DatabasePriors.ipynb

{
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   "source": [
    "from pycalphad import Database, variables as v\n",
    "from pycalphad.variables import Species\n",
    "\n",
    "dbf = Database('AlCoCrNi-2016Liu-minified.TDB')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
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    {
     "name": "stdout",
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     "text": [
      "102862.903225806*((4.65e-11*P + 1.0)**0.8 - 1.0)*exp(9.2e-9*T**2 + 1.7e-5*T) - 1115.9095\n",
      "172788.461538462*((2.6e-11*P + 1.0)**0.8 - 1.0)*exp(9.2e-9*T**2 + 1.7e-5*T) - 3645.714\n",
      "172788.461538462*((2.6e-11*P + 1.0)**0.8 - 1.0)*exp(9.2e-9*T**2 + 1.7e-5*T) - 7287.714\n",
      "102862.903225806*((4.65e-11*P + 1.0)**0.8 - 1.0)*exp(9.2e-9*T**2 + 1.7e-5*T) - 1115.9095\n",
      "172788.461538462*((2.6e-11*P + 1.0)**0.8 - 1.0)*exp(9.2e-9*T**2 + 1.7e-5*T) - 3645.714\n",
      "172788.461538462*((2.6e-11*P + 1.0)**0.8 - 1.0)*exp(9.2e-9*T**2 + 1.7e-5*T) - 7287.714\n",
      "102862.903225806*((4.65e-11*P + 1.0)**0.8 - 1.0)*exp(9.2e-9*T**2 + 1.7e-5*T) - 1115.9095\n",
      "172788.461538462*((2.6e-11*P + 1.0)**0.8 - 1.0)*exp(9.2e-9*T**2 + 1.7e-5*T) - 3645.714\n",
      "172788.461538462*((2.6e-11*P + 1.0)**0.8 - 1.0)*exp(9.2e-9*T**2 + 1.7e-5*T) - 7287.714\n"
     ]
    }
   ],
   "source": [
    "import itertools\n",
    "import string\n",
    "import sympy\n",
    "import numpy as np\n",
    "\n",
    "def genericize(mapping, const_array):\n",
    "    new_array = []\n",
    "    for subl in const_array:\n",
    "        new_array.append(tuple(mapping[x] for x in subl))\n",
    "    return tuple(new_array)\n",
    "def sigfigs(x, n):\n",
    "    \"\"\"Round x to n significant digits\"\"\"\n",
    "    if x != 0:\n",
    "        return np.around(x, -(np.floor(np.log10(np.abs(x)))).astype(np.int) + (n - 1))\n",
    "    else:\n",
    "        return x\n",
    "def average_piecewise(pw):\n",
    "    return sum(x.expr for x in pw.args)/len(pw.args)\n",
    "\n",
    "def categorize_phase(phase_name, constituents, site_ratios):\n",
    "    if phase_name == 'LIQUID' and len(constituents) == 1:\n",
    "        return 'liquid'\n",
    "    elif phase_name == 'GAS' and len(constituents) == 1:\n",
    "        return 'gas'\n",
    "    elif len(constituents) == 1 or \\\n",
    "        (len(constituents) == 2 and len(constituents[1]) == 1 and list(constituents[1])[0] == Species('VA')):\n",
    "        return 'solid'\n",
    "    elif all(len(x) == 1 for x in constituents):\n",
    "        return 'stoichiometric'\n",
    "    else:\n",
    "        return 'complex'\n",
    "\n",
    "def extract_coefficients(expr, polys):\n",
    "    result = {}\n",
    "    for poly in polys:\n",
    "        if poly == 1:\n",
    "            continue\n",
    "        else:\n",
    "            coef = float(expr.coeff(poly))\n",
    "        result[poly] = coef\n",
    "        expr = expr - poly*coef\n",
    "    expr = expr.n()\n",
    "    if isinstance(expr, (sympy.Float, sympy.Integer)):\n",
    "        result[1] = float(expr)\n",
    "        expr = sympy.S.Zero\n",
    "    if expr is not sympy.S.Zero:\n",
    "        raise ValueError(expr)\n",
    "    return tuple(result[p] for p in polys)\n",
    "\n",
    "total_results = []\n",
    "\n",
    "for combo in itertools.combinations(dbf.elements - {'VA', '/-'}, 2):\n",
    "    combo_str = sorted(set(combo) | {'VA'})\n",
    "    combo = [Species(x) for x in combo_str]\n",
    "    combo_dict = dict(zip([c for c in combo if c.number_of_atoms > 0], string.ascii_uppercase))\n",
    "    combo_dict[Species('VA')] = 'VA'\n",
    "    allowed_phases = set()\n",
    "    # TODO: Categorize each phase? solid solution, intermetallic, complex intermetallic, liquid, etc.\n",
    "    for phase_name, phase_obj in dbf.phases.items():\n",
    "        include_phase = True\n",
    "        for sublattice in phase_obj.constituents:\n",
    "            if len(set(sublattice).intersection(combo)) == 0:\n",
    "                # None of the components in a sublattice are active\n",
    "                # We cannot build a model of this phase\n",
    "                include_phase = False\n",
    "                break\n",
    "        if include_phase:\n",
    "            allowed_phases |= {phase_name}\n",
    "    for param in dbf._parameters.all():\n",
    "        if param['phase_name'] in allowed_phases and param['parameter_type'] in ['G', 'L']:\n",
    "            active_pure_elements = [list(x.constituents.keys()) for subl in param['constituent_array'] for x in subl]\n",
    "            active_pure_elements = [el.upper() for constituents in active_pure_elements for el in constituents]\n",
    "            active_pure_elements = set(active_pure_elements)\n",
    "            if not active_pure_elements.issubset(combo_str):\n",
    "                continue\n",
    "            generic_combo = [Species(x) for x in sorted(active_pure_elements)]\n",
    "            gen_combo_dict = dict(zip([c for c in generic_combo if c.number_of_atoms > 0], string.ascii_uppercase))\n",
    "            gen_combo_dict[Species('VA')] = 'VA'\n",
    "            gen_combo_dict[Species('*')] = '*'\n",
    "            ratio_sum = sum(dbf.phases[param['phase_name']].sublattices)\n",
    "            reduced_ratios = tuple(sigfigs(c, 3) for c in dbf.phases[param['phase_name']].sublattices)\n",
    "            param_val = param['parameter'].subs(dbf.symbols).subs(dbf.symbols).subs(dbf.symbols).subs(dbf.symbols)\n",
    "            # If parameter is Piecewise, average it (for now)\n",
    "            param_val = sympy.piecewise_fold(param_val)\n",
    "            pw_atoms = param_val.atoms(sympy.Piecewise)\n",
    "            pw_dict = {key: average_piecewise(key) for key in pw_atoms}\n",
    "            param_val = param_val.subs(pw_dict)\n",
    "            # Cross terms must be listed first\n",
    "            polys = [v.T*sympy.log(1.0e-5*v.P)] + [v.T*sympy.log(v.T), sympy.log(v.T)] + [v.T**n for n in range(-30,0)] + [v.T**n for n in range(1,30)] + [1]\n",
    "            columns = ['system', 'phase_name', 'phase_type', 'site_ratios',\n",
    "                       'parameter_order', 'constituent_array', 'parameter_value'] + \\\n",
    "                        [str(x) for x in polys]\n",
    "            try:\n",
    "                id_tuple = (tuple(c for c in combo_str if c != 'VA'), param['phase_name'],\n",
    "                            categorize_phase(param['phase_name'], dbf.phases[param['phase_name']].constituents, reduced_ratios),\n",
    "                            reduced_ratios, param['parameter_order'],\n",
    "                            genericize(gen_combo_dict, param['constituent_array']),\n",
    "                            param_val) + extract_coefficients(param_val, polys)\n",
    "                total_results.append(id_tuple)\n",
    "            except ValueError as e:\n",
    "                print(e)"
   ]
  },
  {
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       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th>system</th>\n",
       "      <th>phase_name</th>\n",
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       "      <th>T*log(1.0e-5*P)</th>\n",
       "      <th>T*log(T)</th>\n",
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       "      <th>((VA,), (VA,))</th>\n",
       "      <th>0</th>\n",
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       "      <th>((A,),)</th>\n",
       "      <th>0</th>\n",
       "      <td>(CO, NI)</td>\n",
       "      <td>LIQUID</td>\n",
       "      <td>-7.3267e-22*T**7 - 5.78266666666667e-8*T**3 - ...</td>\n",
       "      <td>0.0</td>\n",
       "      <td>-21.862033</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
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       "      <th>(1.0, 1.0)</th>\n",
       "      <th>((A,), (VA,))</th>\n",
       "      <th>0</th>\n",
       "      <td>(CO, NI)</td>\n",
       "      <td>FCC_A1</td>\n",
       "      <td>-2.89133333333333e-8*T**3 - 0.0004424565*T**2 ...</td>\n",
       "      <td>0.0</td>\n",
       "      <td>-10.931017</td>\n",
       "      <td>0.0</td>\n",
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       "    <tr>\n",
       "      <th rowspan=\"2\" valign=\"top\">(1.0, 3.0)</th>\n",
       "      <th>((A,), (VA,))</th>\n",
       "      <th>0</th>\n",
       "      <td>(CO, NI)</td>\n",
       "      <td>BCC_A2</td>\n",
       "      <td>-2.89133333333333e-8*T**3 - 0.0004424565*T**2 ...</td>\n",
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       "    </tr>\n",
       "    <tr>\n",
       "      <th>((A, VA), (VA,))</th>\n",
       "      <th>0</th>\n",
       "      <td>(CO, NI)</td>\n",
       "      <td>BCC_A2</td>\n",
       "      <td>-35.045*T + 96765</td>\n",
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       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>96765.000000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>(1.0, 0.5)</th>\n",
       "      <th>((A,), (VA,))</th>\n",
       "      <th>0</th>\n",
       "      <td>(CO, NI)</td>\n",
       "      <td>HCP_A3</td>\n",
       "      <td>-2.89133333333333e-8*T**3 - 0.0004424565*T**2 ...</td>\n",
       "      <td>0.0</td>\n",
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       "      <td>0.0</td>\n",
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       "    </tr>\n",
       "    <tr>\n",
       "      <th rowspan=\"2\" valign=\"top\">complex</th>\n",
       "      <th rowspan=\"2\" valign=\"top\">(0.5, 0.5, 3.0)</th>\n",
       "      <th>((A,), (VA,), (VA,))</th>\n",
       "      <th>0</th>\n",
       "      <td>(CO, NI)</td>\n",
       "      <td>BCC_B2</td>\n",
       "      <td>-0.2875*T + 25867.5</td>\n",
       "      <td>0.0</td>\n",
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       "      <td>0.0</td>\n",
       "      <td>...</td>\n",
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       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>25867.500000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>((VA,), (A,), (VA,))</th>\n",
       "      <th>0</th>\n",
       "      <td>(CO, NI)</td>\n",
       "      <td>BCC_B2</td>\n",
       "      <td>-0.2875*T + 25867.5</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>...</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>25867.500000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>liquid</th>\n",
       "      <th>(1.0,)</th>\n",
       "      <th>((A,),)</th>\n",
       "      <th>0</th>\n",
       "      <td>(CO, NI)</td>\n",
       "      <td>LIQUID</td>\n",
       "      <td>-1.27439333333333e-21*T**7 - 0.000537855555555...</td>\n",
       "      <td>0.0</td>\n",
       "      <td>-21.610667</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>...</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>-1380.564556</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th rowspan=\"4\" valign=\"top\">solid</th>\n",
       "      <th>(1.0, 1.0)</th>\n",
       "      <th>((A,), (VA,))</th>\n",
       "      <th>0</th>\n",
       "      <td>(CO, NI)</td>\n",
       "      <td>FCC_A1</td>\n",
       "      <td>-0.000806783333333333*T**2 - 10.866*T*log(T) +...</td>\n",
       "      <td>0.0</td>\n",
       "      <td>-10.866000</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>...</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>-5503.302333</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th rowspan=\"2\" valign=\"top\">(1.0, 3.0)</th>\n",
       "      <th>((A,), (VA,))</th>\n",
       "      <th>0</th>\n",
       "      <td>(CO, NI)</td>\n",
       "      <td>BCC_A2</td>\n",
       "      <td>-0.000806783333333333*T**2 - 10.866*T*log(T) +...</td>\n",
       "      <td>0.0</td>\n",
       "      <td>-10.866000</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>...</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>-1145.760333</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>((A, VA), (VA,))</th>\n",
       "      <th>0</th>\n",
       "      <td>(CO, NI)</td>\n",
       "      <td>BCC_A2</td>\n",
       "      <td>-0.22789*T + 24593.23</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>...</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>24593.230000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>(1.0, 0.5)</th>\n",
       "      <th>((A,), (VA,))</th>\n",
       "      <th>0</th>\n",
       "      <td>(CO, NI)</td>\n",
       "      <td>HCP_A3</td>\n",
       "      <td>-0.000806783333333333*T**2 - 10.866*T*log(T) +...</td>\n",
       "      <td>0.0</td>\n",
       "      <td>-10.866000</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>...</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>-4980.302333</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th rowspan=\"2\" valign=\"top\">complex</th>\n",
       "      <th rowspan=\"2\" valign=\"top\">(0.5, 0.5, 3.0)</th>\n",
       "      <th>((VA,), (A,), (VA,))</th>\n",
       "      <th>0</th>\n",
       "      <td>(CO, NI)</td>\n",
       "      <td>BCC_B2</td>\n",
       "      <td>-6.7374925*T + 28302.71</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>...</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>28302.710000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>((A,), (VA,), (VA,))</th>\n",
       "      <th>0</th>\n",
       "      <td>(CO, NI)</td>\n",
       "      <td>BCC_B2</td>\n",
       "      <td>-6.7374925*T + 28302.71</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>...</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>28302.710000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>liquid</th>\n",
       "      <th>(1.0,)</th>\n",
       "      <th>((A, B),)</th>\n",
       "      <th>0</th>\n",
       "      <td>(CO, NI)</td>\n",
       "      <td>LIQUID</td>\n",
       "      <td>1331/2</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>...</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>665.500000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th rowspan=\"3\" valign=\"top\">solid</th>\n",
       "      <th>(1.0, 1.0)</th>\n",
       "      <th>((A, B), (VA,))</th>\n",
       "      <th>0</th>\n",
       "      <td>(CO, NI)</td>\n",
       "      <td>FCC_A1</td>\n",
       "      <td>0.63145*T - 400</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>...</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>-400.000000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>(1.0, 3.0)</th>\n",
       "      <th>((A, B), (VA,))</th>\n",
       "      <th>0</th>\n",
       "      <td>(CO, NI)</td>\n",
       "      <td>BCC_A2</td>\n",
       "      <td>1000</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>...</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>1000.000000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>(1.0, 0.5)</th>\n",
       "      <th>((A, B), (VA,))</th>\n",
       "      <th>0</th>\n",
       "      <td>(CO, NI)</td>\n",
       "      <td>HCP_A3</td>\n",
       "      <td>-0.1925*T - 810</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>...</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>-810.000000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th rowspan=\"11\" valign=\"top\">complex</th>\n",
       "      <th rowspan=\"2\" valign=\"top\">(0.5, 0.5, 3.0)</th>\n",
       "      <th>((A,), (B,), (VA,))</th>\n",
       "      <th>0</th>\n",
       "      <td>(CO, NI)</td>\n",
       "      <td>BCC_B2</td>\n",
       "      <td>-0.832*T + 1932.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>...</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>1932.000000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>((B,), (A,), (VA,))</th>\n",
       "      <th>0</th>\n",
       "      <td>(CO, NI)</td>\n",
       "      <td>BCC_B2</td>\n",
       "      <td>-0.832*T + 1932.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>...</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>1932.000000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th rowspan=\"9\" valign=\"top\">(0.75, 0.25, 1.0)</th>\n",
       "      <th>((B,), (A,), (VA,))</th>\n",
       "      <th>0</th>\n",
       "      <td>(CO, NI)</td>\n",
       "      <td>L12_FCC</td>\n",
       "      <td>0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>...</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.000000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>((A,), (B,), (VA,))</th>\n",
       "      <th>0</th>\n",
       "      <td>(CO, NI)</td>\n",
       "      <td>L12_FCC</td>\n",
       "      <td>0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>...</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.000000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>((A, B), (A,), (VA,))</th>\n",
       "      <th>0</th>\n",
       "      <td>(CO, NI)</td>\n",
       "      <td>L12_FCC</td>\n",
       "      <td>0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>...</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.000000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>((A, B), (B,), (VA,))</th>\n",
       "      <th>0</th>\n",
       "      <td>(CO, NI)</td>\n",
       "      <td>L12_FCC</td>\n",
       "      <td>0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>...</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.000000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>((A, B), (A,), (VA,))</th>\n",
       "      <th>1</th>\n",
       "      <td>(CO, NI)</td>\n",
       "      <td>L12_FCC</td>\n",
       "      <td>0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>...</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.000000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>((A, B), (B,), (VA,))</th>\n",
       "      <th>1</th>\n",
       "      <td>(CO, NI)</td>\n",
       "      <td>L12_FCC</td>\n",
       "      <td>0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>...</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.000000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th rowspan=\"2\" valign=\"top\">((*,), (A, B), (VA,))</th>\n",
       "      <th>0</th>\n",
       "      <td>(CO, NI)</td>\n",
       "      <td>L12_FCC</td>\n",
       "      <td>0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>...</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.000000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>(CO, NI)</td>\n",
       "      <td>L12_FCC</td>\n",
       "      <td>0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>...</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.000000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>((A, B), (*,), (VA,))</th>\n",
       "      <th>0</th>\n",
       "      <td>(CO, NI)</td>\n",
       "      <td>L12_FCC</td>\n",
       "      <td>0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>...</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.000000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>...</th>\n",
       "      <th>...</th>\n",
       "      <th>...</th>\n",
       "      <th>...</th>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>solid</th>\n",
       "      <th>(1.0, 0.5)</th>\n",
       "      <th>((A,), (VA,))</th>\n",
       "      <th>0</th>\n",
       "      <td>(AL, CR)</td>\n",
       "      <td>HCP_A3</td>\n",
       "      <td>-2.46201666666667e-7*T**3 + 0.000315725*T**2 -...</td>\n",
       "      <td>0.0</td>\n",
       "      <td>-12.818000</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>...</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>-5068.714000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th rowspan=\"2\" valign=\"top\">complex</th>\n",
       "      <th rowspan=\"2\" valign=\"top\">(0.5, 0.5, 3.0)</th>\n",
       "      <th>((A,), (VA,), (VA,))</th>\n",
       "      <th>0</th>\n",
       "      <td>(AL, CR)</td>\n",
       "      <td>BCC_B2</td>\n",
       "      <td>0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>...</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.000000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>((VA,), (A,), (VA,))</th>\n",
       "      <th>0</th>\n",
       "      <td>(AL, CR)</td>\n",
       "      <td>BCC_B2</td>\n",
       "      <td>0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>...</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.000000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th rowspan=\"2\" valign=\"top\">liquid</th>\n",
       "      <th rowspan=\"2\" valign=\"top\">(1.0,)</th>\n",
       "      <th rowspan=\"2\" valign=\"top\">((A, B),)</th>\n",
       "      <th>0</th>\n",
       "      <td>(AL, CR)</td>\n",
       "      <td>LIQUID</td>\n",
       "      <td>-14500</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>...</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>-14500.000000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>(AL, CR)</td>\n",
       "      <td>LIQUID</td>\n",
       "      <td>-5500</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>...</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>-5500.000000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th rowspan=\"2\" valign=\"top\">solid</th>\n",
       "      <th>(1.0, 1.0)</th>\n",
       "      <th>((A, B), (VA,))</th>\n",
       "      <th>0</th>\n",
       "      <td>(AL, CR)</td>\n",
       "      <td>FCC_A1</td>\n",
       "      <td>3*T - 22950</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>...</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>-22950.000000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>(1.0, 3.0)</th>\n",
       "      <th>((A, B), (VA,))</th>\n",
       "      <th>0</th>\n",
       "      <td>(AL, CR)</td>\n",
       "      <td>BCC_A2</td>\n",
       "      <td>5*T - 27450</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>...</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>-27450.000000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th rowspan=\"12\" valign=\"top\">complex</th>\n",
       "      <th rowspan=\"2\" valign=\"top\">(0.5, 0.5, 3.0)</th>\n",
       "      <th>((A,), (B,), (VA,))</th>\n",
       "      <th>0</th>\n",
       "      <td>(AL, CR)</td>\n",
       "      <td>BCC_B2</td>\n",
       "      <td>-1000</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>...</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>-1000.000000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>((B,), (A,), (VA,))</th>\n",
       "      <th>0</th>\n",
       "      <td>(AL, CR)</td>\n",
       "      <td>BCC_B2</td>\n",
       "      <td>-1000</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>...</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>-1000.000000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th rowspan=\"10\" valign=\"top\">(0.75, 0.25, 1.0)</th>\n",
       "      <th>((B,), (A,), (VA,))</th>\n",
       "      <th>0</th>\n",
       "      <td>(AL, CR)</td>\n",
       "      <td>L12_FCC</td>\n",
       "      <td>-1245</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>...</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>-1245.000000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>((A,), (B,), (VA,))</th>\n",
       "      <th>0</th>\n",
       "      <td>(AL, CR)</td>\n",
       "      <td>L12_FCC</td>\n",
       "      <td>-1245</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>...</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>-1245.000000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>((A, B), (A,), (VA,))</th>\n",
       "      <th>0</th>\n",
       "      <td>(AL, CR)</td>\n",
       "      <td>L12_FCC</td>\n",
       "      <td>-2490.00000000000</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>...</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>-2490.000000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>((A, B), (B,), (VA,))</th>\n",
       "      <th>0</th>\n",
       "      <td>(AL, CR)</td>\n",
       "      <td>L12_FCC</td>\n",
       "      <td>-2490.00000000000</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>...</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>-2490.000000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>((A, B), (A,), (VA,))</th>\n",
       "      <th>1</th>\n",
       "      <td>(AL, CR)</td>\n",
       "      <td>L12_FCC</td>\n",
       "      <td>0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>...</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.000000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>((A, B), (B,), (VA,))</th>\n",
       "      <th>1</th>\n",
       "      <td>(AL, CR)</td>\n",
       "      <td>L12_FCC</td>\n",
       "      <td>0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>...</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.000000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th rowspan=\"2\" valign=\"top\">((*,), (A, B), (VA,))</th>\n",
       "      <th>0</th>\n",
       "      <td>(AL, CR)</td>\n",
       "      <td>L12_FCC</td>\n",
       "      <td>0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>...</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.000000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>(AL, CR)</td>\n",
       "      <td>L12_FCC</td>\n",
       "      <td>0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>...</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.000000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th rowspan=\"2\" valign=\"top\">((A, B), (*,), (VA,))</th>\n",
       "      <th>0</th>\n",
       "      <td>(AL, CR)</td>\n",
       "      <td>L12_FCC</td>\n",
       "      <td>0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>...</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.000000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>(AL, CR)</td>\n",
       "      <td>L12_FCC</td>\n",
       "      <td>0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>...</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.000000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th rowspan=\"8\" valign=\"top\">stoichiometric</th>\n",
       "      <th>(10.0, 1.0, 2.0)</th>\n",
       "      <th>((A,), (A,), (B,))</th>\n",
       "      <th>0</th>\n",
       "      <td>(AL, CR)</td>\n",
       "      <td>AL11CR2</td>\n",
       "      <td>-9.62500345833333e-6*T**3 + 0.023521515*T**2 -...</td>\n",
       "      <td>0.0</td>\n",
       "      <td>-155.848251</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>...</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>-144305.234000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>(13.0, 2.0)</th>\n",
       "      <th>((A,), (B,))</th>\n",
       "      <th>0</th>\n",
       "      <td>(AL, CR)</td>\n",
       "      <td>AL13CR2</td>\n",
       "      <td>-1.12854762083333e-5*T**3 + 0.027683345*T**2 -...</td>\n",
       "      <td>0.0</td>\n",
       "      <td>-179.523206</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>...</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>-151390.426000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>(4.0, 1.0)</th>\n",
       "      <th>((A,), (B,))</th>\n",
       "      <th>0</th>\n",
       "      <td>(AL, CR)</td>\n",
       "      <td>AL4CR</td>\n",
       "      <td>-3.56714716666667e-6*T**3 + 0.008639385*T**2 -...</td>\n",
       "      <td>0.0</td>\n",
       "      <td>-60.167910</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>...</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>-67065.598000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th rowspan=\"2\" valign=\"top\">(8.0, 5.0)</th>\n",
       "      <th rowspan=\"2\" valign=\"top\">((A,), (B,))</th>\n",
       "      <th>0</th>\n",
       "      <td>(AL, CR)</td>\n",
       "      <td>AL8CR5_H</td>\n",
       "      <td>-7.87289933333333e-6*T**3 + 0.018225945*T**2 -...</td>\n",
       "      <td>0.0</td>\n",
       "      <td>-158.789819</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>...</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>-140835.338000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>(AL, CR)</td>\n",
       "      <td>AL8CR5_L</td>\n",
       "      <td>-7.87289933333333e-6*T**3 + 0.018225945*T**2 -...</td>\n",
       "      <td>0.0</td>\n",
       "      <td>-158.789819</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>...</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>-181726.838000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th rowspan=\"2\" valign=\"top\">(9.0, 4.0)</th>\n",
       "      <th rowspan=\"2\" valign=\"top\">((A,), (B,))</th>\n",
       "      <th>0</th>\n",
       "      <td>(AL, CR)</td>\n",
       "      <td>AL9CR4_H</td>\n",
       "      <td>-8.45693404166667e-6*T**3 + 0.019991135*T**2 -...</td>\n",
       "      <td>0.0</td>\n",
       "      <td>-157.809297</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>...</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>-130714.470000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>(AL, CR)</td>\n",
       "      <td>AL9CR4_L</td>\n",
       "      <td>-8.45693404166667e-6*T**3 + 0.019991135*T**2 -...</td>\n",
       "      <td>0.0</td>\n",
       "      <td>-157.809297</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>...</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>-178872.970000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>(1.0, 2.0)</th>\n",
       "      <th>((A,), (B,))</th>\n",
       "      <th>0</th>\n",
       "      <td>(AL, CR)</td>\n",
       "      <td>ALCR2</td>\n",
       "      <td>-1.32263970833333e-6*T**3 + 0.002712365*T**2 -...</td>\n",
       "      <td>0.0</td>\n",
       "      <td>-37.473477</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>...</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>-34741.774000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th rowspan=\"3\" valign=\"top\">complex</th>\n",
       "      <th rowspan=\"2\" valign=\"top\">(8.0, 18.0, 4.0)</th>\n",
       "      <th>((A,), (A,), (B,))</th>\n",
       "      <th>0</th>\n",
       "      <td>(AL, CR)</td>\n",
       "      <td>SIGMA_SGTE</td>\n",
       "      <td>-1.50988250416667e-5*T**3 + 0.036638455*T**2 -...</td>\n",
       "      <td>0.0</td>\n",
       "      <td>-252.509116</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>...</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>31918.762000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>((A,), (B,), (B,))</th>\n",
       "      <th>0</th>\n",
       "      <td>(AL, CR)</td>\n",
       "      <td>SIGMA_SGTE</td>\n",
       "      <td>-1.20583276666667e-5*T**3 + 0.02359327*T**2 - ...</td>\n",
       "      <td>0.0</td>\n",
       "      <td>-376.695819</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>...</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>-166917.476000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>(3.0, 2.0, 1.0)</th>\n",
       "      <th>((A,), (A,), (VA,))</th>\n",
       "      <th>0</th>\n",
       "      <td>(AL, CR)</td>\n",
       "      <td>AL3NI2</td>\n",
       "      <td>-4.151181875e-6*T**3 + 0.010404575*T**2 - 59.1...</td>\n",
       "      <td>0.0</td>\n",
       "      <td>-59.187387</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>...</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>21125.770000</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "<p>218 rows × 66 columns</p>\n",
       "</div>"
      ],
      "text/plain": [
       "                                                                          system  \\\n",
       "phase_type     site_ratios       constituent_array     parameter_order             \n",
       "solid          (1.0, 3.0)        ((VA,), (VA,))        0                (CO, NI)   \n",
       "liquid         (1.0,)            ((A,),)               0                (CO, NI)   \n",
       "solid          (1.0, 1.0)        ((A,), (VA,))         0                (CO, NI)   \n",
       "               (1.0, 3.0)        ((A,), (VA,))         0                (CO, NI)   \n",
       "                                 ((A, VA), (VA,))      0                (CO, NI)   \n",
       "               (1.0, 0.5)        ((A,), (VA,))         0                (CO, NI)   \n",
       "complex        (0.5, 0.5, 3.0)   ((A,), (VA,), (VA,))  0                (CO, NI)   \n",
       "                                 ((VA,), (A,), (VA,))  0                (CO, NI)   \n",
       "liquid         (1.0,)            ((A,),)               0                (CO, NI)   \n",
       "solid          (1.0, 1.0)        ((A,), (VA,))         0                (CO, NI)   \n",
       "               (1.0, 3.0)        ((A,), (VA,))         0                (CO, NI)   \n",
       "                                 ((A, VA), (VA,))      0                (CO, NI)   \n",
       "               (1.0, 0.5)        ((A,), (VA,))         0                (CO, NI)   \n",
       "complex        (0.5, 0.5, 3.0)   ((VA,), (A,), (VA,))  0                (CO, NI)   \n",
       "                                 ((A,), (VA,), (VA,))  0                (CO, NI)   \n",
       "liquid         (1.0,)            ((A, B),)             0                (CO, NI)   \n",
       "solid          (1.0, 1.0)        ((A, B), (VA,))       0                (CO, NI)   \n",
       "               (1.0, 3.0)        ((A, B), (VA,))       0                (CO, NI)   \n",
       "               (1.0, 0.5)        ((A, B), (VA,))       0                (CO, NI)   \n",
       "complex        (0.5, 0.5, 3.0)   ((A,), (B,), (VA,))   0                (CO, NI)   \n",
       "                                 ((B,), (A,), (VA,))   0                (CO, NI)   \n",
       "               (0.75, 0.25, 1.0) ((B,), (A,), (VA,))   0                (CO, NI)   \n",
       "                                 ((A,), (B,), (VA,))   0                (CO, NI)   \n",
       "                                 ((A, B), (A,), (VA,)) 0                (CO, NI)   \n",
       "                                 ((A, B), (B,), (VA,)) 0                (CO, NI)   \n",
       "                                 ((A, B), (A,), (VA,)) 1                (CO, NI)   \n",
       "                                 ((A, B), (B,), (VA,)) 1                (CO, NI)   \n",
       "                                 ((*,), (A, B), (VA,)) 0                (CO, NI)   \n",
       "                                                       1                (CO, NI)   \n",
       "                                 ((A, B), (*,), (VA,)) 0                (CO, NI)   \n",
       "...                                                                          ...   \n",
       "solid          (1.0, 0.5)        ((A,), (VA,))         0                (AL, CR)   \n",
       "complex        (0.5, 0.5, 3.0)   ((A,), (VA,), (VA,))  0                (AL, CR)   \n",
       "                                 ((VA,), (A,), (VA,))  0                (AL, CR)   \n",
       "liquid         (1.0,)            ((A, B),)             0                (AL, CR)   \n",
       "                                                       1                (AL, CR)   \n",
       "solid          (1.0, 1.0)        ((A, B), (VA,))       0                (AL, CR)   \n",
       "               (1.0, 3.0)        ((A, B), (VA,))       0                (AL, CR)   \n",
       "complex        (0.5, 0.5, 3.0)   ((A,), (B,), (VA,))   0                (AL, CR)   \n",
       "                                 ((B,), (A,), (VA,))   0                (AL, CR)   \n",
       "               (0.75, 0.25, 1.0) ((B,), (A,), (VA,))   0                (AL, CR)   \n",
       "                                 ((A,), (B,), (VA,))   0                (AL, CR)   \n",
       "                                 ((A, B), (A,), (VA,)) 0                (AL, CR)   \n",
       "                                 ((A, B), (B,), (VA,)) 0                (AL, CR)   \n",
       "                                 ((A, B), (A,), (VA,)) 1                (AL, CR)   \n",
       "                                 ((A, B), (B,), (VA,)) 1                (AL, CR)   \n",
       "                                 ((*,), (A, B), (VA,)) 0                (AL, CR)   \n",
       "                                                       1                (AL, CR)   \n",
       "                                 ((A, B), (*,), (VA,)) 0                (AL, CR)   \n",
       "                                                       1                (AL, CR)   \n",
       "stoichiometric (10.0, 1.0, 2.0)  ((A,), (A,), (B,))    0                (AL, CR)   \n",
       "               (13.0, 2.0)       ((A,), (B,))          0                (AL, CR)   \n",
       "               (4.0, 1.0)        ((A,), (B,))          0                (AL, CR)   \n",
       "               (8.0, 5.0)        ((A,), (B,))          0                (AL, CR)   \n",
       "                                                       0                (AL, CR)   \n",
       "               (9.0, 4.0)        ((A,), (B,))          0                (AL, CR)   \n",
       "                                                       0                (AL, CR)   \n",
       "               (1.0, 2.0)        ((A,), (B,))          0                (AL, CR)   \n",
       "complex        (8.0, 18.0, 4.0)  ((A,), (A,), (B,))    0                (AL, CR)   \n",
       "                                 ((A,), (B,), (B,))    0                (AL, CR)   \n",
       "               (3.0, 2.0, 1.0)   ((A,), (A,), (VA,))   0                (AL, CR)   \n",
       "\n",
       "                                                                        phase_name  \\\n",
       "phase_type     site_ratios       constituent_array     parameter_order               \n",
       "solid          (1.0, 3.0)        ((VA,), (VA,))        0                    BCC_A2   \n",
       "liquid         (1.0,)            ((A,),)               0                    LIQUID   \n",
       "solid          (1.0, 1.0)        ((A,), (VA,))         0                    FCC_A1   \n",
       "               (1.0, 3.0)        ((A,), (VA,))         0                    BCC_A2   \n",
       "                                 ((A, VA), (VA,))      0                    BCC_A2   \n",
       "               (1.0, 0.5)        ((A,), (VA,))         0                    HCP_A3   \n",
       "complex        (0.5, 0.5, 3.0)   ((A,), (VA,), (VA,))  0                    BCC_B2   \n",
       "                                 ((VA,), (A,), (VA,))  0                    BCC_B2   \n",
       "liquid         (1.0,)            ((A,),)               0                    LIQUID   \n",
       "solid          (1.0, 1.0)        ((A,), (VA,))         0                    FCC_A1   \n",
       "               (1.0, 3.0)        ((A,), (VA,))         0                    BCC_A2   \n",
       "                                 ((A, VA), (VA,))      0                    BCC_A2   \n",
       "               (1.0, 0.5)        ((A,), (VA,))         0                    HCP_A3   \n",
       "complex        (0.5, 0.5, 3.0)   ((VA,), (A,), (VA,))  0                    BCC_B2   \n",
       "                                 ((A,), (VA,), (VA,))  0                    BCC_B2   \n",
       "liquid         (1.0,)            ((A, B),)             0                    LIQUID   \n",
       "solid          (1.0, 1.0)        ((A, B), (VA,))       0                    FCC_A1   \n",
       "               (1.0, 3.0)        ((A, B), (VA,))       0                    BCC_A2   \n",
       "               (1.0, 0.5)        ((A, B), (VA,))       0                    HCP_A3   \n",
       "complex        (0.5, 0.5, 3.0)   ((A,), (B,), (VA,))   0                    BCC_B2   \n",
       "                                 ((B,), (A,), (VA,))   0                    BCC_B2   \n",
       "               (0.75, 0.25, 1.0) ((B,), (A,), (VA,))   0                   L12_FCC   \n",
       "                                 ((A,), (B,), (VA,))   0                   L12_FCC   \n",
       "                                 ((A, B), (A,), (VA,)) 0                   L12_FCC   \n",
       "                                 ((A, B), (B,), (VA,)) 0                   L12_FCC   \n",
       "                                 ((A, B), (A,), (VA,)) 1                   L12_FCC   \n",
       "                                 ((A, B), (B,), (VA,)) 1                   L12_FCC   \n",
       "                                 ((*,), (A, B), (VA,)) 0                   L12_FCC   \n",
       "                                                       1                   L12_FCC   \n",
       "                                 ((A, B), (*,), (VA,)) 0                   L12_FCC   \n",
       "...                                                                            ...   \n",
       "solid          (1.0, 0.5)        ((A,), (VA,))         0                    HCP_A3   \n",
       "complex        (0.5, 0.5, 3.0)   ((A,), (VA,), (VA,))  0                    BCC_B2   \n",
       "                                 ((VA,), (A,), (VA,))  0                    BCC_B2   \n",
       "liquid         (1.0,)            ((A, B),)             0                    LIQUID   \n",
       "                                                       1                    LIQUID   \n",
       "solid          (1.0, 1.0)        ((A, B), (VA,))       0                    FCC_A1   \n",
       "               (1.0, 3.0)        ((A, B), (VA,))       0                    BCC_A2   \n",
       "complex        (0.5, 0.5, 3.0)   ((A,), (B,), (VA,))   0                    BCC_B2   \n",
       "                                 ((B,), (A,), (VA,))   0                    BCC_B2   \n",
       "               (0.75, 0.25, 1.0) ((B,), (A,), (VA,))   0                   L12_FCC   \n",
       "                                 ((A,), (B,), (VA,))   0                   L12_FCC   \n",
       "                                 ((A, B), (A,), (VA,)) 0                   L12_FCC   \n",
       "                                 ((A, B), (B,), (VA,)) 0                   L12_FCC   \n",
       "                                 ((A, B), (A,), (VA,)) 1                   L12_FCC   \n",
       "                                 ((A, B), (B,), (VA,)) 1                   L12_FCC   \n",
       "                                 ((*,), (A, B), (VA,)) 0                   L12_FCC   \n",
       "                                                       1                   L12_FCC   \n",
       "                                 ((A, B), (*,), (VA,)) 0                   L12_FCC   \n",
       "                                                       1                   L12_FCC   \n",
       "stoichiometric (10.0, 1.0, 2.0)  ((A,), (A,), (B,))    0                   AL11CR2   \n",
       "               (13.0, 2.0)       ((A,), (B,))          0                   AL13CR2   \n",
       "               (4.0, 1.0)        ((A,), (B,))          0                     AL4CR   \n",
       "               (8.0, 5.0)        ((A,), (B,))          0                  AL8CR5_H   \n",
       "                                                       0                  AL8CR5_L   \n",
       "               (9.0, 4.0)        ((A,), (B,))          0                  AL9CR4_H   \n",
       "                                                       0                  AL9CR4_L   \n",
       "               (1.0, 2.0)        ((A,), (B,))          0                     ALCR2   \n",
       "complex        (8.0, 18.0, 4.0)  ((A,), (A,), (B,))    0                SIGMA_SGTE   \n",
       "                                 ((A,), (B,), (B,))    0                SIGMA_SGTE   \n",
       "               (3.0, 2.0, 1.0)   ((A,), (A,), (VA,))   0                    AL3NI2   \n",
       "\n",
       "                                                                                                          parameter_value  \\\n",
       "phase_type     site_ratios       constituent_array     parameter_order                                                      \n",
       "solid          (1.0, 3.0)        ((VA,), (VA,))        0                                                                0   \n",
       "liquid         (1.0,)            ((A,),)               0                -7.3267e-22*T**7 - 5.78266666666667e-8*T**3 - ...   \n",
       "solid          (1.0, 1.0)        ((A,), (VA,))         0                -2.89133333333333e-8*T**3 - 0.0004424565*T**2 ...   \n",
       "               (1.0, 3.0)        ((A,), (VA,))         0                -2.89133333333333e-8*T**3 - 0.0004424565*T**2 ...   \n",
       "                                 ((A, VA), (VA,))      0                                                -35.045*T + 96765   \n",
       "               (1.0, 0.5)        ((A,), (VA,))         0                -2.89133333333333e-8*T**3 - 0.0004424565*T**2 ...   \n",
       "complex        (0.5, 0.5, 3.0)   ((A,), (VA,), (VA,))  0                                              -0.2875*T + 25867.5   \n",
       "                                 ((VA,), (A,), (VA,))  0                                              -0.2875*T + 25867.5   \n",
       "liquid         (1.0,)            ((A,),)               0                -1.27439333333333e-21*T**7 - 0.000537855555555...   \n",
       "solid          (1.0, 1.0)        ((A,), (VA,))         0                -0.000806783333333333*T**2 - 10.866*T*log(T) +...   \n",
       "               (1.0, 3.0)        ((A,), (VA,))         0                -0.000806783333333333*T**2 - 10.866*T*log(T) +...   \n",
       "                                 ((A, VA), (VA,))      0                                            -0.22789*T + 24593.23   \n",
       "               (1.0, 0.5)        ((A,), (VA,))         0                -0.000806783333333333*T**2 - 10.866*T*log(T) +...   \n",
       "complex        (0.5, 0.5, 3.0)   ((VA,), (A,), (VA,))  0                                          -6.7374925*T + 28302.71   \n",
       "                                 ((A,), (VA,), (VA,))  0                                          -6.7374925*T + 28302.71   \n",
       "liquid         (1.0,)            ((A, B),)             0                                                           1331/2   \n",
       "solid          (1.0, 1.0)        ((A, B), (VA,))       0                                                  0.63145*T - 400   \n",
       "               (1.0, 3.0)        ((A, B), (VA,))       0                                                             1000   \n",
       "               (1.0, 0.5)        ((A, B), (VA,))       0                                                  -0.1925*T - 810   \n",
       "complex        (0.5, 0.5, 3.0)   ((A,), (B,), (VA,))   0                                                -0.832*T + 1932.0   \n",
       "                                 ((B,), (A,), (VA,))   0                                                -0.832*T + 1932.0   \n",
       "               (0.75, 0.25, 1.0) ((B,), (A,), (VA,))   0                                                                0   \n",
       "                                 ((A,), (B,), (VA,))   0                                                                0   \n",
       "                                 ((A, B), (A,), (VA,)) 0                                                                0   \n",
       "                                 ((A, B), (B,), (VA,)) 0                                                                0   \n",
       "                                 ((A, B), (A,), (VA,)) 1                                                                0   \n",
       "                                 ((A, B), (B,), (VA,)) 1                                                                0   \n",
       "                                 ((*,), (A, B), (VA,)) 0                                                                0   \n",
       "                                                       1                                                                0   \n",
       "                                 ((A, B), (*,), (VA,)) 0                                                                0   \n",
       "...                                                                                                                   ...   \n",
       "solid          (1.0, 0.5)        ((A,), (VA,))         0                -2.46201666666667e-7*T**3 + 0.000315725*T**2 -...   \n",
       "complex        (0.5, 0.5, 3.0)   ((A,), (VA,), (VA,))  0                                                                0   \n",
       "                                 ((VA,), (A,), (VA,))  0                                                                0   \n",
       "liquid         (1.0,)            ((A, B),)             0                                                           -14500   \n",
       "                                                       1                                                            -5500   \n",
       "solid          (1.0, 1.0)        ((A, B), (VA,))       0                                                      3*T - 22950   \n",
       "               (1.0, 3.0)        ((A, B), (VA,))       0                                                      5*T - 27450   \n",
       "complex        (0.5, 0.5, 3.0)   ((A,), (B,), (VA,))   0                                                            -1000   \n",
       "                                 ((B,), (A,), (VA,))   0                                                            -1000   \n",
       "               (0.75, 0.25, 1.0) ((B,), (A,), (VA,))   0                                                            -1245   \n",
       "                                 ((A,), (B,), (VA,))   0                                                            -1245   \n",
       "                                 ((A, B), (A,), (VA,)) 0                                                -2490.00000000000   \n",
       "                                 ((A, B), (B,), (VA,)) 0                                                -2490.00000000000   \n",
       "                                 ((A, B), (A,), (VA,)) 1                                                                0   \n",
       "                                 ((A, B), (B,), (VA,)) 1                                                                0   \n",
       "                                 ((*,), (A, B), (VA,)) 0                                                                0   \n",
       "                                                       1                                                                0   \n",
       "                                 ((A, B), (*,), (VA,)) 0                                                                0   \n",
       "                                                       1                                                                0   \n",
       "stoichiometric (10.0, 1.0, 2.0)  ((A,), (A,), (B,))    0                -9.62500345833333e-6*T**3 + 0.023521515*T**2 -...   \n",
       "               (13.0, 2.0)       ((A,), (B,))          0                -1.12854762083333e-5*T**3 + 0.027683345*T**2 -...   \n",
       "               (4.0, 1.0)        ((A,), (B,))          0                -3.56714716666667e-6*T**3 + 0.008639385*T**2 -...   \n",
       "               (8.0, 5.0)        ((A,), (B,))          0                -7.87289933333333e-6*T**3 + 0.018225945*T**2 -...   \n",
       "                                                       0                -7.87289933333333e-6*T**3 + 0.018225945*T**2 -...   \n",
       "               (9.0, 4.0)        ((A,), (B,))          0                -8.45693404166667e-6*T**3 + 0.019991135*T**2 -...   \n",
       "                                                       0                -8.45693404166667e-6*T**3 + 0.019991135*T**2 -...   \n",
       "               (1.0, 2.0)        ((A,), (B,))          0                -1.32263970833333e-6*T**3 + 0.002712365*T**2 -...   \n",
       "complex        (8.0, 18.0, 4.0)  ((A,), (A,), (B,))    0                -1.50988250416667e-5*T**3 + 0.036638455*T**2 -...   \n",
       "                                 ((A,), (B,), (B,))    0                -1.20583276666667e-5*T**3 + 0.02359327*T**2 - ...   \n",
       "               (3.0, 2.0, 1.0)   ((A,), (A,), (VA,))   0                -4.151181875e-6*T**3 + 0.010404575*T**2 - 59.1...   \n",
       "\n",
       "                                                                        T*log(1.0e-5*P)  \\\n",
       "phase_type     site_ratios       constituent_array     parameter_order                    \n",
       "solid          (1.0, 3.0)        ((VA,), (VA,))        0                            0.0   \n",
       "liquid         (1.0,)            ((A,),)               0                            0.0   \n",
       "solid          (1.0, 1.0)        ((A,), (VA,))         0                            0.0   \n",
       "               (1.0, 3.0)        ((A,), (VA,))         0                            0.0   \n",
       "                                 ((A, VA), (VA,))      0                            0.0   \n",
       "               (1.0, 0.5)        ((A,), (VA,))         0                            0.0   \n",
       "complex        (0.5, 0.5, 3.0)   ((A,), (VA,), (VA,))  0                            0.0   \n",
       "                                 ((VA,), (A,), (VA,))  0                            0.0   \n",
       "liquid         (1.0,)            ((A,),)               0                            0.0   \n",
       "solid          (1.0, 1.0)        ((A,), (VA,))         0                            0.0   \n",
       "               (1.0, 3.0)        ((A,), (VA,))         0                            0.0   \n",
       "                                 ((A, VA), (VA,))      0                            0.0   \n",
       "               (1.0, 0.5)        ((A,), (VA,))         0                            0.0   \n",
       "complex        (0.5, 0.5, 3.0)   ((VA,), (A,), (VA,))  0                            0.0   \n",
       "                                 ((A,), (VA,), (VA,))  0                            0.0   \n",
       "liquid         (1.0,)            ((A, B),)             0                            0.0   \n",
       "solid          (1.0, 1.0)        ((A, B), (VA,))       0                            0.0   \n",
       "               (1.0, 3.0)        ((A, B), (VA,))       0                            0.0   \n",
       "               (1.0, 0.5)        ((A, B), (VA,))       0                            0.0   \n",
       "complex        (0.5, 0.5, 3.0)   ((A,), (B,), (VA,))   0                            0.0   \n",
       "                                 ((B,), (A,), (VA,))   0                            0.0   \n",
       "               (0.75, 0.25, 1.0) ((B,), (A,), (VA,))   0                            0.0   \n",
       "                                 ((A,), (B,), (VA,))   0                            0.0   \n",
       "                                 ((A, B), (A,), (VA,)) 0                            0.0   \n",
       "                                 ((A, B), (B,), (VA,)) 0                            0.0   \n",
       "                                 ((A, B), (A,), (VA,)) 1                            0.0   \n",
       "                                 ((A, B), (B,), (VA,)) 1                            0.0   \n",
       "                                 ((*,), (A, B), (VA,)) 0                            0.0   \n",
       "                                                       1                            0.0   \n",
       "                                 ((A, B), (*,), (VA,)) 0                            0.0   \n",
       "...                                                                                 ...   \n",
       "solid          (1.0, 0.5)        ((A,), (VA,))         0                            0.0   \n",
       "complex        (0.5, 0.5, 3.0)   ((A,), (VA,), (VA,))  0                            0.0   \n",
       "                                 ((VA,), (A,), (VA,))  0                            0.0   \n",
       "liquid         (1.0,)            ((A, B),)             0                            0.0   \n",
       "                                                       1                            0.0   \n",
       "solid          (1.0, 1.0)        ((A, B), (VA,))       0                            0.0   \n",
       "               (1.0, 3.0)        ((A, B), (VA,))       0                            0.0   \n",
       "complex        (0.5, 0.5, 3.0)   ((A,), (B,), (VA,))   0                            0.0   \n",
       "                                 ((B,), (A,), (VA,))   0                            0.0   \n",
       "               (0.75, 0.25, 1.0) ((B,), (A,), (VA,))   0                            0.0   \n",
       "                                 ((A,), (B,), (VA,))   0                            0.0   \n",
       "                                 ((A, B), (A,), (VA,)) 0                            0.0   \n",
       "                                 ((A, B), (B,), (VA,)) 0                            0.0   \n",
       "                                 ((A, B), (A,), (VA,)) 1                            0.0   \n",
       "                                 ((A, B), (B,), (VA,)) 1                            0.0   \n",
       "                                 ((*,), (A, B), (VA,)) 0                            0.0   \n",
       "                                                       1                            0.0   \n",
       "                                 ((A, B), (*,), (VA,)) 0                            0.0   \n",
       "                                                       1                            0.0   \n",
       "stoichiometric (10.0, 1.0, 2.0)  ((A,), (A,), (B,))    0                            0.0   \n",
       "               (13.0, 2.0)       ((A,), (B,))          0                            0.0   \n",
       "               (4.0, 1.0)        ((A,), (B,))          0                            0.0   \n",
       "               (8.0, 5.0)        ((A,), (B,))          0                            0.0   \n",
       "                                                       0                            0.0   \n",
       "               (9.0, 4.0)        ((A,), (B,))          0                            0.0   \n",
       "                                                       0                            0.0   \n",
       "               (1.0, 2.0)        ((A,), (B,))          0                            0.0   \n",
       "complex        (8.0, 18.0, 4.0)  ((A,), (A,), (B,))    0                            0.0   \n",
       "                                 ((A,), (B,), (B,))    0                            0.0   \n",
       "               (3.0, 2.0, 1.0)   ((A,), (A,), (VA,))   0                            0.0   \n",
       "\n",
       "                                                                          T*log(T)  \\\n",
       "phase_type     site_ratios       constituent_array     parameter_order               \n",
       "solid          (1.0, 3.0)        ((VA,), (VA,))        0                  0.000000   \n",
       "liquid         (1.0,)            ((A,),)               0                -21.862033   \n",
       "solid          (1.0, 1.0)        ((A,), (VA,))         0                -10.931017   \n",
       "               (1.0, 3.0)        ((A,), (VA,))         0                -10.931017   \n",
       "                                 ((A, VA), (VA,))      0                  0.000000   \n",
       "               (1.0, 0.5)        ((A,), (VA,))         0                -10.931017   \n",
       "complex        (0.5, 0.5, 3.0)   ((A,), (VA,), (VA,))  0                  0.000000   \n",
       "                                 ((VA,), (A,), (VA,))  0                  0.000000   \n",
       "liquid         (1.0,)            ((A,),)               0                -21.610667   \n",
       "solid          (1.0, 1.0)        ((A,), (VA,))         0                -10.866000   \n",
       "               (1.0, 3.0)        ((A,), (VA,))         0                -10.866000   \n",
       "                                 ((A, VA), (VA,))      0                  0.000000   \n",
       "               (1.0, 0.5)        ((A,), (VA,))         0                -10.866000   \n",
       "complex        (0.5, 0.5, 3.0)   ((VA,), (A,), (VA,))  0                  0.000000   \n",
       "                                 ((A,), (VA,), (VA,))  0                  0.000000   \n",
       "liquid         (1.0,)            ((A, B),)             0                  0.000000   \n",
       "solid          (1.0, 1.0)        ((A, B), (VA,))       0                  0.000000   \n",
       "               (1.0, 3.0)        ((A, B), (VA,))       0                  0.000000   \n",
       "               (1.0, 0.5)        ((A, B), (VA,))       0                  0.000000   \n",
       "complex        (0.5, 0.5, 3.0)   ((A,), (B,), (VA,))   0                  0.000000   \n",
       "                                 ((B,), (A,), (VA,))   0                  0.000000   \n",
       "               (0.75, 0.25, 1.0) ((B,), (A,), (VA,))   0                  0.000000   \n",
       "                                 ((A,), (B,), (VA,))   0                  0.000000   \n",
       "                                 ((A, B), (A,), (VA,)) 0                  0.000000   \n",
       "                                 ((A, B), (B,), (VA,)) 0                  0.000000   \n",
       "                                 ((A, B), (A,), (VA,)) 1                  0.000000   \n",
       "                                 ((A, B), (B,), (VA,)) 1                  0.000000   \n",
       "                                 ((*,), (A, B), (VA,)) 0                  0.000000   \n",
       "                                                       1                  0.000000   \n",
       "                                 ((A, B), (*,), (VA,)) 0                  0.000000   \n",
       "...                                                                            ...   \n",
       "solid          (1.0, 0.5)        ((A,), (VA,))         0                -12.818000   \n",
       "complex        (0.5, 0.5, 3.0)   ((A,), (VA,), (VA,))  0                  0.000000   \n",
       "                                 ((VA,), (A,), (VA,))  0                  0.000000   \n",
       "liquid         (1.0,)            ((A, B),)             0                  0.000000   \n",
       "                                                       1                  0.000000   \n",
       "solid          (1.0, 1.0)        ((A, B), (VA,))       0                  0.000000   \n",
       "               (1.0, 3.0)        ((A, B), (VA,))       0                  0.000000   \n",
       "complex        (0.5, 0.5, 3.0)   ((A,), (B,), (VA,))   0                  0.000000   \n",
       "                                 ((B,), (A,), (VA,))   0                  0.000000   \n",
       "               (0.75, 0.25, 1.0) ((B,), (A,), (VA,))   0                  0.000000   \n",
       "                                 ((A,), (B,), (VA,))   0                  0.000000   \n",
       "                                 ((A, B), (A,), (VA,)) 0                  0.000000   \n",
       "                                 ((A, B), (B,), (VA,)) 0                  0.000000   \n",
       "                                 ((A, B), (A,), (VA,)) 1                  0.000000   \n",
       "                                 ((A, B), (B,), (VA,)) 1                  0.000000   \n",
       "                                 ((*,), (A, B), (VA,)) 0                  0.000000   \n",
       "                                                       1                  0.000000   \n",
       "                                 ((A, B), (*,), (VA,)) 0                  0.000000   \n",
       "                                                       1                  0.000000   \n",
       "stoichiometric (10.0, 1.0, 2.0)  ((A,), (A,), (B,))    0               -155.848251   \n",
       "               (13.0, 2.0)       ((A,), (B,))          0               -179.523206   \n",
       "               (4.0, 1.0)        ((A,), (B,))          0                -60.167910   \n",
       "               (8.0, 5.0)        ((A,), (B,))          0               -158.789819   \n",
       "                                                       0               -158.789819   \n",
       "               (9.0, 4.0)        ((A,), (B,))          0               -157.809297   \n",
       "                                                       0               -157.809297   \n",
       "               (1.0, 2.0)        ((A,), (B,))          0                -37.473477   \n",
       "complex        (8.0, 18.0, 4.0)  ((A,), (A,), (B,))    0               -252.509116   \n",
       "                                 ((A,), (B,), (B,))    0               -376.695819   \n",
       "               (3.0, 2.0, 1.0)   ((A,), (A,), (VA,))   0                -59.187387   \n",
       "\n",
       "                                                                        log(T)  \\\n",
       "phase_type     site_ratios       constituent_array     parameter_order           \n",
       "solid          (1.0, 3.0)        ((VA,), (VA,))        0                   0.0   \n",
       "liquid         (1.0,)            ((A,),)               0                   0.0   \n",
       "solid          (1.0, 1.0)        ((A,), (VA,))         0                   0.0   \n",
       "               (1.0, 3.0)        ((A,), (VA,))         0                   0.0   \n",
       "                                 ((A, VA), (VA,))      0                   0.0   \n",
       "               (1.0, 0.5)        ((A,), (VA,))         0                   0.0   \n",
       "complex        (0.5, 0.5, 3.0)   ((A,), (VA,), (VA,))  0                   0.0   \n",
       "                                 ((VA,), (A,), (VA,))  0                   0.0   \n",
       "liquid         (1.0,)            ((A,),)               0                   0.0   \n",
       "solid          (1.0, 1.0)        ((A,), (VA,))         0                   0.0   \n",
       "               (1.0, 3.0)        ((A,), (VA,))         0                   0.0   \n",
       "                                 ((A, VA), (VA,))      0                   0.0   \n",
       "               (1.0, 0.5)        ((A,), (VA,))         0                   0.0   \n",
       "complex        (0.5, 0.5, 3.0)   ((VA,), (A,), (VA,))  0                   0.0   \n",
       "                                 ((A,), (VA,), (VA,))  0                   0.0   \n",
       "liquid         (1.0,)            ((A, B),)             0                   0.0   \n",
       "solid          (1.0, 1.0)        ((A, B), (VA,))       0                   0.0   \n",
       "               (1.0, 3.0)        ((A, B), (VA,))       0                   0.0   \n",
       "               (1.0, 0.5)        ((A, B), (VA,))       0                   0.0   \n",
       "complex        (0.5, 0.5, 3.0)   ((A,), (B,), (VA,))   0                   0.0   \n",
       "                                 ((B,), (A,), (VA,))   0                   0.0   \n",
       "               (0.75, 0.25, 1.0) ((B,), (A,), (VA,))   0                   0.0   \n",
       "                                 ((A,), (B,), (VA,))   0                   0.0   \n",
       "                                 ((A, B), (A,), (VA,)) 0                   0.0   \n",
       "                                 ((A, B), (B,), (VA,)) 0                   0.0   \n",
       "                                 ((A, B), (A,), (VA,)) 1                   0.0   \n",
       "                                 ((A, B), (B,), (VA,)) 1                   0.0   \n",
       "                                 ((*,), (A, B), (VA,)) 0                   0.0   \n",
       "                                                       1                   0.0   \n",
       "                                 ((A, B), (*,), (VA,)) 0                   0.0   \n",
       "...                                                                        ...   \n",
       "solid          (1.0, 0.5)        ((A,), (VA,))         0                   0.0   \n",
       "complex        (0.5, 0.5, 3.0)   ((A,), (VA,), (VA,))  0                   0.0   \n",
       "                                 ((VA,), (A,), (VA,))  0                   0.0   \n",
       "liquid         (1.0,)            ((A, B),)             0                   0.0   \n",
       "                                                       1                   0.0   \n",
       "solid          (1.0, 1.0)        ((A, B), (VA,))       0                   0.0   \n",
       "               (1.0, 3.0)        ((A, B), (VA,))       0                   0.0   \n",
       "complex        (0.5, 0.5, 3.0)   ((A,), (B,), (VA,))   0                   0.0   \n",
       "                                 ((B,), (A,), (VA,))   0                   0.0   \n",
       "               (0.75, 0.25, 1.0) ((B,), (A,), (VA,))   0                   0.0   \n",
       "                                 ((A,), (B,), (VA,))   0                   0.0   \n",
       "                                 ((A, B), (A,), (VA,)) 0                   0.0   \n",
       "                                 ((A, B), (B,), (VA,)) 0                   0.0   \n",
       "                                 ((A, B), (A,), (VA,)) 1                   0.0   \n",
       "                                 ((A, B), (B,), (VA,)) 1                   0.0   \n",
       "                                 ((*,), (A, B), (VA,)) 0                   0.0   \n",
       "                                                       1                   0.0   \n",
       "                                 ((A, B), (*,), (VA,)) 0                   0.0   \n",
       "                                                       1                   0.0   \n",
       "stoichiometric (10.0, 1.0, 2.0)  ((A,), (A,), (B,))    0                   0.0   \n",
       "               (13.0, 2.0)       ((A,), (B,))          0                   0.0   \n",
       "               (4.0, 1.0)        ((A,), (B,))          0                   0.0   \n",
       "               (8.0, 5.0)        ((A,), (B,))          0                   0.0   \n",
       "                                                       0                   0.0   \n",
       "               (9.0, 4.0)        ((A,), (B,))          0                   0.0   \n",
       "                                                       0                   0.0   \n",
       "               (1.0, 2.0)        ((A,), (B,))          0                   0.0   \n",
       "complex        (8.0, 18.0, 4.0)  ((A,), (A,), (B,))    0                   0.0   \n",
       "                                 ((A,), (B,), (B,))    0                   0.0   \n",
       "               (3.0, 2.0, 1.0)   ((A,), (A,), (VA,))   0                   0.0   \n",
       "\n",
       "                                                                        T**(-30)  \\\n",
       "phase_type     site_ratios       constituent_array     parameter_order             \n",
       "solid          (1.0, 3.0)        ((VA,), (VA,))        0                     0.0   \n",
       "liquid         (1.0,)            ((A,),)               0                     0.0   \n",
       "solid          (1.0, 1.0)        ((A,), (VA,))         0                     0.0   \n",
       "               (1.0, 3.0)        ((A,), (VA,))         0                     0.0   \n",
       "                                 ((A, VA), (VA,))      0                     0.0   \n",
       "               (1.0, 0.5)        ((A,), (VA,))         0                     0.0   \n",
       "complex        (0.5, 0.5, 3.0)   ((A,), (VA,), (VA,))  0                     0.0   \n",
       "                                 ((VA,), (A,), (VA,))  0                     0.0   \n",
       "liquid         (1.0,)            ((A,),)               0                     0.0   \n",
       "solid          (1.0, 1.0)        ((A,), (VA,))         0                     0.0   \n",
       "               (1.0, 3.0)        ((A,), (VA,))         0                     0.0   \n",
       "                                 ((A, VA), (VA,))      0                     0.0   \n",
       "               (1.0, 0.5)        ((A,), (VA,))         0                     0.0   \n",
       "complex        (0.5, 0.5, 3.0)   ((VA,), (A,), (VA,))  0                     0.0   \n",
       "                                 ((A,), (VA,), (VA,))  0                     0.0   \n",
       "liquid         (1.0,)            ((A, B),)             0                     0.0   \n",
       "solid          (1.0, 1.0)        ((A, B), (VA,))       0                     0.0   \n",
       "               (1.0, 3.0)        ((A, B), (VA,))       0                     0.0   \n",
       "               (1.0, 0.5)        ((A, B), (VA,))       0                     0.0   \n",
       "complex        (0.5, 0.5, 3.0)   ((A,), (B,), (VA,))   0                     0.0   \n",
       "                                 ((B,), (A,), (VA,))   0                     0.0   \n",
       "               (0.75, 0.25, 1.0) ((B,), (A,), (VA,))   0                     0.0   \n",
       "                                 ((A,), (B,), (VA,))   0                     0.0   \n",
       "                                 ((A, B), (A,), (VA,)) 0                     0.0   \n",
       "                                 ((A, B), (B,), (VA,)) 0                     0.0   \n",
       "                                 ((A, B), (A,), (VA,)) 1                     0.0   \n",
       "                                 ((A, B), (B,), (VA,)) 1                     0.0   \n",
       "                                 ((*,), (A, B), (VA,)) 0                     0.0   \n",
       "                                                       1                     0.0   \n",
       "                                 ((A, B), (*,), (VA,)) 0                     0.0   \n",
       "...                                                                          ...   \n",
       "solid          (1.0, 0.5)        ((A,), (VA,))         0                     0.0   \n",
       "complex        (0.5, 0.5, 3.0)   ((A,), (VA,), (VA,))  0                     0.0   \n",
       "                                 ((VA,), (A,), (VA,))  0                     0.0   \n",
       "liquid         (1.0,)            ((A, B),)             0                     0.0   \n",
       "                                                       1                     0.0   \n",
       "solid          (1.0, 1.0)        ((A, B), (VA,))       0                     0.0   \n",
       "               (1.0, 3.0)        ((A, B), (VA,))       0                     0.0   \n",
       "complex        (0.5, 0.5, 3.0)   ((A,), (B,), (VA,))   0                     0.0   \n",
       "                                 ((B,), (A,), (VA,))   0                     0.0   \n",
       "               (0.75, 0.25, 1.0) ((B,), (A,), (VA,))   0                     0.0   \n",
       "                                 ((A,), (B,), (VA,))   0                     0.0   \n",
       "                                 ((A, B), (A,), (VA,)) 0                     0.0   \n",
       "                                 ((A, B), (B,), (VA,)) 0                     0.0   \n",
       "                                 ((A, B), (A,), (VA,)) 1                     0.0   \n",
       "                                 ((A, B), (B,), (VA,)) 1                     0.0   \n",
       "                                 ((*,), (A, B), (VA,)) 0                     0.0   \n",
       "                                                       1                     0.0   \n",
       "                                 ((A, B), (*,), (VA,)) 0                     0.0   \n",
       "                                                       1                     0.0   \n",
       "stoichiometric (10.0, 1.0, 2.0)  ((A,), (A,), (B,))    0                     0.0   \n",
       "               (13.0, 2.0)       ((A,), (B,))          0                     0.0   \n",
       "               (4.0, 1.0)        ((A,), (B,))          0                     0.0   \n",
       "               (8.0, 5.0)        ((A,), (B,))          0                     0.0   \n",
       "                                                       0                     0.0   \n",
       "               (9.0, 4.0)        ((A,), (B,))          0                     0.0   \n",
       "                                                       0                     0.0   \n",
       "               (1.0, 2.0)        ((A,), (B,))          0                     0.0   \n",
       "complex        (8.0, 18.0, 4.0)  ((A,), (A,), (B,))    0                     0.0   \n",
       "                                 ((A,), (B,), (B,))    0                     0.0   \n",
       "               (3.0, 2.0, 1.0)   ((A,), (A,), (VA,))   0                     0.0   \n",
       "\n",
       "                                                                        T**(-29)  \\\n",
       "phase_type     site_ratios       constituent_array     parameter_order             \n",
       "solid          (1.0, 3.0)        ((VA,), (VA,))        0                     0.0   \n",
       "liquid         (1.0,)            ((A,),)               0                     0.0   \n",
       "solid          (1.0, 1.0)        ((A,), (VA,))         0                     0.0   \n",
       "               (1.0, 3.0)        ((A,), (VA,))         0                     0.0   \n",
       "                                 ((A, VA), (VA,))      0                     0.0   \n",
       "               (1.0, 0.5)        ((A,), (VA,))         0                     0.0   \n",
       "complex        (0.5, 0.5, 3.0)   ((A,), (VA,), (VA,))  0                     0.0   \n",
       "                                 ((VA,), (A,), (VA,))  0                     0.0   \n",
       "liquid         (1.0,)            ((A,),)               0                     0.0   \n",
       "solid          (1.0, 1.0)        ((A,), (VA,))         0                     0.0   \n",
       "               (1.0, 3.0)        ((A,), (VA,))         0                     0.0   \n",
       "                                 ((A, VA), (VA,))      0                     0.0   \n",
       "               (1.0, 0.5)        ((A,), (VA,))         0                     0.0   \n",
       "complex        (0.5, 0.5, 3.0)   ((VA,), (A,), (VA,))  0                     0.0   \n",
       "                                 ((A,), (VA,), (VA,))  0                     0.0   \n",
       "liquid         (1.0,)            ((A, B),)             0                     0.0   \n",
       "solid          (1.0, 1.0)        ((A, B), (VA,))       0                     0.0   \n",
       "               (1.0, 3.0)        ((A, B), (VA,))       0                     0.0   \n",
       "               (1.0, 0.5)        ((A, B), (VA,))       0                     0.0   \n",
       "complex        (0.5, 0.5, 3.0)   ((A,), (B,), (VA,))   0                     0.0   \n",
       "                                 ((B,), (A,), (VA,))   0                     0.0   \n",
       "               (0.75, 0.25, 1.0) ((B,), (A,), (VA,))   0                     0.0   \n",
       "                                 ((A,), (B,), (VA,))   0                     0.0   \n",
       "                                 ((A, B), (A,), (VA,)) 0                     0.0   \n",
       "                                 ((A, B), (B,), (VA,)) 0                     0.0   \n",
       "                                 ((A, B), (A,), (VA,)) 1                     0.0   \n",
       "                                 ((A, B), (B,), (VA,)) 1                     0.0   \n",
       "                                 ((*,), (A, B), (VA,)) 0                     0.0   \n",
       "                                                       1                     0.0   \n",
       "                                 ((A, B), (*,), (VA,)) 0                     0.0   \n",
       "...                                                                          ...   \n",
       "solid          (1.0, 0.5)        ((A,), (VA,))         0                     0.0   \n",
       "complex        (0.5, 0.5, 3.0)   ((A,), (VA,), (VA,))  0                     0.0   \n",
       "                                 ((VA,), (A,), (VA,))  0                     0.0   \n",
       "liquid         (1.0,)            ((A, B),)             0                     0.0   \n",
       "                                                       1                     0.0   \n",
       "solid          (1.0, 1.0)        ((A, B), (VA,))       0                     0.0   \n",
       "               (1.0, 3.0)        ((A, B), (VA,))       0                     0.0   \n",
       "complex        (0.5, 0.5, 3.0)   ((A,), (B,), (VA,))   0                     0.0   \n",
       "                                 ((B,), (A,), (VA,))   0                     0.0   \n",
       "               (0.75, 0.25, 1.0) ((B,), (A,), (VA,))   0                     0.0   \n",
       "                                 ((A,), (B,), (VA,))   0                     0.0   \n",
       "                                 ((A, B), (A,), (VA,)) 0                     0.0   \n",
       "                                 ((A, B), (B,), (VA,)) 0                     0.0   \n",
       "                                 ((A, B), (A,), (VA,)) 1                     0.0   \n",
       "                                 ((A, B), (B,), (VA,)) 1                     0.0   \n",
       "                                 ((*,), (A, B), (VA,)) 0                     0.0   \n",
       "                                                       1                     0.0   \n",
       "                                 ((A, B), (*,), (VA,)) 0                     0.0   \n",
       "                                                       1                     0.0   \n",
       "stoichiometric (10.0, 1.0, 2.0)  ((A,), (A,), (B,))    0                     0.0   \n",
       "               (13.0, 2.0)       ((A,), (B,))          0                     0.0   \n",
       "               (4.0, 1.0)        ((A,), (B,))          0                     0.0   \n",
       "               (8.0, 5.0)        ((A,), (B,))          0                     0.0   \n",
       "                                                       0                     0.0   \n",
       "               (9.0, 4.0)        ((A,), (B,))          0                     0.0   \n",
       "                                                       0                     0.0   \n",
       "               (1.0, 2.0)        ((A,), (B,))          0                     0.0   \n",
       "complex        (8.0, 18.0, 4.0)  ((A,), (A,), (B,))    0                     0.0   \n",
       "                                 ((A,), (B,), (B,))    0                     0.0   \n",
       "               (3.0, 2.0, 1.0)   ((A,), (A,), (VA,))   0                     0.0   \n",
       "\n",
       "                                                                        T**(-28)  \\\n",
       "phase_type     site_ratios       constituent_array     parameter_order             \n",
       "solid          (1.0, 3.0)        ((VA,), (VA,))        0                     0.0   \n",
       "liquid         (1.0,)            ((A,),)               0                     0.0   \n",
       "solid          (1.0, 1.0)        ((A,), (VA,))         0                     0.0   \n",
       "               (1.0, 3.0)        ((A,), (VA,))         0                     0.0   \n",
       "                                 ((A, VA), (VA,))      0                     0.0   \n",
       "               (1.0, 0.5)        ((A,), (VA,))         0                     0.0   \n",
       "complex        (0.5, 0.5, 3.0)   ((A,), (VA,), (VA,))  0                     0.0   \n",
       "                                 ((VA,), (A,), (VA,))  0                     0.0   \n",
       "liquid         (1.0,)            ((A,),)               0                     0.0   \n",
       "solid          (1.0, 1.0)        ((A,), (VA,))         0                     0.0   \n",
       "               (1.0, 3.0)        ((A,), (VA,))         0                     0.0   \n",
       "                                 ((A, VA), (VA,))      0                     0.0   \n",
       "               (1.0, 0.5)        ((A,), (VA,))         0                     0.0   \n",
       "complex        (0.5, 0.5, 3.0)   ((VA,), (A,), (VA,))  0                     0.0   \n",
       "                                 ((A,), (VA,), (VA,))  0                     0.0   \n",
       "liquid         (1.0,)            ((A, B),)             0                     0.0   \n",
       "solid          (1.0, 1.0)        ((A, B), (VA,))       0                     0.0   \n",
       "               (1.0, 3.0)        ((A, B), (VA,))       0                     0.0   \n",
       "               (1.0, 0.5)        ((A, B), (VA,))       0                     0.0   \n",
       "complex        (0.5, 0.5, 3.0)   ((A,), (B,), (VA,))   0                     0.0   \n",
       "                                 ((B,), (A,), (VA,))   0                     0.0   \n",
       "               (0.75, 0.25, 1.0) ((B,), (A,), (VA,))   0                     0.0   \n",
       "                                 ((A,), (B,), (VA,))   0                     0.0   \n",
       "                                 ((A, B), (A,), (VA,)) 0                     0.0   \n",
       "                                 ((A, B), (B,), (VA,)) 0                     0.0   \n",
       "                                 ((A, B), (A,), (VA,)) 1                     0.0   \n",
       "                                 ((A, B), (B,), (VA,)) 1                     0.0   \n",
       "                                 ((*,), (A, B), (VA,)) 0                     0.0   \n",
       "                                                       1                     0.0   \n",
       "                                 ((A, B), (*,), (VA,)) 0                     0.0   \n",
       "...                                                                          ...   \n",
       "solid          (1.0, 0.5)        ((A,), (VA,))         0                     0.0   \n",
       "complex        (0.5, 0.5, 3.0)   ((A,), (VA,), (VA,))  0                     0.0   \n",
       "                                 ((VA,), (A,), (VA,))  0                     0.0   \n",
       "liquid         (1.0,)            ((A, B),)             0                     0.0   \n",
       "                                                       1                     0.0   \n",
       "solid          (1.0, 1.0)        ((A, B), (VA,))       0                     0.0   \n",
       "               (1.0, 3.0)        ((A, B), (VA,))       0                     0.0   \n",
       "complex        (0.5, 0.5, 3.0)   ((A,), (B,), (VA,))   0                     0.0   \n",
       "                                 ((B,), (A,), (VA,))   0                     0.0   \n",
       "               (0.75, 0.25, 1.0) ((B,), (A,), (VA,))   0                     0.0   \n",
       "                                 ((A,), (B,), (VA,))   0                     0.0   \n",
       "                                 ((A, B), (A,), (VA,)) 0                     0.0   \n",
       "                                 ((A, B), (B,), (VA,)) 0                     0.0   \n",
       "                                 ((A, B), (A,), (VA,)) 1                     0.0   \n",
       "                                 ((A, B), (B,), (VA,)) 1                     0.0   \n",
       "                                 ((*,), (A, B), (VA,)) 0                     0.0   \n",
       "                                                       1                     0.0   \n",
       "                                 ((A, B), (*,), (VA,)) 0                     0.0   \n",
       "                                                       1                     0.0   \n",
       "stoichiometric (10.0, 1.0, 2.0)  ((A,), (A,), (B,))    0                     0.0   \n",
       "               (13.0, 2.0)       ((A,), (B,))          0                     0.0   \n",
       "               (4.0, 1.0)        ((A,), (B,))          0                     0.0   \n",
       "               (8.0, 5.0)        ((A,), (B,))          0                     0.0   \n",
       "                                                       0                     0.0   \n",
       "               (9.0, 4.0)        ((A,), (B,))          0                     0.0   \n",
       "                                                       0                     0.0   \n",
       "               (1.0, 2.0)        ((A,), (B,))          0                     0.0   \n",
       "complex        (8.0, 18.0, 4.0)  ((A,), (A,), (B,))    0                     0.0   \n",
       "                                 ((A,), (B,), (B,))    0                     0.0   \n",
       "               (3.0, 2.0, 1.0)   ((A,), (A,), (VA,))   0                     0.0   \n",
       "\n",
       "                                                                        T**(-27)  \\\n",
       "phase_type     site_ratios       constituent_array     parameter_order             \n",
       "solid          (1.0, 3.0)        ((VA,), (VA,))        0                     0.0   \n",
       "liquid         (1.0,)            ((A,),)               0                     0.0   \n",
       "solid          (1.0, 1.0)        ((A,), (VA,))         0                     0.0   \n",
       "               (1.0, 3.0)        ((A,), (VA,))         0                     0.0   \n",
       "                                 ((A, VA), (VA,))      0                     0.0   \n",
       "               (1.0, 0.5)        ((A,), (VA,))         0                     0.0   \n",
       "complex        (0.5, 0.5, 3.0)   ((A,), (VA,), (VA,))  0                     0.0   \n",
       "                                 ((VA,), (A,), (VA,))  0                     0.0   \n",
       "liquid         (1.0,)            ((A,),)               0                     0.0   \n",
       "solid          (1.0, 1.0)        ((A,), (VA,))         0                     0.0   \n",
       "               (1.0, 3.0)        ((A,), (VA,))         0                     0.0   \n",
       "                                 ((A, VA), (VA,))      0                     0.0   \n",
       "               (1.0, 0.5)        ((A,), (VA,))         0                     0.0   \n",
       "complex        (0.5, 0.5, 3.0)   ((VA,), (A,), (VA,))  0                     0.0   \n",
       "                                 ((A,), (VA,), (VA,))  0                     0.0   \n",
       "liquid         (1.0,)            ((A, B),)             0                     0.0   \n",
       "solid          (1.0, 1.0)        ((A, B), (VA,))       0                     0.0   \n",
       "               (1.0, 3.0)        ((A, B), (VA,))       0                     0.0   \n",
       "               (1.0, 0.5)        ((A, B), (VA,))       0                     0.0   \n",
       "complex        (0.5, 0.5, 3.0)   ((A,), (B,), (VA,))   0                     0.0   \n",
       "                                 ((B,), (A,), (VA,))   0                     0.0   \n",
       "               (0.75, 0.25, 1.0) ((B,), (A,), (VA,))   0                     0.0   \n",
       "                                 ((A,), (B,), (VA,))   0                     0.0   \n",
       "                                 ((A, B), (A,), (VA,)) 0                     0.0   \n",
       "                                 ((A, B), (B,), (VA,)) 0                     0.0   \n",
       "                                 ((A, B), (A,), (VA,)) 1                     0.0   \n",
       "                                 ((A, B), (B,), (VA,)) 1                     0.0   \n",
       "                                 ((*,), (A, B), (VA,)) 0                     0.0   \n",
       "                                                       1                     0.0   \n",
       "                                 ((A, B), (*,), (VA,)) 0                     0.0   \n",
       "...                                                                          ...   \n",
       "solid          (1.0, 0.5)        ((A,), (VA,))         0                     0.0   \n",
       "complex        (0.5, 0.5, 3.0)   ((A,), (VA,), (VA,))  0                     0.0   \n",
       "                                 ((VA,), (A,), (VA,))  0                     0.0   \n",
       "liquid         (1.0,)            ((A, B),)             0                     0.0   \n",
       "                                                       1                     0.0   \n",
       "solid          (1.0, 1.0)        ((A, B), (VA,))       0                     0.0   \n",
       "               (1.0, 3.0)        ((A, B), (VA,))       0                     0.0   \n",
       "complex        (0.5, 0.5, 3.0)   ((A,), (B,), (VA,))   0                     0.0   \n",
       "                                 ((B,), (A,), (VA,))   0                     0.0   \n",
       "               (0.75, 0.25, 1.0) ((B,), (A,), (VA,))   0                     0.0   \n",
       "                                 ((A,), (B,), (VA,))   0                     0.0   \n",
       "                                 ((A, B), (A,), (VA,)) 0                     0.0   \n",
       "                                 ((A, B), (B,), (VA,)) 0                     0.0   \n",
       "                                 ((A, B), (A,), (VA,)) 1                     0.0   \n",
       "                                 ((A, B), (B,), (VA,)) 1                     0.0   \n",
       "                                 ((*,), (A, B), (VA,)) 0                     0.0   \n",
       "                                                       1                     0.0   \n",
       "                                 ((A, B), (*,), (VA,)) 0                     0.0   \n",
       "                                                       1                     0.0   \n",
       "stoichiometric (10.0, 1.0, 2.0)  ((A,), (A,), (B,))    0                     0.0   \n",
       "               (13.0, 2.0)       ((A,), (B,))          0                     0.0   \n",
       "               (4.0, 1.0)        ((A,), (B,))          0                     0.0   \n",
       "               (8.0, 5.0)        ((A,), (B,))          0                     0.0   \n",
       "                                                       0                     0.0   \n",
       "               (9.0, 4.0)        ((A,), (B,))          0                     0.0   \n",
       "                                                       0                     0.0   \n",
       "               (1.0, 2.0)        ((A,), (B,))          0                     0.0   \n",
       "complex        (8.0, 18.0, 4.0)  ((A,), (A,), (B,))    0                     0.0   \n",
       "                                 ((A,), (B,), (B,))    0                     0.0   \n",
       "               (3.0, 2.0, 1.0)   ((A,), (A,), (VA,))   0                     0.0   \n",
       "\n",
       "                                                                            ...        \\\n",
       "phase_type     site_ratios       constituent_array     parameter_order      ...         \n",
       "solid          (1.0, 3.0)        ((VA,), (VA,))        0                    ...         \n",
       "liquid         (1.0,)            ((A,),)               0                    ...         \n",
       "solid          (1.0, 1.0)        ((A,), (VA,))         0                    ...         \n",
       "               (1.0, 3.0)        ((A,), (VA,))         0                    ...         \n",
       "                                 ((A, VA), (VA,))      0                    ...         \n",
       "               (1.0, 0.5)        ((A,), (VA,))         0                    ...         \n",
       "complex        (0.5, 0.5, 3.0)   ((A,), (VA,), (VA,))  0                    ...         \n",
       "                                 ((VA,), (A,), (VA,))  0                    ...         \n",
       "liquid         (1.0,)            ((A,),)               0                    ...         \n",
       "solid          (1.0, 1.0)        ((A,), (VA,))         0                    ...         \n",
       "               (1.0, 3.0)        ((A,), (VA,))         0                    ...         \n",
       "                                 ((A, VA), (VA,))      0                    ...         \n",
       "               (1.0, 0.5)        ((A,), (VA,))         0                    ...         \n",
       "complex        (0.5, 0.5, 3.0)   ((VA,), (A,), (VA,))  0                    ...         \n",
       "                                 ((A,), (VA,), (VA,))  0                    ...         \n",
       "liquid         (1.0,)            ((A, B),)             0                    ...         \n",
       "solid          (1.0, 1.0)        ((A, B), (VA,))       0                    ...         \n",
       "               (1.0, 3.0)        ((A, B), (VA,))       0                    ...         \n",
       "               (1.0, 0.5)        ((A, B), (VA,))       0                    ...         \n",
       "complex        (0.5, 0.5, 3.0)   ((A,), (B,), (VA,))   0                    ...         \n",
       "                                 ((B,), (A,), (VA,))   0                    ...         \n",
       "               (0.75, 0.25, 1.0) ((B,), (A,), (VA,))   0                    ...         \n",
       "                                 ((A,), (B,), (VA,))   0                    ...         \n",
       "                                 ((A, B), (A,), (VA,)) 0                    ...         \n",
       "                                 ((A, B), (B,), (VA,)) 0                    ...         \n",
       "                                 ((A, B), (A,), (VA,)) 1                    ...         \n",
       "                                 ((A, B), (B,), (VA,)) 1                    ...         \n",
       "                                 ((*,), (A, B), (VA,)) 0                    ...         \n",
       "                                                       1                    ...         \n",
       "                                 ((A, B), (*,), (VA,)) 0                    ...         \n",
       "...                                                                         ...         \n",
       "solid          (1.0, 0.5)        ((A,), (VA,))         0                    ...         \n",
       "complex        (0.5, 0.5, 3.0)   ((A,), (VA,), (VA,))  0                    ...         \n",
       "                                 ((VA,), (A,), (VA,))  0                    ...         \n",
       "liquid         (1.0,)            ((A, B),)             0                    ...         \n",
       "                                                       1                    ...         \n",
       "solid          (1.0, 1.0)        ((A, B), (VA,))       0                    ...         \n",
       "               (1.0, 3.0)        ((A, B), (VA,))       0                    ...         \n",
       "complex        (0.5, 0.5, 3.0)   ((A,), (B,), (VA,))   0                    ...         \n",
       "                                 ((B,), (A,), (VA,))   0                    ...         \n",
       "               (0.75, 0.25, 1.0) ((B,), (A,), (VA,))   0                    ...         \n",
       "                                 ((A,), (B,), (VA,))   0                    ...         \n",
       "                                 ((A, B), (A,), (VA,)) 0                    ...         \n",
       "                                 ((A, B), (B,), (VA,)) 0                    ...         \n",
       "                                 ((A, B), (A,), (VA,)) 1                    ...         \n",
       "                                 ((A, B), (B,), (VA,)) 1                    ...         \n",
       "                                 ((*,), (A, B), (VA,)) 0                    ...         \n",
       "                                                       1                    ...         \n",
       "                                 ((A, B), (*,), (VA,)) 0                    ...         \n",
       "                                                       1                    ...         \n",
       "stoichiometric (10.0, 1.0, 2.0)  ((A,), (A,), (B,))    0                    ...         \n",
       "               (13.0, 2.0)       ((A,), (B,))          0                    ...         \n",
       "               (4.0, 1.0)        ((A,), (B,))          0                    ...         \n",
       "               (8.0, 5.0)        ((A,), (B,))          0                    ...         \n",
       "                                                       0                    ...         \n",
       "               (9.0, 4.0)        ((A,), (B,))          0                    ...         \n",
       "                                                       0                    ...         \n",
       "               (1.0, 2.0)        ((A,), (B,))          0                    ...         \n",
       "complex        (8.0, 18.0, 4.0)  ((A,), (A,), (B,))    0                    ...         \n",
       "                                 ((A,), (B,), (B,))    0                    ...         \n",
       "               (3.0, 2.0, 1.0)   ((A,), (A,), (VA,))   0                    ...         \n",
       "\n",
       "                                                                        T**21  \\\n",
       "phase_type     site_ratios       constituent_array     parameter_order          \n",
       "solid          (1.0, 3.0)        ((VA,), (VA,))        0                  0.0   \n",
       "liquid         (1.0,)            ((A,),)               0                  0.0   \n",
       "solid          (1.0, 1.0)        ((A,), (VA,))         0                  0.0   \n",
       "               (1.0, 3.0)        ((A,), (VA,))         0                  0.0   \n",
       "                                 ((A, VA), (VA,))      0                  0.0   \n",
       "               (1.0, 0.5)        ((A,), (VA,))         0                  0.0   \n",
       "complex        (0.5, 0.5, 3.0)   ((A,), (VA,), (VA,))  0                  0.0   \n",
       "                                 ((VA,), (A,), (VA,))  0                  0.0   \n",
       "liquid         (1.0,)            ((A,),)               0                  0.0   \n",
       "solid          (1.0, 1.0)        ((A,), (VA,))         0                  0.0   \n",
       "               (1.0, 3.0)        ((A,), (VA,))         0                  0.0   \n",
       "                                 ((A, VA), (VA,))      0                  0.0   \n",
       "               (1.0, 0.5)        ((A,), (VA,))         0                  0.0   \n",
       "complex        (0.5, 0.5, 3.0)   ((VA,), (A,), (VA,))  0                  0.0   \n",
       "                                 ((A,), (VA,), (VA,))  0                  0.0   \n",
       "liquid         (1.0,)            ((A, B),)             0                  0.0   \n",
       "solid          (1.0, 1.0)        ((A, B), (VA,))       0                  0.0   \n",
       "               (1.0, 3.0)        ((A, B), (VA,))       0                  0.0   \n",
       "               (1.0, 0.5)        ((A, B), (VA,))       0                  0.0   \n",
       "complex        (0.5, 0.5, 3.0)   ((A,), (B,), (VA,))   0                  0.0   \n",
       "                                 ((B,), (A,), (VA,))   0                  0.0   \n",
       "               (0.75, 0.25, 1.0) ((B,), (A,), (VA,))   0                  0.0   \n",
       "                                 ((A,), (B,), (VA,))   0                  0.0   \n",
       "                                 ((A, B), (A,), (VA,)) 0                  0.0   \n",
       "                                 ((A, B), (B,), (VA,)) 0                  0.0   \n",
       "                                 ((A, B), (A,), (VA,)) 1                  0.0   \n",
       "                                 ((A, B), (B,), (VA,)) 1                  0.0   \n",
       "                                 ((*,), (A, B), (VA,)) 0                  0.0   \n",
       "                                                       1                  0.0   \n",
       "                                 ((A, B), (*,), (VA,)) 0                  0.0   \n",
       "...                                                                       ...   \n",
       "solid          (1.0, 0.5)        ((A,), (VA,))         0                  0.0   \n",
       "complex        (0.5, 0.5, 3.0)   ((A,), (VA,), (VA,))  0                  0.0   \n",
       "                                 ((VA,), (A,), (VA,))  0                  0.0   \n",
       "liquid         (1.0,)            ((A, B),)             0                  0.0   \n",
       "                                                       1                  0.0   \n",
       "solid          (1.0, 1.0)        ((A, B), (VA,))       0                  0.0   \n",
       "               (1.0, 3.0)        ((A, B), (VA,))       0                  0.0   \n",
       "complex        (0.5, 0.5, 3.0)   ((A,), (B,), (VA,))   0                  0.0   \n",
       "                                 ((B,), (A,), (VA,))   0                  0.0   \n",
       "               (0.75, 0.25, 1.0) ((B,), (A,), (VA,))   0                  0.0   \n",
       "                                 ((A,), (B,), (VA,))   0                  0.0   \n",
       "                                 ((A, B), (A,), (VA,)) 0                  0.0   \n",
       "                                 ((A, B), (B,), (VA,)) 0                  0.0   \n",
       "                                 ((A, B), (A,), (VA,)) 1                  0.0   \n",
       "                                 ((A, B), (B,), (VA,)) 1                  0.0   \n",
       "                                 ((*,), (A, B), (VA,)) 0                  0.0   \n",
       "                                                       1                  0.0   \n",
       "                                 ((A, B), (*,), (VA,)) 0                  0.0   \n",
       "                                                       1                  0.0   \n",
       "stoichiometric (10.0, 1.0, 2.0)  ((A,), (A,), (B,))    0                  0.0   \n",
       "               (13.0, 2.0)       ((A,), (B,))          0                  0.0   \n",
       "               (4.0, 1.0)        ((A,), (B,))          0                  0.0   \n",
       "               (8.0, 5.0)        ((A,), (B,))          0                  0.0   \n",
       "                                                       0                  0.0   \n",
       "               (9.0, 4.0)        ((A,), (B,))          0                  0.0   \n",
       "                                                       0                  0.0   \n",
       "               (1.0, 2.0)        ((A,), (B,))          0                  0.0   \n",
       "complex        (8.0, 18.0, 4.0)  ((A,), (A,), (B,))    0                  0.0   \n",
       "                                 ((A,), (B,), (B,))    0                  0.0   \n",
       "               (3.0, 2.0, 1.0)   ((A,), (A,), (VA,))   0                  0.0   \n",
       "\n",
       "                                                                        T**22  \\\n",
       "phase_type     site_ratios       constituent_array     parameter_order          \n",
       "solid          (1.0, 3.0)        ((VA,), (VA,))        0                  0.0   \n",
       "liquid         (1.0,)            ((A,),)               0                  0.0   \n",
       "solid          (1.0, 1.0)        ((A,), (VA,))         0                  0.0   \n",
       "               (1.0, 3.0)        ((A,), (VA,))         0                  0.0   \n",
       "                                 ((A, VA), (VA,))      0                  0.0   \n",
       "               (1.0, 0.5)        ((A,), (VA,))         0                  0.0   \n",
       "complex        (0.5, 0.5, 3.0)   ((A,), (VA,), (VA,))  0                  0.0   \n",
       "                                 ((VA,), (A,), (VA,))  0                  0.0   \n",
       "liquid         (1.0,)            ((A,),)               0                  0.0   \n",
       "solid          (1.0, 1.0)        ((A,), (VA,))         0                  0.0   \n",
       "               (1.0, 3.0)        ((A,), (VA,))         0                  0.0   \n",
       "                                 ((A, VA), (VA,))      0                  0.0   \n",
       "               (1.0, 0.5)        ((A,), (VA,))         0                  0.0   \n",
       "complex        (0.5, 0.5, 3.0)   ((VA,), (A,), (VA,))  0                  0.0   \n",
       "                                 ((A,), (VA,), (VA,))  0                  0.0   \n",
       "liquid         (1.0,)            ((A, B),)             0                  0.0   \n",
       "solid          (1.0, 1.0)        ((A, B), (VA,))       0                  0.0   \n",
       "               (1.0, 3.0)        ((A, B), (VA,))       0                  0.0   \n",
       "               (1.0, 0.5)        ((A, B), (VA,))       0                  0.0   \n",
       "complex        (0.5, 0.5, 3.0)   ((A,), (B,), (VA,))   0                  0.0   \n",
       "                                 ((B,), (A,), (VA,))   0                  0.0   \n",
       "               (0.75, 0.25, 1.0) ((B,), (A,), (VA,))   0                  0.0   \n",
       "                                 ((A,), (B,), (VA,))   0                  0.0   \n",
       "                                 ((A, B), (A,), (VA,)) 0                  0.0   \n",
       "                                 ((A, B), (B,), (VA,)) 0                  0.0   \n",
       "                                 ((A, B), (A,), (VA,)) 1                  0.0   \n",
       "                                 ((A, B), (B,), (VA,)) 1                  0.0   \n",
       "                                 ((*,), (A, B), (VA,)) 0                  0.0   \n",
       "                                                       1                  0.0   \n",
       "                                 ((A, B), (*,), (VA,)) 0                  0.0   \n",
       "...                                                                       ...   \n",
       "solid          (1.0, 0.5)        ((A,), (VA,))         0                  0.0   \n",
       "complex        (0.5, 0.5, 3.0)   ((A,), (VA,), (VA,))  0                  0.0   \n",
       "                                 ((VA,), (A,), (VA,))  0                  0.0   \n",
       "liquid         (1.0,)            ((A, B),)             0                  0.0   \n",
       "                                                       1                  0.0   \n",
       "solid          (1.0, 1.0)        ((A, B), (VA,))       0                  0.0   \n",
       "               (1.0, 3.0)        ((A, B), (VA,))       0                  0.0   \n",
       "complex        (0.5, 0.5, 3.0)   ((A,), (B,), (VA,))   0                  0.0   \n",
       "                                 ((B,), (A,), (VA,))   0                  0.0   \n",
       "               (0.75, 0.25, 1.0) ((B,), (A,), (VA,))   0                  0.0   \n",
       "                                 ((A,), (B,), (VA,))   0                  0.0   \n",
       "                                 ((A, B), (A,), (VA,)) 0                  0.0   \n",
       "                                 ((A, B), (B,), (VA,)) 0                  0.0   \n",
       "                                 ((A, B), (A,), (VA,)) 1                  0.0   \n",
       "                                 ((A, B), (B,), (VA,)) 1                  0.0   \n",
       "                                 ((*,), (A, B), (VA,)) 0                  0.0   \n",
       "                                                       1                  0.0   \n",
       "                                 ((A, B), (*,), (VA,)) 0                  0.0   \n",
       "                                                       1                  0.0   \n",
       "stoichiometric (10.0, 1.0, 2.0)  ((A,), (A,), (B,))    0                  0.0   \n",
       "               (13.0, 2.0)       ((A,), (B,))          0                  0.0   \n",
       "               (4.0, 1.0)        ((A,), (B,))          0                  0.0   \n",
       "               (8.0, 5.0)        ((A,), (B,))          0                  0.0   \n",
       "                                                       0                  0.0   \n",
       "               (9.0, 4.0)        ((A,), (B,))          0                  0.0   \n",
       "                                                       0                  0.0   \n",
       "               (1.0, 2.0)        ((A,), (B,))          0                  0.0   \n",
       "complex        (8.0, 18.0, 4.0)  ((A,), (A,), (B,))    0                  0.0   \n",
       "                                 ((A,), (B,), (B,))    0                  0.0   \n",
       "               (3.0, 2.0, 1.0)   ((A,), (A,), (VA,))   0                  0.0   \n",
       "\n",
       "                                                                        T**23  \\\n",
       "phase_type     site_ratios       constituent_array     parameter_order          \n",
       "solid          (1.0, 3.0)        ((VA,), (VA,))        0                  0.0   \n",
       "liquid         (1.0,)            ((A,),)               0                  0.0   \n",
       "solid          (1.0, 1.0)        ((A,), (VA,))         0                  0.0   \n",
       "               (1.0, 3.0)        ((A,), (VA,))         0                  0.0   \n",
       "                                 ((A, VA), (VA,))      0                  0.0   \n",
       "               (1.0, 0.5)        ((A,), (VA,))         0                  0.0   \n",
       "complex        (0.5, 0.5, 3.0)   ((A,), (VA,), (VA,))  0                  0.0   \n",
       "                                 ((VA,), (A,), (VA,))  0                  0.0   \n",
       "liquid         (1.0,)            ((A,),)               0                  0.0   \n",
       "solid          (1.0, 1.0)        ((A,), (VA,))         0                  0.0   \n",
       "               (1.0, 3.0)        ((A,), (VA,))         0                  0.0   \n",
       "                                 ((A, VA), (VA,))      0                  0.0   \n",
       "               (1.0, 0.5)        ((A,), (VA,))         0                  0.0   \n",
       "complex        (0.5, 0.5, 3.0)   ((VA,), (A,), (VA,))  0                  0.0   \n",
       "                                 ((A,), (VA,), (VA,))  0                  0.0   \n",
       "liquid         (1.0,)            ((A, B),)             0                  0.0   \n",
       "solid          (1.0, 1.0)        ((A, B), (VA,))       0                  0.0   \n",
       "               (1.0, 3.0)        ((A, B), (VA,))       0                  0.0   \n",
       "               (1.0, 0.5)        ((A, B), (VA,))       0                  0.0   \n",
       "complex        (0.5, 0.5, 3.0)   ((A,), (B,), (VA,))   0                  0.0   \n",
       "                                 ((B,), (A,), (VA,))   0                  0.0   \n",
       "               (0.75, 0.25, 1.0) ((B,), (A,), (VA,))   0                  0.0   \n",
       "                                 ((A,), (B,), (VA,))   0                  0.0   \n",
       "                                 ((A, B), (A,), (VA,)) 0                  0.0   \n",
       "                                 ((A, B), (B,), (VA,)) 0                  0.0   \n",
       "                                 ((A, B), (A,), (VA,)) 1                  0.0   \n",
       "                                 ((A, B), (B,), (VA,)) 1                  0.0   \n",
       "                                 ((*,), (A, B), (VA,)) 0                  0.0   \n",
       "                                                       1                  0.0   \n",
       "                                 ((A, B), (*,), (VA,)) 0                  0.0   \n",
       "...                                                                       ...   \n",
       "solid          (1.0, 0.5)        ((A,), (VA,))         0                  0.0   \n",
       "complex        (0.5, 0.5, 3.0)   ((A,), (VA,), (VA,))  0                  0.0   \n",
       "                                 ((VA,), (A,), (VA,))  0                  0.0   \n",
       "liquid         (1.0,)            ((A, B),)             0                  0.0   \n",
       "                                                       1                  0.0   \n",
       "solid          (1.0, 1.0)        ((A, B), (VA,))       0                  0.0   \n",
       "               (1.0, 3.0)        ((A, B), (VA,))       0                  0.0   \n",
       "complex        (0.5, 0.5, 3.0)   ((A,), (B,), (VA,))   0                  0.0   \n",
       "                                 ((B,), (A,), (VA,))   0                  0.0   \n",
       "               (0.75, 0.25, 1.0) ((B,), (A,), (VA,))   0                  0.0   \n",
       "                                 ((A,), (B,), (VA,))   0                  0.0   \n",
       "                                 ((A, B), (A,), (VA,)) 0                  0.0   \n",
       "                                 ((A, B), (B,), (VA,)) 0                  0.0   \n",
       "                                 ((A, B), (A,), (VA,)) 1                  0.0   \n",
       "                                 ((A, B), (B,), (VA,)) 1                  0.0   \n",
       "                                 ((*,), (A, B), (VA,)) 0                  0.0   \n",
       "                                                       1                  0.0   \n",
       "                                 ((A, B), (*,), (VA,)) 0                  0.0   \n",
       "                                                       1                  0.0   \n",
       "stoichiometric (10.0, 1.0, 2.0)  ((A,), (A,), (B,))    0                  0.0   \n",
       "               (13.0, 2.0)       ((A,), (B,))          0                  0.0   \n",
       "               (4.0, 1.0)        ((A,), (B,))          0                  0.0   \n",
       "               (8.0, 5.0)        ((A,), (B,))          0                  0.0   \n",
       "                                                       0                  0.0   \n",
       "               (9.0, 4.0)        ((A,), (B,))          0                  0.0   \n",
       "                                                       0                  0.0   \n",
       "               (1.0, 2.0)        ((A,), (B,))          0                  0.0   \n",
       "complex        (8.0, 18.0, 4.0)  ((A,), (A,), (B,))    0                  0.0   \n",
       "                                 ((A,), (B,), (B,))    0                  0.0   \n",
       "               (3.0, 2.0, 1.0)   ((A,), (A,), (VA,))   0                  0.0   \n",
       "\n",
       "                                                                        T**24  \\\n",
       "phase_type     site_ratios       constituent_array     parameter_order          \n",
       "solid          (1.0, 3.0)        ((VA,), (VA,))        0                  0.0   \n",
       "liquid         (1.0,)            ((A,),)               0                  0.0   \n",
       "solid          (1.0, 1.0)        ((A,), (VA,))         0                  0.0   \n",
       "               (1.0, 3.0)        ((A,), (VA,))         0                  0.0   \n",
       "                                 ((A, VA), (VA,))      0                  0.0   \n",
       "               (1.0, 0.5)        ((A,), (VA,))         0                  0.0   \n",
       "complex        (0.5, 0.5, 3.0)   ((A,), (VA,), (VA,))  0                  0.0   \n",
       "                                 ((VA,), (A,), (VA,))  0                  0.0   \n",
       "liquid         (1.0,)            ((A,),)               0                  0.0   \n",
       "solid          (1.0, 1.0)        ((A,), (VA,))         0                  0.0   \n",
       "               (1.0, 3.0)        ((A,), (VA,))         0                  0.0   \n",
       "                                 ((A, VA), (VA,))      0                  0.0   \n",
       "               (1.0, 0.5)        ((A,), (VA,))         0                  0.0   \n",
       "complex        (0.5, 0.5, 3.0)   ((VA,), (A,), (VA,))  0                  0.0   \n",
       "                                 ((A,), (VA,), (VA,))  0                  0.0   \n",
       "liquid         (1.0,)            ((A, B),)             0                  0.0   \n",
       "solid          (1.0, 1.0)        ((A, B), (VA,))       0                  0.0   \n",
       "               (1.0, 3.0)        ((A, B), (VA,))       0                  0.0   \n",
       "               (1.0, 0.5)        ((A, B), (VA,))       0                  0.0   \n",
       "complex        (0.5, 0.5, 3.0)   ((A,), (B,), (VA,))   0                  0.0   \n",
       "                                 ((B,), (A,), (VA,))   0                  0.0   \n",
       "               (0.75, 0.25, 1.0) ((B,), (A,), (VA,))   0                  0.0   \n",
       "                                 ((A,), (B,), (VA,))   0                  0.0   \n",
       "                                 ((A, B), (A,), (VA,)) 0                  0.0   \n",
       "                                 ((A, B), (B,), (VA,)) 0                  0.0   \n",
       "                                 ((A, B), (A,), (VA,)) 1                  0.0   \n",
       "                                 ((A, B), (B,), (VA,)) 1                  0.0   \n",
       "                                 ((*,), (A, B), (VA,)) 0                  0.0   \n",
       "                                                       1                  0.0   \n",
       "                                 ((A, B), (*,), (VA,)) 0                  0.0   \n",
       "...                                                                       ...   \n",
       "solid          (1.0, 0.5)        ((A,), (VA,))         0                  0.0   \n",
       "complex        (0.5, 0.5, 3.0)   ((A,), (VA,), (VA,))  0                  0.0   \n",
       "                                 ((VA,), (A,), (VA,))  0                  0.0   \n",
       "liquid         (1.0,)            ((A, B),)             0                  0.0   \n",
       "                                                       1                  0.0   \n",
       "solid          (1.0, 1.0)        ((A, B), (VA,))       0                  0.0   \n",
       "               (1.0, 3.0)        ((A, B), (VA,))       0                  0.0   \n",
       "complex        (0.5, 0.5, 3.0)   ((A,), (B,), (VA,))   0                  0.0   \n",
       "                                 ((B,), (A,), (VA,))   0                  0.0   \n",
       "               (0.75, 0.25, 1.0) ((B,), (A,), (VA,))   0                  0.0   \n",
       "                                 ((A,), (B,), (VA,))   0                  0.0   \n",
       "                                 ((A, B), (A,), (VA,)) 0                  0.0   \n",
       "                                 ((A, B), (B,), (VA,)) 0                  0.0   \n",
       "                                 ((A, B), (A,), (VA,)) 1                  0.0   \n",
       "                                 ((A, B), (B,), (VA,)) 1                  0.0   \n",
       "                                 ((*,), (A, B), (VA,)) 0                  0.0   \n",
       "                                                       1                  0.0   \n",
       "                                 ((A, B), (*,), (VA,)) 0                  0.0   \n",
       "                                                       1                  0.0   \n",
       "stoichiometric (10.0, 1.0, 2.0)  ((A,), (A,), (B,))    0                  0.0   \n",
       "               (13.0, 2.0)       ((A,), (B,))          0                  0.0   \n",
       "               (4.0, 1.0)        ((A,), (B,))          0                  0.0   \n",
       "               (8.0, 5.0)        ((A,), (B,))          0                  0.0   \n",
       "                                                       0                  0.0   \n",
       "               (9.0, 4.0)        ((A,), (B,))          0                  0.0   \n",
       "                                                       0                  0.0   \n",
       "               (1.0, 2.0)        ((A,), (B,))          0                  0.0   \n",
       "complex        (8.0, 18.0, 4.0)  ((A,), (A,), (B,))    0                  0.0   \n",
       "                                 ((A,), (B,), (B,))    0                  0.0   \n",
       "               (3.0, 2.0, 1.0)   ((A,), (A,), (VA,))   0                  0.0   \n",
       "\n",
       "                                                                        T**25  \\\n",
       "phase_type     site_ratios       constituent_array     parameter_order          \n",
       "solid          (1.0, 3.0)        ((VA,), (VA,))        0                  0.0   \n",
       "liquid         (1.0,)            ((A,),)               0                  0.0   \n",
       "solid          (1.0, 1.0)        ((A,), (VA,))         0                  0.0   \n",
       "               (1.0, 3.0)        ((A,), (VA,))         0                  0.0   \n",
       "                                 ((A, VA), (VA,))      0                  0.0   \n",
       "               (1.0, 0.5)        ((A,), (VA,))         0                  0.0   \n",
       "complex        (0.5, 0.5, 3.0)   ((A,), (VA,), (VA,))  0                  0.0   \n",
       "                                 ((VA,), (A,), (VA,))  0                  0.0   \n",
       "liquid         (1.0,)            ((A,),)               0                  0.0   \n",
       "solid          (1.0, 1.0)        ((A,), (VA,))         0                  0.0   \n",
       "               (1.0, 3.0)        ((A,), (VA,))         0                  0.0   \n",
       "                                 ((A, VA), (VA,))      0                  0.0   \n",
       "               (1.0, 0.5)        ((A,), (VA,))         0                  0.0   \n",
       "complex        (0.5, 0.5, 3.0)   ((VA,), (A,), (VA,))  0                  0.0   \n",
       "                                 ((A,), (VA,), (VA,))  0                  0.0   \n",
       "liquid         (1.0,)            ((A, B),)             0                  0.0   \n",
       "solid          (1.0, 1.0)        ((A, B), (VA,))       0                  0.0   \n",
       "               (1.0, 3.0)        ((A, B), (VA,))       0                  0.0   \n",
       "               (1.0, 0.5)        ((A, B), (VA,))       0                  0.0   \n",
       "complex        (0.5, 0.5, 3.0)   ((A,), (B,), (VA,))   0                  0.0   \n",
       "                                 ((B,), (A,), (VA,))   0                  0.0   \n",
       "               (0.75, 0.25, 1.0) ((B,), (A,), (VA,))   0                  0.0   \n",
       "                                 ((A,), (B,), (VA,))   0                  0.0   \n",
       "                                 ((A, B), (A,), (VA,)) 0                  0.0   \n",
       "                                 ((A, B), (B,), (VA,)) 0                  0.0   \n",
       "                                 ((A, B), (A,), (VA,)) 1                  0.0   \n",
       "                                 ((A, B), (B,), (VA,)) 1                  0.0   \n",
       "                                 ((*,), (A, B), (VA,)) 0                  0.0   \n",
       "                                                       1                  0.0   \n",
       "                                 ((A, B), (*,), (VA,)) 0                  0.0   \n",
       "...                                                                       ...   \n",
       "solid          (1.0, 0.5)        ((A,), (VA,))         0                  0.0   \n",
       "complex        (0.5, 0.5, 3.0)   ((A,), (VA,), (VA,))  0                  0.0   \n",
       "                                 ((VA,), (A,), (VA,))  0                  0.0   \n",
       "liquid         (1.0,)            ((A, B),)             0                  0.0   \n",
       "                                                       1                  0.0   \n",
       "solid          (1.0, 1.0)        ((A, B), (VA,))       0                  0.0   \n",
       "               (1.0, 3.0)        ((A, B), (VA,))       0                  0.0   \n",
       "complex        (0.5, 0.5, 3.0)   ((A,), (B,), (VA,))   0                  0.0   \n",
       "                                 ((B,), (A,), (VA,))   0                  0.0   \n",
       "               (0.75, 0.25, 1.0) ((B,), (A,), (VA,))   0                  0.0   \n",
       "                                 ((A,), (B,), (VA,))   0                  0.0   \n",
       "                                 ((A, B), (A,), (VA,)) 0                  0.0   \n",
       "                                 ((A, B), (B,), (VA,)) 0                  0.0   \n",
       "                                 ((A, B), (A,), (VA,)) 1                  0.0   \n",
       "                                 ((A, B), (B,), (VA,)) 1                  0.0   \n",
       "                                 ((*,), (A, B), (VA,)) 0                  0.0   \n",
       "                                                       1                  0.0   \n",
       "                                 ((A, B), (*,), (VA,)) 0                  0.0   \n",
       "                                                       1                  0.0   \n",
       "stoichiometric (10.0, 1.0, 2.0)  ((A,), (A,), (B,))    0                  0.0   \n",
       "               (13.0, 2.0)       ((A,), (B,))          0                  0.0   \n",
       "               (4.0, 1.0)        ((A,), (B,))          0                  0.0   \n",
       "               (8.0, 5.0)        ((A,), (B,))          0                  0.0   \n",
       "                                                       0                  0.0   \n",
       "               (9.0, 4.0)        ((A,), (B,))          0                  0.0   \n",
       "                                                       0                  0.0   \n",
       "               (1.0, 2.0)        ((A,), (B,))          0                  0.0   \n",
       "complex        (8.0, 18.0, 4.0)  ((A,), (A,), (B,))    0                  0.0   \n",
       "                                 ((A,), (B,), (B,))    0                  0.0   \n",
       "               (3.0, 2.0, 1.0)   ((A,), (A,), (VA,))   0                  0.0   \n",
       "\n",
       "                                                                        T**26  \\\n",
       "phase_type     site_ratios       constituent_array     parameter_order          \n",
       "solid          (1.0, 3.0)        ((VA,), (VA,))        0                  0.0   \n",
       "liquid         (1.0,)            ((A,),)               0                  0.0   \n",
       "solid          (1.0, 1.0)        ((A,), (VA,))         0                  0.0   \n",
       "               (1.0, 3.0)        ((A,), (VA,))         0                  0.0   \n",
       "                                 ((A, VA), (VA,))      0                  0.0   \n",
       "               (1.0, 0.5)        ((A,), (VA,))         0                  0.0   \n",
       "complex        (0.5, 0.5, 3.0)   ((A,), (VA,), (VA,))  0                  0.0   \n",
       "                                 ((VA,), (A,), (VA,))  0                  0.0   \n",
       "liquid         (1.0,)            ((A,),)               0                  0.0   \n",
       "solid          (1.0, 1.0)        ((A,), (VA,))         0                  0.0   \n",
       "               (1.0, 3.0)        ((A,), (VA,))         0                  0.0   \n",
       "                                 ((A, VA), (VA,))      0                  0.0   \n",
       "               (1.0, 0.5)        ((A,), (VA,))         0                  0.0   \n",
       "complex        (0.5, 0.5, 3.0)   ((VA,), (A,), (VA,))  0                  0.0   \n",
       "                                 ((A,), (VA,), (VA,))  0                  0.0   \n",
       "liquid         (1.0,)            ((A, B),)             0                  0.0   \n",
       "solid          (1.0, 1.0)        ((A, B), (VA,))       0                  0.0   \n",
       "               (1.0, 3.0)        ((A, B), (VA,))       0                  0.0   \n",
       "               (1.0, 0.5)        ((A, B), (VA,))       0                  0.0   \n",
       "complex        (0.5, 0.5, 3.0)   ((A,), (B,), (VA,))   0                  0.0   \n",
       "                                 ((B,), (A,), (VA,))   0                  0.0   \n",
       "               (0.75, 0.25, 1.0) ((B,), (A,), (VA,))   0                  0.0   \n",
       "                                 ((A,), (B,), (VA,))   0                  0.0   \n",
       "                                 ((A, B), (A,), (VA,)) 0                  0.0   \n",
       "                                 ((A, B), (B,), (VA,)) 0                  0.0   \n",
       "                                 ((A, B), (A,), (VA,)) 1                  0.0   \n",
       "                                 ((A, B), (B,), (VA,)) 1                  0.0   \n",
       "                                 ((*,), (A, B), (VA,)) 0                  0.0   \n",
       "                                                       1                  0.0   \n",
       "                                 ((A, B), (*,), (VA,)) 0                  0.0   \n",
       "...                                                                       ...   \n",
       "solid          (1.0, 0.5)        ((A,), (VA,))         0                  0.0   \n",
       "complex        (0.5, 0.5, 3.0)   ((A,), (VA,), (VA,))  0                  0.0   \n",
       "                                 ((VA,), (A,), (VA,))  0                  0.0   \n",
       "liquid         (1.0,)            ((A, B),)             0                  0.0   \n",
       "                                                       1                  0.0   \n",
       "solid          (1.0, 1.0)        ((A, B), (VA,))       0                  0.0   \n",
       "               (1.0, 3.0)        ((A, B), (VA,))       0                  0.0   \n",
       "complex        (0.5, 0.5, 3.0)   ((A,), (B,), (VA,))   0                  0.0   \n",
       "                                 ((B,), (A,), (VA,))   0                  0.0   \n",
       "               (0.75, 0.25, 1.0) ((B,), (A,), (VA,))   0                  0.0   \n",
       "                                 ((A,), (B,), (VA,))   0                  0.0   \n",
       "                                 ((A, B), (A,), (VA,)) 0                  0.0   \n",
       "                                 ((A, B), (B,), (VA,)) 0                  0.0   \n",
       "                                 ((A, B), (A,), (VA,)) 1                  0.0   \n",
       "                                 ((A, B), (B,), (VA,)) 1                  0.0   \n",
       "                                 ((*,), (A, B), (VA,)) 0                  0.0   \n",
       "                                                       1                  0.0   \n",
       "                                 ((A, B), (*,), (VA,)) 0                  0.0   \n",
       "                                                       1                  0.0   \n",
       "stoichiometric (10.0, 1.0, 2.0)  ((A,), (A,), (B,))    0                  0.0   \n",
       "               (13.0, 2.0)       ((A,), (B,))          0                  0.0   \n",
       "               (4.0, 1.0)        ((A,), (B,))          0                  0.0   \n",
       "               (8.0, 5.0)        ((A,), (B,))          0                  0.0   \n",
       "                                                       0                  0.0   \n",
       "               (9.0, 4.0)        ((A,), (B,))          0                  0.0   \n",
       "                                                       0                  0.0   \n",
       "               (1.0, 2.0)        ((A,), (B,))          0                  0.0   \n",
       "complex        (8.0, 18.0, 4.0)  ((A,), (A,), (B,))    0                  0.0   \n",
       "                                 ((A,), (B,), (B,))    0                  0.0   \n",
       "               (3.0, 2.0, 1.0)   ((A,), (A,), (VA,))   0                  0.0   \n",
       "\n",
       "                                                                        T**27  \\\n",
       "phase_type     site_ratios       constituent_array     parameter_order          \n",
       "solid          (1.0, 3.0)        ((VA,), (VA,))        0                  0.0   \n",
       "liquid         (1.0,)            ((A,),)               0                  0.0   \n",
       "solid          (1.0, 1.0)        ((A,), (VA,))         0                  0.0   \n",
       "               (1.0, 3.0)        ((A,), (VA,))         0                  0.0   \n",
       "                                 ((A, VA), (VA,))      0                  0.0   \n",
       "               (1.0, 0.5)        ((A,), (VA,))         0                  0.0   \n",
       "complex        (0.5, 0.5, 3.0)   ((A,), (VA,), (VA,))  0                  0.0   \n",
       "                                 ((VA,), (A,), (VA,))  0                  0.0   \n",
       "liquid         (1.0,)            ((A,),)               0                  0.0   \n",
       "solid          (1.0, 1.0)        ((A,), (VA,))         0                  0.0   \n",
       "               (1.0, 3.0)        ((A,), (VA,))         0                  0.0   \n",
       "                                 ((A, VA), (VA,))      0                  0.0   \n",
       "               (1.0, 0.5)        ((A,), (VA,))         0                  0.0   \n",
       "complex        (0.5, 0.5, 3.0)   ((VA,), (A,), (VA,))  0                  0.0   \n",
       "                                 ((A,), (VA,), (VA,))  0                  0.0   \n",
       "liquid         (1.0,)            ((A, B),)             0                  0.0   \n",
       "solid          (1.0, 1.0)        ((A, B), (VA,))       0                  0.0   \n",
       "               (1.0, 3.0)        ((A, B), (VA,))       0                  0.0   \n",
       "               (1.0, 0.5)        ((A, B), (VA,))       0                  0.0   \n",
       "complex        (0.5, 0.5, 3.0)   ((A,), (B,), (VA,))   0                  0.0   \n",
       "                                 ((B,), (A,), (VA,))   0                  0.0   \n",
       "               (0.75, 0.25, 1.0) ((B,), (A,), (VA,))   0                  0.0   \n",
       "                                 ((A,), (B,), (VA,))   0                  0.0   \n",
       "                                 ((A, B), (A,), (VA,)) 0                  0.0   \n",
       "                                 ((A, B), (B,), (VA,)) 0                  0.0   \n",
       "                                 ((A, B), (A,), (VA,)) 1                  0.0   \n",
       "                                 ((A, B), (B,), (VA,)) 1                  0.0   \n",
       "                                 ((*,), (A, B), (VA,)) 0                  0.0   \n",
       "                                                       1                  0.0   \n",
       "                                 ((A, B), (*,), (VA,)) 0                  0.0   \n",
       "...                                                                       ...   \n",
       "solid          (1.0, 0.5)        ((A,), (VA,))         0                  0.0   \n",
       "complex        (0.5, 0.5, 3.0)   ((A,), (VA,), (VA,))  0                  0.0   \n",
       "                                 ((VA,), (A,), (VA,))  0                  0.0   \n",
       "liquid         (1.0,)            ((A, B),)             0                  0.0   \n",
       "                                                       1                  0.0   \n",
       "solid          (1.0, 1.0)        ((A, B), (VA,))       0                  0.0   \n",
       "               (1.0, 3.0)        ((A, B), (VA,))       0                  0.0   \n",
       "complex        (0.5, 0.5, 3.0)   ((A,), (B,), (VA,))   0                  0.0   \n",
       "                                 ((B,), (A,), (VA,))   0                  0.0   \n",
       "               (0.75, 0.25, 1.0) ((B,), (A,), (VA,))   0                  0.0   \n",
       "                                 ((A,), (B,), (VA,))   0                  0.0   \n",
       "                                 ((A, B), (A,), (VA,)) 0                  0.0   \n",
       "                                 ((A, B), (B,), (VA,)) 0                  0.0   \n",
       "                                 ((A, B), (A,), (VA,)) 1                  0.0   \n",
       "                                 ((A, B), (B,), (VA,)) 1                  0.0   \n",
       "                                 ((*,), (A, B), (VA,)) 0                  0.0   \n",
       "                                                       1                  0.0   \n",
       "                                 ((A, B), (*,), (VA,)) 0                  0.0   \n",
       "                                                       1                  0.0   \n",
       "stoichiometric (10.0, 1.0, 2.0)  ((A,), (A,), (B,))    0                  0.0   \n",
       "               (13.0, 2.0)       ((A,), (B,))          0                  0.0   \n",
       "               (4.0, 1.0)        ((A,), (B,))          0                  0.0   \n",
       "               (8.0, 5.0)        ((A,), (B,))          0                  0.0   \n",
       "                                                       0                  0.0   \n",
       "               (9.0, 4.0)        ((A,), (B,))          0                  0.0   \n",
       "                                                       0                  0.0   \n",
       "               (1.0, 2.0)        ((A,), (B,))          0                  0.0   \n",
       "complex        (8.0, 18.0, 4.0)  ((A,), (A,), (B,))    0                  0.0   \n",
       "                                 ((A,), (B,), (B,))    0                  0.0   \n",
       "               (3.0, 2.0, 1.0)   ((A,), (A,), (VA,))   0                  0.0   \n",
       "\n",
       "                                                                        T**28  \\\n",
       "phase_type     site_ratios       constituent_array     parameter_order          \n",
       "solid          (1.0, 3.0)        ((VA,), (VA,))        0                  0.0   \n",
       "liquid         (1.0,)            ((A,),)               0                  0.0   \n",
       "solid          (1.0, 1.0)        ((A,), (VA,))         0                  0.0   \n",
       "               (1.0, 3.0)        ((A,), (VA,))         0                  0.0   \n",
       "                                 ((A, VA), (VA,))      0                  0.0   \n",
       "               (1.0, 0.5)        ((A,), (VA,))         0                  0.0   \n",
       "complex        (0.5, 0.5, 3.0)   ((A,), (VA,), (VA,))  0                  0.0   \n",
       "                                 ((VA,), (A,), (VA,))  0                  0.0   \n",
       "liquid         (1.0,)            ((A,),)               0                  0.0   \n",
       "solid          (1.0, 1.0)        ((A,), (VA,))         0                  0.0   \n",
       "               (1.0, 3.0)        ((A,), (VA,))         0                  0.0   \n",
       "                                 ((A, VA), (VA,))      0                  0.0   \n",
       "               (1.0, 0.5)        ((A,), (VA,))         0                  0.0   \n",
       "complex        (0.5, 0.5, 3.0)   ((VA,), (A,), (VA,))  0                  0.0   \n",
       "                                 ((A,), (VA,), (VA,))  0                  0.0   \n",
       "liquid         (1.0,)            ((A, B),)             0                  0.0   \n",
       "solid          (1.0, 1.0)        ((A, B), (VA,))       0                  0.0   \n",
       "               (1.0, 3.0)        ((A, B), (VA,))       0                  0.0   \n",
       "               (1.0, 0.5)        ((A, B), (VA,))       0                  0.0   \n",
       "complex        (0.5, 0.5, 3.0)   ((A,), (B,), (VA,))   0                  0.0   \n",
       "                                 ((B,), (A,), (VA,))   0                  0.0   \n",
       "               (0.75, 0.25, 1.0) ((B,), (A,), (VA,))   0                  0.0   \n",
       "                                 ((A,), (B,), (VA,))   0                  0.0   \n",
       "                                 ((A, B), (A,), (VA,)) 0                  0.0   \n",
       "                                 ((A, B), (B,), (VA,)) 0                  0.0   \n",
       "                                 ((A, B), (A,), (VA,)) 1                  0.0   \n",
       "                                 ((A, B), (B,), (VA,)) 1                  0.0   \n",
       "                                 ((*,), (A, B), (VA,)) 0                  0.0   \n",
       "                                                       1                  0.0   \n",
       "                                 ((A, B), (*,), (VA,)) 0                  0.0   \n",
       "...                                                                       ...   \n",
       "solid          (1.0, 0.5)        ((A,), (VA,))         0                  0.0   \n",
       "complex        (0.5, 0.5, 3.0)   ((A,), (VA,), (VA,))  0                  0.0   \n",
       "                                 ((VA,), (A,), (VA,))  0                  0.0   \n",
       "liquid         (1.0,)            ((A, B),)             0                  0.0   \n",
       "                                                       1                  0.0   \n",
       "solid          (1.0, 1.0)        ((A, B), (VA,))       0                  0.0   \n",
       "               (1.0, 3.0)        ((A, B), (VA,))       0                  0.0   \n",
       "complex        (0.5, 0.5, 3.0)   ((A,), (B,), (VA,))   0                  0.0   \n",
       "                                 ((B,), (A,), (VA,))   0                  0.0   \n",
       "               (0.75, 0.25, 1.0) ((B,), (A,), (VA,))   0                  0.0   \n",
       "                                 ((A,), (B,), (VA,))   0                  0.0   \n",
       "                                 ((A, B), (A,), (VA,)) 0                  0.0   \n",
       "                                 ((A, B), (B,), (VA,)) 0                  0.0   \n",
       "                                 ((A, B), (A,), (VA,)) 1                  0.0   \n",
       "                                 ((A, B), (B,), (VA,)) 1                  0.0   \n",
       "                                 ((*,), (A, B), (VA,)) 0                  0.0   \n",
       "                                                       1                  0.0   \n",
       "                                 ((A, B), (*,), (VA,)) 0                  0.0   \n",
       "                                                       1                  0.0   \n",
       "stoichiometric (10.0, 1.0, 2.0)  ((A,), (A,), (B,))    0                  0.0   \n",
       "               (13.0, 2.0)       ((A,), (B,))          0                  0.0   \n",
       "               (4.0, 1.0)        ((A,), (B,))          0                  0.0   \n",
       "               (8.0, 5.0)        ((A,), (B,))          0                  0.0   \n",
       "                                                       0                  0.0   \n",
       "               (9.0, 4.0)        ((A,), (B,))          0                  0.0   \n",
       "                                                       0                  0.0   \n",
       "               (1.0, 2.0)        ((A,), (B,))          0                  0.0   \n",
       "complex        (8.0, 18.0, 4.0)  ((A,), (A,), (B,))    0                  0.0   \n",
       "                                 ((A,), (B,), (B,))    0                  0.0   \n",
       "               (3.0, 2.0, 1.0)   ((A,), (A,), (VA,))   0                  0.0   \n",
       "\n",
       "                                                                        T**29  \\\n",
       "phase_type     site_ratios       constituent_array     parameter_order          \n",
       "solid          (1.0, 3.0)        ((VA,), (VA,))        0                  0.0   \n",
       "liquid         (1.0,)            ((A,),)               0                  0.0   \n",
       "solid          (1.0, 1.0)        ((A,), (VA,))         0                  0.0   \n",
       "               (1.0, 3.0)        ((A,), (VA,))         0                  0.0   \n",
       "                                 ((A, VA), (VA,))      0                  0.0   \n",
       "               (1.0, 0.5)        ((A,), (VA,))         0                  0.0   \n",
       "complex        (0.5, 0.5, 3.0)   ((A,), (VA,), (VA,))  0                  0.0   \n",
       "                                 ((VA,), (A,), (VA,))  0                  0.0   \n",
       "liquid         (1.0,)            ((A,),)               0                  0.0   \n",
       "solid          (1.0, 1.0)        ((A,), (VA,))         0                  0.0   \n",
       "               (1.0, 3.0)        ((A,), (VA,))         0                  0.0   \n",
       "                                 ((A, VA), (VA,))      0                  0.0   \n",
       "               (1.0, 0.5)        ((A,), (VA,))         0                  0.0   \n",
       "complex        (0.5, 0.5, 3.0)   ((VA,), (A,), (VA,))  0                  0.0   \n",
       "                                 ((A,), (VA,), (VA,))  0                  0.0   \n",
       "liquid         (1.0,)            ((A, B),)             0                  0.0   \n",
       "solid          (1.0, 1.0)        ((A, B), (VA,))       0                  0.0   \n",
       "               (1.0, 3.0)        ((A, B), (VA,))       0                  0.0   \n",
       "               (1.0, 0.5)        ((A, B), (VA,))       0                  0.0   \n",
       "complex        (0.5, 0.5, 3.0)   ((A,), (B,), (VA,))   0                  0.0   \n",
       "                                 ((B,), (A,), (VA,))   0                  0.0   \n",
       "               (0.75, 0.25, 1.0) ((B,), (A,), (VA,))   0                  0.0   \n",
       "                                 ((A,), (B,), (VA,))   0                  0.0   \n",
       "                                 ((A, B), (A,), (VA,)) 0                  0.0   \n",
       "                                 ((A, B), (B,), (VA,)) 0                  0.0   \n",
       "                                 ((A, B), (A,), (VA,)) 1                  0.0   \n",
       "                                 ((A, B), (B,), (VA,)) 1                  0.0   \n",
       "                                 ((*,), (A, B), (VA,)) 0                  0.0   \n",
       "                                                       1                  0.0   \n",
       "                                 ((A, B), (*,), (VA,)) 0                  0.0   \n",
       "...                                                                       ...   \n",
       "solid          (1.0, 0.5)        ((A,), (VA,))         0                  0.0   \n",
       "complex        (0.5, 0.5, 3.0)   ((A,), (VA,), (VA,))  0                  0.0   \n",
       "                                 ((VA,), (A,), (VA,))  0                  0.0   \n",
       "liquid         (1.0,)            ((A, B),)             0                  0.0   \n",
       "                                                       1                  0.0   \n",
       "solid          (1.0, 1.0)        ((A, B), (VA,))       0                  0.0   \n",
       "               (1.0, 3.0)        ((A, B), (VA,))       0                  0.0   \n",
       "complex        (0.5, 0.5, 3.0)   ((A,), (B,), (VA,))   0                  0.0   \n",
       "                                 ((B,), (A,), (VA,))   0                  0.0   \n",
       "               (0.75, 0.25, 1.0) ((B,), (A,), (VA,))   0                  0.0   \n",
       "                                 ((A,), (B,), (VA,))   0                  0.0   \n",
       "                                 ((A, B), (A,), (VA,)) 0                  0.0   \n",
       "                                 ((A, B), (B,), (VA,)) 0                  0.0   \n",
       "                                 ((A, B), (A,), (VA,)) 1                  0.0   \n",
       "                                 ((A, B), (B,), (VA,)) 1                  0.0   \n",
       "                                 ((*,), (A, B), (VA,)) 0                  0.0   \n",
       "                                                       1                  0.0   \n",
       "                                 ((A, B), (*,), (VA,)) 0                  0.0   \n",
       "                                                       1                  0.0   \n",
       "stoichiometric (10.0, 1.0, 2.0)  ((A,), (A,), (B,))    0                  0.0   \n",
       "               (13.0, 2.0)       ((A,), (B,))          0                  0.0   \n",
       "               (4.0, 1.0)        ((A,), (B,))          0                  0.0   \n",
       "               (8.0, 5.0)        ((A,), (B,))          0                  0.0   \n",
       "                                                       0                  0.0   \n",
       "               (9.0, 4.0)        ((A,), (B,))          0                  0.0   \n",
       "                                                       0                  0.0   \n",
       "               (1.0, 2.0)        ((A,), (B,))          0                  0.0   \n",
       "complex        (8.0, 18.0, 4.0)  ((A,), (A,), (B,))    0                  0.0   \n",
       "                                 ((A,), (B,), (B,))    0                  0.0   \n",
       "               (3.0, 2.0, 1.0)   ((A,), (A,), (VA,))   0                  0.0   \n",
       "\n",
       "                                                                                    1  \n",
       "phase_type     site_ratios       constituent_array     parameter_order                 \n",
       "solid          (1.0, 3.0)        ((VA,), (VA,))        0                     0.000000  \n",
       "liquid         (1.0,)            ((A,),)               0                  4849.556000  \n",
       "solid          (1.0, 1.0)        ((A,), (VA,))         0                 -2600.775833  \n",
       "               (1.0, 3.0)        ((A,), (VA,))         0                 -1345.570833  \n",
       "                                 ((A, VA), (VA,))      0                 96765.000000  \n",
       "               (1.0, 0.5)        ((A,), (VA,))         0                 -2814.570833  \n",
       "complex        (0.5, 0.5, 3.0)   ((A,), (VA,), (VA,))  0                 25867.500000  \n",
       "                                 ((VA,), (A,), (VA,))  0                 25867.500000  \n",
       "liquid         (1.0,)            ((A,),)               0                 -1380.564556  \n",
       "solid          (1.0, 1.0)        ((A,), (VA,))         0                 -5503.302333  \n",
       "               (1.0, 3.0)        ((A,), (VA,))         0                 -1145.760333  \n",
       "                                 ((A, VA), (VA,))      0                 24593.230000  \n",
       "               (1.0, 0.5)        ((A,), (VA,))         0                 -4980.302333  \n",
       "complex        (0.5, 0.5, 3.0)   ((VA,), (A,), (VA,))  0                 28302.710000  \n",
       "                                 ((A,), (VA,), (VA,))  0                 28302.710000  \n",
       "liquid         (1.0,)            ((A, B),)             0                   665.500000  \n",
       "solid          (1.0, 1.0)        ((A, B), (VA,))       0                  -400.000000  \n",
       "               (1.0, 3.0)        ((A, B), (VA,))       0                  1000.000000  \n",
       "               (1.0, 0.5)        ((A, B), (VA,))       0                  -810.000000  \n",
       "complex        (0.5, 0.5, 3.0)   ((A,), (B,), (VA,))   0                  1932.000000  \n",
       "                                 ((B,), (A,), (VA,))   0                  1932.000000  \n",
       "               (0.75, 0.25, 1.0) ((B,), (A,), (VA,))   0                     0.000000  \n",
       "                                 ((A,), (B,), (VA,))   0                     0.000000  \n",
       "                                 ((A, B), (A,), (VA,)) 0                     0.000000  \n",
       "                                 ((A, B), (B,), (VA,)) 0                     0.000000  \n",
       "                                 ((A, B), (A,), (VA,)) 1                     0.000000  \n",
       "                                 ((A, B), (B,), (VA,)) 1                     0.000000  \n",
       "                                 ((*,), (A, B), (VA,)) 0                     0.000000  \n",
       "                                                       1                     0.000000  \n",
       "                                 ((A, B), (*,), (VA,)) 0                     0.000000  \n",
       "...                                                                               ...  \n",
       "solid          (1.0, 0.5)        ((A,), (VA,))         0                 -5068.714000  \n",
       "complex        (0.5, 0.5, 3.0)   ((A,), (VA,), (VA,))  0                     0.000000  \n",
       "                                 ((VA,), (A,), (VA,))  0                     0.000000  \n",
       "liquid         (1.0,)            ((A, B),)             0                -14500.000000  \n",
       "                                                       1                 -5500.000000  \n",
       "solid          (1.0, 1.0)        ((A, B), (VA,))       0                -22950.000000  \n",
       "               (1.0, 3.0)        ((A, B), (VA,))       0                -27450.000000  \n",
       "complex        (0.5, 0.5, 3.0)   ((A,), (B,), (VA,))   0                 -1000.000000  \n",
       "                                 ((B,), (A,), (VA,))   0                 -1000.000000  \n",
       "               (0.75, 0.25, 1.0) ((B,), (A,), (VA,))   0                 -1245.000000  \n",
       "                                 ((A,), (B,), (VA,))   0                 -1245.000000  \n",
       "                                 ((A, B), (A,), (VA,)) 0                 -2490.000000  \n",
       "                                 ((A, B), (B,), (VA,)) 0                 -2490.000000  \n",
       "                                 ((A, B), (A,), (VA,)) 1                     0.000000  \n",
       "                                 ((A, B), (B,), (VA,)) 1                     0.000000  \n",
       "                                 ((*,), (A, B), (VA,)) 0                     0.000000  \n",
       "                                                       1                     0.000000  \n",
       "                                 ((A, B), (*,), (VA,)) 0                     0.000000  \n",
       "                                                       1                     0.000000  \n",
       "stoichiometric (10.0, 1.0, 2.0)  ((A,), (A,), (B,))    0               -144305.234000  \n",
       "               (13.0, 2.0)       ((A,), (B,))          0               -151390.426000  \n",
       "               (4.0, 1.0)        ((A,), (B,))          0                -67065.598000  \n",
       "               (8.0, 5.0)        ((A,), (B,))          0               -140835.338000  \n",
       "                                                       0               -181726.838000  \n",
       "               (9.0, 4.0)        ((A,), (B,))          0               -130714.470000  \n",
       "                                                       0               -178872.970000  \n",
       "               (1.0, 2.0)        ((A,), (B,))          0                -34741.774000  \n",
       "complex        (8.0, 18.0, 4.0)  ((A,), (A,), (B,))    0                 31918.762000  \n",
       "                                 ((A,), (B,), (B,))    0               -166917.476000  \n",
       "               (3.0, 2.0, 1.0)   ((A,), (A,), (VA,))   0                 21125.770000  \n",
       "\n",
       "[218 rows x 66 columns]"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "import pandas as pd\n",
    "from IPython.display import display\n",
    "\n",
    "df = pd.DataFrame(total_results, columns=columns)\n",
    "for p in polys:\n",
    "    df[str(p)] = pd.to_numeric(df[str(p)])\n",
    "multi_df = df.set_index(['phase_type', 'site_ratios', 'constituent_array', 'parameter_order'])\n",
    "display(multi_df)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {
    "collapsed": false,
    "deletable": true,
    "editable": true
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "-\n",
      "AL-CO\n",
      "stoichiometric    4\n",
      "solid             3\n",
      "complex           3\n",
      "liquid            1\n",
      "-\n",
      "AL-CR\n",
      "stoichiometric    8\n",
      "complex           4\n",
      "solid             3\n",
      "liquid            1\n",
      "-\n",
      "AL-NI\n",
      "solid             3\n",
      "complex           3\n",
      "stoichiometric    2\n",
      "liquid            1\n",
      "-\n",
      "CO-CR\n",
      "complex    3\n",
      "solid      3\n",
      "liquid     1\n",
      "-\n",
      "CO-NI\n",
      "solid      3\n",
      "complex    2\n",
      "liquid     1\n",
      "-\n",
      "CR-NI\n",
      "complex    3\n",
      "solid      3\n",
      "liquid     1\n"
     ]
    }
   ],
   "source": [
    "for system_name, system_df in df.groupby('system'):\n",
    "    system_df = system_df.drop_duplicates(subset='phase_name')\n",
    "    print('-')\n",
    "    print('-'.join(system_name))\n",
    "    print(system_df['phase_type'].value_counts().to_string())"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 54,
   "metadata": {
    "collapsed": false,
    "deletable": true,
    "editable": true,
    "scrolled": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "phase_type      site_ratios        constituent_array      parameter_order\n",
       "complex         (0.5, 0.5, 3.0)    ((A,), (B,), (VA,))    0                   6\n",
       "                                   ((A,), (VA,), (VA,))   0                  12\n",
       "                                   ((B,), (A,), (VA,))    0                   6\n",
       "                                   ((VA,), (A,), (VA,))   0                  12\n",
       "                (0.75, 0.25, 1.0)  ((*,), (A, B), (VA,))  0                   6\n",
       "                                                          1                   6\n",
       "                                   ((A,), (B,), (VA,))    0                   6\n",
       "                                   ((A, B), (*,), (VA,))  0                   6\n",
       "                                                          1                   6\n",
       "                                   ((A, B), (A,), (VA,))  0                   6\n",
       "                                                          1                   6\n",
       "                                   ((A, B), (B,), (VA,))  0                   6\n",
       "                                                          1                   6\n",
       "                                   ((B,), (A,), (VA,))    0                   6\n",
       "                (3.0, 2.0, 1.0)    ((A,), (*,), (B, VA))  0                   1\n",
       "                                   ((A,), (A,), (B,))     0                   1\n",
       "                                   ((A,), (A,), (VA,))    0                   3\n",
       "                                   ((A,), (A, B), (*,))   0                   1\n",
       "                                   ((A,), (B,), (B,))     0                   1\n",
       "                                   ((A,), (B,), (VA,))    0                   1\n",
       "                (8.0, 18.0, 4.0)   ((A,), (A,), (B,))     0                   2\n",
       "                                   ((A,), (B,), (B,))     0                   2\n",
       "                                   ((B,), (A,), (A,))     0                   1\n",
       "                                   ((B,), (B,), (A,))     0                   1\n",
       "liquid          (1.0,)             ((A,),)                0                   9\n",
       "                                   ((A, B),)              0                   6\n",
       "                                                          1                   5\n",
       "                                                          2                   2\n",
       "                                                          3                   2\n",
       "                                                          4                   1\n",
       "solid           (1.0, 0.5)         ((A,), (VA,))          0                  12\n",
       "                                   ((A, B), (VA,))        0                   2\n",
       "                (1.0, 1.0)         ((A,), (VA,))          0                   9\n",
       "                                   ((A, B), (VA,))        0                   6\n",
       "                                                          1                   2\n",
       "                                                          2                   2\n",
       "                                                          3                   1\n",
       "                (1.0, 3.0)         ((A,), (VA,))          0                   9\n",
       "                                   ((A, B), (VA,))        0                   6\n",
       "                                                          1                   2\n",
       "                                   ((A, VA), (VA,))       0                  12\n",
       "                                   ((VA,), (VA,))         0                   6\n",
       "stoichiometric  (0.375, 0.625)     ((A,), (B,))           0                   1\n",
       "                (0.75, 0.25)       ((A,), (B,))           0                   1\n",
       "                (1.0, 2.0)         ((A,), (B,))           0                   1\n",
       "                (3.0, 1.0)         ((A,), (B,))           0                   1\n",
       "                (4.0, 1.0)         ((A,), (B,))           0                   1\n",
       "                (5.0, 2.0)         ((A,), (B,))           0                   1\n",
       "                (8.0, 5.0)         ((A,), (B,))           0                   2\n",
       "                (9.0, 2.0)         ((A,), (B,))           0                   1\n",
       "                (9.0, 4.0)         ((A,), (B,))           0                   2\n",
       "                (10.0, 1.0, 2.0)   ((A,), (A,), (B,))     0                   1\n",
       "                (13.0, 2.0)        ((A,), (B,))           0                   1\n",
       "                (13.0, 4.0)        ((A,), (B,))           0                   1\n",
       "dtype: int64"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "import numpy as np\n",
    "\n",
    "def frac_nonzero(x):\n",
    "    return np.count_nonzero(x)/np.size(x)\n",
    "def fnz_var(x):\n",
    "    fnz = frac_nonzero(x)\n",
    "    return fnz*(1-fnz)\n",
    "\n",
    "mdc = (multi_df.drop(columns=['system', 'phase_name', 'parameter_value'])\n",
    "                .groupby(level=[0,1,2,3])\n",
    "                .agg([frac_nonzero, fnz_var])\n",
    "    )\n",
    "#display(mdc)\n",
    "mdl = (multi_df.drop(columns=['system', 'phase_name', 'parameter_value'])\n",
    "                .groupby(level=[0,1,2,3])\n",
    "                .apply(np.size, axis=0)\n",
    "    )\n",
    "display(mdl)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 50,
   "metadata": {
    "collapsed": false,
    "deletable": true,
    "editable": true
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "complex           18\n",
       "solid             18\n",
       "stoichiometric    14\n",
       "liquid             6\n",
       "Name: phase_type, dtype: int64"
      ]
     },
     "execution_count": 50,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "df.drop_duplicates(subset=['phase_name', 'system'])['phase_type'].value_counts()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
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