OpenMC_NEA_Training_nov25/course/live_notebooks/Lattices.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Universes\n",
    "\n",
    "A universe is a collection of cells. At a minimum, there must be one \"root\" universe, which gets passed to `openmc.Geometry(root)`. But you can also use universes to repeat a collection of cells multiple times throughout a geometry. Here, we will explore some basic features of universes and reinforce concepts as to how neutrons \"see\" boundary conditions on different surfaces as they walk through the geometry.\n",
    "\n",
    "We'll start by making a simple universe - say, an infinite region of space divided into four quadrants, each with a different material. For illustration, let's fill each quadrant with a different mixture of two base materials, material A and material B."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [],
   "source": [
    "import openmc"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [],
   "source": [
    "model = openmc.Model()\n",
    "\n",
    "mat_a = openmc.Material()\n",
    "mat_a.add_element('U', 1.0, enrichment=4.0)\n",
    "mat_a.add_element('O', 2.0)\n",
    "mat_a.set_density('g/cc', 11.0)\n",
    "\n",
    "mat_b = openmc.Material()\n",
    "mat_b.add_element('H', 2.0)\n",
    "mat_b.add_element('O', 1.0)\n",
    "mat_b.set_density('g/cc', 1.0)\n",
    "\n",
    "q1 = openmc.Material.mix_materials([mat_a, mat_b], [0.1, 0.9])\n",
    "q2 = openmc.Material.mix_materials([mat_a, mat_b], [0.2, 0.8])\n",
    "q3 = openmc.Material.mix_materials([mat_a, mat_b], [0.3, 0.7])\n",
    "q4 = openmc.Material.mix_materials([mat_a, mat_b], [0.4, 0.6])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [],
   "source": [
    "horizontal = openmc.YPlane(y0 = 0)\n",
    "vertical = openmc.XPlane(x0 = 0)\n",
    "\n",
    "quad1_cell = openmc.Cell(region = +horizontal & +vertical, fill = q1)\n",
    "quad2_cell = openmc.Cell(region = +horizontal & -vertical, fill = q2)\n",
    "quad3_cell = openmc.Cell(region = -horizontal & -vertical, fill = q3)\n",
    "quad4_cell = openmc.Cell(region = -horizontal & +vertical, fill = q4)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [],
   "source": [
    "universe = openmc.Universe()\n",
    "universe.add_cells([quad1_cell, quad2_cell, quad3_cell, quad4_cell])"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Let's plot our universe to confirm we know what we've built. Note that because the cells are infinite, that the universe extends to infinity."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<Axes: xlabel='x [cm]', ylabel='y [cm]'>"
      ]
     },
     "execution_count": 9,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 258.065x259.74 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "universe.plot(width=(3, 3))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<Axes: xlabel='x [cm]', ylabel='y [cm]'>"
      ]
     },
     "execution_count": 10,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": "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",
      "text/plain": [
       "<Figure size 258.065x259.74 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "universe.plot(width=(10, 10))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Now let's suppose that I want to fill this universe into an enclosing cell, a cylinder of radius 5 cm. Let's first create this cylinder, and then we will fill it with our universe."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [],
   "source": [
    "big_cylinder = openmc.ZCylinder(r=5)\n",
    "big_cell = openmc.Cell(region=-big_cylinder, fill=universe)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<Axes: xlabel='x [cm]', ylabel='y [cm]'>"
      ]
     },
     "execution_count": 12,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": "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",
      "text/plain": [
       "<Figure size 258.065x259.74 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "big_universe = openmc.Universe(cells=[big_cell])\n",
    "big_universe.plot(width=(10.0, 10.0))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We can see that our `big_cell`, the large cylinder, has been filled with the universe we declared earlier. Let's increase the complexity a bit to understand how this filling works. What if we had made our universe so that the intersection of the `horizontal` and `vertical` surfaces occurred at (1, 1) instead of (0, 0)?"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<Axes: xlabel='x [cm]', ylabel='y [cm]'>"
      ]
     },
     "execution_count": 13,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 258.065x259.74 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "horizontal.y0 = 1\n",
    "vertical.x0 = 1\n",
    "big_universe.plot(width=(10.0, 10.0))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We see that when we fill a universe inside of another cell, that there's (by default) no transformation of coordinates. It's as if we are directly underlaying the filled universe into a \"higher-up\" cell. You can shift the position of the universe (_without_ actually modifying the filling universe itself) filling a cell with the `Cell.translation` attribute. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<Axes: xlabel='x [cm]', ylabel='y [cm]'>"
      ]
     },
     "execution_count": 14,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": "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",
      "text/plain": [
       "<Figure size 258.065x259.74 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "big_cell.translation = [0, 2.0, 0]\n",
    "big_universe.plot(width=(10.0, 10.0))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<Axes: xlabel='x [cm]', ylabel='y [cm]'>"
      ]
     },
     "execution_count": 15,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 258.065x259.74 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "universe.plot(width=(10.0, 10.0))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "There are similar adjustments you can make (_without_ actually changing the filling universe itself), like rotations. The `Cell.rotation` method lists the rotation angles (in degrees) for rotations about the x, y, and z axes."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<Axes: xlabel='x [cm]', ylabel='y [cm]'>"
      ]
     },
     "execution_count": 16,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": "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",
      "text/plain": [
       "<Figure size 258.065x259.74 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "big_cell.rotation = [0, 0, -45]\n",
    "big_cell.plot(width=(10.0, 10.0))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<Axes: xlabel='x [cm]', ylabel='y [cm]'>"
      ]
     },
     "execution_count": 17,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 258.065x259.74 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "universe.plot(width=(10.0, 10.0))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "If we wanted to run transport on this overall geometry, we would need to assign some universe to the root universe."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {},
   "outputs": [],
   "source": [
    "model.geometry = openmc.Geometry(big_universe)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Then, let's assign some simple settings and try to run."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {},
   "outputs": [],
   "source": [
    "model.settings = openmc.Settings()\n",
    "model.settings.particles = 100\n",
    "model.settings.inactive = 10\n",
    "model.settings.batches = 20"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "                                %%%%%%%%%%%%%%%\n",
      "                           %%%%%%%%%%%%%%%%%%%%%%%%\n",
      "                        %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%\n",
      "                      %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%\n",
      "                    %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%\n",
      "                   %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%\n",
      "                                    %%%%%%%%%%%%%%%%%%%%%%%%\n",
      "                                     %%%%%%%%%%%%%%%%%%%%%%%%\n",
      "                 ###############      %%%%%%%%%%%%%%%%%%%%%%%%\n",
      "                ##################     %%%%%%%%%%%%%%%%%%%%%%%\n",
      "                ###################     %%%%%%%%%%%%%%%%%%%%%%%\n",
      "                ####################     %%%%%%%%%%%%%%%%%%%%%%\n",
      "                #####################     %%%%%%%%%%%%%%%%%%%%%\n",
      "                ######################     %%%%%%%%%%%%%%%%%%%%\n",
      "                #######################     %%%%%%%%%%%%%%%%%%\n",
      "                 #######################     %%%%%%%%%%%%%%%%%\n",
      "                 ######################     %%%%%%%%%%%%%%%%%\n",
      "                  ####################     %%%%%%%%%%%%%%%%%\n",
      "                    #################     %%%%%%%%%%%%%%%%%\n",
      "                     ###############     %%%%%%%%%%%%%%%%\n",
      "                       ############     %%%%%%%%%%%%%%%\n",
      "                          ########     %%%%%%%%%%%%%%\n",
      "                                      %%%%%%%%%%%\n",
      "\n",
      "                 | The OpenMC Monte Carlo Code\n",
      "       Copyright | 2011-2025 MIT, UChicago Argonne LLC, and contributors\n",
      "         License | https://docs.openmc.org/en/latest/license.html\n",
      "         Version | 0.15.3\n",
      "     Commit Hash | 27e38e894697bb32a1dac7848d2618818b6b8daf\n",
      "       Date/Time | 2025-11-25 08:45:14\n",
      "  OpenMP Threads | 2\n",
      "\n",
      " Reading model XML file 'model.xml' ...\n",
      " Reading chain file: /home/ubuntu/data/depletion_chains/chain_endfb71_pwr.xml...\n",
      " Reading cross sections XML file...\n",
      " ERROR: No boundary conditions were applied to any surfaces!\n",
      "Memory leak detected!\n",
      "Compile in DEBUG mode with --enable-reference-counting\n",
      "for more information\n"
     ]
    },
    {
     "ename": "RuntimeError",
     "evalue": "No boundary conditions were applied to any surfaces! Memory leak detected! Compile in DEBUG mode with --enable-reference-counting for more information",
     "output_type": "error",
     "traceback": [
      "\u001b[0;31m---------------------------------------------------------------------------\u001b[0m",
      "\u001b[0;31mRuntimeError\u001b[0m                              Traceback (most recent call last)",
      "Cell \u001b[0;32mIn[20], line 1\u001b[0m\n\u001b[0;32m----> 1\u001b[0m \u001b[43mmodel\u001b[49m\u001b[38;5;241;43m.\u001b[39;49m\u001b[43mrun\u001b[49m\u001b[43m(\u001b[49m\u001b[43m)\u001b[49m\n",
      "File \u001b[0;32m~/openmc/openmc/model/model.py:871\u001b[0m, in \u001b[0;36mModel.run\u001b[0;34m(self, particles, threads, geometry_debug, restart_file, tracks, output, cwd, openmc_exec, mpi_args, event_based, export_model_xml, apply_tally_results, **export_kwargs)\u001b[0m\n\u001b[1;32m    869\u001b[0m         \u001b[38;5;28mself\u001b[39m\u001b[38;5;241m.\u001b[39mexport_to_xml(\u001b[38;5;241m*\u001b[39m\u001b[38;5;241m*\u001b[39mexport_kwargs)\n\u001b[1;32m    870\u001b[0m     path_input \u001b[38;5;241m=\u001b[39m export_kwargs\u001b[38;5;241m.\u001b[39mget(\u001b[38;5;124m\"\u001b[39m\u001b[38;5;124mpath\u001b[39m\u001b[38;5;124m\"\u001b[39m, \u001b[38;5;28;01mNone\u001b[39;00m)\n\u001b[0;32m--> 871\u001b[0m     \u001b[43mopenmc\u001b[49m\u001b[38;5;241;43m.\u001b[39;49m\u001b[43mrun\u001b[49m\u001b[43m(\u001b[49m\u001b[43mparticles\u001b[49m\u001b[43m,\u001b[49m\u001b[43m \u001b[49m\u001b[43mthreads\u001b[49m\u001b[43m,\u001b[49m\u001b[43m \u001b[49m\u001b[43mgeometry_debug\u001b[49m\u001b[43m,\u001b[49m\u001b[43m \u001b[49m\u001b[43mrestart_file\u001b[49m\u001b[43m,\u001b[49m\n\u001b[1;32m    872\u001b[0m \u001b[43m               \u001b[49m\u001b[43mtracks\u001b[49m\u001b[43m,\u001b[49m\u001b[43m \u001b[49m\u001b[43moutput\u001b[49m\u001b[43m,\u001b[49m\u001b[43m \u001b[49m\u001b[43mPath\u001b[49m\u001b[43m(\u001b[49m\u001b[38;5;124;43m'\u001b[39;49m\u001b[38;5;124;43m.\u001b[39;49m\u001b[38;5;124;43m'\u001b[39;49m\u001b[43m)\u001b[49m\u001b[43m,\u001b[49m\u001b[43m \u001b[49m\u001b[43mopenmc_exec\u001b[49m\u001b[43m,\u001b[49m\u001b[43m \u001b[49m\u001b[43mmpi_args\u001b[49m\u001b[43m,\u001b[49m\n\u001b[1;32m    873\u001b[0m \u001b[43m               \u001b[49m\u001b[43mevent_based\u001b[49m\u001b[43m,\u001b[49m\u001b[43m \u001b[49m\u001b[43mpath_input\u001b[49m\u001b[43m)\u001b[49m\n\u001b[1;32m    875\u001b[0m \u001b[38;5;66;03m# Get output directory and return the last statepoint written\u001b[39;00m\n\u001b[1;32m    876\u001b[0m \u001b[38;5;28;01mif\u001b[39;00m \u001b[38;5;28mself\u001b[39m\u001b[38;5;241m.\u001b[39msettings\u001b[38;5;241m.\u001b[39moutput \u001b[38;5;129;01mand\u001b[39;00m \u001b[38;5;124m'\u001b[39m\u001b[38;5;124mpath\u001b[39m\u001b[38;5;124m'\u001b[39m \u001b[38;5;129;01min\u001b[39;00m \u001b[38;5;28mself\u001b[39m\u001b[38;5;241m.\u001b[39msettings\u001b[38;5;241m.\u001b[39moutput:\n",
      "File \u001b[0;32m~/openmc/openmc/executor.py:314\u001b[0m, in \u001b[0;36mrun\u001b[0;34m(particles, threads, geometry_debug, restart_file, tracks, output, cwd, openmc_exec, mpi_args, event_based, path_input)\u001b[0m\n\u001b[1;32m    261\u001b[0m \u001b[38;5;250m\u001b[39m\u001b[38;5;124;03m\"\"\"Run an OpenMC simulation.\u001b[39;00m\n\u001b[1;32m    262\u001b[0m \n\u001b[1;32m    263\u001b[0m \u001b[38;5;124;03mParameters\u001b[39;00m\n\u001b[0;32m   (...)\u001b[0m\n\u001b[1;32m    305\u001b[0m \n\u001b[1;32m    306\u001b[0m \u001b[38;5;124;03m\"\"\"\u001b[39;00m\n\u001b[1;32m    308\u001b[0m args \u001b[38;5;241m=\u001b[39m _process_CLI_arguments(\n\u001b[1;32m    309\u001b[0m     volume\u001b[38;5;241m=\u001b[39m\u001b[38;5;28;01mFalse\u001b[39;00m, geometry_debug\u001b[38;5;241m=\u001b[39mgeometry_debug, particles\u001b[38;5;241m=\u001b[39mparticles,\n\u001b[1;32m    310\u001b[0m     restart_file\u001b[38;5;241m=\u001b[39mrestart_file, threads\u001b[38;5;241m=\u001b[39mthreads, tracks\u001b[38;5;241m=\u001b[39mtracks,\n\u001b[1;32m    311\u001b[0m     event_based\u001b[38;5;241m=\u001b[39mevent_based, openmc_exec\u001b[38;5;241m=\u001b[39mopenmc_exec, mpi_args\u001b[38;5;241m=\u001b[39mmpi_args,\n\u001b[1;32m    312\u001b[0m     path_input\u001b[38;5;241m=\u001b[39mpath_input)\n\u001b[0;32m--> 314\u001b[0m \u001b[43m_run\u001b[49m\u001b[43m(\u001b[49m\u001b[43margs\u001b[49m\u001b[43m,\u001b[49m\u001b[43m \u001b[49m\u001b[43moutput\u001b[49m\u001b[43m,\u001b[49m\u001b[43m \u001b[49m\u001b[43mcwd\u001b[49m\u001b[43m)\u001b[49m\n",
      "File \u001b[0;32m~/openmc/openmc/executor.py:125\u001b[0m, in \u001b[0;36m_run\u001b[0;34m(args, output, cwd)\u001b[0m\n\u001b[1;32m    122\u001b[0m     error_msg \u001b[38;5;241m=\u001b[39m \u001b[38;5;124m'\u001b[39m\u001b[38;5;124mOpenMC aborted unexpectedly.\u001b[39m\u001b[38;5;124m'\u001b[39m\n\u001b[1;32m    123\u001b[0m error_msg \u001b[38;5;241m=\u001b[39m \u001b[38;5;124m'\u001b[39m\u001b[38;5;124m \u001b[39m\u001b[38;5;124m'\u001b[39m\u001b[38;5;241m.\u001b[39mjoin(error_msg\u001b[38;5;241m.\u001b[39msplit())\n\u001b[0;32m--> 125\u001b[0m \u001b[38;5;28;01mraise\u001b[39;00m \u001b[38;5;167;01mRuntimeError\u001b[39;00m(error_msg)\n",
      "\u001b[0;31mRuntimeError\u001b[0m: No boundary conditions were applied to any surfaces! Memory leak detected! Compile in DEBUG mode with --enable-reference-counting for more information"
     ]
    }
   ],
   "source": [
    "model.run()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "When we try and run, we get an error: `No boundary conditions were applied to any surfaces!` Let's think about the history of a neutron which is initially sampled somewhere inside the geometry but manages to make it to the edge of the cylinder. The neutron may try to cross that cylinder, which is by default a `transmission` boundary type (because we did not set it ourselves). The neutron will try to cross the surface, but because there is no universe or cell on the other side, OpenMC will not be able to sample the next material's cross sections to continue the transport. The fix is that we should set a boundary condition to the `big_cylinder` (the _surface_)."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "metadata": {},
   "outputs": [],
   "source": [
    "big_cylinder.boundary_type = 'vacuum'"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "                                %%%%%%%%%%%%%%%\n",
      "                           %%%%%%%%%%%%%%%%%%%%%%%%\n",
      "                        %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%\n",
      "                      %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%\n",
      "                    %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%\n",
      "                   %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%\n",
      "                                    %%%%%%%%%%%%%%%%%%%%%%%%\n",
      "                                     %%%%%%%%%%%%%%%%%%%%%%%%\n",
      "                 ###############      %%%%%%%%%%%%%%%%%%%%%%%%\n",
      "                ##################     %%%%%%%%%%%%%%%%%%%%%%%\n",
      "                ###################     %%%%%%%%%%%%%%%%%%%%%%%\n",
      "                ####################     %%%%%%%%%%%%%%%%%%%%%%\n",
      "                #####################     %%%%%%%%%%%%%%%%%%%%%\n",
      "                ######################     %%%%%%%%%%%%%%%%%%%%\n",
      "                #######################     %%%%%%%%%%%%%%%%%%\n",
      "                 #######################     %%%%%%%%%%%%%%%%%\n",
      "                 ######################     %%%%%%%%%%%%%%%%%\n",
      "                  ####################     %%%%%%%%%%%%%%%%%\n",
      "                    #################     %%%%%%%%%%%%%%%%%\n",
      "                     ###############     %%%%%%%%%%%%%%%%\n",
      "                       ############     %%%%%%%%%%%%%%%\n",
      "                          ########     %%%%%%%%%%%%%%\n",
      "                                      %%%%%%%%%%%\n",
      "\n",
      "                 | The OpenMC Monte Carlo Code\n",
      "       Copyright | 2011-2025 MIT, UChicago Argonne LLC, and contributors\n",
      "         License | https://docs.openmc.org/en/latest/license.html\n",
      "         Version | 0.15.3\n",
      "     Commit Hash | 27e38e894697bb32a1dac7848d2618818b6b8daf\n",
      "       Date/Time | 2025-11-25 08:47:12\n",
      "  OpenMP Threads | 2\n",
      "\n",
      " Reading model XML file 'model.xml' ...\n",
      " Reading chain file: /home/ubuntu/data/depletion_chains/chain_endfb71_pwr.xml...\n",
      " Reading cross sections XML file...\n",
      " Reading U234 from /home/ubuntu/data/endfb71_hdf5/U234.h5\n",
      " Reading U235 from /home/ubuntu/data/endfb71_hdf5/U235.h5\n",
      " Reading U238 from /home/ubuntu/data/endfb71_hdf5/U238.h5\n",
      " Reading U236 from /home/ubuntu/data/endfb71_hdf5/U236.h5\n",
      " Reading O16 from /home/ubuntu/data/endfb71_hdf5/O16.h5\n",
      " Reading O17 from /home/ubuntu/data/endfb71_hdf5/O17.h5\n",
      " Reading H1 from /home/ubuntu/data/endfb71_hdf5/H1.h5\n",
      " Reading H2 from /home/ubuntu/data/endfb71_hdf5/H2.h5\n",
      " Minimum neutron data temperature: 294 K\n",
      " Maximum neutron data temperature: 294 K\n",
      " Preparing distributed cell instances...\n",
      " Writing summary.h5 file...\n",
      " Maximum neutron transport energy: 20000000 eV for U235\n",
      " Initializing source particles...\n",
      "\n",
      " ====================>     K EIGENVALUE SIMULATION     <====================\n",
      "\n",
      "  Bat./Gen.      k            Average k\n",
      "  =========   ========   ====================\n",
      "        1/1    0.12401\n",
      "        2/1    0.16261\n",
      "        3/1    0.14271\n",
      "        4/1    0.22176\n",
      "        5/1    0.15142\n",
      "        6/1    0.16074\n",
      "        7/1    0.21338\n",
      "        8/1    0.17334\n",
      "        9/1    0.14500\n",
      "       10/1    0.09403\n",
      "       11/1    0.11025\n",
      "       12/1    0.18847    0.14936 +/- 0.03911\n",
      "       13/1    0.21225    0.17032 +/- 0.03081\n",
      "       14/1    0.08748    0.14961 +/- 0.03006\n",
      "       15/1    0.07917    0.13552 +/- 0.02722\n",
      "       16/1    0.20650    0.14735 +/- 0.02517\n",
      "       17/1    0.22479    0.15841 +/- 0.02398\n",
      "       18/1    0.10792    0.15210 +/- 0.02171\n",
      "       19/1    0.23095    0.16086 +/- 0.02105\n",
      "       20/1    0.11252    0.15603 +/- 0.01944\n",
      " Creating state point statepoint.20.h5...\n",
      "\n",
      " =======================>     TIMING STATISTICS     <=======================\n",
      "\n",
      " Total time for initialization     = 3.4103e-01 seconds\n",
      "   Reading cross sections          = 1.6408e-01 seconds\n",
      " Total time in simulation          = 1.0520e-02 seconds\n",
      "   Time in transport only          = 9.0307e-03 seconds\n",
      "   Time in inactive batches        = 4.9895e-03 seconds\n",
      "   Time in active batches          = 5.5303e-03 seconds\n",
      "   Time synchronizing fission bank = 8.2479e-05 seconds\n",
      "     Sampling source sites         = 7.7320e-05 seconds\n",
      "     SEND/RECV source sites        = 2.8850e-06 seconds\n",
      "   Time accumulating tallies       = 3.6930e-06 seconds\n",
      "   Time writing statepoints        = 1.2142e-03 seconds\n",
      " Total time for finalization       = 1.6030e-06 seconds\n",
      " Total time elapsed                = 3.5396e-01 seconds\n",
      " Calculation Rate (inactive)       = 200423 particles/second\n",
      " Calculation Rate (active)         = 180822 particles/second\n",
      "\n",
      " ============================>     RESULTS     <============================\n",
      "\n",
      " k-effective (Collision)     = 0.15502 +/- 0.01873\n",
      " k-effective (Track-length)  = 0.15603 +/- 0.01944\n",
      " k-effective (Absorption)    = 0.12164 +/- 0.01390\n",
      " Combined k-effective        = 0.12525 +/- 0.01883\n",
      " Leakage Fraction            = 0.88900 +/- 0.01433\n",
      "\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "PosixPath('/home/ubuntu/openmc-nea-course/notebooks/lattices/statepoint.20.h5')"
      ]
     },
     "execution_count": 22,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "model.run()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Materials, Cells, etc. Outside the Root Universe\n",
    "\n",
    "Let's suppose we built our universe in such a way that two of our quadrants are completely cut off by the enclosing cylinder. We can do this a few different ways, but let's just change the `horizontal` and `vertical` planes in our initial model so that they intersect at (-10, 0, 0), which will be outside our cylinder."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "metadata": {},
   "outputs": [],
   "source": [
    "horizontal.y0 = 0\n",
    "vertical.x0 = -10"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<Axes: xlabel='x [cm]', ylabel='y [cm]'>"
      ]
     },
     "execution_count": 24,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": "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",
      "text/plain": [
       "<Figure size 258.065x259.74 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "universe.plot(width=(30.0, 30.0))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Let's now plot our geometry, undoing the rotation we added before to make this simpler to understand. You can see that we don't see the materials in the 2nd and 3rd quadrant at all - they've been completely chopped off. However, those materials still exist in the OpenMC model - neutrons will just never reach them. The same idea applies to the cells - the `quad2_cell` and `quad3_cell` still exist in memory, but neutrons never reach there."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 25,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<Axes: xlabel='x [cm]', ylabel='y [cm]'>"
      ]
     },
     "execution_count": 25,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": "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",
      "text/plain": [
       "<Figure size 258.065x259.74 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "big_cell.rotation = [0, 0, 0]\n",
    "big_cell.translation = [0, 0, 0]\n",
    "big_universe.plot(width=(10.0, 10.0))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 26,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "{7: Material\n",
       " \tID             =\t7\n",
       " \tName           =\t(0.1)-(0.9)\n",
       " \tTemperature    =\tNone\n",
       " \tDensity        =\t2.314727435439738 [g/cm3]\n",
       " \tVolume         =\tNone [cm^3]\n",
       " \tDepletable     =\tTrue\n",
       " \tS(a,b) Tables  \n",
       " \tNuclides       \n",
       " \tU234           =\t1.2063713366049352e-05 [ao]\n",
       " \tU235           =\t0.0013496893451669524 [ao]\n",
       " \tU238           =\t0.03196539804932208 [ao]\n",
       " \tU236           =\t6.182225478255921e-06 [ao]\n",
       " \tO16            =\t0.36652769999999996 [ao]\n",
       " \tO17            =\t0.0001389666666666667 [ao]\n",
       " \tH1             =\t0.5999065560000001 [ao]\n",
       " \tH2             =\t9.344400000000001e-05 [ao],\n",
       " 8: Material\n",
       " \tID             =\t8\n",
       " \tName           =\t(0.2)-(0.8)\n",
       " \tTemperature    =\tNone\n",
       " \tDensity        =\t3.540610447480913 [g/cm3]\n",
       " \tVolume         =\tNone [cm^3]\n",
       " \tDepletable     =\tTrue\n",
       " \tS(a,b) Tables  \n",
       " \tNuclides       \n",
       " \tU234           =\t2.4127426732098704e-05 [ao]\n",
       " \tU235           =\t0.0026993786903339047 [ao]\n",
       " \tU238           =\t0.06393079609864416 [ao]\n",
       " \tU236           =\t1.2364450956511845e-05 [ao]\n",
       " \tO16            =\t0.3998484    [ao]\n",
       " \tO17            =\t0.00015160000000000003 [ao]\n",
       " \tH1             =\t0.5332502720000001 [ao]\n",
       " \tH2             =\t8.306133333333334e-05 [ao],\n",
       " 9: Material\n",
       " \tID             =\t9\n",
       " \tName           =\t(0.3)-(0.7)\n",
       " \tTemperature    =\tNone\n",
       " \tDensity        =\t4.686360363370276 [g/cm3]\n",
       " \tVolume         =\tNone [cm^3]\n",
       " \tDepletable     =\tTrue\n",
       " \tS(a,b) Tables  \n",
       " \tNuclides       \n",
       " \tU234           =\t3.619114009814806e-05 [ao]\n",
       " \tU235           =\t0.004049068035500858 [ao]\n",
       " \tU238           =\t0.09589619414796624 [ao]\n",
       " \tU236           =\t1.854667643476777e-05 [ao]\n",
       " \tO16            =\t0.4331691    [ao]\n",
       " \tO17            =\t0.00016423333333333336 [ao]\n",
       " \tH1             =\t0.46659398800000007 [ao]\n",
       " \tH2             =\t7.267866666666667e-05 [ao],\n",
       " 10: Material\n",
       " \tID             =\t10\n",
       " \tName           =\t(0.4)-(0.6)\n",
       " \tTemperature    =\tNone\n",
       " \tDensity        =\t5.759585677120354 [g/cm3]\n",
       " \tVolume         =\tNone [cm^3]\n",
       " \tDepletable     =\tTrue\n",
       " \tS(a,b) Tables  \n",
       " \tNuclides       \n",
       " \tU234           =\t4.825485346419741e-05 [ao]\n",
       " \tU235           =\t0.0053987573806678095 [ao]\n",
       " \tU238           =\t0.12786159219728832 [ao]\n",
       " \tU236           =\t2.4728901913023687e-05 [ao]\n",
       " \tO16            =\t0.4664898    [ao]\n",
       " \tO17            =\t0.00017686666666666667 [ao]\n",
       " \tH1             =\t0.39993770400000006 [ao]\n",
       " \tH2             =\t6.2296e-05   [ao]}"
      ]
     },
     "execution_count": 26,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "all_materials = model.geometry.get_all_materials()\n",
    "all_materials"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 27,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "{5: Cell\n",
       " \tID             =\t5\n",
       " \tName           =\t\n",
       " \tFill           =\t2\n",
       " \tRegion         =\t-3\n",
       " \tRotation       =\t[0 0 0]\n",
       " \tTranslation    =\t[0 0 0]\n",
       " \tVolume         =\tNone,\n",
       " 1: Cell\n",
       " \tID             =\t1\n",
       " \tName           =\t\n",
       " \tFill           =\tMaterial 7\n",
       " \tRegion         =\t(1 2)\n",
       " \tRotation       =\tNone\n",
       " \tTemperature    =\tNone\n",
       " \tDensity        =\tNone\n",
       " \tTranslation    =\tNone\n",
       " \tVolume         =\tNone,\n",
       " 2: Cell\n",
       " \tID             =\t2\n",
       " \tName           =\t\n",
       " \tFill           =\tMaterial 8\n",
       " \tRegion         =\t(1 -2)\n",
       " \tRotation       =\tNone\n",
       " \tTemperature    =\tNone\n",
       " \tDensity        =\tNone\n",
       " \tTranslation    =\tNone\n",
       " \tVolume         =\tNone,\n",
       " 3: Cell\n",
       " \tID             =\t3\n",
       " \tName           =\t\n",
       " \tFill           =\tMaterial 9\n",
       " \tRegion         =\t(-1 -2)\n",
       " \tRotation       =\tNone\n",
       " \tTemperature    =\tNone\n",
       " \tDensity        =\tNone\n",
       " \tTranslation    =\tNone\n",
       " \tVolume         =\tNone,\n",
       " 4: Cell\n",
       " \tID             =\t4\n",
       " \tName           =\t\n",
       " \tFill           =\tMaterial 10\n",
       " \tRegion         =\t(-1 2)\n",
       " \tRotation       =\tNone\n",
       " \tTemperature    =\tNone\n",
       " \tDensity        =\tNone\n",
       " \tTranslation    =\tNone\n",
       " \tVolume         =\tNone}"
      ]
     },
     "execution_count": 27,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "all_cells = model.geometry.get_all_cells()\n",
    "all_cells"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Boundary Conditions When Filled\n",
    "\n",
    "When a universe is filled inside a cell, the boundary conditions on all the various surfaces are unaffected - to understand the boundary conditions in your problem, just think about the process of a neutron walk. Whenever that neutron crosses a surface, that surface's boundary condition will be applied to the neutron. To explore this concept, let's make our filling universe finite in extent. We can do this by placing our original `universe` inside a surface to create a new cell."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 29,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<Axes: xlabel='x [cm]', ylabel='y [cm]'>"
      ]
     },
     "execution_count": 29,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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eeK4HyDW38+fPw2QyYcuWLQgODkZJSQmSkpJQW1uLtWvXWh2blJRk8eFBV1dX0eUS0VNkETSjR4/G6NGjzftBQUEoLS3Fpk2bnhk0rq6u0Gq1okskIitkcenUEL1eb9Nzpnbu3IkuXbqgX79+SE1Nxb1796z2NxqNMBgMFhsRvRhZzGieVlZWhg0bNjxzNjNp0iQEBATAz88PP//8M9577z2Ulpbim2++aXRMRkYGli9f3tQlE7VpDn329uLFi7F69Wqrfc6dO4eQkBDzflVVFUaMGIGoqChs3brVrvMdPnwYo0aNQllZGXr06NFgH6PRaPGUTYPBAH9/fz57mxymNTx726EzmkWLFmHq1KlW+wQFBZn/ffXqVYwcORKRkZH47LPP7D5feHg4AFgNGpVKBZVKZfexiahxDg0aLy8veHl52dS3qqoKI0eOxODBg5GVlQUnJ/uXl4qLiwE8/gY6ETUfWSwGV1VVISoqCt26dcPatWtx/fp16HQ66HQ6iz4hISE4efIkAKC8vBzp6ekoKipCRUUFDhw4gISEBLz22msICwtz1EshapNksRicm5uLsrIylJWV1Xum95Mlprq6OpSWlprfVVIqlcjLy0NmZiZqa2vh7++PCRMmYMmSJc1eP1Fb59DFYDmwdbHLkbgY3Lq1hsVgWVw6EZG8MWiISDgGDREJx6AhIuEYNEQkHIOGiIRj0BCRcAwaIhKOQUNEwjFoiEg4Bg0RCcegISLhGDREJByDhoiEY9AQkXAMGiISjkFDRMIxaIhIOAYNEQnHoCEi4WTxFASyriXfvJoI4IyGiJoBg4aIhJNN0AQGBkKhUFhsq1atsjrm/v37mDNnDjw9PdGpUydMmDABNTW8zCBqbrIJGgBYsWIFqqurzdu8efOs9k9OTsZ3332HvXv34ujRo7h69Sr++Mc/NlO1RPSErBaD3dzcoNVqbeqr1+uxbds27Nq1C6+//joAICsrC6GhoTh+/DiGDx/e4Dij0Qij0WjeNxgML144URsnqxnNqlWr4OnpiYEDB2LNmjV4+PBho32LiopQV1eH6Ohoc1tISAi6deuGwsLCRsdlZGRAo9GYN39//yZ9DURtkWxmNPPnz8egQYPQuXNnFBQUIDU1FdXV1Vi3bl2D/XU6HZRKJdzd3S3afXx8oNPpGj1PamoqUlJSzPsGg4FhQ/SCHBo0ixcvxurVq632OXfuHEJCQiz++MPCwqBUKvH2228jIyMDKpWqyWpSqVRNejwicnDQLFq0CFOnTrXaJygoqMH28PBwPHz4EBUVFejdu3e9n2u1Wjx48AC3b9+2mNXU1NTYvM5DRE3DoUHj5eUFLy+v5xpbXFwMJycneHt7N/jzwYMHo3379sjPz8eECRMAAKWlpaisrERERMRz10xE9pPFGk1hYSFOnDiBkSNHws3NDYWFhUhOTsbkyZPh4eEBAKiqqsKoUaPw97//HcOGDYNGo8GMGTOQkpKCzp07Q61WY968eYiIiGj0HSciEkMWQaNSqfDVV19h2bJlMBqN6N69O5KTky3Wberq6lBaWop79+6Z29avXw8nJydMmDABRqMRMTEx+PTTTx3xEojaNIUkSZKji2jJDAYDNBoN9Ho91Gq1o8shalFs/fuQ1edoiEieGDREJByDhoiEY9AQkXAMGiISjkFDRMIxaIhIOAYNEQnHoCEi4Rg0RCQcg4aIhGPQEJFwDBoiEo5BQ0TCMWiISDgGDREJx6AhIuEYNEQkHIOGiIRj0BCRcAwaIhKOQUNEwskiaI4cOQKFQtHg9uOPPzY6Lioqql7/WbNmNWPlRATI5AFykZGRqK6utmhbunQp8vPzMWTIEKtjk5KSsGLFCvO+q6urkBqJqHGyCBqlUgmtVmver6urw/79+zFv3jwoFAqrY11dXS3GElHzk0XQPO3AgQO4efMmpk2b9sy+O3fuxI4dO6DVajF+/HgsXbrU6qzGaDTCaDSa9/V6PYDHT+QjIktP/i6e+cBbSYbGjBkjjRkz5pn9tmzZIuXk5Eg///yztGPHDqlr167Sm2++aXVMWlqaBIAbN252bJcvX7b6d+XQZ28vXrwYq1evttrn3LlzCAkJMe9fuXIFAQEB2LNnDyZMmGDX+Q4fPoxRo0ahrKwMPXr0aLDP0zMak8mEX375BZ6ens+8TBPFYDDA398fly9fbvPP/+bv4rGW8nuQJAl37tyBn58fnJwaf2/JoUFz/fp13Lx502qfoKAgKJVK8356ejo2bNiAqqoqtG/f3q7z1dbWolOnTsjJyUFMTMxz1ewItj5IvS3g7+Ixuf0eHLpG4+XlBS8vL5v7S5KErKwsJCQk2B0yAFBcXAwA8PX1tXssET0/WXyO5onDhw/j4sWLmDlzZr2fVVVVISQkBCdPngQAlJeXIz09HUVFRaioqMCBAweQkJCA1157DWFhYc1dOlGbJqt3nbZt24bIyEiLNZsn6urqUFpainv37gF4/JZ4Xl4eMjMzUVtbC39/f0yYMAFLlixp7rJfmEqlQlpaGlQqlaNLcTj+Lh6T2+/BoWs0RNQ2yOrSiYjkiUFDRMIxaIhIOAYNEQnHoJGZwMDAere+WLVqlaPLahaffPIJAgMD4eLigvDwcPNHGdqSZcuW1fv/b+hd2JZGVm9v02MrVqxAUlKSed/Nzc2B1TSP3bt3IyUlBZs3b0Z4eDgyMzMRExOD0tJSeHt7O7q8ZtW3b1/k5eWZ99u1a/l/xpzRyJCbmxu0Wq1569ixo6NLEm7dunVISkrCtGnT0KdPH2zevBmurq7Yvn27o0trdu3atbP4/+/SpYujS3omBo0MrVq1Cp6enhg4cCDWrFmDhw8fOrokoR48eICioiJER0eb25ycnBAdHY3CwkIHVuYYFy5cgJ+fH4KCgvDWW2+hsrLS0SU9U8ufc5GF+fPnY9CgQejcuTMKCgqQmpqK6upqrFu3ztGlCXPjxg08evQIPj4+Fu0+Pj44f/68g6pyjPDwcGRnZ6N3796orq7G8uXL8eqrr6KkpKRlX0LbdAMYEuq999575v0+zp071+DYbdu2Se3atZPu37/fzFU3n6qqKgmAVFBQYNH+7rvvSsOGDXNQVS3DrVu3JLVaLW3dutXRpVjFGU0LsGjRIkydOtVqn6CgoAbbw8PD8fDhQ1RUVKB3794CqnO8Ll26wNnZGTU1NRbtNTU1bf42re7u7ujVqxfKysocXYpVDJoWwN7bZfxacXExnJycWvU7L0qlEoMHD0Z+fj5iY2MBPL4hWX5+PubOnevY4hzs7t27KC8vx5QpUxxdilUMGhkpLCzEiRMnMHLkSLi5uaGwsBDJycmYPHkyPDw8HF2eUCkpKUhMTMSQIUMwbNgw87fybblvdGvyzjvvYPz48QgICMDVq1eRlpYGZ2dnxMfHO7o06xx97Ua2KyoqksLDwyWNRiO5uLhIoaGh0sqVK1v1+syvbdiwQerWrZukVCqlYcOGScePH3d0Sc0uLi5O8vX1lZRKpdS1a1cpLi5OKisrc3RZz8TbRBCRcPwcDREJx6AhIuEYNEQkHIOGiIRj0BCRcAwaIhKOQUNEwjFoiEg4Bg21GBUVFebbUw4YMEDoubKzs83nWrhwodBzEYOGWqC8vDzk5+cLPUdcXByqq6sREREh9Dz0GL9USS2Op6cnPD09hZ6jQ4cO6NChA5RKpdDz0GOc0ZAQ169fh1arxcqVK81tBQUFUCqVzzVb2b59O/r27QuVSgVfX1+L20MoFAps2bIF48aNg6urK0JDQ1FYWIiysjJERUWhY8eOiIyMRHl5eZO8NrIfg4aE8PLywvbt27Fs2TKcOnUKd+7cwZQpUzB37lyMGjXKrmNt2rQJc+bMwZ/+9CecPXsWBw4cQHBwsEWf9PR0JCQkoLi4GCEhIZg0aRLefvttpKam4tSpU5Akqc3fu8ahHPztcWrl/vznP0u9evWSJk2aJPXv39/qLS0uXrwoAZBOnz5t0e7n5yd98MEHjY4DIC1ZssS8X1hYKAGQtm3bZm778ssvJRcXl3pjR4wYIS1YsMD2F0TPhTMaEmrt2rV4+PAh9u7di507d0KlUtk1/tq1a7h69eozZ0FhYWHmfz+5iXn//v0t2u7fvw+DwWDX+alpMGhIqPLycly9ehUmkwkVFRV2j+/QoYNN/dq3b2/+t0KhaLTNZDLZXQO9OAYNCfPgwQNMnjwZcXFxSE9Px8yZM3Ht2jW7juHm5obAwEDhb3eTWHx7m4T54IMPoNfr8fHHH6NTp044dOgQpk+fjoMHD9p1nGXLlmHWrFnw9vbGmDFjcOfOHfz73//GvHnzBFVOTY0zGhLiyJEjyMzMxBdffAG1Wg0nJyd88cUX+OGHH7Bp0ya7jpWYmIjMzEx8+umn6Nu3L8aNG4cLFy4IqpxE4D2DqcWoqKhA9+7dcfr0aeFfQXgiKioKAwYMQGZmZrOcr63ijIZanMjISERGRgo9x86dO9GpUyf88MMPQs9Dj3FGQy3GkyduAoBKpYK/v7+wc925c8f85Et3d3d06dJF2LmIQUNEzYCXTkQkHIOGiIRj0BCRcAwaIhKOQUNEwjFoiEg4Bg0RCcegISLh/gdqqrdhMPCFuAAAAABJRU5ErkJggg==",
      "text/plain": [
       "<Figure size 258.065x259.74 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "rectangle = openmc.model.RectangularPrism(width=9, height=9, boundary_type='vacuum')\n",
    "finite_universe = openmc.Universe()\n",
    "finite_universe.add_cell(openmc.Cell(region=-rectangle, fill=universe))\n",
    "\n",
    "finite_universe.plot(width=(15, 15))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 30,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<Axes: xlabel='x [cm]', ylabel='y [cm]'>"
      ]
     },
     "execution_count": 30,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 258.065x259.74 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "big_cell.fill = finite_universe\n",
    "big_universe.plot(width=(10, 10))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 31,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "                                %%%%%%%%%%%%%%%\n",
      "                           %%%%%%%%%%%%%%%%%%%%%%%%\n",
      "                        %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%\n",
      "                      %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%\n",
      "                    %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%\n",
      "                   %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%\n",
      "                                    %%%%%%%%%%%%%%%%%%%%%%%%\n",
      "                                     %%%%%%%%%%%%%%%%%%%%%%%%\n",
      "                 ###############      %%%%%%%%%%%%%%%%%%%%%%%%\n",
      "                ##################     %%%%%%%%%%%%%%%%%%%%%%%\n",
      "                ###################     %%%%%%%%%%%%%%%%%%%%%%%\n",
      "                ####################     %%%%%%%%%%%%%%%%%%%%%%\n",
      "                #####################     %%%%%%%%%%%%%%%%%%%%%\n",
      "                ######################     %%%%%%%%%%%%%%%%%%%%\n",
      "                #######################     %%%%%%%%%%%%%%%%%%\n",
      "                 #######################     %%%%%%%%%%%%%%%%%\n",
      "                 ######################     %%%%%%%%%%%%%%%%%\n",
      "                  ####################     %%%%%%%%%%%%%%%%%\n",
      "                    #################     %%%%%%%%%%%%%%%%%\n",
      "                     ###############     %%%%%%%%%%%%%%%%\n",
      "                       ############     %%%%%%%%%%%%%%%\n",
      "                          ########     %%%%%%%%%%%%%%\n",
      "                                      %%%%%%%%%%%\n",
      "\n",
      "                 | The OpenMC Monte Carlo Code\n",
      "       Copyright | 2011-2025 MIT, UChicago Argonne LLC, and contributors\n",
      "         License | https://docs.openmc.org/en/latest/license.html\n",
      "         Version | 0.15.3\n",
      "     Commit Hash | 27e38e894697bb32a1dac7848d2618818b6b8daf\n",
      "       Date/Time | 2025-11-25 08:59:28\n",
      "  OpenMP Threads | 2\n",
      "\n",
      " Reading model XML file 'model.xml' ...\n",
      " Reading chain file: /home/ubuntu/data/depletion_chains/chain_endfb71_pwr.xml...\n",
      " Reading cross sections XML file...\n",
      " Reading U234 from /home/ubuntu/data/endfb71_hdf5/U234.h5\n",
      " Reading U235 from /home/ubuntu/data/endfb71_hdf5/U235.h5\n",
      " Reading U238 from /home/ubuntu/data/endfb71_hdf5/U238.h5\n",
      " Reading U236 from /home/ubuntu/data/endfb71_hdf5/U236.h5\n",
      " Reading O16 from /home/ubuntu/data/endfb71_hdf5/O16.h5\n",
      " Reading O17 from /home/ubuntu/data/endfb71_hdf5/O17.h5\n",
      " Reading H1 from /home/ubuntu/data/endfb71_hdf5/H1.h5\n",
      " Reading H2 from /home/ubuntu/data/endfb71_hdf5/H2.h5\n",
      " Minimum neutron data temperature: 294 K\n",
      " Maximum neutron data temperature: 294 K\n",
      " Preparing distributed cell instances...\n",
      " Writing summary.h5 file...\n",
      " Maximum neutron transport energy: 20000000 eV for U235\n",
      " Initializing source particles...\n",
      "\n",
      " ====================>     K EIGENVALUE SIMULATION     <====================\n",
      "\n",
      "  Bat./Gen.      k            Average k\n",
      "  =========   ========   ====================\n",
      "        1/1    0.17738\n",
      "        2/1    0.17054\n",
      "        3/1    0.20795\n",
      "        4/1    0.14030\n",
      "        5/1    0.07530\n",
      "        6/1    0.20859\n",
      "        7/1    0.11350\n",
      "        8/1    0.09676\n",
      "        9/1    0.12651\n",
      "       10/1    0.23507\n",
      "       11/1    0.18905\n",
      "       12/1    0.19389    0.19147 +/- 0.00242\n",
      "       13/1    0.18617    0.18971 +/- 0.00225\n",
      "       14/1    0.11350    0.17066 +/- 0.01912\n",
      "       15/1    0.08379    0.15328 +/- 0.02283\n",
      "       16/1    0.15315    0.15326 +/- 0.01864\n",
      "       17/1    0.11722    0.14811 +/- 0.01657\n",
      "       18/1    0.19701    0.15422 +/- 0.01560\n",
      "       19/1    0.11963    0.15038 +/- 0.01428\n",
      "       20/1    0.18579    0.15392 +/- 0.01326\n",
      " Creating state point statepoint.20.h5...\n",
      "\n",
      " =======================>     TIMING STATISTICS     <=======================\n",
      "\n",
      " Total time for initialization     = 3.3451e-01 seconds\n",
      "   Reading cross sections          = 1.6221e-01 seconds\n",
      " Total time in simulation          = 1.1985e-02 seconds\n",
      "   Time in transport only          = 1.0366e-02 seconds\n",
      "   Time in inactive batches        = 5.6336e-03 seconds\n",
      "   Time in active batches          = 6.3516e-03 seconds\n",
      "   Time synchronizing fission bank = 8.9363e-05 seconds\n",
      "     Sampling source sites         = 7.9982e-05 seconds\n",
      "     SEND/RECV source sites        = 7.0610e-06 seconds\n",
      "   Time accumulating tallies       = 6.6810e-06 seconds\n",
      "   Time writing statepoints        = 1.3227e-03 seconds\n",
      " Total time for finalization       = 2.0260e-06 seconds\n",
      " Total time elapsed                = 3.4924e-01 seconds\n",
      " Calculation Rate (inactive)       = 177507 particles/second\n",
      " Calculation Rate (active)         = 157440 particles/second\n",
      "\n",
      " ============================>     RESULTS     <============================\n",
      "\n",
      " k-effective (Collision)     = 0.15193 +/- 0.01183\n",
      " k-effective (Track-length)  = 0.15392 +/- 0.01326\n",
      " k-effective (Absorption)    = 0.15145 +/- 0.02764\n",
      " Combined k-effective        = 0.15095 +/- 0.01184\n",
      " Leakage Fraction            = 0.87400 +/- 0.01492\n",
      "\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "PosixPath('/home/ubuntu/openmc-nea-course/notebooks/lattices/statepoint.20.h5')"
      ]
     },
     "execution_count": 31,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "model.run()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Our model has correctly defined all boundary conditions - any time a neutron would leave the rectangular prism surface defining our square, the neutron encounters a vacuum boundary condition. If a neutron instead first passes through the cylinder, it also sees a vacuum boundary condition. So, our model effectively has the following boundaries.\n",
    "\n",
    "<img src=\"bcs.png\" alt=\"drawing\" width=\"=100\"/>\n",
    "\n",
    "If the boundary conditions on `rectangle` had instead been `transmission`, then we would have a problem - the neutron would try to cross the red surfaces, but OpenMC would not be able to find any material on the other side."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We'll use this universe again later - let's remove the translation so that our quadrants have an origin at (0, 0)."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 32,
   "metadata": {},
   "outputs": [],
   "source": [
    "horizontal.x0 = 0\n",
    "vertical.y0 = 0"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Lattices\n",
    "\n",
    "Lattices are a convenient way to (i) repeat a universe multiple times in space, while (ii) automatically translating that universe's origin to different positions in space. \n",
    "\n",
    "In this section, we will build one of the assemblies from the BEAVRS benchmark. This is a Pressurized Water Reactor (PWR) assembly with fuel pins, guide tubes, and borosilicate glass burnable poisons. A diagram of the assembly is plotted below.\n",
    "\n",
    "<img src=\"assembly_diagram.png\" alt=\"drawing\" width=\"=150\"/>\n",
    "\n",
    "In order to build this geometry, we will need to define four universes -- one for a fuel pin (the lilac square with nothing indicated in them), one for a poison pin (B), one for an instrumentation pin (I), and one for a guide tube (G). \n",
    "\n",
    "Before we can discuss lattices, we need to build the materials, cells, and universes for each of these."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Fuel pin universe\n",
    "\n",
    "To build our fuel pin universe, we will require three materials. Note that we treat the helium gap as vacuum by setting `fill=None`."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 33,
   "metadata": {},
   "outputs": [],
   "source": [
    "uo2 = openmc.Material(name='uo2')\n",
    "uo2.add_element('U', 1.0, enrichment=3.0)\n",
    "uo2.add_nuclide('O16', 2.0)\n",
    "uo2.set_density('g/cm3', 10.0)\n",
    "\n",
    "zirconium = openmc.Material(name='zirconium')\n",
    "zirconium.add_element('Zr', 1.0)\n",
    "zirconium.set_density('g/cm3', 6.6)\n",
    "\n",
    "water = openmc.Material(name='water')\n",
    "water.add_nuclide('H1', 2)\n",
    "water.add_nuclide('O16', 1)\n",
    "water.set_density('g/cm3', 0.7)\n",
    "water.add_s_alpha_beta('c_H_in_H2O')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 37,
   "metadata": {},
   "outputs": [],
   "source": [
    "pitch = 1.26\n",
    "\n",
    "fuel_or = openmc.ZCylinder(r=0.39)\n",
    "clad_ir = openmc.ZCylinder(r=0.40)\n",
    "clad_or = openmc.ZCylinder(r=0.46)\n",
    "\n",
    "fuel = openmc.Cell(region = -fuel_or, fill=uo2)\n",
    "gap = openmc.Cell(region = +fuel_or & -clad_ir, fill=None)\n",
    "clad = openmc.Cell(region = +clad_ir & -clad_or, fill=zirconium)\n",
    "moderator = openmc.Cell(region = +clad_or, fill=water)\n",
    "\n",
    "fuel_pin = openmc.Universe(cells=[fuel, gap, clad, moderator])"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "When building a complex geometry, it is helpful to plot each universe as you go along. Let's plot this pincell now. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 38,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<Axes: xlabel='x [cm]', ylabel='y [cm]'>"
      ]
     },
     "execution_count": 38,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": "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",
      "text/plain": [
       "<Figure size 258.065x259.74 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "fuel_pin.plot(width=(10*pitch, 10*pitch))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Guide tube universe\n",
    "A guide tube is an annulus of zirconium within which water flows. These tubes are used to receive control rods."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 39,
   "metadata": {},
   "outputs": [],
   "source": [
    "guide_clad_ir = openmc.ZCylinder(r=0.56)\n",
    "guide_clad_or = openmc.ZCylinder(r=0.60)\n",
    "\n",
    "guide_inner = openmc.Cell(region=-guide_clad_ir, fill=water)\n",
    "guide_clad = openmc.Cell(region=+guide_clad_ir & -guide_clad_or, fill=zirconium)\n",
    "guide_outer = openmc.Cell(region=+guide_clad_or, fill=water)\n",
    "\n",
    "guide_tube = openmc.Universe()\n",
    "guide_tube.add_cells([guide_inner, guide_clad, guide_outer])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 41,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<Axes: xlabel='x [cm]', ylabel='y [cm]'>"
      ]
     },
     "execution_count": 41,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": "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",
      "text/plain": [
       "<Figure size 258.065x259.74 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "guide_tube.plot(width=(10*pitch, 10*pitch), color_by='material')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Pyrex burnable poison universe\n",
    "The burnable absorber universe is a series of annular cylinders enclosing an annular pyrex layer. The geometry is defined as follows:\n",
    "\n",
    "- R < 0.21 cm, void\n",
    "- 0.21 cm < R < 0.23 cm, zirconium\n",
    "- 0.23 cm < R < 0.24 cm, void\n",
    "- 0.24 cm < R < 0.43 cm, pyrex\n",
    "- 0.43 cm < R < 0.44 cm, void\n",
    "- 0.44 cm < R < 0.48 cm, zirconium\n",
    "- 0.48 cm < R < 0.56 cm, water\n",
    "- 0.56 cm < R < 0.60 cm, zirconium\n",
    "- 0.60 cm < R, water"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 42,
   "metadata": {},
   "outputs": [],
   "source": [
    "pyrex = openmc.Material(name='pyrex')\n",
    "pyrex.add_element('B', 0.49)\n",
    "pyrex.add_element('O', 4.7)\n",
    "pyrex.add_element('Al', 0.17)\n",
    "pyrex.add_element('Si', 1.8)\n",
    "pyrex.set_density('g/cm3', 2.26)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "To create the geometry, we're going to use some advanced features. First, we'll use a [list comprehension](https://docs.python.org/3/tutorial/datastructures.html#list-comprehensions), which is a way of creating a list in Python that embeds a for loop."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 43,
   "metadata": {},
   "outputs": [],
   "source": [
    "radii = [0.21, 0.23, 0.24, 0.43, 0.44, 0.48, 0.56, 0.60]\n",
    "cyls = [openmc.ZCylinder(r=r0) for r0 in radii]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 44,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[Surface\n",
       " \tID                 =\t23\n",
       " \tName               =\t\n",
       " \tType               =\tz-cylinder\n",
       " \tBoundary           =\ttransmission\n",
       " \tCoefficients       \n",
       " x0                  =\t0.0\n",
       " y0                  =\t0.0\n",
       " r                   =\t0.21,\n",
       " Surface\n",
       " \tID                 =\t24\n",
       " \tName               =\t\n",
       " \tType               =\tz-cylinder\n",
       " \tBoundary           =\ttransmission\n",
       " \tCoefficients       \n",
       " x0                  =\t0.0\n",
       " y0                  =\t0.0\n",
       " r                   =\t0.23,\n",
       " Surface\n",
       " \tID                 =\t25\n",
       " \tName               =\t\n",
       " \tType               =\tz-cylinder\n",
       " \tBoundary           =\ttransmission\n",
       " \tCoefficients       \n",
       " x0                  =\t0.0\n",
       " y0                  =\t0.0\n",
       " r                   =\t0.24,\n",
       " Surface\n",
       " \tID                 =\t26\n",
       " \tName               =\t\n",
       " \tType               =\tz-cylinder\n",
       " \tBoundary           =\ttransmission\n",
       " \tCoefficients       \n",
       " x0                  =\t0.0\n",
       " y0                  =\t0.0\n",
       " r                   =\t0.43,\n",
       " Surface\n",
       " \tID                 =\t27\n",
       " \tName               =\t\n",
       " \tType               =\tz-cylinder\n",
       " \tBoundary           =\ttransmission\n",
       " \tCoefficients       \n",
       " x0                  =\t0.0\n",
       " y0                  =\t0.0\n",
       " r                   =\t0.44,\n",
       " Surface\n",
       " \tID                 =\t28\n",
       " \tName               =\t\n",
       " \tType               =\tz-cylinder\n",
       " \tBoundary           =\ttransmission\n",
       " \tCoefficients       \n",
       " x0                  =\t0.0\n",
       " y0                  =\t0.0\n",
       " r                   =\t0.48,\n",
       " Surface\n",
       " \tID                 =\t29\n",
       " \tName               =\t\n",
       " \tType               =\tz-cylinder\n",
       " \tBoundary           =\ttransmission\n",
       " \tCoefficients       \n",
       " x0                  =\t0.0\n",
       " y0                  =\t0.0\n",
       " r                   =\t0.56,\n",
       " Surface\n",
       " \tID                 =\t30\n",
       " \tName               =\t\n",
       " \tType               =\tz-cylinder\n",
       " \tBoundary           =\ttransmission\n",
       " \tCoefficients       \n",
       " x0                  =\t0.0\n",
       " y0                  =\t0.0\n",
       " r                   =\t0.6]"
      ]
     },
     "execution_count": 44,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "cyls"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "To create this pin, we're going to use a function provided by OpenMC specifically for this purpose, [`openmc.model.pin`](https://docs.openmc.org/en/stable/pythonapi/model.html)."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 45,
   "metadata": {},
   "outputs": [],
   "source": [
    "mats = [None, zirconium, None, pyrex, None, zirconium, water, zirconium, water]\n",
    "burn = openmc.model.pin(cyls, mats)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 47,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<Axes: xlabel='x [cm]', ylabel='y [cm]'>"
      ]
     },
     "execution_count": 47,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": "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",
      "text/plain": [
       "<Figure size 258.065x259.74 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "burn.plot(width=(5*pitch, 5*pitch), color_by='material')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Lattices in OpenMC\n",
    "\n",
    "OpenMC has `RectLattice` and `HexLattice` objects, to place universes within a rectangular or hexagonal lattice, respectively. The `RectLattice` can be built in 1-D, 2-D, or 3-D, whereas the `HexLattice` can be built in 2-D or 3-D. For our fuel assembly, we will use a 2-D `RectLattice` (infinite in the vertical direction).\n",
    "\n",
    "When creating a rectangular lattice, we need to define:\n",
    "\n",
    "- The lower-left coordinates of the lattice (`.lower_left`)\n",
    "- The size of each lattice element (`.pitch`)\n",
    "- The 2D arrangement of universes (`.universes`)\n",
    "- (optionally) A universe that is used outside of the defined region (`.outer`); this is only relevant if the lattice is filled inside another cell whose boundary allows some \"open space\" outside the nominal edges of the lattice and the surface defining the cell."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 48,
   "metadata": {},
   "outputs": [],
   "source": [
    "lattice = openmc.RectLattice()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 49,
   "metadata": {},
   "outputs": [],
   "source": [
    "lattice.lower_left = (0, 0)\n",
    "lattice.pitch = (pitch, pitch)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 52,
   "metadata": {},
   "outputs": [],
   "source": [
    "lattice.universes = [\n",
    "    [fuel_pin, burn], \n",
    "    [guide_tube, fuel_pin]\n",
    "]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 54,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<Axes: xlabel='x [cm]', ylabel='y [cm]'>"
      ]
     },
     "execution_count": 54,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 258.065x259.74 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "example_univ = openmc.Universe(cells=[openmc.Cell(fill=lattice)])\n",
    "example_univ.plot(width=(2*pitch, 2*pitch), origin=(pitch, pitch, 0), color_by='material')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "By default, the extent of a lattice only covers the actual lattice \"slots.\" If we try to plot our geometry but with a wider width (so that we are including regions of space outside our 2x2 lattice), OpenMC will throw an error."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 55,
   "metadata": {},
   "outputs": [
    {
     "ename": "RuntimeError",
     "evalue": "Particle -1 left lattice 11, but it has no outer definition. ERROR: Particle -1 left lattice 11, but it has no outer definition.",
     "output_type": "error",
     "traceback": [
      "\u001b[0;31m---------------------------------------------------------------------------\u001b[0m",
      "\u001b[0;31mRuntimeError\u001b[0m                              Traceback (most recent call last)",
      "Cell \u001b[0;32mIn[55], line 1\u001b[0m\n\u001b[0;32m----> 1\u001b[0m \u001b[43mexample_univ\u001b[49m\u001b[38;5;241;43m.\u001b[39;49m\u001b[43mplot\u001b[49m\u001b[43m(\u001b[49m\u001b[43mwidth\u001b[49m\u001b[38;5;241;43m=\u001b[39;49m\u001b[43m(\u001b[49m\u001b[38;5;241;43m3\u001b[39;49m\u001b[38;5;241;43m*\u001b[39;49m\u001b[43mpitch\u001b[49m\u001b[43m,\u001b[49m\u001b[43m \u001b[49m\u001b[38;5;241;43m3\u001b[39;49m\u001b[38;5;241;43m*\u001b[39;49m\u001b[43mpitch\u001b[49m\u001b[43m)\u001b[49m\u001b[43m,\u001b[49m\u001b[43m \u001b[49m\u001b[43morigin\u001b[49m\u001b[38;5;241;43m=\u001b[39;49m\u001b[43m(\u001b[49m\u001b[43mpitch\u001b[49m\u001b[43m,\u001b[49m\u001b[43m \u001b[49m\u001b[43mpitch\u001b[49m\u001b[43m,\u001b[49m\u001b[43m \u001b[49m\u001b[38;5;241;43m0\u001b[39;49m\u001b[43m)\u001b[49m\u001b[43m)\u001b[49m\n",
      "File \u001b[0;32m~/openmc/openmc/universe.py:340\u001b[0m, in \u001b[0;36mUniverseBase.plot\u001b[0;34m(self, *args, **kwargs)\u001b[0m\n\u001b[1;32m    338\u001b[0m model \u001b[38;5;241m=\u001b[39m openmc\u001b[38;5;241m.\u001b[39mModel()\n\u001b[1;32m    339\u001b[0m model\u001b[38;5;241m.\u001b[39mgeometry \u001b[38;5;241m=\u001b[39m openmc\u001b[38;5;241m.\u001b[39mGeometry(\u001b[38;5;28mself\u001b[39m)\n\u001b[0;32m--> 340\u001b[0m \u001b[38;5;28;01mreturn\u001b[39;00m \u001b[43mmodel\u001b[49m\u001b[38;5;241;43m.\u001b[39;49m\u001b[43mplot\u001b[49m\u001b[43m(\u001b[49m\u001b[38;5;241;43m*\u001b[39;49m\u001b[43margs\u001b[49m\u001b[43m,\u001b[49m\u001b[43m \u001b[49m\u001b[38;5;241;43m*\u001b[39;49m\u001b[38;5;241;43m*\u001b[39;49m\u001b[43mkwargs\u001b[49m\u001b[43m)\u001b[49m\n",
      "File \u001b[0;32m~/openmc/openmc/model/model.py:1176\u001b[0m, in \u001b[0;36mModel.plot\u001b[0;34m(self, origin, width, pixels, basis, color_by, colors, seed, openmc_exec, axes, legend, axis_units, outline, show_overlaps, overlap_color, n_samples, plane_tolerance, legend_kwargs, source_kwargs, contour_kwargs, **kwargs)\u001b[0m\n\u001b[1;32m   1173\u001b[0m \u001b[38;5;28mself\u001b[39m\u001b[38;5;241m.\u001b[39mplots\u001b[38;5;241m.\u001b[39mappend(plot)\n\u001b[1;32m   1175\u001b[0m \u001b[38;5;66;03m# Run OpenMC in geometry plotting mode\u001b[39;00m\n\u001b[0;32m-> 1176\u001b[0m \u001b[38;5;28;43mself\u001b[39;49m\u001b[38;5;241;43m.\u001b[39;49m\u001b[43mplot_geometry\u001b[49m\u001b[43m(\u001b[49m\u001b[38;5;28;43;01mFalse\u001b[39;49;00m\u001b[43m,\u001b[49m\u001b[43m \u001b[49m\u001b[43mcwd\u001b[49m\u001b[38;5;241;43m=\u001b[39;49m\u001b[43mtmpdir\u001b[49m\u001b[43m,\u001b[49m\u001b[43m \u001b[49m\u001b[43mopenmc_exec\u001b[49m\u001b[38;5;241;43m=\u001b[39;49m\u001b[43mopenmc_exec\u001b[49m\u001b[43m)\u001b[49m\n\u001b[1;32m   1178\u001b[0m \u001b[38;5;66;03m# Undo changes to model\u001b[39;00m\n\u001b[1;32m   1179\u001b[0m \u001b[38;5;28mself\u001b[39m\u001b[38;5;241m.\u001b[39mplots\u001b[38;5;241m.\u001b[39mpop()\n",
      "File \u001b[0;32m~/openmc/openmc/model/model.py:1378\u001b[0m, in \u001b[0;36mModel.plot_geometry\u001b[0;34m(self, output, cwd, openmc_exec, export_model_xml, **export_kwargs)\u001b[0m\n\u001b[1;32m   1376\u001b[0m     \u001b[38;5;28mself\u001b[39m\u001b[38;5;241m.\u001b[39mexport_to_xml(\u001b[38;5;241m*\u001b[39m\u001b[38;5;241m*\u001b[39mexport_kwargs)\n\u001b[1;32m   1377\u001b[0m path_input \u001b[38;5;241m=\u001b[39m export_kwargs\u001b[38;5;241m.\u001b[39mget(\u001b[38;5;124m\"\u001b[39m\u001b[38;5;124mpath\u001b[39m\u001b[38;5;124m\"\u001b[39m, \u001b[38;5;28;01mNone\u001b[39;00m)\n\u001b[0;32m-> 1378\u001b[0m \u001b[43mopenmc\u001b[49m\u001b[38;5;241;43m.\u001b[39;49m\u001b[43mplot_geometry\u001b[49m\u001b[43m(\u001b[49m\u001b[43moutput\u001b[49m\u001b[38;5;241;43m=\u001b[39;49m\u001b[43moutput\u001b[49m\u001b[43m,\u001b[49m\u001b[43m \u001b[49m\u001b[43mopenmc_exec\u001b[49m\u001b[38;5;241;43m=\u001b[39;49m\u001b[43mopenmc_exec\u001b[49m\u001b[43m,\u001b[49m\n\u001b[1;32m   1379\u001b[0m \u001b[43m                     \u001b[49m\u001b[43mpath_input\u001b[49m\u001b[38;5;241;43m=\u001b[39;49m\u001b[43mpath_input\u001b[49m\u001b[43m)\u001b[49m\n",
      "File \u001b[0;32m~/openmc/openmc/executor.py:154\u001b[0m, in \u001b[0;36mplot_geometry\u001b[0;34m(output, openmc_exec, cwd, path_input)\u001b[0m\n\u001b[1;32m    152\u001b[0m \u001b[38;5;28;01mif\u001b[39;00m path_input \u001b[38;5;129;01mis\u001b[39;00m \u001b[38;5;129;01mnot\u001b[39;00m \u001b[38;5;28;01mNone\u001b[39;00m:\n\u001b[1;32m    153\u001b[0m     args \u001b[38;5;241m+\u001b[39m\u001b[38;5;241m=\u001b[39m [path_input]\n\u001b[0;32m--> 154\u001b[0m \u001b[43m_run\u001b[49m\u001b[43m(\u001b[49m\u001b[43margs\u001b[49m\u001b[43m,\u001b[49m\u001b[43m \u001b[49m\u001b[43moutput\u001b[49m\u001b[43m,\u001b[49m\u001b[43m \u001b[49m\u001b[43mcwd\u001b[49m\u001b[43m)\u001b[49m\n",
      "File \u001b[0;32m~/openmc/openmc/executor.py:125\u001b[0m, in \u001b[0;36m_run\u001b[0;34m(args, output, cwd)\u001b[0m\n\u001b[1;32m    122\u001b[0m     error_msg \u001b[38;5;241m=\u001b[39m \u001b[38;5;124m'\u001b[39m\u001b[38;5;124mOpenMC aborted unexpectedly.\u001b[39m\u001b[38;5;124m'\u001b[39m\n\u001b[1;32m    123\u001b[0m error_msg \u001b[38;5;241m=\u001b[39m \u001b[38;5;124m'\u001b[39m\u001b[38;5;124m \u001b[39m\u001b[38;5;124m'\u001b[39m\u001b[38;5;241m.\u001b[39mjoin(error_msg\u001b[38;5;241m.\u001b[39msplit())\n\u001b[0;32m--> 125\u001b[0m \u001b[38;5;28;01mraise\u001b[39;00m \u001b[38;5;167;01mRuntimeError\u001b[39;00m(error_msg)\n",
      "\u001b[0;31mRuntimeError\u001b[0m: Particle -1 left lattice 11, but it has no outer definition. ERROR: Particle -1 left lattice 11, but it has no outer definition."
     ]
    }
   ],
   "source": [
    "example_univ.plot(width=(3*pitch, 3*pitch), origin=(pitch, pitch, 0))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "If we ever want to plot or have neutrons track through regions outside the lattice, but which are not also \"chopped off\" by some containing cell, we can specify the `.outer` parameter for the lattice. As an example, let's set the outer universe to an infinite universe of water."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 56,
   "metadata": {},
   "outputs": [],
   "source": [
    "all_water = openmc.Universe()\n",
    "all_water.add_cell(openmc.Cell(fill=water))\n",
    "lattice.outer = all_water"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 57,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<Axes: xlabel='x [cm]', ylabel='y [cm]'>"
      ]
     },
     "execution_count": 57,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": "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",
      "text/plain": [
       "<Figure size 258.065x259.74 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "example_univ.plot(width=(3*pitch, 3*pitch), origin=(pitch, pitch, 0), color_by='material')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## What exactly does `outer` mean?\n",
    "\n",
    "To get a better sense of what the outer universe does, let's change the outer universe to the quadrant universe we created earlier. We could also try with a `burn` universe."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 58,
   "metadata": {},
   "outputs": [],
   "source": [
    "lattice.outer = universe"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 61,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<Axes: xlabel='x [cm]', ylabel='y [cm]'>"
      ]
     },
     "execution_count": 61,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAQ0AAAEHCAYAAAC0iRNuAAAAOnRFWHRTb2Z0d2FyZQBNYXRwbG90bGliIHZlcnNpb24zLjEwLjMsIGh0dHBzOi8vbWF0cGxvdGxpYi5vcmcvZiW1igAAAAlwSFlzAAAPYQAAD2EBqD+naQAAG0pJREFUeJzt3XtQVOf9P/D3gZ+uXFa8AUIhiqXG1mtivKD9RoxETTCJ/SNja6OIic0FjIZOJqGJMdY0aLWVxHtrvYxjok0zitHEbwm/QU3VxHih4owmWm1QvKypXRDNYtjn+8dy1l257Hl2z+Hssu8XszNyOJcPyL55znPOeR5FCCFARKRRhNkFEFFoYWgQkRSGBhFJYWgQkRSGBhFJYWgQkRSGBhFJYWgQkZT/Z3YBbcnpdKK6uhpWqxWKophdDlFQEUKgtrYWycnJiIhouT0RVqFRXV2N1NRUs8sgCmpVVVVISUlp8ethFRpWqxUAsOmDRxEd3cHkaoiCy82bt5Hz5Mfu90lLwio01FOS6OgOiI5haBA1x9epOztCiUgKQ4OIpDA0iEgKQ4OIpDA0iEgKQ4OIpDA0iEgKQ4OIpDA0iEgKQ4OIpDA0iEgKQ4OIpDA0iEhKWD3lqhKNH0R0h9b3RFiGRnm3A7DEspFF5MlhcWpaj+8cIpLC0CAiKQwNIpLC0CAiKQwNIpISsqGxaNEiKIqCuXPnml0KUVgJydA4fPgw1q5di0GDBpldClHYCbnQuHHjBn75y1/iz3/+M7p27Wp2OURhJ+RCIy8vD9nZ2cjKyvK5rsPhQE1NjdeLiAITUneEbt26FUePHsXhw4c1rV9UVIQFCxYYXBVReAmZlkZVVRXmzJmDLVu2oFOnTpq2KSwshN1ud7+qqqoMrpKo/QuZlsaRI0dw9epV3H///e5lDQ0N2LdvH1asWAGHw4HIyEivbSwWCywWS1uXStSuhUxojBs3DidOnPBalpubi379+uGVV15pEhhEZIyQCQ2r1YoBAwZ4LYuJiUH37t2bLCci44RMaOhKNL6I6A6N74mQDo3y8nK/tht7fTSi6zvoWwxRiLtZdxurUOJzvZC5ekJEwYGhQURSGBpEJIWhQURSGBpEJIWhQURSGBpEJIWhQURSGBpEJIWhQURSGBpEJIWhQURSGBpEJIWhQURSGBpEJCWkx9Pwl2j8IKI7tL4nwjI0yrsdgCWWjSwiTw6LU9N6fOcQkRSGBhFJYWgQkRSGBhFJYWgQkRSGBhFJYWgQkRSGBhFJYWgQkRSGBhFJYWgQkRSGBhFJYWgQkRSGBhFJYWgQkZSwHE8DovEV5vgjcFHMLiBYaPyFCMvQGHt9NKLrO5hdhqmEAD4sfd7kGgR2LX03oH1Epq6AEALOC7P93sem0o4B1dBe3Ky7jVUo8bleWIYGhabI1OXNLBVQlKZfa6jyP0SodQwNCnpqIGwoOalpfSGAmZNd2zA89MfQoKAVmboCgPAOC+H7xFtRFGwoOcnwMAhDg6SMn57cZJkQAqWbL+l6nCaB0RgWgz7d53Pbf2Y9CKBpeDA49MHQIE3GT0+GEAKihb/0D09LgqIougRIc4GhhkXFrv9F9ufftbjt7pFRGNz4b8/wWL/jJINDJwwNapXashBC4Ksp8xB9+dUm6wgI3EpajL5bF7q38Tc8WgoMX2Ghyj50CzhUcic8FAX/HPc/DA4d8eYuapFn6+LCmLpmAwMAFCiIvvQqLoypw4UxdRBCQFEUPDwtSep4LQVGyrwSTYHhKfvQLaTMK3Hto2w/IFxXWdbvOImIlOauwpBWDA1qlhoYX02Zhwtj6qS29T84mg+MQHgFRyOFd3MFJGRCo6ioCMOGDYPVakVCQgImT56M06dPm11Wu+QZGC21LnxRg0MrVyujkccpScvu3nfLx1KDg60NfYRMaOzduxd5eXk4dOgQSktLcfv2bYwfPx51dXJ/BUk7fwNDpbZQtLU2GlsZQmBwY6ugtVMS25Ia7H600P2yLbG799Ocit1/Z2tDJyETGnv27MGMGTPQv39/DB48GBs3bsQ333yDI0eOmF1au6K2MmRPSZojIPDVz+dJn6YIIVo9Ldn9aCEyTl7DnIRn3K+Mym89wqNpcGQfusXWhk40XT0pKCiQ3vHrr7+Obt26SW+nld3u+svS2jEcDgccDof785qaGsPqaS/cpyUIrJUB3Okg9XWaEpm6XPPdnrsfLcSchGeaO5hr+UnAtkRB/MtxTVap2P13DFYU96VY8o+m0CguLkZGRgY6dtT2YM9nn32G/Px8w0LD6XRi7ty5GD16NAYMGNDiekVFRViwYIEhNbRHaisj0NMST2prQ70c2/rKrfdltBgY3gfEF/9/EYC3cffzq9mHbuHCJG11U8s036exfft2JCQkaFrXarX6XZAWeXl5qKysxGeffdbqeoWFhV6tpJqaGqSmphpaGwWu+b4M4TswAFeLI/EZ2Jb0aLa1QYHTFBobNmxAXJz2/4C1a9ciMTHR76Jak5+fj127dmHfvn1ISUlpdV2LxQKLxdJkuWj8CG9t0xOonqIERsC2xI4MbWcwHq2NotZrUxREpi6HgPzpd3uk9T2hKTRycnKkDj516lSp9bUQQmD27NnYvn07ysvLkZaW5ve+yrsdgCU2ZPqADeHqZmi78TTUzlC9n1HRQ1n3/b5XCgMOi1PTegHdRn7jxg04nd4H6ty5cyC7bFFeXh7ee+89lJSUwGq14vLlywCAuLg4REVFGXJM0ovQ56E2AV0bSK7Be/L122GYkP5ze+7cOWRnZyMmJgZxcXHo2rUrunbtii5duqBr165G1AgAWL16Nex2OzIzM5GUlOR+bdu2zbBjhhv1Koeep24CAjeTFge4FwXxL3fBO7Z1WlfH8If068wlb9ItjaeeegpCCKxfvx6JiYlQ2uguGZm7C8k/pZsv4eFpSbiVtFiHfggXBQru3faW1P/f7pFRrvsq7qaO7drar5wA3rm6DvEbW+/PIP9Jh0ZFRQWOHDmCe++914h6yGSKoqDv1oW63Nzloi0shHAd+59ZD7qeTj3U9Oau7E+KsPuRdXeuotwdHo2Bkf1J84Hx8UiexupB+vRk2LBhqKqqMqIWCgJ6tujUUxNf/RkNVbMxc3J/r2W7W3iDZ39ShHeursM7V+86VfERGAAwaNIE3tilA+mWxrp16/Dcc8/h4sWLGDBgADp08B7Ve9CgQboVR22vdPMljJ+ejJS9MQG3NmRPTbS0NgA0BoOAbUkP97L4l+OQ3colVs9WhhBA7hP9AxrBPJxJh4bNZsPZs2eRm5vrXqaO2KQoChoaGnQtkNqe+n8ZaHCk7ovVfNXE1drwvp28xb4NAK7OUe33DrGVoR/p0Jg5cybuu+8+vP/++23aEUptR+0Q9QwOAQFFw/VOdT2ZwPDa/q7Wxm78vZXg0ObCW5PdgcFWRuCk+zT+/e9/Y/HixRgxYgR69+6NXr16eb2ofSjdfMl9WpGyNwa3Gi+bNnc37Z3PXcP++RsYat+GEHAN05f1IAZnj2+xf8OXj0dGNQmMmZNbflaJtJFuaTz00EOoqKhAenq6EfVQEFHf9A9PS3L3TXz183kA4HFJ1hUU9257y/WZWBjQjVyuN3Z/rN9x8k6LQ1FwIVugYrf2VsfFtyZDAE0CI9DZ2MiP0Hjsscfw0ksv4cSJExg4cGCTjtDHH39ct+IoOKinKwC8nlZV+7KAhe5WSaB3fTovzEZEyvImwQEhfIbHxyOjMGjSBABgYBhIEZLX2CIiWj6jCfaO0JqaGsTFxeGFgz347IkA7FvfD2gfgT5L0tpcrhEpy92D5QAeI23dNd7n3Tw7O9Xf7NYDQ2Da0c/9Kb/dcdxwYlXGNdjt9lYfB5Fuadz9rAmFLyMfPlPf4LlP3B0evgfRuTssALYw9MR5TyiotRQercl9Qr1RjGFhBOnQePHFF5Geno4XX3zRa/mKFStw5swZFBcX61UbkZtneGhdl4whHRoffvghdu7c2WT5qFGjsGjRotAIDfXBpzCmIDR/BPoHghKaPwgjaPw5SIfGt99+2+woXp07d8a1a9dkd2eKsddHI7q+g+8V2zEhgDURo2S30rCOxM1+QuCxl82+OVAg6z/axr5t727W3cYq+J6cSjo00tPTsWfPHuTnew9e8sknn6BPnz6yu6Ogdyco7sn4l89Vvzmk/g6YHQZkFOnQKCgoQH5+Pmw2Gx566CEAQFlZGf7whz+ExqkJaeQKi3syzrn//fh9rd9NKQTwkVLJ8Gjn/Hr2xOFw4He/+x0WLnTd6NO7d2+sXr0a06dP171AMoOQCguVorjWZXi0b35dcn3++efx/PPPw2azISoqCrGxsXrXRaa5Exhaw+Jud4eHEAqqDqXBiOAI1sGK27OA7tOIj4/Xqw4KCoEHhidFAR4bMgAfHa9E6shzugTH+OnJrko9bmT2nPJRvbWdQWIcTfdS33///bh+/brmnf70pz/FxYsX/S6KzKBvYKjU4FAUgdSR5/zez/jpyXh4WhKEEO6pIy+MqcOFMXWoGnMDX02Zh69+Ps8dJjJzx5IcTS2N48ePo6KiQvM0i8ePH/eaQ5WCnTGBoXK3OI5Vwp95CNTpIr+aMs89ZaTnXLMKFPfyqjE3cCtpMfpuXejejq0OfWk+PRk3bpzmYds4ME8oMiYwVIoCPHbfAOzESVQd0n5p3nMWey2TUqszul0YU4eUvTFBPUlTqNIUGufOyTcrfU2ZSMFC4J6MfxkaGJ4UTfMQuHgGhj8YHMbQFBockYv0INPaCDQwVGpwkH7Ce1CJsNe2rQyVouHhH7UPQw8XxtS5WxsUOIYGtSm1tdHalRT1sqrauakHztCnH4YGtXsCd8Y2pcAxNCjo6HlqAty5osJTFH1Ih0ZOTg727dtnRC1EbnqempC+pG8jt9vtyMrKQq9evZCbm4ucnBz84Ac/MKI2wzQ3d0fYUZTGG7qCixktgbD/XWik9ecgHRo7duyAzWbD5s2bsWnTJsyfPx9ZWVl4+umn8cQTTzSZ0iAYlXc7wNHIBSBueIzyHSTU6RK0zuimh7LuLY9uHk4cFm2Dhvv1zomPj0dBQQEqKirw+eefIz09HdOmTUNycjJeeuklfP311/7sltqY6wGy4HSr52KzS6AWBPTn9tKlSygtLUVpaSkiIyPx6KOP4sSJE/jJT36CZcuW6VUjhSPdGxk8BdGLdGjcvn0bH374ISZNmoRevXrhgw8+wNy5c1FdXY1Nmzbh008/xV//+lf89re/NaJeCgOKoqDv1oW69TUICNxMWsyH13Qi3aeRlJQEp9OJX/ziF/jiiy8wZMiQJuuMHTsWXbp00aE8MpxQZ2pvo8MJYOcx9Tby5kNBvRHrVtJijzlj/adAcc9FS4GTbmksW7YM1dXVWLlyZbOBAQBdunTx6yE3amsKvjnUBx8drzS7EC9qa8Bz3lj/Cb9nsafmSYfGtGnT0KlTJyNqIbOIO1MZGnoYAXx03PcMaYArOBRFCehhM/W0hPQV3tcdCW3d2hACmsfTEEIEEBwCt5IWu09L2MrQD0ODXAxubci0MlSlmy81GxytdZCqX0vdZ2VgGIShQXC3No5VGhIcamDItDJUanAAQOq+WKTsjcGtFk85XK0LtQ+DgWEMzhpPjRqDA5V47L4Bul1NCSQwVOobX73FvO/WhS0OKSnEQoaFwRga5ME7OIDALsXqERiePIOgpWdUGBbGC7nQWLlyJZYsWYLLly9j8ODBWL58OYYPH252We2IKzh24iQUCL/CQz3F2XnM1YehR2DcjeFgnpAKjW3btqGgoABr1qzBiBEjUFxcjAkTJuD06dNISEgwu7x2RHHffHV3eGhhZFiQ+UIqNP74xz9i1qxZyM3NBQCsWbMGu3fvxvr16/Hqqxx/QX/e4eH1lcaWR3MdpwyL9i1kQqO+vh5HjhxBYWGhe1lERASysrJw8ODBZrdxOBxekzbV1NS4/uF7XNt2z/We1/5DuPuJ2Hsy/gW02Fehcb8K2uauMl+CoISgoPHnEDKhce3aNTQ0NCAxMdFreWJiIk6dOtXsNkVFRViwYEGT5WOvj0Z0ffCP+2G0rKzpOuwk8F2Y7j8Pml1BULhZdxurUOJzvXZ9n0ZhYSHsdrv7VVVVZXZJRCEvZFoaPXr0QGRkJK5cueK1/MqVK+jZs2ez21gsFlgslrYojyhshExLo2PHjhg6dCjKysrcy5xOJ8rKypCRkWFiZUThJWRaGgBQUFCAnJwcPPDAAxg+fDiKi4tRV1fnvppCRMYLqdCYMmUKbDYb3njjDVy+fBlDhgzBnj17mnSOEpFxQio0ACA/Px/5+flml0EUtkKmT4OIggNDg4ikMDSISApDg4ikMDSISApDg4ikMDSISApDg4ikMDSISErI3RGqB9H4QUR3aH1PhGVolHc7AEssG1lEnhwWp6b1+M4hIikMDSKSwtAgIikMDSKSwtAgIikMDSKSwtAgIikMDSKSwtAgIikMDSKSwtAgIikMDSKSwtAgIikMDSKSwtAgIilhOZ4GROOLiO7Q+J4Iy9AYe300ous7mF0GUVC5WXcbq1Dicz2enhCRFIYGEUlhaBCRFIYGEUlhaBCRFIYGEUlhaBCRFIYGEUlhaBCRFIYGEUlhaBCRFIYGEUlhaBCRFIYGEUkJidA4f/48nn76aaSlpSEqKgo//OEPMX/+fNTX1/u1P8EPfvCj2Q8tQmI8jVOnTsHpdGLt2rVIT09HZWUlZs2ahbq6OixdulR6f+XdDsASGxJ5SdRmHBanpvVCIjQmTpyIiRMnuj/v06cPTp8+jdWrV/sVGkTkv5AIjebY7XZ069at1XUcDgccDof785qaGqPLImr3QrKNfubMGSxfvhzPPvtsq+sVFRUhLi7O/UpNTW2jConaL1ND49VXX4WiKK2+Tp065bXNxYsXMXHiRDz55JOYNWtWq/svLCyE3W53v6qqqoz8dojCgqmnJ7/+9a8xY8aMVtfp06eP+9/V1dUYO3YsRo0ahT/96U8+92+xWGCxWAItk4g8mBoa8fHxiI+P17TuxYsXMXbsWAwdOhQbNmxARERInlkRhbyQ6Ai9ePEiMjMz0atXLyxduhQ2m839tZ49e5pYGVH4CYnQKC0txZkzZ3DmzBmkpKR4fU0IznpE1JZCoo0/Y8YMCCGafRFR2wqJ0CCi4MHQICIpDA0iksLQICIpDA0iksLQICIpIXGfhl7US7T1ddrGDSAKJ+r7wtetDGEVGrW1tQCAdVn/MbkSouBVW1uLuLi4Fr+uiDC6Q8rpdKK6uhpWqxWKomjapqamBqmpqaiqqkLnzp0NrrBt8HsKDW39PQkhUFtbi+Tk5Faf7QqrlkZEREST29C16ty5c7v5ZVTxewoNbfk9tdbCULEjlIikMDSISApDwweLxYL58+e3q8F8+D2FhmD9nsKqI5SIAseWBhFJYWgQkRSGBhFJYWgQkRSGhgS9J6I2y8qVK9G7d2906tQJI0aMwBdffGF2SX4rKirCsGHDYLVakZCQgMmTJ+P06dNml6WbRYsWQVEUzJ071+xS3BgaEjwnoj558iSWLVuGNWvW4De/+Y3ZpWm2bds2FBQUYP78+Th69CgGDx6MCRMm4OrVq2aX5pe9e/ciLy8Phw4dQmlpKW7fvo3x48ejrq7O7NICdvjwYaxduxaDBg0yuxRvggLy+9//XqSlpZldhmbDhw8XeXl57s8bGhpEcnKyKCoqMrEq/Vy9elUAEHv37jW7lIDU1taKH/3oR6K0tFSMGTNGzJkzx+yS3NjSCJCWiaiDRX19PY4cOYKsrCz3soiICGRlZeHgwYMmVqYfu90OACHzf9KSvLw8ZGdne/1fBYuwemBNb+pE1EuXLjW7FE2uXbuGhoYGJCYmei1PTExsMmduKHI6nZg7dy5Gjx6NAQMGmF2O37Zu3YqjR4/i8OHDZpfSLLY0YPxE1NQ28vLyUFlZia1bt5pdit+qqqowZ84cbNmyBZ06dTK7nGbxNnIANpsN3377bavr9OnTBx07dgTgmog6MzMTI0eOxMaNG0NmXtn6+npER0fjb3/7GyZPnuxenpOTg//+978oKSkxr7gA5efno6SkBPv27UNaWprZ5fhtx44d+NnPfobIyEj3soaGBiiKgoiICDgcDq+vmYGnJwifiag7duyIoUOHoqyszB0aTqcTZWVlyM/PN7c4PwkhMHv2bGzfvh3l5eUhHRgAMG7cOJw4ccJrWW5uLvr164dXXnnF9MAAGBpS2sNE1AUFBcjJycEDDzyA4cOHo7i4GHV1dcjNzTW7NL/k5eXhvffeQ0lJCaxWKy5fvgzANZhMVFSUydXJs1qtTfpjYmJi0L1796Dpp2FoSGgPE1FPmTIFNpsNb7zxBi5fvowhQ4Zgz549TTpHQ8Xq1asBAJmZmV7LN2zYgBkzZrR9QWGAfRpEJCV0TsiJKCgwNIhICkODiKQwNIhICkODiKQwNIhICkODiKQwNMgQ58+fdz/sN2TIEEOPtXHjRvexgmmEq/aKoUGG+vTTT1FWVmboMaZMmYJLly4hIyPD0OOQC28jJ0N1794d3bt3N/QYUVFRiIqKcj+FTMZiS4N8stls6NmzJ95++233sgMHDqBjx45+tSLWr1+P/v37w2KxICkpyesJW0VRsHbtWkyaNAnR0dH48Y9/jIMHD+LMmTPIzMxETEwMRo0ahbNnz+ryvZE8hgb5FB8fj/Xr1+PNN9/El19+idraWkybNg35+fkYN26c1L5Wr16NvLw8/OpXv8KJEyewc+dOpKene62zcOFCTJ8+HcePH0e/fv0wdepUPPvssygsLMSXX34JIUTIPsrfLpg4PimFmBdeeEH07dtXTJ06VQwcOFB89913La577tw5AUAcO3bMa3lycrJ47bXXWtwOgHj99dfdnx88eFAAEH/5y1/cy95//33RqVOnJtsG2wC87RVbGqTZ0qVL8f333+ODDz7Ali1bpGczv3r1Kqqrq322TjyH7Fcf2R84cKDXsu+++w41NTVSxyd9MDRIs7Nnz6K6uhpOpxPnz5+X3l7roDgdOnRw/1tRlBaXOZ1O6RoocAwN0qS+vh5PPfUUpkyZgoULF+KZZ56RnmDJarWid+/ehl+CJWPxkitp8tprr8Fut+Pdd99FbGwsPv74Y8ycORO7du2S2s+bb76J5557DgkJCXjkkUdQW1uLf/zjH5g9e7ZBlZPe2NIgn8rLy1FcXIzNmzejc+fOiIiIwObNm7F//373cHta5eTkoLi4GKtWrUL//v0xadIkfP311wZVTkbgcH9kiPPnzyMtLQ3Hjh0z/DZyVWZmJoYMGYLi4uI2OV64YkuDDDVq1CiMGjXK0GNs2bIFsbGx2L9/v6HHIRe2NMgQ33//vfsKi8ViQWpqqmHHqq2txZUrVwAAXbp0QY8ePQw7FjE0iEgST0+ISApDg4ikMDSISApDg4ikMDSISApDg4ikMDSISApDg4ikMDSISMr/ARlqxEKc7ZgRAAAAAElFTkSuQmCC",
      "text/plain": [
       "<Figure size 258.065x259.74 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "example_univ.plot(width=(6*pitch, 6*pitch), origin=(pitch, pitch, 0))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 63,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<Axes: xlabel='x [cm]', ylabel='y [cm]'>"
      ]
     },
     "execution_count": 63,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 258.065x259.74 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "lattice.outer = burn\n",
    "example_univ.plot(width=(6.5*pitch, 6.5*pitch), origin=(pitch, pitch, 0), color_by='material')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# The BEAVRS Assembly\n",
    "\n",
    "<img src=\"assembly_diagram.png\" alt=\"drawing\" width=\"350\"/>\n",
    "\n",
    "To make things a little easier, we'll create lists of (row, column) positions for the guide tubes and burnable poison rods:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 64,
   "metadata": {},
   "outputs": [],
   "source": [
    "guide_tube_positions = [\n",
    "    (2, 5), (2, 8), (2, 11),\n",
    "    (5, 2), (5, 5), (5, 8), (5, 11), (5, 14),\n",
    "    (8, 2), (8, 5), (8, 8), (8, 11), (8, 14),\n",
    "    (11, 2), (11, 5), (11, 8), (11, 11), (11, 14),\n",
    "    (14, 5), (14, 8), (14, 11)\n",
    "]\n",
    "\n",
    "burn_positions = [(3, 3), (3, 13), (13, 3), (13, 13)] "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 65,
   "metadata": {},
   "outputs": [],
   "source": [
    "lattice = openmc.RectLattice()\n",
    "assembly_pitch = 17*pitch\n",
    "\n",
    "lattice.lower_left = (-assembly_pitch/2, -assembly_pitch/2)\n",
    "lattice.pitch = (pitch, pitch)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 99,
   "metadata": {},
   "outputs": [],
   "source": [
    "lattice.universes = [[fuel_pin] * 17] * 17\n",
    "\n",
    "import numpy as np\n",
    "lattice.universes = np.tile(fuel_pin, (17, 17))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 100,
   "metadata": {},
   "outputs": [],
   "source": [
    "for row, col in guide_tube_positions:\n",
    "    lattice.universes[row, col] = guide_tube\n",
    "\n",
    "for row, col in burn_positions:\n",
    "    lattice.universes[row, col] = burn"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 101,
   "metadata": {},
   "outputs": [],
   "source": [
    "lattice.outer = all_water"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Now we just have to add the boundary conditions and root universe to finish the geometry. Because each of our cells we used in constructing the lattice uses `transmission` boundary conditions (the default), we need to place the lattice inside some other containing cell, which has boundary conditions."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 102,
   "metadata": {},
   "outputs": [],
   "source": [
    "outer_surface = openmc.model.RectangularPrism(assembly_pitch, assembly_pitch, boundary_type='reflective')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 103,
   "metadata": {},
   "outputs": [],
   "source": [
    "root = openmc.Universe(cells=[openmc.Cell(region=-outer_surface, fill=lattice)])\n",
    "\n",
    "model.geometry = openmc.Geometry(root)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": 104,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<Axes: xlabel='x [cm]', ylabel='y [cm]'>"
      ]
     },
     "execution_count": 104,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 774.194x779.221 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "root.plot(width=(20*pitch, 20*pitch), origin=(0, 0, 0), \n",
    "          color_by='material', pixels=[600,600])"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "To run this input file, now all we need to do is specify some run settings."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 74,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "                                %%%%%%%%%%%%%%%\n",
      "                           %%%%%%%%%%%%%%%%%%%%%%%%\n",
      "                        %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%\n",
      "                      %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%\n",
      "                    %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%\n",
      "                   %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%\n",
      "                                    %%%%%%%%%%%%%%%%%%%%%%%%\n",
      "                                     %%%%%%%%%%%%%%%%%%%%%%%%\n",
      "                 ###############      %%%%%%%%%%%%%%%%%%%%%%%%\n",
      "                ##################     %%%%%%%%%%%%%%%%%%%%%%%\n",
      "                ###################     %%%%%%%%%%%%%%%%%%%%%%%\n",
      "                ####################     %%%%%%%%%%%%%%%%%%%%%%\n",
      "                #####################     %%%%%%%%%%%%%%%%%%%%%\n",
      "                ######################     %%%%%%%%%%%%%%%%%%%%\n",
      "                #######################     %%%%%%%%%%%%%%%%%%\n",
      "                 #######################     %%%%%%%%%%%%%%%%%\n",
      "                 ######################     %%%%%%%%%%%%%%%%%\n",
      "                  ####################     %%%%%%%%%%%%%%%%%\n",
      "                    #################     %%%%%%%%%%%%%%%%%\n",
      "                     ###############     %%%%%%%%%%%%%%%%\n",
      "                       ############     %%%%%%%%%%%%%%%\n",
      "                          ########     %%%%%%%%%%%%%%\n",
      "                                      %%%%%%%%%%%\n",
      "\n",
      "                 | The OpenMC Monte Carlo Code\n",
      "       Copyright | 2011-2025 MIT, UChicago Argonne LLC, and contributors\n",
      "         License | https://docs.openmc.org/en/latest/license.html\n",
      "         Version | 0.15.3\n",
      "     Commit Hash | 27e38e894697bb32a1dac7848d2618818b6b8daf\n",
      "       Date/Time | 2025-11-25 09:34:08\n",
      "  OpenMP Threads | 2\n",
      "\n",
      " Reading model XML file 'model.xml' ...\n",
      " Reading chain file: /home/ubuntu/data/depletion_chains/chain_endfb71_pwr.xml...\n",
      " Reading cross sections XML file...\n",
      " Reading U234 from /home/ubuntu/data/endfb71_hdf5/U234.h5\n",
      " Reading U235 from /home/ubuntu/data/endfb71_hdf5/U235.h5\n",
      " Reading U238 from /home/ubuntu/data/endfb71_hdf5/U238.h5\n",
      " Reading U236 from /home/ubuntu/data/endfb71_hdf5/U236.h5\n",
      " Reading O16 from /home/ubuntu/data/endfb71_hdf5/O16.h5\n",
      " Reading Zr90 from /home/ubuntu/data/endfb71_hdf5/Zr90.h5\n",
      " Reading Zr91 from /home/ubuntu/data/endfb71_hdf5/Zr91.h5\n",
      " Reading Zr92 from /home/ubuntu/data/endfb71_hdf5/Zr92.h5\n",
      " Reading Zr94 from /home/ubuntu/data/endfb71_hdf5/Zr94.h5\n",
      " Reading Zr96 from /home/ubuntu/data/endfb71_hdf5/Zr96.h5\n",
      " Reading H1 from /home/ubuntu/data/endfb71_hdf5/H1.h5\n",
      " Reading B10 from /home/ubuntu/data/endfb71_hdf5/B10.h5\n",
      " Reading B11 from /home/ubuntu/data/endfb71_hdf5/B11.h5\n",
      " Reading O17 from /home/ubuntu/data/endfb71_hdf5/O17.h5\n",
      " Reading Al27 from /home/ubuntu/data/endfb71_hdf5/Al27.h5\n",
      " Reading Si28 from /home/ubuntu/data/endfb71_hdf5/Si28.h5\n",
      " Reading Si29 from /home/ubuntu/data/endfb71_hdf5/Si29.h5\n",
      " Reading Si30 from /home/ubuntu/data/endfb71_hdf5/Si30.h5\n",
      " Reading c_H_in_H2O from /home/ubuntu/data/endfb71_hdf5/c_H_in_H2O.h5\n",
      " Minimum neutron data temperature: 294 K\n",
      " Maximum neutron data temperature: 294 K\n",
      " Preparing distributed cell instances...\n",
      " Writing summary.h5 file...\n",
      " Maximum neutron transport energy: 20000000 eV for U235\n",
      " Initializing source particles...\n",
      "\n",
      " ====================>     K EIGENVALUE SIMULATION     <====================\n",
      "\n",
      "  Bat./Gen.      k            Average k\n",
      "  =========   ========   ====================\n",
      "        1/1    1.33547\n",
      "        2/1    1.29624\n",
      "        3/1    1.28443\n",
      "        4/1    1.27685\n",
      "        5/1    1.36602\n",
      "        6/1    1.39199\n",
      "        7/1    1.33805\n",
      "        8/1    1.30845\n",
      "        9/1    1.28665\n",
      "       10/1    1.24115\n",
      "       11/1    1.31420\n",
      "       12/1    1.41264    1.36342 +/- 0.04922\n",
      "       13/1    1.35806    1.36163 +/- 0.02848\n",
      "       14/1    1.23023    1.32878 +/- 0.03853\n",
      "       15/1    1.30614    1.32425 +/- 0.03019\n",
      "       16/1    1.28189    1.31719 +/- 0.02564\n",
      "       17/1    1.38215    1.32647 +/- 0.02357\n",
      "       18/1    1.28799    1.32166 +/- 0.02097\n",
      "       19/1    1.22838    1.31130 +/- 0.02120\n",
      "       20/1    1.37137    1.31730 +/- 0.01989\n",
      "       21/1    1.36590    1.32172 +/- 0.01853\n",
      "       22/1    1.31276    1.32097 +/- 0.01693\n",
      "       23/1    1.33851    1.32232 +/- 0.01563\n",
      "       24/1    1.34451    1.32391 +/- 0.01456\n",
      "       25/1    1.28174    1.32110 +/- 0.01384\n",
      "       26/1    1.38889    1.32533 +/- 0.01362\n",
      "       27/1    1.30326    1.32404 +/- 0.01286\n",
      "       28/1    1.22248    1.31839 +/- 0.01338\n",
      "       29/1    1.26835    1.31576 +/- 0.01292\n",
      "       30/1    1.31014    1.31548 +/- 0.01226\n",
      "       31/1    1.36387    1.31778 +/- 0.01189\n",
      "       32/1    1.28235    1.31617 +/- 0.01145\n",
      "       33/1    1.31069    1.31593 +/- 0.01094\n",
      "       34/1    1.41989    1.32027 +/- 0.01134\n",
      "       35/1    1.29602    1.31930 +/- 0.01092\n",
      "       36/1    1.37343    1.32138 +/- 0.01069\n",
      "       37/1    1.29861    1.32053 +/- 0.01033\n",
      "       38/1    1.31562    1.32036 +/- 0.00995\n",
      "       39/1    1.34029    1.32105 +/- 0.00963\n",
      "       40/1    1.32987    1.32134 +/- 0.00930\n",
      "       41/1    1.36543    1.32276 +/- 0.00911\n",
      "       42/1    1.42015    1.32581 +/- 0.00933\n",
      "       43/1    1.35849    1.32680 +/- 0.00910\n",
      "       44/1    1.30173    1.32606 +/- 0.00886\n",
      "       45/1    1.32554    1.32604 +/- 0.00860\n",
      "       46/1    1.32270    1.32595 +/- 0.00836\n",
      "       47/1    1.33713    1.32625 +/- 0.00814\n",
      "       48/1    1.37162    1.32745 +/- 0.00801\n",
      "       49/1    1.34892    1.32800 +/- 0.00782\n",
      "       50/1    1.34012    1.32830 +/- 0.00763\n",
      " Creating state point statepoint.50.h5...\n",
      "\n",
      " =======================>     TIMING STATISTICS     <=======================\n",
      "\n",
      " Total time for initialization     = 1.4560e+00 seconds\n",
      "   Reading cross sections          = 1.2814e+00 seconds\n",
      " Total time in simulation          = 1.9308e+00 seconds\n",
      "   Time in transport only          = 1.9241e+00 seconds\n",
      "   Time in inactive batches        = 3.8017e-01 seconds\n",
      "   Time in active batches          = 1.5506e+00 seconds\n",
      "   Time synchronizing fission bank = 2.6672e-03 seconds\n",
      "     Sampling source sites         = 2.3251e-03 seconds\n",
      "     SEND/RECV source sites        = 3.2964e-04 seconds\n",
      "   Time accumulating tallies       = 2.0729e-05 seconds\n",
      "   Time writing statepoints        = 1.4864e-03 seconds\n",
      " Total time for finalization       = 2.3400e-06 seconds\n",
      " Total time elapsed                = 3.3914e+00 seconds\n",
      " Calculation Rate (inactive)       = 26304.3 particles/second\n",
      " Calculation Rate (active)         = 25796.4 particles/second\n",
      "\n",
      " ============================>     RESULTS     <============================\n",
      "\n",
      " k-effective (Collision)     = 1.32661 +/- 0.00611\n",
      " k-effective (Track-length)  = 1.32830 +/- 0.00763\n",
      " k-effective (Absorption)    = 1.32639 +/- 0.00520\n",
      " Combined k-effective        = 1.32679 +/- 0.00434\n",
      " Leakage Fraction            = 0.00000 +/- 0.00000\n",
      "\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "PosixPath('/home/ubuntu/openmc-nea-course/notebooks/lattices/statepoint.50.h5')"
      ]
     },
     "execution_count": 74,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "model.settings.batches = 50\n",
    "model.settings.inactive = 10\n",
    "model.settings.particles = 1000\n",
    "model.run()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Hexagonal Lattices\n",
    "OpenMC also allows you to define hexagonal lattices. They are a little trickier, but as we'll see there are some helper methods that demystify how to assign universes.\n",
    "\n",
    "We need to set the center of the lattice, the pitch, an outer universe (which is applied to all lattice elements outside of those that are defined), and a list of universes. Let's start with the easy ones first. Note that for a 2D lattice, we only need to specify a single number for the pitch."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 75,
   "metadata": {},
   "outputs": [],
   "source": [
    "hex_lat = openmc.HexLattice()\n",
    "hex_lat.center = (0, 0)\n",
    "hex_lat.pitch = [pitch]\n",
    "hex_lat.outer = all_water"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Now we need to set the universes property on our lattice. It needs to be set to a list of lists of Universes, where each list of Universes corresponds to a ring of the lattice. The rings are ordered from outermost to innermost, and within each ring the indexing starts at the \"top\". To help visualize the proper indices, we can use the `show_indices()` helper method."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 81,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "            (0, 0)\n",
      "      (0,11)      (0, 1)\n",
      "(0,10)      (1, 0)      (0, 2)\n",
      "      (1, 5)      (1, 1)\n",
      "(0, 9)      (2, 0)      (0, 3)\n",
      "      (1, 4)      (1, 2)\n",
      "(0, 8)      (1, 3)      (0, 4)\n",
      "      (0, 7)      (0, 5)\n",
      "            (0, 6)\n"
     ]
    }
   ],
   "source": [
    "print(hex_lat.show_indices(num_rings=3))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 84,
   "metadata": {},
   "outputs": [],
   "source": [
    "ring2 = [guide_tube] + [fuel_pin] * 11\n",
    "ring1 = [burn] + [fuel_pin] * 5\n",
    "ring0 = [fuel_pin]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 85,
   "metadata": {},
   "outputs": [],
   "source": [
    "hex_lat.universes = [ring2, ring1, ring0]"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Let's set up a lattice where the first element in each ring is the guide tube universe and all other elements are regular fuel pin universes. From the diagram above, we see that the outer ring has 12 elements, the middle ring has 6, and the innermost degenerate ring has a single element."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Now let's put our lattice inside a circular cell."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 89,
   "metadata": {},
   "outputs": [],
   "source": [
    "hex_lat.outer = universe\n",
    "main_cell = openmc.Cell(region=-big_cylinder, fill=hex_lat)\n",
    "root = openmc.Universe(cells=[main_cell])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 91,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<Axes: xlabel='x [cm]', ylabel='y [cm]'>"
      ]
     },
     "execution_count": 91,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 645.161x649.351 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "root.plot(width=(12, 12), color_by='material', pixels=(500, 500))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Now let's say we want our hexagonal lattice orientated such that flat sides are parallel to the y-axis instead of the x-axis. This can be achieved by changing the orientation of the lattice from `y` to `x`:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 96,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "            (0, 8)      (0, 9)      (0,10)\n",
      "\n",
      "      (0, 7)      (1, 4)      (1, 5)      (0,11)\n",
      "\n",
      "(0, 6)      (1, 3)      (2, 0)      (1, 0)      (0, 0)\n",
      "\n",
      "      (0, 5)      (1, 2)      (1, 1)      (0, 1)\n",
      "\n",
      "            (0, 4)      (0, 3)      (0, 2)\n"
     ]
    }
   ],
   "source": [
    "hex_lat.orientation = 'x'\n",
    "print(hex_lat.show_indices(num_rings=3, orientation='x'))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 93,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<Axes: xlabel='x [cm]', ylabel='y [cm]'>"
      ]
     },
     "execution_count": 93,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 258.065x259.74 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "root.plot(width=(8, 8), color_by='material')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We could also have accomplished this using the `rotation` attribute for the `main_cell`."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 97,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<Axes: xlabel='x [cm]', ylabel='y [cm]'>"
      ]
     },
     "execution_count": 97,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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2X4ssy03AntyjiUhgBHJ03AyzO0H/DUuDgmIcnSTy9BUlIon2q+s6dp7LEy4gtl7a7NixA3fccQeqqqrO76T1j+30m61yhMS85aZZmwNRtpPh8c0aPsmw3JSduxAROb+zmGKS6GatjOdYogqZBMtPWy077733XgwdOhTbt2/Hl19+icOHD4f8lziPVetHEbaTIfEZbS+FWm7C/twDsefsXccuIgCgaTg6bgbm7F0XkX+0v4VMEfE35/xljlMf+2IWkiNHjmDBggXIycnBgAEDkJmZGfIhIrFq/chjOxkiIhbMnoLmUpwetnbkbixk40gk2r0Qw0bnPzGY+vj70OHP31jM0WLbhVNtLZiF5Be/+AU++eQTGW1JKkR5tBhtJ80WM6+IBLDqYasy9wCxRyI6ls/PR+aGpcHP8vn50QVF03D0xvv9WyUYlciec0TGNJQiYRaSX/7yl3jwwQfx1FNP4c0338Q777wT8iHEFTLgEENqFrdLm3OPNhqJaXCl68j8+1JomobSfW8EPwCQuWFpTDEJXOLEGpXYjRMvb5iFZPr06fjqq68wd+5cTJgwAePHjw9+br31VhltDOH555/HgAED0LZtW+Tk5ODjjz+WHtMyKicMFeRfa9k/V1HuMS9pdB2ZG5YGhcOI1ioWscRk6uPvR48l+d5IOE4RsmgwC0lLS0vMj+xvbNasWYPi4mKUlpZiz549uOqqq3D99dfj+PHjUuNaRZT1I4vtpMxrdpb9qsg9JnFEJBjHKCYEM86ZJswEf/jDHzBt2jRMmTIFl19+OV588UW0b98eL7/8suqmRSLQvxY47yHrCpyWe+ulTOLVBIiWR2EWkt/85jd47rnnIpb/8Y9/xKxZs0S0KSpNTU3YvXs3CgoKgstSUlJQUFCA7du3R93G5/OhoaEh5AMgaNkp4h9BqEJkP+btz8yPyAdusIaTm5uLZ555BosXL7bcmHicPHkSzc3N6NWrV8jyXr164cCBA1G3KSsrw9NPPx2xXLRlJ1luEnYjw/LTVsvOb775Bp07d45Y3qlTJ5w8edJyQ2Qwe/Zs1NfXBz/V1dWqm2QZ1UZPKhGRuxO/6UgmmIXk4osvxqZNmyKWb9y4Ueocrd27d0dqairq6upCltfV1SEjIyPqNmlpaejUqVPIxzYEusUBLrM3cFruut/fxsyDbU97xNBKNMxCUlxcjEceeQSlpaWoqKhARUUF5syZg5KSEjz44IMy2ggAaNOmDYYNG4bNmzcHl7W0tGDz5s0YOXKktLg8iPKQZTF6Mj64JPoeDsvXnCpyj4mm4ciN98cVk4CIRH2QLcGQiEY7Ft+1efbZZ7F8+XLk5+cjPz8fr776KpYuXYpp06bJaGOQ4uJivPTSS1i5ciU+//xz3H///Th79iymTJkiNS4Pym7ICnCqA1pfouttbT925h4oZg3+KQEiMIhJYH3jJ6aIAFg+/xdRl9v9XIfdz62wYOmO4/3334+vvvoKdXV1aGhowJdffol77rlHdNsimDhxIhYuXIg5c+YgOzsb+/btw6ZNmyJuwKpGpO0kwGf2ZLeQ2Z27sZgD///00Akxn1I9Mm5GUDieHjohKCwxH6lvvSwyPjkbrS1eH5VwfXXRo0cPdOzYUVRbTFFUVIQjR47A5/PhX//6F3JycmyNbxZRhtQsJtjRYvPYToqwvbQzd+OopH+cB8umPvEBjo6bgaPjZuDIuBlxXu7TTT+gJntUYvfLgayYEpKf/vSnOH36tOmd/vznP0dNTY3lRiUbc4dOwMO1wxgLWvfPC2Lx/gCvmIiwvQTsyT3aqCR4iWN5pKAHL2nijUZC7knZMCpx4mUNwOC09/7775v28s3NzcW///1v5zvtCWLEBVsAEzNnodVHFoi0fQyu31pwxvsSoub+NOehy+/bGy227NzDJ/8JmdjoxvtjHp8YOwuORMInSko0sZHoKTJjxZZhqmWLZWfg4Jjaqabhiy++SH4haf1zXHdqNBp7zfX/YEZQEOolC0C4by5LbNXxRcWOJSYAcKR1OoC4gtLav1lFxLgOIHa+3YipFlvbmF73pHATN+lCcuTIEeZG9e3bF6mpqczbyUSYkMS0P4RfUEyKSTxkTtnn5Ni88Y1iAkTOCD9n77rIt3k1/zcz4aMw43yzZtokWkyiiUj49IoiTdykC0mywC0kJmbtDooJwDacVoCTv07kIVZBJxKz8EsHUb403L44rfuJN0erCEEhITEJl5Awupe5SVCSkWgFDcQvamMp8M4Ib0VQrAhIxD5g3RWShMQkloSE0zuEBEUt4aOQeNMVmrXXlBE7Iv7qeZZnibc6OiEhMQmTkAg2H0p0/4SQD8uljd2xg/EF2kywCoqvsQUv5JKQJCQoJNtahSTaH1eie5mo0UmiQybLclN1bNXxpcZu3bdorxrAhKC0ppVbPdI+y85JkyZh6tSpGD1avU2gVfJPj0K7pgsiryUZ74OwosHfUawKSvg1dCxkWW6qiq06vtTYEgUkQITNbIw+/z+csx6DdUQyfvx4bNiwAZmZmZgyZQomTZqEH//4x5YbYCfhTnshSg37PVTNXu5EdGSD9aURo+UlIO55hvAHy8zGBsTYjQJJmrvAyxizxOvztlp2AsCJEyewatUqrFy5Ev/5z39QUFCAqVOn4pZbbonwAnYSMiw7eWGy/IQ5wylRlpvh8VljAwItPy3Ed3TuCkQkEbYLiZE9e/ZgxYoV+POf/4yOHTvirrvuwowZM3DJJZfw7FYKbhMS1o4cut/zHrpWC4rHo8b4royV+Emfe5IJCddz4l9//TXKy8tRXl6O1NRU3Hjjjfj0009x+eWXY9GiRTy79jw8hQTwW27yGl0ZLTdZ31r1cu5uhVlIzp07hzfffBM33XQTMjMzsW7dOsyaNQvHjh3DypUr8d5772Ht2rWYO3eujPZ6Dw5rB27LTfCZbAUsNwP7ZMbLubsMZiHp3bs3pk2bhszMTHz88cfYtWsXpk+fHjIUys/PR5cuXUS201OI6sxAqMEUa4fm9XixUsxezt3NMAvJokWLcOzYMTz//PPIzs6Ouk6XLl1w+PBh3rZ5HlFmTYE3bc10aFEG4AGsOuV5OXc3wiwkd999N9q2bSujLYQRwW51zAh8DCRQzKZHBV7O3aW4yrLTC8iYUs/KmVHGmTRRXl7O3e0wP9maDDjLbpPevfEqzumDfmy17EwGRFt28kKWn95DhuUmL7ZadhIEQYRDQkJIx8sXb17JnYTEYYjyhDFixfZSlOUmYN6fxsu5ux0SEgcjskMD5jqzeO9ga969Xs7djZCQOBCxZ2aL3r2CvINZz8hezt3NkJA4nLnZE7jOjryWnzzFbOWywoiXc3cbJCQOhd+/l8/yM4A1y01wWX56OXe3QkICQMjlsARCCqr3AtOdWoeO//VewGW7abxfMHfoBIaC9hcxbyF5OXdbENznSUh04LpT16gREz3w0YNzd4YT0akNRRX+L7wjA3yd2Rg7vKBjxeYt4ljxkyr3wLEOHH+7kdDnvTmL/PbuSOvg19DAnJUirQ8TEmWm+kQTQrO+hyL6bKgyftLkHmWiZ5X9Ljw2+dqYxGhHMa4pL+o60g9sgpnqzUwIHatj2zWUVhnftbknmFqRxyEvIQksVgKxfWfI18YULHO2ChcUBr8ccudLIhjsJlT2OYBvzlZPvrRnhrheICxYMNzi9b8hHIAFv5qIPudfaDG+vfYqJCQJ0KDhulPXsB9YAY59JCguRIDhFZegSHSKjAcJiQmYD6zgs0GEoAgynYoaywahihVfZWwh8QVbTDCNihUJSAASEgYSCorkg6kBSK+bY3l0YsZ6UrblZrz4wa9bJcaXkrtk2824o2LFAhKAbrZyoNLyk+VyJ6rtZSwEW24G4puKHRZfVGxAUu42+PZGhJTY55Q67bkJJzrt8SLa8lOk5WZE/ASGU0aHPOGxITh3Bzrl8aLMac8uqqqqMHXqVGRlZaFdu3a46KKLUFpaiqamJtVNczQRRfx1ScLZ2Rdm7A661AHWnOqixZ+zd11CnxoNGtrXlvgnX7bokhcttorcvYYrhOTAgQNoaWnBsmXLsH//fixatAgvvvgiHnvsMdVNcyysRWwkpKBhbQb0ENtLE0VsxFjQXJabUJO7F3GFkIwdOxYrVqzAmDFjMHDgQNx88814+OGH8de//lV105wPh0eMVdtJEW55QpzqFOTuVVwhJNGor69H165d467j8/nQ0NAQ8vEComwveYtZhO0lq+WmU3L3Gq4UksrKSixZsgT33Xdf3PXKysrQuXPn4Kdfv342tdAZiDB6Yi1mYyGLcMtjsdw0oiJ3L6NUSEpKSqBpWtzPgQMHQrapqanB2LFjMWHCBEybNi3u/mfPno36+vrgp7q6WmY6jkC0fy1grZhFudWxOOU5JXcvovSBtIceegiTJ0+Ou87AgQOD/3/s2DHk5+cjNzcXf/rTnxLuPy0tDWlpabzNJFgR7N37+4xdQG9huyMkoFRIevTogR49ephat6amBvn5+Rg2bBhWrFiBlBRXXpURRFLiikfka2pqkJeXh8zMTCxcuBAnTpwI/i4jI4N5f87y/uWFXuJTRfL0IT9J7/1bXl6OyspKVFZWom/fviG/s3ITzGnev7yQd7D9ONG7l5ek9/6dPHkydF2P+iGSHxpzOR9XCAmhFuZCFmi5CZz3p1EBiZg5SEiSDBn+uVaMpsRZbpo3mnJK7l6EhCSJEVPMbI5xoovZaiGryN3LkJAkISKLmeeMzGu5acX20im5ew0SkiQnYDtpBau2l/yWm2JsL1Xk7lVISJKUcJc6Ng/bUO9cLttLg5iYtdzkFRHVuXsRT86QNmN7d3HPkRj/enbf4m+NPeLCLTGnW4w2S1jg/RHN0GAdOjT4h/PGM7Ep60nAXHwdwTdqjfGNRW7acpM1NsTmrus6dp7LCyRiL5L6HDntmUSokMSyP7SrU+nG2Innb43mEGd8GS58GG+miANTDSaa3T6WO10gfrRLiETxI2IDinJXedzFGmqRkJhEiJDEmbXbFh/XuPGtFZURliISHVt1fOuxVR93MfFJSEzCLSQm/WqkdCwrlp8iLR1MTnYsxcyLyfZSZe6qjzvf6IiExCSWhcSid4go60VrsQUVtEXLBSHxVcbmiq/yuFuPTUJiEmYhEWQ+ZPlMIcCxz3JRCfJssTxCEGD3oD53lcedXVBISEwSFJJt3ZGWHkdIJLiXMR1YKfFNFpUE0yemglYZX0ps1cfdvM2s70wLXsglIUlIQEjW/v1mbO+3I/ofVrKLe9wDa4P9YtwRgmTTp7gFbYNrndrcVR/3OKOj1j5PTnsmMTrttetwQeiBtdlDNdx60d7YYQVts/VkSPxWlMRWkrvK467H7fMkJCaJZtkZ+OOqNmFWQaCoks160gzezj16n096y06ZaNA8KSKA/6TkxUICvJ67+D7veSEhCIIfEhKCILghISEIAgAw5uf/z/K2nhSS/xu1UnUTCMJR3HgtnzOiJ4VE0zTcMHqt6mYQhCPgFRHAo0ICkJgQBCBGRAAPCwlBEOJwhdOeLAKjko0f3sYwFR9BuB8NmrDRCOBxIQHOi8lD+9k9hAnCrfxhSJ3Q/dGlDfxi8uzgWtXNIAhbEC0iAAlJEBITwgvIEBGAhCQEEhMimZElIgAJSQQkJkQyIlNEABKSqJCYEMmEbBEBSEhiQmJCJAN2iAhAQhIXEhPCzdglIgAJSUKki4kOKH0WTnVs1fFVxpYY304RAUhITCFFTFo7UsGp0bju1DX2F1VrPJWxKXc58e0WEcCjc7ZamZMS8Fs+CnkCNsZM9bb4yMaY5NoW28nW+JR7+GJxufOICE99kJAwwiUmJmaql9apTc6SrzI+5c4Xm3ckQkJiEhFCAlgQEwtWF0I7tQWvHmFnScrdltxFXM6QkJhElJAAJsVEgFcOV1FxxlcZW3V8N+Uu6p6Ip4TE5/MhJycHn3zyCfbu3Yvs7GzT24oUkgAxBUWwYx/TWVKw2RdzUVHuQmKHxI8SW/RNVZ76cN23No888gj69OmjuhlBIr7RMdyVFxoHWuK7/IbYIuMHfFBY4ouEco+MreKbmXi4akSyceNGFBcX480338TgwYMdMSIJEBiZFHwj32wr6llSsmdx1PiG2IA98T2fe7et0kTEE5c2dXV1GDZsGN5++210794dWVlZCYXE5/PB5/MFf66vr0f//v1RXV0tXEgAv5iUfzRJ+H5jxoOOLV23ATqQf3qUbXFVx1YdX2VsHsuIRDQ0NKBfv3749ttv0blzZ7aNdRfQ0tKijx07Vp83b56u67p++PBhHYC+d+/euNuVlpYGBoT0oQ99TH4OHTrEXKNKRyQlJSVYsGBB3HU+//xz/OMf/8DatWtRUVGB1NRUVFVVWRqRfPvtt8jMzMTRo0fZFddBBM4cskZWdkF5OIvAiP306dPo0qUL07ZKheTEiRP45ptv4q4zcOBA3Hbbbfjb3/4GTTt/67q5uRmpqam48847sXKlOcMrmfdI7ITycBaUh+LJn3v06IEePXokXO+5557D/Pnzgz8fO3YM119/PdasWYOcnByZTSQIwgSumEW+f//+IT937NgRAHDRRRehb9++KppEEIQB1z1HwkNaWhpKS0uRlpamuilcUB7OgvJw0de/BEE4F0+NSAiCkAMJCUEQ3JCQEATBDQkJQRDceF5IfD4fsrOzoWka9u3bp7o5TFRVVWHq1KnIyspCu3btcNFFF6G0tBRNTU2qm5aQ559/HgMGDEDbtm2Rk5ODjz/+WHWTmCgrK8Pw4cORnp6Onj17Yvz48Th48KDqZnHzzDPPQNM0zJo1i2k7zwuJ06YlYOHAgQNoaWnBsmXLsH//fixatAgvvvgiHnvsMdVNi8uaNWtQXFyM0tJS7NmzB1dddRWuv/56HD9+XHXTTFNRUYHCwkLs2LED5eXlOHfuHMaMGYOzZ8+qbppldu7ciWXLluHKK69k35j57ZwkYsOGDfqgQYP0/fv360DilwDdwO9+9zs9KytLdTPiMmLECL2wsDD4c3Nzs96nTx+9rKxMYav4OH78uA5Ar6ioUN0USzQ2NuqXXHKJXl5erl977bX6zJkzmbb37Iikrq4O06ZNw6pVq9C+fXvVzRFGfX09unbtqroZMWlqasLu3btRUFAQXJaSkoKCggJs375dYcv4qK+vBwBH/+3jUVhYiHHjxoUcFxZc8Yi8aHRdx+TJkzF9+nRcffXVqKqqUt0kIVRWVmLJkiVYuHCh6qbE5OTJk2hubkavXr1Clvfq1QsHDhxQ1Co+WlpaMGvWLIwaNQpDhgxR3RxmVq9ejT179mDnzp2W95FUI5KSkhJomhb3c+DAASxZsgSNjY2YPXu26iZHxWweRmpqajB27FhMmDAB06ZNU9Ryb1JYWIjPPvsMq1evVt0UZqqrqzFz5ky89tpraNu2reX9JNUj8nZPSyALs3m0adMGgP9t6Ly8PPzsZz/DK6+8gpQU554fmpqa0L59e7zxxhsYP358cPmkSZPw7bffYv369eoaZ4GioiKsX78eH374IbKyslQ3h5m3334bt956K1JTU4PLmpuboWkaUlJS4PP5Qn4Xi6QSErMcPXoUDQ0NwZ8D0xK88cYbyMnJcdUbxTU1NcjPz8ewYcPw6quvmjroqsnJycGIESOwZMkSAP5Lg/79+6OoqAglJSWKW2cOXdfxwAMP4K233sKWLVtwySWXqG6SJRobG3HkyJGQZVOmTMGgQYPw6KOPmr5U8+Q9kmSZlqCmpgZ5eXnIzMzEwoULceLEieDvMjIEWItKori4GJMmTcLVV1+NESNGYPHixTh79iymTJmiummmKSwsxOuvv47169cjPT0dtbV+J4HOnTujXbt2iltnnvT09Aix6NChA7p168Z0v8eTQpIslJeXo7KyEpWVlREC6OSB5sSJE3HixAnMmTMHtbW1yM7OxqZNmyJuwDqZpUuXAgDy8vJClq9YsQKTJ0+2v0GK8eSlDUEQYnHuXTmCIFwDCQlBENyQkBAEwQ0JCUEQ3JCQEATBDQkJQRDckJAQBMENCQlBENyQkBBSqKqqCr6pHM/oXQSvvPJKMBbrFIGEGEhICKm899572Lx5s9QYEydOxNdff42RI0dKjUPEht61IaTSrVs3dOvWTWqMdu3aoV27dsFpFQj7oREJkZATJ04gIyMDv/3tb4PLtm3bhjZt2lgabbz88ssYPHgw0tLS0Lt3bxQVFQV/p2kali1bhptuugnt27fHT37yE2zfvh2VlZXIy8tDhw4dkJubi0OHDgnJjRADCQmRkB49euDll1/GU089hV27dqGxsRF33303ioqKcN111zHta+nSpSgsLMSvf/1rfPrpp3jnnXdw8cUXh6wzb9483HPPPdi3bx8GDRqEO+64A/fddx9mz56NXbt2Qdf1EPEhHIDImaiJ5GbGjBn6pZdeqt9xxx36FVdcoX///fcx1z18+HDUmfn79OmjP/744zG3A6A/8cQTwZ+3b9+uA9CXL18eXPaXv/xFb9u2bcS2VmY/J8RAIxLCNAsXLsQPP/yAdevW4bXXXkNaWhrT9sePH8exY8cSjmKMviqBOUquuOKKkGXff/99yCx3hFpISAjTHDp0CMeOHUNLS4ulmffNzhx24YUXBv8/MK9utGUtLS3MbSDkQEJCmKKpqQl33XUXJk6ciHnz5uFXv/oVszNeeno6BgwYIP3rYMJ+6OtfwhSPP/446uvr8dxzz6Fjx47YsGED7r33Xrz77rtM+3nqqacwffp09OzZEzfccAMaGxvx0Ucf4YEHHpDUcsIOaERCJGTLli1YvHgxVq1ahU6dOiElJQWrVq3C1q1bg3OXmmXSpElYvHgxXnjhBQwePBg33XQTvvjiC0ktJ+yC5mwlpFBVVYWsrCzs3btX+iPyAfLy8pCdnY3FixfbEo84D41ICKnk5uYiNzdXaozXXnsNHTt2xNatW6XGIWJDIxJCCj/88EPwm520tDT069dPWqzGxkbU1dUBALp06YLu3btLi0VEh4SEIAhu6NKGIAhuSEgIguCGhIQgCG5ISAiC4IaEhCAIbkhICILghoSEIAhuSEgIguDm/wPK0wVTEMjncgAAAABJRU5ErkJggg==",
      "text/plain": [
       "<Figure size 258.065x259.74 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "root.plot(width=(8, 8), color_by='material')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  }
 ],
 "metadata": {
  "anaconda-cloud": {},
  "kernelspec": {
   "display_name": "Python 3 (ipykernel)",
   "language": "python",
   "name": "python3"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.12.4"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 4
}