>51.675308</td>\n",
       "      <td>2.781350</td>\n",
       "      <td>13.715738</td>\n",
       "      <td>1.928249</td>\n",
       "      <td>9.827054</td>\n",
       "      <td>0.201220</td>\n",
       "      <td>6.297788</td>\n",
       "      <td>10.497260</td>\n",
       "      <td>2.518187</td>\n",
       "      <td>0.522361</td>\n",
       "      <td>0.269056</td>\n",
       "      <td>0.150063</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>51.702115</td>\n",
       "      <td>2.883721</td>\n",
       "      <td>13.621032</td>\n",
       "      <td>1.962512</td>\n",
       "      <td>10.073308</td>\n",
       "      <td>0.209695</td>\n",
       "      <td>6.161487</td>\n",
       "      <td>10.256404</td>\n",
       "      <td>2.553387</td>\n",
       "      <td>0.543127</td>\n",
       "      <td>0.280389</td>\n",
       "      <td>0.149155</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>51.718628</td>\n",
       "      <td>3.071538</td>\n",
       "      <td>13.405281</td>\n",
       "      <td>2.025025</td>\n",
       "      <td>10.442040</td>\n",
       "      <td>0.224702</td>\n",
       "      <td>5.881070</td>\n",
       "      <td>10.018574</td>\n",
       "      <td>2.603312</td>\n",
       "      <td>0.579522</td>\n",
       "      <td>0.300455</td>\n",
       "      <td>0.148573</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "    SiO2_Liq  TiO2_Liq  Al2O3_Liq  Fe2O3_Liq    FeO_Liq   MnO_Liq   MgO_Liq  \\\n",
       "0  51.621424  2.610058  13.572588   1.881698   9.456264  0.186471  6.720022   \n",
       "1  51.632661  2.650201  13.762974   1.886144   9.514574  0.190198  6.519464   \n",
       "2  51.675308  2.781350  13.715738   1.928249   9.827054  0.201220  6.297788   \n",
       "3  51.702115  2.883721  13.621032   1.962512  10.073308  0.209695  6.161487   \n",
       "4  51.718628  3.071538  13.405281   2.025025  10.442040  0.224702  5.881070   \n",
       "\n",
       "     CaO_Liq  Na2O_Liq   K2O_Liq  P2O5_Liq  Fe3Fet_Liq  \n",
       "0  11.009907  2.414668  0.485357  0.249335    0.151860  \n",
       "1  10.850404  2.459237  0.495057  0.254318    0.151373  \n",
       "2  10.497260  2.518187  0.522361  0.269056    0.150063  \n",
       "3  10.256404  2.553387  0.543127  0.280389    0.149155  \n",
       "4  10.018574  2.603312  0.579522  0.300455    0.148573  "
      ]
     },
     "execution_count": 21,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Calculate oxides using Kress 1991 and 3 kbar, and \n",
    "myLiquids_Fe3_Kress_norm_QFM=pt.convert_fo2_to_fe_partition(liq_comps=Liqs, T_K=T_HT87, \n",
    "                            P_kbar=3, fo2=\"QFM\", model=\"Kress1991\", renorm=True)\n",
    "myLiquids_Fe3_Kress_norm_QFM.head()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "id": "d355afda-7836-4007-b1f5-5427e87e5f16",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Text(0, 0.5, 'Fe3Fet Liq')"
      ]
     },
     "execution_count": 22,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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97UB45plw9dV5R2NmzaRk+3lIag9MBgYCNcBMSdMj4rlab3sHOBYY2sBtdo6It+u5d8/svq83a9DW/CT4zW+gpsZrQMxakVLu57E1MCciXo2IZcBN1FmpHhELImImUOyI6kXAj/F6k8qwYg1I375pDchTT+UdkZmtolImj+5A7c0earJjhQrgPkmzJH2656mkvYE3IuIfjV0saZSkaknVCxcuLCZuK4UuXdIU3rXWSlN4a2ryjsjMVkEhm0FdV8ix+i6t51gxLYXtImIrYAhwjKQdJX0Z+Anw06YujogrIqIqIqq6detWxMdayXTvnhLI4sVeA2JW4QppeXy99otsLOPbBVxXA/Ss9boHMK/QwCJiXva4AJhG6gbbFOgN/EPSa9k9n5S0QaH3tZx985ufrQEZNsz7gJhVqMbWeUyQtBjoV2vb2cXAAuDOAu49E+gjqbekjsBwYHohQUnqJKnziufAIOCZiHg6ItaLiF4R0YuUoLaKiDcLua+ViQEDYMoUeOAB+OEPvQbErAI1VtvqPOA8SedFxIRibxwRH0saA9wLtAemRMSzkkZn5y/PWgzVQBdguaTjgb5AV2CapBUx3hgRM4qNwcrYYYelNSCnnQYbbww/+1neEZlZERRN/NYnqR1p86feEXFONk12w4h4oiUCbA5VVVVRXV1fcWDLVQQcdVRaiX755em5mZUNSbMioqq+c4WMeUwGvstnuwcuyY6ZrRoJLrssDZ4ffTTcdVfeEZlZgQpJHttExDHAhwAR8S7QsaRRWdvRoQNMnQpbbgkHHQQzZ+YdkZkVoJDk8VE2wyoAJHUDlpc0Kmtb1lwz7QOy/vqwxx7wyit5R2RmTSgkefyKNFV2PUk/Ax4Fzi1pVNb2rL8+3HMPfPIJDBkCb3+hKo2ZlZEmk0dE3EAqBXIeMB8YGhG3lDowa4M22wymT0+zsPbeGz74IO+IzKwBja3zuK/Wy30jYnJEXBoRzzd0jdkq2247uOGGtIXtoYemloiZlZ3GWh61a3ocUOpAzD41bBhcdBFMmwbHH+9FhGZlqLGS7P4Xa/k57rjUfXXhhWkR4ckn5x2RmdXSWPLYRNJ0UoHDFc8/FRF7lzQys1/8IlXf/fGPU1HFQw5p+hozaxGNJY/ae29MKnUgZl/Qrh1ccw289Vba0naDDWCXXfKOysxovLbVQy0ZiFm9Vl8d7rgDtt8e9t0XHnkE+vXLOyqzNq+x2VYbSPq1pMmSviLpTElPSbpZ0oYtGaS1cWuvndaAdO6c1oC87t2HzfLW2Gyrq4HnSLsB/gX4ANgTeAS4vOSRmdXWs2dKIEuWpATy7rt5R2TWpjWWPNaPiEsiYiKwdkT8PCJej4hLgP9oofjMPvPNb6YurJdfhqFD4cMP847IrM1qLHnUPndtEdeZlc7OO8O118LDD8PIkbDcZdbM8tDYbKs7Ja0ZEUsi4rQVByV9FXip9KGZNWD48DSF9+ST0xTeCy/MOyKzNqex2VY/beD4HGD/kkVkVoiTToK5c9NK9J494YQT8o7IrE1psvtJ0vqSrpJ0T/a6r6Qflj40s0ZIqcWx//5w4olw8815R2TWphQydnE1aR/yjbLXLwHHlyges8K1bw/XXQc77JD2RH/IS5PMWkohyaNrRNxMtgFURHwMuNSplYcViwg33RT22QeeeSbviMzahEKSx/uSvsJnOwluC7xXyM0lDZb0oqQ5ksbXc35zSY9JWippXJ1zr0l6WtJsSdW1jv9C0gvZgsVpktYuJBZrxdZdF2bMgE6dYPDgNBZiZiVVSPI4EZgObCrpr6Rpu2ObuijbunYyMAToCxwsqW+dt70DHEvDtbN2jogtIqKq1rH7gW9ERD9SF9qEAn4Ga+023jglkCVLYLfd4J138o7IrFVrrDzJxgAR8SSwE/A94Cjg6xHxVAH33hqYExGvRsQy4CY+X2yRiFgQETOBjwoNOCLuy7rOAB4HehR6rbVyKxYRvvKKdyI0K7HGWh531Ho+NSKejYhnIqLQL/rupNImK9RkxwoVwH2SZkka1cB7fgDcU98JSaMkVUuqXrhwYREfaxWtf3+4/nr4n/9JJdy9E6G1ZfPnl+zWjSUP1Xq+yUrcW/UcK2aDqe0iYitSt9cxknb83M2lnwAfAzfUd3FEXBERVRFR1a1bt/reYq3VAQfAxRenVsiYMd6J0NqeCLjsMujdO3XnlkChOwmuzL++GqBnrdc9gHmFXhwR87LHBZKmkbrBHgaQNJJUpHHXCH8zWD3GjoV582DixLQK/bTTmr7GrDVYvBiOPBKmToXdd4fvfKckH9NY8viWpEWkFsQa2XOy1xERXZq490ygj6TewBvAcKCgreAkdQLaRcTi7Pkg4Ozs3GDgFGCniPh3IfezNurcc1MCOf102HBD+KHXtlor99RTqeU9Zw6cd17ahbNdaUoRNlaepP2q3DgiPpY0hrTAsD0wJSKelTQ6O3+5pA2AaqALsFzS8aSZWV2BaZJWxHhjRKxoe10KfAm4Pzv/eESMXpVYrZWS4Mor006ERx0F668Pe+6Zd1RmzS8CpkxJ3bTrrAN/+QvsuGPT160CtYVen6qqqqiurm76jdY6LVmSqvE++yz8+c+w7bZ5R2TWfN5/H44+OlWbHjAAbrgB1luvWW4taVadpRKfcml1a/3WXBP++EfYaKPU8njxxbwjMmsezz8PW2+dyvSceWYaHG+mxNEUJw9rG9ZbD+69N9XD2m23NBZiVsmuvx6qqmDhQrjvPjjjjPT3u4U4eVjbsemmcPfd8PbbaRbKewVV2TErP7//fSoGWlUFs2en7qoW5uRhbcu3vw23357GP/bbD5YuzTsis+J8+CGMHw9bbgkPPJC6Y3Pg5GFtz6BBaWbKn//srWyt8kyeDK+/DuefDx0aW21RWvl9slmeDjsslW445ZS0BuTCC9PUXrNy9u678LOfpV+Acuiqqs3Jw9quk09OA+e//GVahT5uXJOXmOVq4kT4v/+Dn/8870icPKwNW7GV7fz5KZFssAGMGJF3VGb1mzs31Ww79FDYYou8o3HysDauXbu0uGrBAjjiiDSld9CgvKMy+6Izzkgryc85J+9IAA+Ym8GXvpQq8PbtC8OGwZNP5h2R2ec98wxcc00qP9KrV97RAE4eZslaa8E996QtbYcMSRtKmZWL8eOhc2c49dS8I/mUk4fZChttlFahf/xxWoX+1lt5R2QGDz2UyutMmABf+Ure0XzKycOsts03T/9Q581LLZBFi5q+xqxUIlJZ9R494Nhj847mc5w8zOradlu47TZ4+mkYOjSt6DXLw623whNPwNlnwxpr5B3N5zh5mNVnyBD43e/SvggjRngvdGt5H32Uxji+8Q34/vfzjuYLPFXXrCEjRqSKpSeeCMccA7/+tVehW8u54oq0I+Bdd7VotdxCOXmYNeaEE9IakIkT006EZ52Vd0TWFixenP6u7bRTqgBdhpw8zJpy7rkpgZx9NnTrlubam5XSpEmp1Xv++WXb2nXyMGuKBL/5TdoH5NhjUwI56KC8o7LW6s034YIL4IAD0i6BZaqkA+aSBkt6UdIcSePrOb+5pMckLZU0rs651yQ9LWm2pOpax9eVdL+kl7PHdUr5M5gBqfT1TTfB9tunirz33593RNZanXVW2mfm3HPzjqRRJUsektoDk4EhQF/gYEl967ztHeBYYFIDt9k5IraoswH7eOCBiOgDPJC9Niu9NdaA6dPTWpB994WZM/OOyFqbl16C3/4WjjoKvvrVvKNpVClbHlsDcyLi1YhYBtwE7FP7DRGxICJmAh8Vcd99gGuy59cAQ5shVrPCrL12WoXerVsayHzxxbwjstbknHNSrbXTT887kiaVMnl0B+bWel2THStUAPdJmiVpVK3j60fEfIDscb36LpY0SlK1pOqFCxcWGbpZIzbcEO67L42FDBoEb7yRd0TWGrzyStqbfPToNLOvzJUyedQ3RSCKuH67iNiK1O11jKQdi/nwiLgiIqoioqpbt27FXGrWtD59YMaMtLPbbrvBO+/kHZFVup//PI2tnXRS3pEUpJTJowboWet1D2BeoRdHxLzscQEwjdQNBvCWpA0BsscFzRKtWbG22iqVcn/5ZdhrL/j3v/OOyCpVTQ1cfTX84AepQGcFKGXymAn0kdRbUkdgODC9kAsldZLUecVzYBDwTHZ6OjAyez4SuLNZozYrxi67wA03wGOPwYEHppISZsWaNAmWL09FECtEyZJHRHwMjAHuBZ4Hbo6IZyWNljQaQNIGkmqAE4HTJNVI6gKsDzwq6R/AE8AfI2JGduuJwEBJLwMDs9dm+dl/f7jsslSN90c/Sl8CZoVasCCVIhkxomw2eipESRcJRsTdwN11jl1e6/mbpO6suhYB32rgnv8Cdm3GMM1W3ejR6UvgjDPSTKxJDc0+N6vjootS5eYJE/KOpCheYW7WXE4/PSWQCy5Ie6FXUBeE5eTdd2Hy5LSafLPN8o6mKE4eZs1Fgl/9Cv71LzjllLSl7Y9+lHdUVs4uvTQVQSyj7WUL5eRh1pzatYNrrkm/UR51VEog++2Xd1RWjpYsgV/+Ms3U+1a9vfRlzZtBmTW3jh3TToRbbw0HH5w2lDKr6/LL0/qgn/wk70hWipOHWSl06pRmX/XpA3vvDdXVTV9jbccHH6SxsV13hW22yTualeLkYVYq666b6mB17Zq2tXUdLIM0lfvcc1Pp9QptdYCTh1lpde+e6mC1awcDB8LcuU1fY63Xyy+nhaX//d9pLKx//7wjWmlOHmal1qdPaoG8914qpPj223lHZC3t44/TroD9+sHs2XDllXDrrWW7S2AhnDzMWsIWW8Bdd8Frr6UurEWL8o7IWsrs2Wlc45RTYPBgeO45+OEPKzpxgJOHWcvZYYf02+bs2TB0aFpVbK3Xhx+mMY2qqlS2/5Zb4PbbK6bwYVOcPMxa0h57pOqpf/kLDB+eujOs9Xn00dTaPPfctG3xc8+lGmgV3tqozcnDrKUdeihccgnceacLKbY2ixfDmDGplbl0aRrr+t3v0sy7VsYrzM3yMGZMWiB2xhnpi+WCC1rVb6Vt0t13pwKZNTVw3HFpRtWaa+YdVck4eZjl5fTTUx2siy5KCeS00/KOyIoVkcawLrgg7evSty/89a/w3e/mHVnJOXmY5UVKiePdd1MiWXvt1CKx8vbBB/DAA2n23F13pcHw1VaDn/40FTj80pfyjrBFOHmY5aldO7jqqrQGZOxYWGedNCZi5eWNNz5LFg88kBLImmum/ev33BN23z2V4W9DnDzM8rbaajB1avoCGjkSunRJlVYtPyu6o+68E6ZPh7//PR3v3RuOPDIljB13bDOtjPo4eZiVg9VXT19Uu+6aNgaaMaOiS1dUpGXL4KGHPksYc+emrsXvfQ8mTkwJ/T//0xMbMk4eZuWic2e45570G+1ee6W1IFVVeUfVur33Xvpvfued6fG992CNNVIZmbPOSi2Mbt3yjrIslXSdh6TBkl6UNEfS+HrOby7pMUlLJY2r53x7SX+XdFetY1tIelzSbEnVkrYu5c9g1qK+8pVUSLFr189KWVjzmjs3bf06aFBKDAcfnMYxhg1LSeTtt+GOO+CII5w4GlGyloek9sBkYCBQA8yUND0iav9reAc4FhjawG2OA54HutQ6dj5wVkTcI2n37HX/5o3eLEfdu8Of/gTbb5++4B59FHr1yjuqyhWRkvDtt6ek8OST6fhmm8EJJ8A++6TaU+3b5xpmpSllt9XWwJyIeBVA0k3APsCnySMiFgALJO1R92JJPYA9gJ8BJ9Y6FXyWTNYC5pUkerM8bbppaoHstBMMGJASyAYb5B1V5Vi+HGbOhGnTUtJ4+eU0VrHttvDzn6eEsdlmeUdZ0UqZPLoDtTcvqAGK2TLrl8CPgc51jh8P3CtpEqnb7Xv1XSxpFDAKYOONNy7iY83KxDe/mVYtDxiQ9gJ56KFWWeai2Xz8MTz88GctjDfegA4d0v4ZJ56YEsaGG+YdZatRyjGP+qYkREEXSnsCCyJiVj2n/ws4ISJ6AicAV9V3j4i4IiKqIqKqm/strVJtu236InzppVTKffHivCMqLx99lOpH/ehHqWW2664wZUraP/6662DBgnR+9GgnjmZWypZHDdCz1useFN7FtB2wdzamsTrQRdL1ETECGEkaCwG4BbiymeI1K08DBsDNN6cB3aFD097oq6+ed1T5WbYsjQndcksa4H733TRTba+90n+jwYPhy1/OO8pWr5TJYybQR1Jv4A1gOHBIIRdGxARgAoCk/sC4LHFASkA7AQ8CuwAvN2fQZmVpn31SKffDDoMDD4TbbkuLC9uKDz+E++9PCWP69DSldq21YO+907qYgQPbdkLNQcmSR0R8LGkMcC/QHpgSEc9KGp2dv1zSBkA1aQB8uaTjgb4R0dg2a0cCF0vqAHxINq5h1uqNGJF2IDzmGDj88NQt064V76rwwQepy+mWW+APf0hdduusk/b+3n//1EXVhld4562kiwQj4m7g7jrHLq/1/E1Sd1Zj93iQ1MpY8fpR4NvNGadZxTj66JRAJkxIZUwuu6x1rXheujTNMps6NXVJLVmS1r4cdFBKGDvvDB075h2l4RXmZpVn/PjUbTNxYkogEydWdgL56KO0SG/q1DS19r330qyy4cNTF13//m2ri65COHmYVaJzz00tkPPPT6XcJ0zIO6LiLF+eptX+/vdp/OZf/0qJcOjQlDQGDHDCKHNOHmaVSEpb2S5alPaQ6NIljYWUsxWVam+8MSWNN96ATp3SoPdBB6Xy5h70rhhOHmaVql27tD/2in2zO3eG738/76i+aM6clCxuvBFeeCEt3BsyBCZNStNrO3XKO0JbCU4eZpWsQwe46ab0JXzEEemLeNiwvKOCN99Ma1NuuAGeeCId22mnVEtq2LA0CG4VzcnDrNKtvnpahT5oUKoQe+ed6Tf7lrZkSSoNcv31aQB8+XLYckv4xS9St1TPnk3fwyqGk4dZa9CpU1p5vssuaR3EjBnpN/1S++STlCiuvTbNlPr3v9Nue6eeCocckjZPslbJycOstVh77bSobqed0iZGf/pTKjVeCk89lRLGjTfC/Pnpsw87LP353vcqe+qwFcTJw6w16dYtJY0ddkhdVw8+CP36Nc+933orJYtrroF//CNNpd1995Qw9tzTq73bmFZc28Csjdpoo9SV1KlTqvn04osrf69ly9I4xl57pU2qTjwxrfC+9FKYNy+NtQwb5sTRBrnlYdYa9eqVWiA77pgW3D3ySHG7Ec6enUqb33hjWsC34YZw0kkwciT07VuioK2SOHmYtVabbZbqRPXvn4oIPvJIapU05J13UrKYMgX+/vfUwhg6NE0BHjAgTQs2y7jbyqw1+9a30syrBQtSF9bbb3/+/PLlqdT58OGpdTF2bBrsvvTSNBA+dWraH8OJw+rw3wiz1m6bbVJJ8yFDUgmQe+5JLYs//CHtjTF3bip1ftRR8IMfwBZb5B2xVQAnD7O2oH//VIBw6NC0XWsErLFGao384hdpsynXlbIiOHmYtRW7755mTs2YkVohu+ySEojZSnDyMGtL9twz/TFbRR4wNzOzojl5mJlZ0Zw8zMysaCVNHpIGS3pR0hxJ4+s5v7mkxyQtlTSunvPtJf1d0l11jo/N7vuspPNL+TOYmdkXlWzAXFJ7YDIwEKgBZkqaHhHP1XrbO8CxwNAGbnMc8DzQpdZ9dwb2AfpFxFJJ65UgfDMza0QpWx5bA3Mi4tWIWAbcRPrS/1RELIiImcBHdS+W1APYA7iyzqn/AiZGxNIV9yhF8GZm1rBSJo/uwNxar2uyY4X6JfBjYHmd418DdpD0N0kPSfpOfRdLGiWpWlL1woULi/hYMzNrSimTR327wURBF0p7AgsiYlY9pzsA6wDbAicDN0tf3HkmIq6IiKqIqOrWrVsRYZuZWVNKuUiwBqi9aXEPYF6B124H7C1pd2B1oIuk6yNiRHbf2yMigCckLQe6Ag02L2bNmvW2pH+uxM/QFXi7yXeVl0qMGSoz7kqMGSoz7kqMGSoz7tox/0dDbypl8pgJ9JHUG3gDGA4cUsiFETEBmAAgqT8wLkscAHcAuwAPSvoa0JEm/udExEo1PSRVR0TVylybl0qMGSoz7kqMGSoz7kqMGSoz7kJjLlnyiIiPJY0B7gXaA1Mi4llJo7Pzl0vaAKgmzaZaLul4oG9ELGrk1lOAKZKeAZYBI7NWiJmZtZCS1raKiLuBu+scu7zW8zdJ3VmN3eNB4MFar5cBIxp6v5mZlZ5XmDfuirwDWAmVGDNUZtyVGDNUZtyVGDNUZtwFxSz3+JiZWbHc8jAzs6I5eZiZWdGcPOrRVEHHciRpiqQF2Sy0iiGpp6S/SHo+K3R5XN4xNUXS6pKekPSPLOaz8o6pUA0VGy1nkl6T9LSk2ZKq846nEJLWlnSrpBeyv9vfzTumpkjaLPtvvOLPomwGbP3v95jH52UFHV+iVkFH4OA6BR3LjqQdgSXAtRHxjbzjKZSkDYENI+JJSZ2BWcDQcv7vnVU06BQRSyStBjwKHBcRj+ccWpMknQhUAV0ioiK2FJT0GlAVERWz2E7SNcAjEXGlpI7AlyPi/3IOq2DZ9+AbwDYRUe8Ca7c8vqjJgo7lKCIeJlUprigRMT8insyeLyZVUS6mBlqLi2RJ9nK17E/Z/xbWSLFRa0aSugA7AldBWl5QSYkjsyvwSkOJA5w86rOqBR1tJUnqBWwJ/C3nUJqUdf/MBhYA90dE2cdMw8VGy10A90maJWlU3sEUYBNSuaTfZV2EV0rqlHdQRRoO/L6xNzh5fNFKF3S0lSdpTeA24PgmKgyUhYj4JCK2IC1y3VpSWXcVNlFstNxtFxFbAUOAY7Iu2nLWAdgK+HVEbAm8D1TE2ClA1s22N3BLY+9z8viiVSnoaCshGze4DbghIm7PO55iZN0RDwKD842kSSuKjb5G6ordRdL1+YZUmIiYlz0uAKaRupbLWQ1QU6s1eispmVSKIcCTEfFWY29y8viiTws6Zhl4ODA955harWzw+Srg+Yi4MO94CiGpm6S1s+drAAOAF3INqgkRMSEiekREL9Lf6T/XKjZatiR1yiZSkHX9DALKekZhVnZprqTNskO7AmU7AaQeB9NElxWUuLZVJWqooGPOYTVJ0u+B/kBXSTXAGRFxVb5RFWQ74DDg6WwMAeDUrC5audoQuCabkdIOuDkiKmbqa4VZH5iWbdnTAbgxImbkG1JBxgI3ZL+AvgockXM8BZH0ZdJM06OafK+n6pqZWbHcbWVmZkVz8jAzs6I5eZiZWdGcPMzMrGhOHmZmVjQnD7MiSQpJ19V63UHSwkIq1UrqIelOSS9LekXSxdl0zrrv61VfhWRJZ0sasOo/hdmqcfIwK977wDeyBYKQ5sW/0dRF2YLI24E7IqIP8DVgTeBnhX5wRPw0Iv5UfMhmzcvJw2zl3EOqUAt1VuRmK9Dvl/SkpN9I+qekrsAuwIcR8TtI9bGAE4AfZIuzmiTpakn7Z88HZ/tFPCrpV5W0R4dVPicPs5VzEzBc0upAPz5fCfgMUvmPrUi1mDbOjn+dtF/Jp7IikK8DXy3mw7PP/S2wF7ADsMFK/AxmK83Jw2wlRMRTQC9Sq6NuKZXtScmFrJTGu9lxUX+F5oaON2Zz4H8j4uVIZSIqosihtR5OHmYrbzowiS8WkauvrD/As6Rd/D57Y9o4qCfwykp8vmsLWW6cPMxW3hTg7Ih4us7xR4EDASQNAtbJjj8AfFnS97Nz7YELgKsj4t9FfvYLQG9Jm2avD16J+M1WmpOH2UqKiJqIuLieU2cBgyQ9SdobYT6wOOte2hc4QNLLwEvAh8CpDXzEZpJqav05oNZnfwiMAv4o6VGgwe1CzUrBVXXNmpmkLwGfZOX9v0vaUW6LEn9mf2BcROxZys8xW8H7eZg1v42BmyW1A5YBR+Ycj1mzc8vDzMyK5jEPMzMrmpOHmZkVzcnDzMyK5uRhZmZFc/IwM7Oi/T/dKF+fwIeiwQAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.plot(myLiquids_Fe3_Kress_norm_QFM['MgO_Liq'], myLiquids_Fe3_Kress_norm_QFM['Fe3Fet_Liq'], '-r')\n",
    "plt.xlabel('MgO Liq')\n",
    "plt.ylabel('Fe3Fet Liq')"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "17557f0e-7588-448c-a134-df4c127df756",
   "metadata": {},
   "source": [
    "### 1c: At buffer with offset (here NNO+1)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "id": "57e4c833-cc99-44ce-9eae-46709ae57492",
   "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>SiO2_Liq</th>\n",
       "      <th>TiO2_Liq</th>\n",
       "      <th>Al2O3_Liq</th>\n",
       "      <th>Fe2O3_Liq</th>\n",
       "      <th>FeO_Liq</th>\n",
       "      <th>MnO_Liq</th>\n",
       "      <th>MgO_Liq</th>\n",
       "      <th>CaO_Liq</th>\n",
       "      <th>Na2O_Liq</th>\n",
       "      <th>K2O_Liq</th>\n",
       "      <th>P2O5_Liq</th>\n",
       "      <th>Fe3Fet_Liq</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>51.546390</td>\n",
       "      <td>2.606264</td>\n",
       "      <td>13.552860</td>\n",
       "      <td>3.339932</td>\n",
       "      <td>8.127207</td>\n",
       "      <td>0.186200</td>\n",
       "      <td>6.710254</td>\n",
       "      <td>10.993904</td>\n",
       "      <td>2.411158</td>\n",
       "      <td>0.484651</td>\n",
       "      <td>0.248972</td>\n",
       "      <td>0.269955</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>51.557365</td>\n",
       "      <td>2.646336</td>\n",
       "      <td>13.742904</td>\n",
       "      <td>3.349248</td>\n",
       "      <td>8.180990</td>\n",
       "      <td>0.189920</td>\n",
       "      <td>6.509957</td>\n",
       "      <td>10.834581</td>\n",
       "      <td>2.455651</td>\n",
       "      <td>0.494335</td>\n",
       "      <td>0.253947</td>\n",
       "      <td>0.269205</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>51.598076</td>\n",
       "      <td>2.777193</td>\n",
       "      <td>13.695239</td>\n",
       "      <td>3.427946</td>\n",
       "      <td>8.459594</td>\n",
       "      <td>0.200919</td>\n",
       "      <td>6.288375</td>\n",
       "      <td>10.481571</td>\n",
       "      <td>2.514423</td>\n",
       "      <td>0.521581</td>\n",
       "      <td>0.268654</td>\n",
       "      <td>0.267191</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>51.623335</td>\n",
       "      <td>2.879327</td>\n",
       "      <td>13.600278</td>\n",
       "      <td>3.491627</td>\n",
       "      <td>8.678603</td>\n",
       "      <td>0.209376</td>\n",
       "      <td>6.152098</td>\n",
       "      <td>10.240776</td>\n",
       "      <td>2.549497</td>\n",
       "      <td>0.542300</td>\n",
       "      <td>0.279962</td>\n",
       "      <td>0.265793</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>51.637241</td>\n",
       "      <td>3.066705</td>\n",
       "      <td>13.384186</td>\n",
       "      <td>3.604510</td>\n",
       "      <td>9.000728</td>\n",
       "      <td>0.224349</td>\n",
       "      <td>5.871815</td>\n",
       "      <td>10.002808</td>\n",
       "      <td>2.599216</td>\n",
       "      <td>0.578610</td>\n",
       "      <td>0.299982</td>\n",
       "      <td>0.264891</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "    SiO2_Liq  TiO2_Liq  Al2O3_Liq  Fe2O3_Liq   FeO_Liq   MnO_Liq   MgO_Liq  \\\n",
       "0  51.546390  2.606264  13.552860   3.339932  8.127207  0.186200  6.710254   \n",
       "1  51.557365  2.646336  13.742904   3.349248  8.180990  0.189920  6.509957   \n",
       "2  51.598076  2.777193  13.695239   3.427946  8.459594  0.200919  6.288375   \n",
       "3  51.623335  2.879327  13.600278   3.491627  8.678603  0.209376  6.152098   \n",
       "4  51.637241  3.066705  13.384186   3.604510  9.000728  0.224349  5.871815   \n",
       "\n",
       "     CaO_Liq  Na2O_Liq   K2O_Liq  P2O5_Liq  Fe3Fet_Liq  \n",
       "0  10.993904  2.411158  0.484651  0.248972    0.269955  \n",
       "1  10.834581  2.455651  0.494335  0.253947    0.269205  \n",
       "2  10.481571  2.514423  0.521581  0.268654    0.267191  \n",
       "3  10.240776  2.549497  0.542300  0.279962    0.265793  \n",
       "4  10.002808  2.599216  0.578610  0.299982    0.264891  "
      ]
     },
     "execution_count": 24,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Calculate oxides using Kress 1991 and 3 kbar, and \n",
    "myLiquids_Fe3_Kress_norm_NNO1=pt.convert_fo2_to_fe_partition(liq_comps=Liqs, T_K=T_HT87, \n",
    "                            P_kbar=3, fo2=\"NNO\", fo2_offset=1, model=\"Kress1991\", renorm=True)\n",
    "myLiquids_Fe3_Kress_norm_NNO1.head()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 25,
   "id": "fdd34d45-bcd2-42f2-b9a1-a42a59fb05fd",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Text(0, 0.5, 'Fe3Fet Liq')"
      ]
     },
     "execution_count": 25,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.plot(myLiquids_Fe3_Kress_norm_NNO1['MgO_Liq'], myLiquids_Fe3_Kress_norm_NNO1['Fe3Fet_Liq'], '-r')\n",
    "plt.xlabel('MgO Liq')\n",
    "plt.ylabel('Fe3Fet Liq')"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "06239684-5423-4b68-8360-003d403e86dc",
   "metadata": {},
   "source": [
    "### 1d: With different normalization routines:\n",
    "- So far, we used Norm=True, this renormalizes the other oxides to account for the changing FeO and Fe2O3 amount, can also put false, doesn't affect the Fe3FeT but affects the oxide concs.  You can see this by comparing the other oxide contents"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 29,
   "id": "cbeab65c-5bfe-4dcc-9fd6-79f592592320",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Original\n"
     ]
    },
    {
     "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>SiO2_Liq</th>\n",
       "      <th>TiO2_Liq</th>\n",
       "      <th>Al2O3_Liq</th>\n",
       "      <th>FeOt_Liq</th>\n",
       "      <th>MnO_Liq</th>\n",
       "      <th>MgO_Liq</th>\n",
       "      <th>CaO_Liq</th>\n",
       "      <th>Na2O_Liq</th>\n",
       "      <th>K2O_Liq</th>\n",
       "      <th>Cr2O3_Liq</th>\n",
       "      <th>P2O5_Liq</th>\n",
       "      <th>H2O_Liq</th>\n",
       "      <th>Fe3Fet_Liq</th>\n",
       "      <th>NiO_Liq</th>\n",
       "      <th>CoO_Liq</th>\n",
       "      <th>CO2_Liq</th>\n",
       "      <th>Sample_ID_Liq</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>51.456179</td>\n",
       "      <td>2.60169</td>\n",
       "      <td>13.529073</td>\n",
       "      <td>11.11461</td>\n",
       "      <td>0.185873</td>\n",
       "      <td>6.698477</td>\n",
       "      <td>10.974609</td>\n",
       "      <td>2.406926</td>\n",
       "      <td>0.483801</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.248535</td>\n",
       "      <td>0.508277</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "    SiO2_Liq  TiO2_Liq  Al2O3_Liq  FeOt_Liq   MnO_Liq   MgO_Liq    CaO_Liq  \\\n",
       "0  51.456179   2.60169  13.529073  11.11461  0.185873  6.698477  10.974609   \n",
       "\n",
       "   Na2O_Liq   K2O_Liq  Cr2O3_Liq  P2O5_Liq   H2O_Liq  Fe3Fet_Liq  NiO_Liq  \\\n",
       "0  2.406926  0.483801        0.0  0.248535  0.508277         0.0      0.0   \n",
       "\n",
       "   CoO_Liq  CO2_Liq  Sample_ID_Liq  \n",
       "0      0.0      0.0              0  "
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "No Norm\n"
     ]
    },
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
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       "\n",
       "    .dataframe tbody tr th {\n",
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       "    }\n",
       "\n",
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       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>SiO2_Liq</th>\n",
       "      <th>TiO2_Liq</th>\n",
       "      <th>Al2O3_Liq</th>\n",
       "      <th>FeOt_Liq</th>\n",
       "      <th>MnO_Liq</th>\n",
       "      <th>MgO_Liq</th>\n",
       "      <th>CaO_Liq</th>\n",
       "      <th>Na2O_Liq</th>\n",
       "      <th>K2O_Liq</th>\n",
       "      <th>Cr2O3_Liq</th>\n",
       "      <th>P2O5_Liq</th>\n",
       "      <th>H2O_Liq</th>\n",
       "      <th>Fe3Fet_Liq</th>\n",
       "      <th>NiO_Liq</th>\n",
       "      <th>CoO_Liq</th>\n",
       "      <th>CO2_Liq</th>\n",
       "      <th>Sample_ID_Liq</th>\n",
       "      <th>FeO_Liq</th>\n",
       "      <th>Fe2O3_Liq</th>\n",
       "      <th>XFe3Fe2</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>51.456179</td>\n",
       "      <td>2.60169</td>\n",
       "      <td>13.529073</td>\n",
       "      <td>11.11461</td>\n",
       "      <td>0.185873</td>\n",
       "      <td>6.698477</td>\n",
       "      <td>10.974609</td>\n",
       "      <td>2.406926</td>\n",
       "      <td>0.483801</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.248535</td>\n",
       "      <td>0.508277</td>\n",
       "      <td>0.227286</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0</td>\n",
       "      <td>8.589075</td>\n",
       "      <td>2.807726</td>\n",
       "      <td>0.147152</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "    SiO2_Liq  TiO2_Liq  Al2O3_Liq  FeOt_Liq   MnO_Liq   MgO_Liq    CaO_Liq  \\\n",
       "0  51.456179   2.60169  13.529073  11.11461  0.185873  6.698477  10.974609   \n",
       "\n",
       "   Na2O_Liq   K2O_Liq  Cr2O3_Liq  P2O5_Liq   H2O_Liq  Fe3Fet_Liq  NiO_Liq  \\\n",
       "0  2.406926  0.483801        0.0  0.248535  0.508277    0.227286      0.0   \n",
       "\n",
       "   CoO_Liq  CO2_Liq  Sample_ID_Liq   FeO_Liq  Fe2O3_Liq   XFe3Fe2  \n",
       "0      0.0      0.0              0  8.589075   2.807726  0.147152  "
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Renorm\n"
     ]
    },
    {
     "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>SiO2_Liq</th>\n",
       "      <th>TiO2_Liq</th>\n",
       "      <th>Al2O3_Liq</th>\n",
       "      <th>Fe2O3_Liq</th>\n",
       "      <th>FeO_Liq</th>\n",
       "      <th>MnO_Liq</th>\n",
       "      <th>MgO_Liq</th>\n",
       "      <th>CaO_Liq</th>\n",
       "      <th>Na2O_Liq</th>\n",
       "      <th>K2O_Liq</th>\n",
       "      <th>P2O5_Liq</th>\n",
       "      <th>Fe3Fet_Liq</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>51.573474</td>\n",
       "      <td>2.607633</td>\n",
       "      <td>13.559981</td>\n",
       "      <td>2.813568</td>\n",
       "      <td>8.606944</td>\n",
       "      <td>0.186298</td>\n",
       "      <td>6.71378</td>\n",
       "      <td>10.99968</td>\n",
       "      <td>2.412425</td>\n",
       "      <td>0.484906</td>\n",
       "      <td>0.249103</td>\n",
       "      <td>0.227286</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "    SiO2_Liq  TiO2_Liq  Al2O3_Liq  Fe2O3_Liq   FeO_Liq   MnO_Liq  MgO_Liq  \\\n",
       "0  51.573474  2.607633  13.559981   2.813568  8.606944  0.186298  6.71378   \n",
       "\n",
       "    CaO_Liq  Na2O_Liq   K2O_Liq  P2O5_Liq  Fe3Fet_Liq  \n",
       "0  10.99968  2.412425  0.484906  0.249103    0.227286  "
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "logfo2=-7.58429552677443\n",
    "print('Original')\n",
    "display(Liqs.loc[[0]])\n",
    "\n",
    "# No renormalizatoin\n",
    "myLiquids_Fe3_Kress_nonorm=pt.convert_fo2_to_fe_partition(liq_comps=Liqs.loc[[0]], T_K=T_HT87.loc[[0]], \n",
    "                            P_kbar=3, fo2=10**logfo2, model=\"Kress1991\", renorm=False)\n",
    "print('No Norm')\n",
    "display(myLiquids_Fe3_Kress_nonorm)\n",
    "\n",
    "\n",
    "# With renormalization \n",
    "myLiquids_Fe3_Kress_norm=pt.convert_fo2_to_fe_partition(liq_comps=Liqs.loc[[0]], T_K=T_HT87.loc[[0]], \n",
    "                            P_kbar=3, fo2=10**logfo2, model=\"Kress1991\", renorm=True)\n",
    "print('Renorm')\n",
    "display(myLiquids_Fe3_Kress_norm)\n"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "7b60f781-3b38-4d32-9476-b27d9fea166d",
   "metadata": {},
   "source": [
    "## Converting from FeO and Fe2O3 proportions to fo2\n",
    "- This function goes the other way, it takes a liquid with FeO and Fe2O3, and a temperature and pressure, and converts to a buffer position/delta fo2 vlaue"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 41,
   "id": "85f460c6-3651-4138-8de5-3617f9dcdc5e",
   "metadata": {},
   "outputs": [],
   "source": [
    "## The inversion isn't quite perfect, but is very close\n",
    "calc_fo2=pt.convert_fe_partition_to_fo2(liq_comps=myLiquids_Fe3_Kress_norm_NNO1,\n",
    "                                        T_K=T_HT87, P_kbar=3, model=\"Kress1991\", renorm=False)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 42,
   "id": "40a913db-27d4-4909-9164-986eb846800c",
   "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>DeltaQFM</th>\n",
       "      <th>DeltaNNO</th>\n",
       "      <th>fo2_calc</th>\n",
       "      <th>SiO2_Liq</th>\n",
       "      <th>TiO2_Liq</th>\n",
       "      <th>Al2O3_Liq</th>\n",
       "      <th>Fe2O3_Liq</th>\n",
       "      <th>FeO_Liq</th>\n",
       "      <th>MnO_Liq</th>\n",
       "      <th>MgO_Liq</th>\n",
       "      <th>CaO_Liq</th>\n",
       "      <th>Na2O_Liq</th>\n",
       "      <th>K2O_Liq</th>\n",
       "      <th>P2O5_Liq</th>\n",
       "      <th>Fe3Fet_Liq</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>1.587252</td>\n",
       "      <td>0.980283</td>\n",
       "      <td>7.999607e-08</td>\n",
       "      <td>51.546390</td>\n",
       "      <td>2.606264</td>\n",
       "      <td>13.552860</td>\n",
       "      <td>3.339932</td>\n",
       "      <td>8.127207</td>\n",
       "      <td>0.186200</td>\n",
       "      <td>6.710254</td>\n",
       "      <td>10.993904</td>\n",
       "      <td>2.411158</td>\n",
       "      <td>0.484651</td>\n",
       "      <td>0.248972</td>\n",
       "      <td>0.269955</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>1.587349</td>\n",
       "      <td>0.980431</td>\n",
       "      <td>7.139051e-08</td>\n",
       "      <td>51.557365</td>\n",
       "      <td>2.646336</td>\n",
       "      <td>13.742904</td>\n",
       "      <td>3.349248</td>\n",
       "      <td>8.180990</td>\n",
       "      <td>0.189920</td>\n",
       "      <td>6.509957</td>\n",
       "      <td>10.834581</td>\n",
       "      <td>2.455651</td>\n",
       "      <td>0.494335</td>\n",
       "      <td>0.253947</td>\n",
       "      <td>0.269205</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>1.587300</td>\n",
       "      <td>0.980439</td>\n",
       "      <td>6.284887e-08</td>\n",
       "      <td>51.598076</td>\n",
       "      <td>2.777193</td>\n",
       "      <td>13.695239</td>\n",
       "      <td>3.427946</td>\n",
       "      <td>8.459594</td>\n",
       "      <td>0.200919</td>\n",
       "      <td>6.288375</td>\n",
       "      <td>10.481571</td>\n",
       "      <td>2.514423</td>\n",
       "      <td>0.521581</td>\n",
       "      <td>0.268654</td>\n",
       "      <td>0.267191</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>1.587231</td>\n",
       "      <td>0.980406</td>\n",
       "      <td>5.807824e-08</td>\n",
       "      <td>51.623335</td>\n",
       "      <td>2.879327</td>\n",
       "      <td>13.600278</td>\n",
       "      <td>3.491627</td>\n",
       "      <td>8.678603</td>\n",
       "      <td>0.209376</td>\n",
       "      <td>6.152098</td>\n",
       "      <td>10.240776</td>\n",
       "      <td>2.549497</td>\n",
       "      <td>0.542300</td>\n",
       "      <td>0.279962</td>\n",
       "      <td>0.265793</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>1.586615</td>\n",
       "      <td>0.979863</td>\n",
       "      <td>4.928451e-08</td>\n",
       "      <td>51.637241</td>\n",
       "      <td>3.066705</td>\n",
       "      <td>13.384186</td>\n",
       "      <td>3.604510</td>\n",
       "      <td>9.000728</td>\n",
       "      <td>0.224349</td>\n",
       "      <td>5.871815</td>\n",
       "      <td>10.002808</td>\n",
       "      <td>2.599216</td>\n",
       "      <td>0.578610</td>\n",
       "      <td>0.299982</td>\n",
       "      <td>0.264891</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>5</th>\n",
       "      <td>1.586086</td>\n",
       "      <td>0.979386</td>\n",
       "      <td>4.382653e-08</td>\n",
       "      <td>51.638351</td>\n",
       "      <td>3.199578</td>\n",
       "      <td>13.221434</td>\n",
       "      <td>3.682642</td>\n",
       "      <td>9.209909</td>\n",
       "      <td>0.234892</td>\n",
       "      <td>5.673066</td>\n",
       "      <td>9.879096</td>\n",
       "      <td>2.629078</td>\n",
       "      <td>0.603989</td>\n",
       "      <td>0.314080</td>\n",
       "      <td>0.264593</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>6</th>\n",
       "      <td>1.585330</td>\n",
       "      <td>0.978706</td>\n",
       "      <td>3.698529e-08</td>\n",
       "      <td>51.634502</td>\n",
       "      <td>3.398218</td>\n",
       "      <td>12.978289</td>\n",
       "      <td>3.796698</td>\n",
       "      <td>9.516734</td>\n",
       "      <td>0.250723</td>\n",
       "      <td>5.387579</td>\n",
       "      <td>9.701648</td>\n",
       "      <td>2.668614</td>\n",
       "      <td>0.641860</td>\n",
       "      <td>0.335248</td>\n",
       "      <td>0.264151</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>7</th>\n",
       "      <td>1.584851</td>\n",
       "      <td>0.978275</td>\n",
       "      <td>3.316046e-08</td>\n",
       "      <td>51.628396</td>\n",
       "      <td>3.530278</td>\n",
       "      <td>12.816809</td>\n",
       "      <td>3.870774</td>\n",
       "      <td>9.716984</td>\n",
       "      <td>0.261292</td>\n",
       "      <td>5.205129</td>\n",
       "      <td>9.588480</td>\n",
       "      <td>2.691642</td>\n",
       "      <td>0.666987</td>\n",
       "      <td>0.349380</td>\n",
       "      <td>0.263860</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>8</th>\n",
       "      <td>1.584167</td>\n",
       "      <td>0.977661</td>\n",
       "      <td>2.831006e-08</td>\n",
       "      <td>51.614145</td>\n",
       "      <td>3.727939</td>\n",
       "      <td>12.575476</td>\n",
       "      <td>3.979141</td>\n",
       "      <td>10.011395</td>\n",
       "      <td>0.277175</td>\n",
       "      <td>4.942417</td>\n",
       "      <td>9.425986</td>\n",
       "      <td>2.721464</td>\n",
       "      <td>0.704516</td>\n",
       "      <td>0.370618</td>\n",
       "      <td>0.263425</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>9</th>\n",
       "      <td>1.583734</td>\n",
       "      <td>0.977274</td>\n",
       "      <td>2.556757e-08</td>\n",
       "      <td>51.601373</td>\n",
       "      <td>3.859495</td>\n",
       "      <td>12.415173</td>\n",
       "      <td>4.049654</td>\n",
       "      <td>10.203931</td>\n",
       "      <td>0.287788</td>\n",
       "      <td>4.774137</td>\n",
       "      <td>9.322264</td>\n",
       "      <td>2.738345</td>\n",
       "      <td>0.729436</td>\n",
       "      <td>0.384809</td>\n",
       "      <td>0.263138</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>10</th>\n",
       "      <td>1.583119</td>\n",
       "      <td>0.976725</td>\n",
       "      <td>2.205359e-08</td>\n",
       "      <td>51.577516</td>\n",
       "      <td>4.056607</td>\n",
       "      <td>12.175604</td>\n",
       "      <td>4.152968</td>\n",
       "      <td>10.487474</td>\n",
       "      <td>0.303752</td>\n",
       "      <td>4.531307</td>\n",
       "      <td>9.173226</td>\n",
       "      <td>2.759398</td>\n",
       "      <td>0.766683</td>\n",
       "      <td>0.406155</td>\n",
       "      <td>0.262708</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>11</th>\n",
       "      <td>1.582732</td>\n",
       "      <td>0.976380</td>\n",
       "      <td>2.004672e-08</td>\n",
       "      <td>51.558600</td>\n",
       "      <td>4.187924</td>\n",
       "      <td>12.016501</td>\n",
       "      <td>4.220276</td>\n",
       "      <td>10.673160</td>\n",
       "      <td>0.314429</td>\n",
       "      <td>4.375443</td>\n",
       "      <td>9.078035</td>\n",
       "      <td>2.770713</td>\n",
       "      <td>0.791434</td>\n",
       "      <td>0.420430</td>\n",
       "      <td>0.262423</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>12</th>\n",
       "      <td>1.582732</td>\n",
       "      <td>0.976380</td>\n",
       "      <td>2.004672e-08</td>\n",
       "      <td>51.558600</td>\n",
       "      <td>4.187924</td>\n",
       "      <td>12.016501</td>\n",
       "      <td>4.220276</td>\n",
       "      <td>10.673160</td>\n",
       "      <td>0.314429</td>\n",
       "      <td>4.375443</td>\n",
       "      <td>9.078035</td>\n",
       "      <td>2.770713</td>\n",
       "      <td>0.791434</td>\n",
       "      <td>0.420430</td>\n",
       "      <td>0.262423</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>13</th>\n",
       "      <td>1.582544</td>\n",
       "      <td>0.976214</td>\n",
       "      <td>1.913018e-08</td>\n",
       "      <td>51.548269</td>\n",
       "      <td>4.253568</td>\n",
       "      <td>11.937139</td>\n",
       "      <td>4.253476</td>\n",
       "      <td>10.765036</td>\n",
       "      <td>0.319778</td>\n",
       "      <td>4.299228</td>\n",
       "      <td>9.031643</td>\n",
       "      <td>2.775586</td>\n",
       "      <td>0.803787</td>\n",
       "      <td>0.427583</td>\n",
       "      <td>0.262280</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>14</th>\n",
       "      <td>1.582362</td>\n",
       "      <td>0.976051</td>\n",
       "      <td>1.826626e-08</td>\n",
       "      <td>51.537371</td>\n",
       "      <td>4.319209</td>\n",
       "      <td>11.857907</td>\n",
       "      <td>4.286379</td>\n",
       "      <td>10.856281</td>\n",
       "      <td>0.325135</td>\n",
       "      <td>4.224120</td>\n",
       "      <td>8.986032</td>\n",
       "      <td>2.779949</td>\n",
       "      <td>0.816127</td>\n",
       "      <td>0.434746</td>\n",
       "      <td>0.262138</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>15</th>\n",
       "      <td>1.582183</td>\n",
       "      <td>0.975893</td>\n",
       "      <td>1.745137e-08</td>\n",
       "      <td>51.525916</td>\n",
       "      <td>4.384849</td>\n",
       "      <td>11.778808</td>\n",
       "      <td>4.318990</td>\n",
       "      <td>10.946905</td>\n",
       "      <td>0.330500</td>\n",
       "      <td>4.150092</td>\n",
       "      <td>8.941187</td>\n",
       "      <td>2.783811</td>\n",
       "      <td>0.828454</td>\n",
       "      <td>0.441920</td>\n",
       "      <td>0.261996</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>16</th>\n",
       "      <td>1.582009</td>\n",
       "      <td>0.975739</td>\n",
       "      <td>1.668222e-08</td>\n",
       "      <td>51.513916</td>\n",
       "      <td>4.450493</td>\n",
       "      <td>11.699847</td>\n",
       "      <td>4.351312</td>\n",
       "      <td>11.036914</td>\n",
       "      <td>0.335874</td>\n",
       "      <td>4.077119</td>\n",
       "      <td>8.897096</td>\n",
       "      <td>2.787183</td>\n",
       "      <td>0.840768</td>\n",
       "      <td>0.449106</td>\n",
       "      <td>0.261855</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>17</th>\n",
       "      <td>1.581827</td>\n",
       "      <td>0.975579</td>\n",
       "      <td>1.589241e-08</td>\n",
       "      <td>51.529100</td>\n",
       "      <td>4.496905</td>\n",
       "      <td>11.625147</td>\n",
       "      <td>4.382480</td>\n",
       "      <td>11.122869</td>\n",
       "      <td>0.341191</td>\n",
       "      <td>3.998756</td>\n",
       "      <td>8.848689</td>\n",
       "      <td>2.792709</td>\n",
       "      <td>0.854256</td>\n",
       "      <td>0.456956</td>\n",
       "      <td>0.261735</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>18</th>\n",
       "      <td>1.581695</td>\n",
       "      <td>0.975511</td>\n",
       "      <td>1.375841e-08</td>\n",
       "      <td>52.612734</td>\n",
       "      <td>4.263861</td>\n",
       "      <td>11.713650</td>\n",
       "      <td>4.246476</td>\n",
       "      <td>10.710464</td>\n",
       "      <td>0.327012</td>\n",
       "      <td>3.766118</td>\n",
       "      <td>8.463650</td>\n",
       "      <td>2.870163</td>\n",
       "      <td>0.979760</td>\n",
       "      <td>0.463878</td>\n",
       "      <td>0.262946</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>19</th>\n",
       "      <td>1.581520</td>\n",
       "      <td>0.975392</td>\n",
       "      <td>1.214620e-08</td>\n",
       "      <td>53.545497</td>\n",
       "      <td>4.063865</td>\n",
       "      <td>11.790118</td>\n",
       "      <td>4.128805</td>\n",
       "      <td>10.357587</td>\n",
       "      <td>0.314846</td>\n",
       "      <td>3.566451</td>\n",
       "      <td>8.133268</td>\n",
       "      <td>2.936798</td>\n",
       "      <td>1.087593</td>\n",
       "      <td>0.469841</td>\n",
       "      <td>0.263994</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>20</th>\n",
       "      <td>1.581327</td>\n",
       "      <td>0.975246</td>\n",
       "      <td>1.094722e-08</td>\n",
       "      <td>54.320717</td>\n",
       "      <td>3.898105</td>\n",
       "      <td>11.853887</td>\n",
       "      <td>4.030598</td>\n",
       "      <td>10.065866</td>\n",
       "      <td>0.304765</td>\n",
       "      <td>3.400949</td>\n",
       "      <td>7.859484</td>\n",
       "      <td>2.992153</td>\n",
       "      <td>1.177063</td>\n",
       "      <td>0.474801</td>\n",
       "      <td>0.264868</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>21</th>\n",
       "      <td>1.581123</td>\n",
       "      <td>0.975083</td>\n",
       "      <td>9.993273e-09</td>\n",
       "      <td>54.998878</td>\n",
       "      <td>3.753437</td>\n",
       "      <td>11.909834</td>\n",
       "      <td>3.944379</td>\n",
       "      <td>9.811827</td>\n",
       "      <td>0.295969</td>\n",
       "      <td>3.256496</td>\n",
       "      <td>7.620568</td>\n",
       "      <td>3.040558</td>\n",
       "      <td>1.255220</td>\n",
       "      <td>0.479143</td>\n",
       "      <td>0.265636</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>22</th>\n",
       "      <td>1.580911</td>\n",
       "      <td>0.974907</td>\n",
       "      <td>9.198004e-09</td>\n",
       "      <td>55.614102</td>\n",
       "      <td>3.622435</td>\n",
       "      <td>11.960703</td>\n",
       "      <td>3.865888</td>\n",
       "      <td>9.582234</td>\n",
       "      <td>0.288004</td>\n",
       "      <td>3.125681</td>\n",
       "      <td>7.404243</td>\n",
       "      <td>3.084456</td>\n",
       "      <td>1.326045</td>\n",
       "      <td>0.483083</td>\n",
       "      <td>0.266334</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>23</th>\n",
       "      <td>1.580231</td>\n",
       "      <td>0.974324</td>\n",
       "      <td>7.416449e-09</td>\n",
       "      <td>57.204632</td>\n",
       "      <td>3.284890</td>\n",
       "      <td>12.092753</td>\n",
       "      <td>3.661803</td>\n",
       "      <td>8.992664</td>\n",
       "      <td>0.267487</td>\n",
       "      <td>2.788582</td>\n",
       "      <td>6.846957</td>\n",
       "      <td>3.197883</td>\n",
       "      <td>1.508776</td>\n",
       "      <td>0.493280</td>\n",
       "      <td>0.268149</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>24</th>\n",
       "      <td>1.579221</td>\n",
       "      <td>0.973432</td>\n",
       "      <td>5.683154e-09</td>\n",
       "      <td>59.154871</td>\n",
       "      <td>2.871874</td>\n",
       "      <td>12.255080</td>\n",
       "      <td>3.408360</td>\n",
       "      <td>8.274897</td>\n",
       "      <td>0.242386</td>\n",
       "      <td>2.376084</td>\n",
       "      <td>6.165149</td>\n",
       "      <td>3.336912</td>\n",
       "      <td>1.732547</td>\n",
       "      <td>0.505790</td>\n",
       "      <td>0.270403</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>25</th>\n",
       "      <td>1.578437</td>\n",
       "      <td>0.972719</td>\n",
       "      <td>4.846800e-09</td>\n",
       "      <td>60.316296</td>\n",
       "      <td>2.627669</td>\n",
       "      <td>12.352587</td>\n",
       "      <td>3.256571</td>\n",
       "      <td>7.852786</td>\n",
       "      <td>0.227552</td>\n",
       "      <td>2.132128</td>\n",
       "      <td>5.762176</td>\n",
       "      <td>3.419607</td>\n",
       "      <td>1.865233</td>\n",
       "      <td>0.513254</td>\n",
       "      <td>0.271747</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>26</th>\n",
       "      <td>1.577633</td>\n",
       "      <td>0.971978</td>\n",
       "      <td>4.206919e-09</td>\n",
       "      <td>61.346095</td>\n",
       "      <td>2.412078</td>\n",
       "      <td>12.439490</td>\n",
       "      <td>3.121347</td>\n",
       "      <td>7.481528</td>\n",
       "      <td>0.214461</td>\n",
       "      <td>1.916728</td>\n",
       "      <td>5.406509</td>\n",
       "      <td>3.492877</td>\n",
       "      <td>1.982573</td>\n",
       "      <td>0.519881</td>\n",
       "      <td>0.272940</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>27</th>\n",
       "      <td>1.576543</td>\n",
       "      <td>0.970962</td>\n",
       "      <td>3.560534e-09</td>\n",
       "      <td>62.556232</td>\n",
       "      <td>2.160024</td>\n",
       "      <td>12.542227</td>\n",
       "      <td>2.961789</td>\n",
       "      <td>7.049199</td>\n",
       "      <td>0.199161</td>\n",
       "      <td>1.664854</td>\n",
       "      <td>4.990808</td>\n",
       "      <td>3.578904</td>\n",
       "      <td>2.120038</td>\n",
       "      <td>0.527678</td>\n",
       "      <td>0.274342</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>28</th>\n",
       "      <td>1.575718</td>\n",
       "      <td>0.970186</td>\n",
       "      <td>3.184888e-09</td>\n",
       "      <td>63.363583</td>\n",
       "      <td>1.992753</td>\n",
       "      <td>12.611191</td>\n",
       "      <td>2.855025</td>\n",
       "      <td>6.763360</td>\n",
       "      <td>0.189011</td>\n",
       "      <td>1.497674</td>\n",
       "      <td>4.715018</td>\n",
       "      <td>3.636246</td>\n",
       "      <td>2.211458</td>\n",
       "      <td>0.532887</td>\n",
       "      <td>0.275275</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>29</th>\n",
       "      <td>1.574891</td>\n",
       "      <td>0.969404</td>\n",
       "      <td>2.877135e-09</td>\n",
       "      <td>64.098829</td>\n",
       "      <td>1.841131</td>\n",
       "      <td>12.674334</td>\n",
       "      <td>2.757645</td>\n",
       "      <td>6.505031</td>\n",
       "      <td>0.179815</td>\n",
       "      <td>1.346111</td>\n",
       "      <td>4.465098</td>\n",
       "      <td>3.688427</td>\n",
       "      <td>2.294479</td>\n",
       "      <td>0.537637</td>\n",
       "      <td>0.276122</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>30</th>\n",
       "      <td>1.574065</td>\n",
       "      <td>0.968618</td>\n",
       "      <td>2.621649e-09</td>\n",
       "      <td>64.771438</td>\n",
       "      <td>1.703098</td>\n",
       "      <td>12.732418</td>\n",
       "      <td>2.668493</td>\n",
       "      <td>6.270519</td>\n",
       "      <td>0.171445</td>\n",
       "      <td>1.208111</td>\n",
       "      <td>4.237641</td>\n",
       "      <td>3.736124</td>\n",
       "      <td>2.370207</td>\n",
       "      <td>0.541988</td>\n",
       "      <td>0.276893</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>31</th>\n",
       "      <td>1.572966</td>\n",
       "      <td>0.967569</td>\n",
       "      <td>2.343280e-09</td>\n",
       "      <td>65.583633</td>\n",
       "      <td>1.537408</td>\n",
       "      <td>12.803026</td>\n",
       "      <td>2.560853</td>\n",
       "      <td>5.989896</td>\n",
       "      <td>0.161403</td>\n",
       "      <td>1.042426</td>\n",
       "      <td>3.964702</td>\n",
       "      <td>3.793663</td>\n",
       "      <td>2.461326</td>\n",
       "      <td>0.547249</td>\n",
       "      <td>0.277817</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>32</th>\n",
       "      <td>1.572146</td>\n",
       "      <td>0.966783</td>\n",
       "      <td>2.170925e-09</td>\n",
       "      <td>66.136981</td>\n",
       "      <td>1.425242</td>\n",
       "      <td>12.851474</td>\n",
       "      <td>2.487602</td>\n",
       "      <td>5.800502</td>\n",
       "      <td>0.154609</td>\n",
       "      <td>0.930241</td>\n",
       "      <td>3.780003</td>\n",
       "      <td>3.832823</td>\n",
       "      <td>2.523170</td>\n",
       "      <td>0.550840</td>\n",
       "      <td>0.278441</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>33</th>\n",
       "      <td>1.571302</td>\n",
       "      <td>0.965970</td>\n",
       "      <td>2.020282e-09</td>\n",
       "      <td>66.659137</td>\n",
       "      <td>1.320178</td>\n",
       "      <td>12.897561</td>\n",
       "      <td>2.418719</td>\n",
       "      <td>5.623593</td>\n",
       "      <td>0.148248</td>\n",
       "      <td>0.825132</td>\n",
       "      <td>3.607073</td>\n",
       "      <td>3.869732</td>\n",
       "      <td>2.581271</td>\n",
       "      <td>0.554235</td>\n",
       "      <td>0.279022</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>34</th>\n",
       "      <td>1.570115</td>\n",
       "      <td>0.964823</td>\n",
       "      <td>1.845036e-09</td>\n",
       "      <td>67.320571</td>\n",
       "      <td>1.188397</td>\n",
       "      <td>12.956564</td>\n",
       "      <td>2.331963</td>\n",
       "      <td>5.402444</td>\n",
       "      <td>0.140275</td>\n",
       "      <td>0.693250</td>\n",
       "      <td>3.390294</td>\n",
       "      <td>3.916410</td>\n",
       "      <td>2.654442</td>\n",
       "      <td>0.558545</td>\n",
       "      <td>0.279746</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>35</th>\n",
       "      <td>1.569236</td>\n",
       "      <td>0.963970</td>\n",
       "      <td>1.736422e-09</td>\n",
       "      <td>67.764932</td>\n",
       "      <td>1.100791</td>\n",
       "      <td>12.996645</td>\n",
       "      <td>2.274078</td>\n",
       "      <td>5.255923</td>\n",
       "      <td>0.134980</td>\n",
       "      <td>0.605547</td>\n",
       "      <td>3.246275</td>\n",
       "      <td>3.947716</td>\n",
       "      <td>2.703295</td>\n",
       "      <td>0.561449</td>\n",
       "      <td>0.280221</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>36</th>\n",
       "      <td>1.568370</td>\n",
       "      <td>0.963128</td>\n",
       "      <td>1.643674e-09</td>\n",
       "      <td>68.168968</td>\n",
       "      <td>1.021921</td>\n",
       "      <td>13.033462</td>\n",
       "      <td>2.221829</td>\n",
       "      <td>5.124396</td>\n",
       "      <td>0.130216</td>\n",
       "      <td>0.526562</td>\n",
       "      <td>3.116695</td>\n",
       "      <td>3.976137</td>\n",
       "      <td>2.747456</td>\n",
       "      <td>0.564096</td>\n",
       "      <td>0.280645</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>37</th>\n",
       "      <td>1.567206</td>\n",
       "      <td>0.961992</td>\n",
       "      <td>1.539031e-09</td>\n",
       "      <td>68.657179</td>\n",
       "      <td>0.928027</td>\n",
       "      <td>13.078620</td>\n",
       "      <td>2.159486</td>\n",
       "      <td>4.968416</td>\n",
       "      <td>0.124551</td>\n",
       "      <td>0.432482</td>\n",
       "      <td>2.962573</td>\n",
       "      <td>4.010397</td>\n",
       "      <td>2.800356</td>\n",
       "      <td>0.567305</td>\n",
       "      <td>0.281140</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>38</th>\n",
       "      <td>1.566354</td>\n",
       "      <td>0.961159</td>\n",
       "      <td>1.473449e-09</td>\n",
       "      <td>68.983138</td>\n",
       "      <td>0.866257</td>\n",
       "      <td>13.109207</td>\n",
       "      <td>2.118394</td>\n",
       "      <td>4.866183</td>\n",
       "      <td>0.120829</td>\n",
       "      <td>0.370557</td>\n",
       "      <td>2.861274</td>\n",
       "      <td>4.033219</td>\n",
       "      <td>2.835374</td>\n",
       "      <td>0.569456</td>\n",
       "      <td>0.281459</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>39</th>\n",
       "      <td>1.565521</td>\n",
       "      <td>0.960342</td>\n",
       "      <td>1.417047e-09</td>\n",
       "      <td>69.277768</td>\n",
       "      <td>0.811201</td>\n",
       "      <td>13.137225</td>\n",
       "      <td>2.081729</td>\n",
       "      <td>4.775369</td>\n",
       "      <td>0.117516</td>\n",
       "      <td>0.315335</td>\n",
       "      <td>2.771067</td>\n",
       "      <td>4.053804</td>\n",
       "      <td>2.866770</td>\n",
       "      <td>0.571406</td>\n",
       "      <td>0.281738</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>40</th>\n",
       "      <td>1.564441</td>\n",
       "      <td>0.959282</td>\n",
       "      <td>1.353801e-09</td>\n",
       "      <td>69.626379</td>\n",
       "      <td>0.747242</td>\n",
       "      <td>13.170940</td>\n",
       "      <td>2.039103</td>\n",
       "      <td>4.670311</td>\n",
       "      <td>0.113672</td>\n",
       "      <td>0.251141</td>\n",
       "      <td>2.666395</td>\n",
       "      <td>4.078091</td>\n",
       "      <td>2.903531</td>\n",
       "      <td>0.573723</td>\n",
       "      <td>0.282053</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>41</th>\n",
       "      <td>1.563655</td>\n",
       "      <td>0.958509</td>\n",
       "      <td>1.313931e-09</td>\n",
       "      <td>69.857694</td>\n",
       "      <td>0.705689</td>\n",
       "      <td>13.193732</td>\n",
       "      <td>2.011406</td>\n",
       "      <td>4.602379</td>\n",
       "      <td>0.111179</td>\n",
       "      <td>0.209403</td>\n",
       "      <td>2.598487</td>\n",
       "      <td>4.094157</td>\n",
       "      <td>2.927632</td>\n",
       "      <td>0.575268</td>\n",
       "      <td>0.282251</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>42</th>\n",
       "      <td>1.562891</td>\n",
       "      <td>0.957756</td>\n",
       "      <td>1.279569e-09</td>\n",
       "      <td>70.065498</td>\n",
       "      <td>0.669123</td>\n",
       "      <td>13.214572</td>\n",
       "      <td>1.987043</td>\n",
       "      <td>4.542868</td>\n",
       "      <td>0.108990</td>\n",
       "      <td>0.172645</td>\n",
       "      <td>2.538813</td>\n",
       "      <td>4.108545</td>\n",
       "      <td>2.949032</td>\n",
       "      <td>0.576662</td>\n",
       "      <td>0.282419</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>43</th>\n",
       "      <td>1.562148</td>\n",
       "      <td>0.957023</td>\n",
       "      <td>1.250000e-09</td>\n",
       "      <td>70.251670</td>\n",
       "      <td>0.637130</td>\n",
       "      <td>13.233607</td>\n",
       "      <td>1.965748</td>\n",
       "      <td>4.491067</td>\n",
       "      <td>0.107078</td>\n",
       "      <td>0.140454</td>\n",
       "      <td>2.486686</td>\n",
       "      <td>4.121392</td>\n",
       "      <td>2.967954</td>\n",
       "      <td>0.577917</td>\n",
       "      <td>0.282560</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>44</th>\n",
       "      <td>1.561192</td>\n",
       "      <td>0.956077</td>\n",
       "      <td>1.217011e-09</td>\n",
       "      <td>70.469170</td>\n",
       "      <td>0.600944</td>\n",
       "      <td>13.256412</td>\n",
       "      <td>1.941707</td>\n",
       "      <td>4.432888</td>\n",
       "      <td>0.104923</td>\n",
       "      <td>0.103998</td>\n",
       "      <td>2.427862</td>\n",
       "      <td>4.136333</td>\n",
       "      <td>2.989668</td>\n",
       "      <td>0.579393</td>\n",
       "      <td>0.282708</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>45</th>\n",
       "      <td>1.560499</td>\n",
       "      <td>0.955392</td>\n",
       "      <td>1.196463e-09</td>\n",
       "      <td>70.611226</td>\n",
       "      <td>0.578222</td>\n",
       "      <td>13.271741</td>\n",
       "      <td>1.926656</td>\n",
       "      <td>4.396676</td>\n",
       "      <td>0.103574</td>\n",
       "      <td>0.081069</td>\n",
       "      <td>2.391034</td>\n",
       "      <td>4.146039</td>\n",
       "      <td>3.003551</td>\n",
       "      <td>0.580365</td>\n",
       "      <td>0.282794</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>46</th>\n",
       "      <td>1.559812</td>\n",
       "      <td>0.954711</td>\n",
       "      <td>1.179003e-09</td>\n",
       "      <td>70.737740</td>\n",
       "      <td>0.558946</td>\n",
       "      <td>13.285850</td>\n",
       "      <td>1.913944</td>\n",
       "      <td>4.366299</td>\n",
       "      <td>0.102436</td>\n",
       "      <td>0.061577</td>\n",
       "      <td>2.359909</td>\n",
       "      <td>4.154628</td>\n",
       "      <td>3.015600</td>\n",
       "      <td>0.581238</td>\n",
       "      <td>0.282857</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>47</th>\n",
       "      <td>1.558883</td>\n",
       "      <td>0.953788</td>\n",
       "      <td>1.159793e-09</td>\n",
       "      <td>70.886236</td>\n",
       "      <td>0.538023</td>\n",
       "      <td>13.303220</td>\n",
       "      <td>1.900261</td>\n",
       "      <td>4.333956</td>\n",
       "      <td>0.101211</td>\n",
       "      <td>0.040344</td>\n",
       "      <td>2.326343</td>\n",
       "      <td>4.164613</td>\n",
       "      <td>3.029184</td>\n",
       "      <td>0.582277</td>\n",
       "      <td>0.282910</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>48</th>\n",
       "      <td>1.557488</td>\n",
       "      <td>0.952397</td>\n",
       "      <td>1.144100e-09</td>\n",
       "      <td>71.036962</td>\n",
       "      <td>0.523079</td>\n",
       "      <td>13.323848</td>\n",
       "      <td>1.890969</td>\n",
       "      <td>4.313347</td>\n",
       "      <td>0.100377</td>\n",
       "      <td>0.024876</td>\n",
       "      <td>2.303243</td>\n",
       "      <td>4.174388</td>\n",
       "      <td>3.040906</td>\n",
       "      <td>0.583383</td>\n",
       "      <td>0.282883</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "    DeltaQFM  DeltaNNO      fo2_calc   SiO2_Liq  TiO2_Liq  Al2O3_Liq  \\\n",
       "0   1.587252  0.980283  7.999607e-08  51.546390  2.606264  13.552860   \n",
       "1   1.587349  0.980431  7.139051e-08  51.557365  2.646336  13.742904   \n",
       "2   1.587300  0.980439  6.284887e-08  51.598076  2.777193  13.695239   \n",
       "3   1.587231  0.980406  5.807824e-08  51.623335  2.879327  13.600278   \n",
       "4   1.586615  0.979863  4.928451e-08  51.637241  3.066705  13.384186   \n",
       "5   1.586086  0.979386  4.382653e-08  51.638351  3.199578  13.221434   \n",
       "6   1.585330  0.978706  3.698529e-08  51.634502  3.398218  12.978289   \n",
       "7   1.584851  0.978275  3.316046e-08  51.628396  3.530278  12.816809   \n",
       "8   1.584167  0.977661  2.831006e-08  51.614145  3.727939  12.575476   \n",
       "9   1.583734  0.977274  2.556757e-08  51.601373  3.859495  12.415173   \n",
       "10  1.583119  0.976725  2.205359e-08  51.577516  4.056607  12.175604   \n",
       "11  1.582732  0.976380  2.004672e-08  51.558600  4.187924  12.016501   \n",
       "12  1.582732  0.976380  2.004672e-08  51.558600  4.187924  12.016501   \n",
       "13  1.582544  0.976214  1.913018e-08  51.548269  4.253568  11.937139   \n",
       "14  1.582362  0.976051  1.826626e-08  51.537371  4.319209  11.857907   \n",
       "15  1.582183  0.975893  1.745137e-08  51.525916  4.384849  11.778808   \n",
       "16  1.582009  0.975739  1.668222e-08  51.513916  4.450493  11.699847   \n",
       "17  1.581827  0.975579  1.589241e-08  51.529100  4.496905  11.625147   \n",
       "18  1.581695  0.975511  1.375841e-08  52.612734  4.263861  11.713650   \n",
       "19  1.581520  0.975392  1.214620e-08  53.545497  4.063865  11.790118   \n",
       "20  1.581327  0.975246  1.094722e-08  54.320717  3.898105  11.853887   \n",
       "21  1.581123  0.975083  9.993273e-09  54.998878  3.753437  11.909834   \n",
       "22  1.580911  0.974907  9.198004e-09  55.614102  3.622435  11.960703   \n",
       "23  1.580231  0.974324  7.416449e-09  57.204632  3.284890  12.092753   \n",
       "24  1.579221  0.973432  5.683154e-09  59.154871  2.871874  12.255080   \n",
       "25  1.578437  0.972719  4.846800e-09  60.316296  2.627669  12.352587   \n",
       "26  1.577633  0.971978  4.206919e-09  61.346095  2.412078  12.439490   \n",
       "27  1.576543  0.970962  3.560534e-09  62.556232  2.160024  12.542227   \n",
       "28  1.575718  0.970186  3.184888e-09  63.363583  1.992753  12.611191   \n",
       "29  1.574891  0.969404  2.877135e-09  64.098829  1.841131  12.674334   \n",
       "30  1.574065  0.968618  2.621649e-09  64.771438  1.703098  12.732418   \n",
       "31  1.572966  0.967569  2.343280e-09  65.583633  1.537408  12.803026   \n",
       "32  1.572146  0.966783  2.170925e-09  66.136981  1.425242  12.851474   \n",
       "33  1.571302  0.965970  2.020282e-09  66.659137  1.320178  12.897561   \n",
       "34  1.570115  0.964823  1.845036e-09  67.320571  1.188397  12.956564   \n",
       "35  1.569236  0.963970  1.736422e-09  67.764932  1.100791  12.996645   \n",
       "36  1.568370  0.963128  1.643674e-09  68.168968  1.021921  13.033462   \n",
       "37  1.567206  0.961992  1.539031e-09  68.657179  0.928027  13.078620   \n",
       "38  1.566354  0.961159  1.473449e-09  68.983138  0.866257  13.109207   \n",
       "39  1.565521  0.960342  1.417047e-09  69.277768  0.811201  13.137225   \n",
       "40  1.564441  0.959282  1.353801e-09  69.626379  0.747242  13.170940   \n",
       "41  1.563655  0.958509  1.313931e-09  69.857694  0.705689  13.193732   \n",
       "42  1.562891  0.957756  1.279569e-09  70.065498  0.669123  13.214572   \n",
       "43  1.562148  0.957023  1.250000e-09  70.251670  0.637130  13.233607   \n",
       "44  1.561192  0.956077  1.217011e-09  70.469170  0.600944  13.256412   \n",
       "45  1.560499  0.955392  1.196463e-09  70.611226  0.578222  13.271741   \n",
       "46  1.559812  0.954711  1.179003e-09  70.737740  0.558946  13.285850   \n",
       "47  1.558883  0.953788  1.159793e-09  70.886236  0.538023  13.303220   \n",
       "48  1.557488  0.952397  1.144100e-09  71.036962  0.523079  13.323848   \n",
       "\n",
       "    Fe2O3_Liq    FeO_Liq   MnO_Liq   MgO_Liq    CaO_Liq  Na2O_Liq   K2O_Liq  \\\n",
       "0    3.339932   8.127207  0.186200  6.710254  10.993904  2.411158  0.484651   \n",
       "1    3.349248   8.180990  0.189920  6.509957  10.834581  2.455651  0.494335   \n",
       "2    3.427946   8.459594  0.200919  6.288375  10.481571  2.514423  0.521581   \n",
       "3    3.491627   8.678603  0.209376  6.152098  10.240776  2.549497  0.542300   \n",
       "4    3.604510   9.000728  0.224349  5.871815  10.002808  2.599216  0.578610   \n",
       "5    3.682642   9.209909  0.234892  5.673066   9.879096  2.629078  0.603989   \n",
       "6    3.796698   9.516734  0.250723  5.387579   9.701648  2.668614  0.641860   \n",
       "7    3.870774   9.716984  0.261292  5.205129   9.588480  2.691642  0.666987   \n",
       "8    3.979141  10.011395  0.277175  4.942417   9.425986  2.721464  0.704516   \n",
       "9    4.049654  10.203931  0.287788  4.774137   9.322264  2.738345  0.729436   \n",
       "10   4.152968  10.487474  0.303752  4.531307   9.173226  2.759398  0.766683   \n",
       "11   4.220276  10.673160  0.314429  4.375443   9.078035  2.770713  0.791434   \n",
       "12   4.220276  10.673160  0.314429  4.375443   9.078035  2.770713  0.791434   \n",
       "13   4.253476  10.765036  0.319778  4.299228   9.031643  2.775586  0.803787   \n",
       "14   4.286379  10.856281  0.325135  4.224120   8.986032  2.779949  0.816127   \n",
       "15   4.318990  10.946905  0.330500  4.150092   8.941187  2.783811  0.828454   \n",
       "16   4.351312  11.036914  0.335874  4.077119   8.897096  2.787183  0.840768   \n",
       "17   4.382480  11.122869  0.341191  3.998756   8.848689  2.792709  0.854256   \n",
       "18   4.246476  10.710464  0.327012  3.766118   8.463650  2.870163  0.979760   \n",
       "19   4.128805  10.357587  0.314846  3.566451   8.133268  2.936798  1.087593   \n",
       "20   4.030598  10.065866  0.304765  3.400949   7.859484  2.992153  1.177063   \n",
       "21   3.944379   9.811827  0.295969  3.256496   7.620568  3.040558  1.255220   \n",
       "22   3.865888   9.582234  0.288004  3.125681   7.404243  3.084456  1.326045   \n",
       "23   3.661803   8.992664  0.267487  2.788582   6.846957  3.197883  1.508776   \n",
       "24   3.408360   8.274897  0.242386  2.376084   6.165149  3.336912  1.732547   \n",
       "25   3.256571   7.852786  0.227552  2.132128   5.762176  3.419607  1.865233   \n",
       "26   3.121347   7.481528  0.214461  1.916728   5.406509  3.492877  1.982573   \n",
       "27   2.961789   7.049199  0.199161  1.664854   4.990808  3.578904  2.120038   \n",
       "28   2.855025   6.763360  0.189011  1.497674   4.715018  3.636246  2.211458   \n",
       "29   2.757645   6.505031  0.179815  1.346111   4.465098  3.688427  2.294479   \n",
       "30   2.668493   6.270519  0.171445  1.208111   4.237641  3.736124  2.370207   \n",
       "31   2.560853   5.989896  0.161403  1.042426   3.964702  3.793663  2.461326   \n",
       "32   2.487602   5.800502  0.154609  0.930241   3.780003  3.832823  2.523170   \n",
       "33   2.418719   5.623593  0.148248  0.825132   3.607073  3.869732  2.581271   \n",
       "34   2.331963   5.402444  0.140275  0.693250   3.390294  3.916410  2.654442   \n",
       "35   2.274078   5.255923  0.134980  0.605547   3.246275  3.947716  2.703295   \n",
       "36   2.221829   5.124396  0.130216  0.526562   3.116695  3.976137  2.747456   \n",
       "37   2.159486   4.968416  0.124551  0.432482   2.962573  4.010397  2.800356   \n",
       "38   2.118394   4.866183  0.120829  0.370557   2.861274  4.033219  2.835374   \n",
       "39   2.081729   4.775369  0.117516  0.315335   2.771067  4.053804  2.866770   \n",
       "40   2.039103   4.670311  0.113672  0.251141   2.666395  4.078091  2.903531   \n",
       "41   2.011406   4.602379  0.111179  0.209403   2.598487  4.094157  2.927632   \n",
       "42   1.987043   4.542868  0.108990  0.172645   2.538813  4.108545  2.949032   \n",
       "43   1.965748   4.491067  0.107078  0.140454   2.486686  4.121392  2.967954   \n",
       "44   1.941707   4.432888  0.104923  0.103998   2.427862  4.136333  2.989668   \n",
       "45   1.926656   4.396676  0.103574  0.081069   2.391034  4.146039  3.003551   \n",
       "46   1.913944   4.366299  0.102436  0.061577   2.359909  4.154628  3.015600   \n",
       "47   1.900261   4.333956  0.101211  0.040344   2.326343  4.164613  3.029184   \n",
       "48   1.890969   4.313347  0.100377  0.024876   2.303243  4.174388  3.040906   \n",
       "\n",
       "    P2O5_Liq  Fe3Fet_Liq  \n",
       "0   0.248972    0.269955  \n",
       "1   0.253947    0.269205  \n",
       "2   0.268654    0.267191  \n",
       "3   0.279962    0.265793  \n",
       "4   0.299982    0.264891  \n",
       "5   0.314080    0.264593  \n",
       "6   0.335248    0.264151  \n",
       "7   0.349380    0.263860  \n",
       "8   0.370618    0.263425  \n",
       "9   0.384809    0.263138  \n",
       "10  0.406155    0.262708  \n",
       "11  0.420430    0.262423  \n",
       "12  0.420430    0.262423  \n",
       "13  0.427583    0.262280  \n",
       "14  0.434746    0.262138  \n",
       "15  0.441920    0.261996  \n",
       "16  0.449106    0.261855  \n",
       "17  0.456956    0.261735  \n",
       "18  0.463878    0.262946  \n",
       "19  0.469841    0.263994  \n",
       "20  0.474801    0.264868  \n",
       "21  0.479143    0.265636  \n",
       "22  0.483083    0.266334  \n",
       "23  0.493280    0.268149  \n",
       "24  0.505790    0.270403  \n",
       "25  0.513254    0.271747  \n",
       "26  0.519881    0.272940  \n",
       "27  0.527678    0.274342  \n",
       "28  0.532887    0.275275  \n",
       "29  0.537637    0.276122  \n",
       "30  0.541988    0.276893  \n",
       "31  0.547249    0.277817  \n",
       "32  0.550840    0.278441  \n",
       "33  0.554235    0.279022  \n",
       "34  0.558545    0.279746  \n",
       "35  0.561449    0.280221  \n",
       "36  0.564096    0.280645  \n",
       "37  0.567305    0.281140  \n",
       "38  0.569456    0.281459  \n",
       "39  0.571406    0.281738  \n",
       "40  0.573723    0.282053  \n",
       "41  0.575268    0.282251  \n",
       "42  0.576662    0.282419  \n",
       "43  0.577917    0.282560  \n",
       "44  0.579393    0.282708  \n",
       "45  0.580365    0.282794  \n",
       "46  0.581238    0.282857  \n",
       "47  0.582277    0.282910  \n",
       "48  0.583383    0.282883  "
      ]
     },
     "execution_count": 42,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "calc_fo2"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "10550e84-3149-4cfc-9279-33f63b0d968e",
   "metadata": {},
   "outputs": [],
   "source": []
  }
 ],
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