Quenching-amorphous-ZnO.ipynb

{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 5,
   "id": "2f591eb1",
   "metadata": {},
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "import scipy\n",
    "import math"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "c0fc65e5",
   "metadata": {},
   "source": [
    "## Question\n",
    "\n",
    "Is it possible to quench amorphous silicon at a rate of 100 K/ps, or is this limited by the thermal conductivity of the material (ie, no matter how good your contact, there is an inherent limitation from the rate at which heat can travel through bulk material).\n",
    "\n",
    "Should be able to get an upper bound to the quench rate using simple heat diffusion equation (e.g. https://en.wikipedia.org/wiki/Heat_equation)\n",
    "\n",
    "\n",
    "In this very, VERY simple classical model there is a slab of a-ZnO sandwiched between heat sinks.\n",
    "\n",
    "The key parameters are the thermal diffusivity of a-ZnO, the material thickness, and the difference in temperature between a-ZnO and the heat sink. We assume this is 5000K, which may not be realistic for experimental studies (?). "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "fd8a998b",
   "metadata": {},
   "outputs": [],
   "source": [
    "# This is actually a 1D problem. the characteristic  time is L**2 / D"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 94,
   "id": "9996e17a",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "9.999999999999999e-09"
      ]
     },
     "execution_count": 94,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "(100E-9)**2 / 1E-6"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "d8a8e5ac",
   "metadata": {},
   "source": [
    "This gives 10ns as the characteristic time over which heat diffuses through the system."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "500287fe",
   "metadata": {},
   "source": [
    "## Key model parameters\n",
    "\n",
    "Couldn't find thermal diffusivity of a-ZnO from a quick scan of literature, but diffusivity for a-IZO is about 1E-6 (A quick scan of literature (https://doi.org/10.1116/1.2743644). 100nm for typical film thickness. These values can be adjusted to explore other diffusivites, material thickness or temperature difference. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 191,
   "id": "484f3a0d",
   "metadata": {},
   "outputs": [],
   "source": [
    "D = 1E-6\n",
    "material_width = 100E-9  "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 192,
   "id": "f58bcc68",
   "metadata": {},
   "outputs": [],
   "source": [
    "T_contact = 0\n",
    "T_material = 5000\n",
    "T_target = 300"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "675c4741",
   "metadata": {},
   "source": [
    "## Model Implementation - FTCS method\n",
    "\n",
    "Solve the heat diffusion equation by calculating the laplacian in space using finite difference method, and evolving the system forward in time using Euler's method. Very basic, UG level numerical methods. From symmetry it can be reduced to a 1D problem."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 193,
   "id": "02d3f8a5",
   "metadata": {},
   "outputs": [],
   "source": [
    "def calculate_laplacian(temperature, Nx, h):\n",
    "\n",
    "    laplacian = temperature * 0\n",
    "\n",
    "    # assume that the temperature at the boundaries remains fixed\n",
    "    for i in range(1,Nx-1):\n",
    "\n",
    "            laplacian[i] = (temperature[i+1]+temperature[i-1]- 2*temperature[i]) / (h**2)\n",
    "            \n",
    "    return laplacian\n",
    "\n",
    "def evolve_system(initial_temperature, T_max, D, Nx, h, t_step): \n",
    "\n",
    "    N_t_steps = int(np.ceil(T_max/t_step))\n",
    "    temperature = initial_temperature\n",
    "    \n",
    "    for i in range(N_t_steps+1):\n",
    "        \n",
    "        laplacian_temperature = calculate_laplacian(temperature, Nx, h) \n",
    "        D_laplacian_temperature = D*laplacian_temperature\n",
    "        temperature = temperature + (t_step*D_laplacian_temperature)\n",
    "        \n",
    "    return temperature"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "616e5ee1",
   "metadata": {},
   "source": [
    "## Numerical parameters\n",
    "\n",
    "To maintain numerical stability, the time step is determined from the diffusivity and the space step."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 201,
   "id": "1e7d25c8",
   "metadata": {},
   "outputs": [],
   "source": [
    "def determine_tstep(D,h):\n",
    "    # We are using the FTCS scheme which is only stable if time_step < h*2 / 2*D\n",
    "    return ((h**2)/(2*D))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 202,
   "id": "0588bdc0",
   "metadata": {},
   "outputs": [],
   "source": [
    "Nx = 100\n",
    "h = material_width / Nx\n",
    "t_step = determine_tstep(D,h)\n",
    "\n",
    "if t_step > 1E-13:\n",
    "    t_step = 1E-13"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "7398a368",
   "metadata": {},
   "source": [
    "## Initial conditions"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 203,
   "id": "8d281c4f",
   "metadata": {},
   "outputs": [],
   "source": [
    "initial_temperature = np.zeros(Nx)+T_material\n",
    "initial_temperature[-1] = T_contact\n",
    "initial_temperature[0] = T_contact"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 204,
   "id": "f0c6d6ba",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Text(0.5, 1.0, 'initial temperature')"
      ]
     },
     "execution_count": 204,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.scatter([h*i for i in range(Nx)],initial_temperature)\n",
    "plt.title(\"initial temperature\")"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "a74036d6",
   "metadata": {},
   "source": [
    "## Average temperature loss\n",
    "\n",
    "the material will not cool at the same rate across the whole sample. The edges closest to the heat sink will cool fastest. To give a single rate across the whole material, we calculate the mean average change."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 205,
   "id": "e2f04bfd",
   "metadata": {},
   "outputs": [],
   "source": [
    "def calc_average_temp_lost(initial_temperature,current_temperature):\n",
    "    return np.average(initial_temperature[1:-1] - current_temperature[1:-1])"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "124cef96",
   "metadata": {},
   "source": [
    "## Evolve system"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 206,
   "id": "a6701511",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "The maximum temperature is  5000.0\n",
      "The mean average temperature drop from the initial temperature is  77.95894079183672\n"
     ]
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "time=1E-12\n",
    "temp = evolve_system(initial_temperature, time, D, Nx, h, t_step)\n",
    "plt.scatter([h*i for i in range(Nx)],temp)\n",
    "plt.title(\"T = {} s\".format(time))\n",
    "print(\"The maximum temperature is \",np.max(temp))\n",
    "print(\"The mean average temperature drop from the initial temperature is \",calc_average_temp_lost(initial_temperature,temp))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 207,
   "id": "98a6e16b",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "The maximum temperature is  5000.0\n",
      "The mean average temperature drop from the initial temperature is  121.7841667770306\n"
     ]
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "time=2E-12\n",
    "temp = evolve_system(initial_temperature, time, D, Nx, h, t_step)\n",
    "plt.scatter([h*i for i in range(Nx)],temp)\n",
    "plt.title(\"T = {} s\".format(time))\n",
    "print(\"The maximum temperature is \",np.max(temp))\n",
    "print(\"The mean average temperature drop from the initial temperature is \",calc_average_temp_lost(initial_temperature,temp))"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "fa4592c0",
   "metadata": {},
   "source": [
    "**This suggests that 100nm film with diffusivity at 1E-6 has an initial heat-diffusion-limited average cooling rate of about 60K/ps.**"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 208,
   "id": "e75b09a2",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "The maximum temperature is  2324.767881439422\n",
      "The mean average temperature drop from the initial temperature is  3504.631229056738\n"
     ]
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "time=1E-9\n",
    "temp = evolve_system(initial_temperature, time, D, Nx, h, t_step)\n",
    "plt.scatter([h*i for i in range(Nx)],temp)\n",
    "plt.title(\"T = {} s\".format(time))\n",
    "print(\"The maximum temperature is \",np.max(temp))\n",
    "print(\"The mean average temperature drop from the initial temperature is \",calc_average_temp_lost(initial_temperature,temp))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 209,
   "id": "4d37beb0",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "The maximum temperature is  0.26949319451838916\n",
      "The mean average temperature drop from the initial temperature is  4999.826677371451\n"
     ]
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "time=1E-8\n",
    "temp = evolve_system(initial_temperature, time, D, Nx, h, t_step)\n",
    "plt.scatter([h*i for i in range(Nx)],temp)\n",
    "plt.title(\"T = {} s\".format(time))\n",
    "print(\"The maximum temperature is \",np.max(temp))\n",
    "print(\"The mean average temperature drop from the initial temperature is \",calc_average_temp_lost(initial_temperature,temp))"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "ad950533",
   "metadata": {},
   "source": [
    "**This is in line with the calculated characteristic time: it takes about 10ns to equilibriate**"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 210,
   "id": "8fcbc8b1",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Text(0, 0.5, 'average temperature decrease per ps (K/ps)')"
      ]
     },
     "execution_count": 210,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "times = np.arange(1E-12,1E-11,1E-12)\n",
    "\n",
    "average_temp_change = []\n",
    "previous_temp = initial_temperature\n",
    "for time in times:\n",
    "    updated_temp = evolve_system(initial_temperature, time, D, Nx, h, t_step)\n",
    "    average_temp_change.append(calc_average_temp_lost(previous_temp,updated_temp))\n",
    "    previous_temp = updated_temp\n",
    "    \n",
    "plt.scatter(times,average_temp_change)\n",
    "plt.xlabel(\"time (s)\")\n",
    "plt.ylabel(\"average temperature decrease per ps (K/ps)\")\n"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "3b46fc2a",
   "metadata": {},
   "source": [
    "\n",
    "**As the system equilibriates the rate of cooling slows, as would be expected for a diffusion process**"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 212,
   "id": "b01a08ec",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "The maximum temperature is  280.578286513957\n",
      "The mean average temperature drop from the initial temperature is  4819.548073488267\n"
     ]
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "time=3.1E-9\n",
    "temp = evolve_system(initial_temperature, time, D, Nx, h, t_step)\n",
    "plt.scatter([h*i for i in range(Nx)],temp)\n",
    "plt.title(\"T = {} s\".format(time))\n",
    "print(\"The maximum temperature is \",np.max(temp))\n",
    "print(\"The mean average temperature drop from the initial temperature is \",calc_average_temp_lost(initial_temperature,temp))"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "229046e0",
   "metadata": {},
   "source": [
    "It takes about 3ns for the temperature across the whole sample to drop to 300K or below. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 180,
   "id": "12161f33",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "1.5666666666666667"
      ]
     },
     "execution_count": 180,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "(4700/3E-9)*1E-12"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "71c98000",
   "metadata": {},
   "source": [
    "That is an average of 1.6K/ps."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "7e9021dc",
   "metadata": {},
   "source": [
    "## Varying thickness"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 225,
   "id": "11e8d9ae",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "1e-13\n",
      "The maximum temperature is  5000.0\n",
      "The mean average temperature drop from the initial temperature is  287.1295765769284\n"
     ]
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# material_width = 100E-9, average drop in temp 121 \n",
    "\n",
    "material_width = 50E-9\n",
    "Nx = 100\n",
    "h = material_width / Nx\n",
    "\n",
    "initial_temperature = np.zeros(Nx)+T_material\n",
    "initial_temperature[-1] = T_contact\n",
    "initial_temperature[0] = T_contact\n",
    "\n",
    "t_step = determine_tstep(D,h)\n",
    "\n",
    "if t_step > 1E-13:\n",
    "    t_step = 1E-13\n",
    "    \n",
    "print(t_step)\n",
    "    \n",
    "time=2E-12\n",
    "temp = evolve_system(initial_temperature, time, D, Nx, h, t_step)\n",
    "plt.scatter([h*i for i in range(Nx)],temp)\n",
    "plt.title(\"T = {} s\".format(time))\n",
    "print(\"The maximum temperature is \",np.max(temp))\n",
    "print(\"The mean average temperature drop from the initial temperature is \",calc_average_temp_lost(initial_temperature,temp))"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "cd09b602",
   "metadata": {},
   "source": [
    "**So the thermal-diffusion limited quench rate is highly sensitive to the thickness, as you would imagine. At 50nm the initial thermal-diffusion limited quench rate is about 150 K/ps.**"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "27ff2469",
   "metadata": {},
   "source": [
    "## Varying Diffusivity"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 226,
   "id": "2b7503b3",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "9.999999999999997e-14\n",
      "The maximum temperature is  5000.0\n",
      "The mean average temperature drop from the initial temperature is  335.12572852932675\n"
     ]
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# material_width = 100E-9, D = 1E-9, average drop in temp 121 \n",
    "\n",
    "D = 5E-6\n",
    "material_width = 100E-9\n",
    "Nx = 100\n",
    "h = material_width / Nx\n",
    "\n",
    "initial_temperature = np.zeros(Nx)+T_material\n",
    "initial_temperature[-1] = T_contact\n",
    "initial_temperature[0] = T_contact\n",
    "\n",
    "t_step = determine_tstep(D,h)\n",
    "\n",
    "if t_step > 1E-13:\n",
    "    t_step = 1E-13\n",
    "    \n",
    "print(t_step)\n",
    "    \n",
    "time=2E-12\n",
    "temp = evolve_system(initial_temperature, time, D, Nx, h, t_step)\n",
    "plt.scatter([h*i for i in range(Nx)],temp)\n",
    "plt.title(\"T = {} s\".format(time))\n",
    "print(\"The maximum temperature is \",np.max(temp))\n",
    "print(\"The mean average temperature drop from the initial temperature is \",calc_average_temp_lost(initial_temperature,temp))"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "b88e1130",
   "metadata": {},
   "source": [
    "**So the thermal-diffusion limited quench rate is highly sensitive to the diffusivity, as you would imagine. At D=5E-6 the initial thermal-diffusion limited quench rate is about 160 K/ps.**\n"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "9e2a6f46",
   "metadata": {},
   "source": [
    "## Final notes\n",
    "\n",
    "- More accurate values for D are needed for a-ZnO, to understand if there are material intrinsic reasons that a quench rate of 100K/ps is not possible.\n",
    "- The model is very, very simple. For example, D will itself by dependent on temperature (as the thermal conducitivty is dependent on temperature), which is not accounted for here (but could be with relatively small adjustments...understanding the form of the T-dependence is the challenging part).\n",
    "- Assuming that a-ZnO has a similar thermal diffusivity compared to a-IZO, the film needs to be below 100nm to achieve a quench rate of 100K/ps."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "fea1e9d8",
   "metadata": {},
   "source": [
    "# Convergence tests\n",
    "\n",
    "## Convergence with time step"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 213,
   "id": "673be970",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "The maximum temperature is  0.26964062235786906\n",
      "The mean average temperature drop from the initial temperature is  4999.826582554287\n"
     ]
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Results for Nx = 100, t_step = 1E-13, time = 1E-8, delta T = 5000\n",
    "# The maximum temperature is  0.26949319451838916\n",
    "# The mean average temperature drop from the initial temperature is  4999.826677371451\n",
    "\n",
    "t_step=1E-14\n",
    "time=1E-8\n",
    "temp = evolve_system(initial_temperature, time, D, Nx, h, t_step)\n",
    "plt.scatter([h*i for i in range(Nx)],temp)\n",
    "plt.title(\"T = {} s\".format(time))\n",
    "print(\"The maximum temperature is \",np.max(temp))\n",
    "print(\"The mean average temperature drop from the initial temperature is \",calc_average_temp_lost(initial_temperature,temp))"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "00f978ad",
   "metadata": {},
   "source": [
    "## Convergence with Nx"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 219,
   "id": "5ae29466",
   "metadata": {
    "scrolled": true
   },
   "outputs": [],
   "source": [
    "# Results for Nx = 100, t_step = 1E-13, time = 1E-8, delta T = 5000\n",
    "# The maximum temperature is  0.26949319451838916\n",
    "# The mean average temperature drop from the initial temperature is  4999.826677371451\n",
    "\n",
    "t_steps = []\n",
    "temps_lost = []\n",
    "\n",
    "for Nx in [100,110,120,130]:\n",
    "    \n",
    "    h = material_width / Nx\n",
    "    t_step = determine_tstep(D,h)\n",
    "\n",
    "    if t_step > 1E-13:\n",
    "        t_step = 1E-13\n",
    "        \n",
    "    t_steps.append(t_step)\n",
    "\n",
    "    initial_temperature = np.zeros(Nx)+T_material\n",
    "    initial_temperature[-1] = T_contact\n",
    "    initial_temperature[0] = T_contact\n",
    "\n",
    "    time=1E-8\n",
    "    temp = evolve_system(initial_temperature, time, D, Nx, h, t_step)\n",
    "    temps_lost.append(calc_average_temp_lost(initial_temperature,temp))\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 220,
   "id": "c512cc22",
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.collections.PathCollection at 0x7fcd13b22200>"
      ]
     },
     "execution_count": 220,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.scatter([100,110,120,130],temps_lost)"
   ]
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3 (ipykernel)",
   "language": "python",
   "name": "python3"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.10.10"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 5
}