{
"cells": [
{
"cell_type": "markdown",
"id": "957f2a96-0f00-4056-9bd9-dd23c93ca1e7",
"metadata": {},
"source": [
"In battery engineering, controlling how metal grows at the microscopic level is a critical safety requirement. If electrodeposition is uneven, it can form sharp, needle-like dendrites that grow across the electrolyte and cause massive internal short circuits. Therefore, understanding and suppressing this dendrite formation is essential to preventing catastrophic battery failure.\n",
"\n",
"In this tutorial, we will build a minimal kinetic Monte Carlo (KMC) model for metal electrodeposition using pyZacros. By explicitly simulating individual atomic events (such as ion diffusion in the electrolyte, electrochemical reduction at the interface, and surface self-diffusion on the electrode), we can visualize how macroscopic morphologies develop from the electrode.\n",
"\n",
"Inspired by the work of Vishnugopi et al. **Surface diffusion manifestation in electrodeposition of metal anodes** [Phys. Chem. Chem. Phys., 2020,22, 11286-11295](https://pubs.rsc.org/en/content/articlelanding/2020/cp/d0cp01352h), the core goal of this tutorial is to show how the competition between different surface diffusion pathways dictates whether a deposited film grows smooth and flat, or rough and fractal. Here we describe a simplified model. For surface diffusion, we will specifically include terrace diffusion and step-detachment (diffusion away from a step edge). By the end, you will have run a short simulation and visualized the direct link between atomic-scale kinetics and the resulting electrodeposition morphology."
]
},
{
"cell_type": "markdown",
"id": "51936f1e-7f48-4484-8658-8d6232aa2ca4",
"metadata": {},
"source": [
"OK, let's start!\n",
"\n",
"First, we import the main packages we need:"
]
},
{
"cell_type": "code",
"execution_count": 1,
"id": "4fc56b18-5eb3-4a8e-a9d8-75ac1da14629",
"metadata": {},
"outputs": [],
"source": [
"import scm.pyzacros as pz\n",
"import math"
]
},
{
"cell_type": "markdown",
"id": "64891f9d-faa4-4911-b930-c99e312ea0ad",
"metadata": {},
"source": [
"Next, we configure our environment for reproducibility and visualization. We set a deterministic random seed and import the `matplotlib` tools needed to visualize the simulation results."
]
},
{
"cell_type": "code",
"execution_count": 2,
"id": "d0d8a847-cc66-4e45-b678-12019ed45414",
"metadata": {},
"outputs": [],
"source": [
"import random\n",
"\n",
"random_seed = 100\n",
"random.seed(random_seed)\n",
"\n",
"%matplotlib inline\n",
"import matplotlib.pyplot as plt\n",
"import matplotlib.animation as animation\n",
"\n",
"plt.rcParams[\"figure.figsize\"] = [7, 7]\n",
"\n",
"from IPython.display import HTML"
]
},
{
"cell_type": "markdown",
"id": "dee77320-46ae-4c35-ae6e-af775d6394d2",
"metadata": {},
"source": [
"Now, define a convenient set of physical constants:"
]
},
{
"cell_type": "code",
"execution_count": 3,
"id": "6cde657e-efd0-4d6b-aa24-373878bb0d47",
"metadata": {},
"outputs": [],
"source": [
"kB = 8.6173e-05 # Boltzmann constant in eV/K\n",
"F = 96487.0 # Faraday constant in C/mol\n",
"R = 8.314 # Gas constant in J/mol/K\n",
"N_a = 6.022e23 # Avogadro constant in 1/mol"
]
},
{
"cell_type": "markdown",
"id": "4de28ba2-538c-4f20-8d46-e341cb85efea",
"metadata": {},
"source": [
"To reproduce these morphological changes, this tutorial will guide you through the complete setup of the pyZacros simulation. We will start from the ground up by defining the species and their energetic cluster expansions. With the physical entities established, we will build a 2D lattice and populate it with our initial electrode surface and electrolyte ions. From there, we will encode the actual physics (ion transport, reduction, and surface diffusion) into a network of elemental reactions. Finally, we will wrap these components into a ZacrosJob calculation, execute the KMC simulation, and animate the results to watch our metal deposit grow dynamically over time."
]
},
{
"cell_type": "markdown",
"id": "e0365e3e-7ed7-4780-906f-d58d13f86e73",
"metadata": {},
"source": [
"Species and Energetics (Clusters)\n",
"---------------------------------\n",
"\n",
"We first need to define the fundamental building blocks of our system. As shown in the diagram below, we allow each lattice site to take on one of three states: an empty site `*` (representing the background solvent), a solid deposited metal atom `M`, or a solvated metal cation `M+`."
]
},
{
"cell_type": "markdown",
"id": "58f94c84-50a1-4a60-b62c-75fe9c95c416",
"metadata": {
"tags": [
"html_base64_image"
]
},
"source": [
""
]
},
{
"cell_type": "code",
"execution_count": 4,
"id": "4c8089da-5ba8-45a7-b89f-120f9e7db9fd",
"metadata": {},
"outputs": [],
"source": [
"s = pz.Species(\"*\", denticity=1, kind=pz.Species.SURFACE)\n",
"M = pz.Species(\"M\", denticity=1, kind=pz.Species.SURFACE, mass=1.0)\n",
"Mp = pz.Species(\"M+\", denticity=1, kind=pz.Species.SURFACE, mass=1.0)"
]
},
{
"cell_type": "markdown",
"id": "84426190-0a62-4e87-97d8-0b113fd0cfb4",
"metadata": {},
"source": [
"Next, we use Clusters to define the energetics of these species. To keep this model minimal, we will stick to one-site energetic terms for `M` and `M+` and assign them a baseline energy of zero. We also intentionally omit lateral interactions. In pyZacros, this means our cluster expansion is simply a single site (`s`) occupied by either an `M` or `M+` species."
]
},
{
"cell_type": "code",
"execution_count": 5,
"id": "6727d2a9-e483-491e-9dae-137994ec7c6f",
"metadata": {},
"outputs": [],
"source": [
"M_cluster = pz.Cluster(label=\"M\", site_types=[\"s\"], species=[M])\n",
"Mp_cluster = pz.Cluster(label=\"Mp\", site_types=[\"s\"], species=[Mp])"
]
},
{
"cell_type": "markdown",
"id": "ec7ac229-1f25-40f3-8506-10579f58c887",
"metadata": {},
"source": [
"The Lattice\n",
"-----------\n",
"\n",
"Our first step is to construct a 2D square lattice with nearest-neighbor connectivity. We set the distance between adjacent sites to 3.5 Å ($a = 3.5$), which corresponds to the atomic spacing of our metal electrode. The lattice has periodic boundary conditions along both axes. Following the reference paper, we map the liquid electrolyte onto this same crystalline structure. We capture the physical difference between the liquid and solid phases indirectly by assigning different kinetic rates to their respective diffusion mechanisms. For the simulation size, we intentionally chose a 100 x 100 grid. This specific scale strikes the perfect balance: it lets us track individual atomic hops while providing a large enough canvas to clearly see macroscopic features like nucleation density, growth front roughness, and island coalescence.\n",
"\n",
"The code below creates this lattice and plots it so we can verify the setup is correct before moving on."
]
},
{
"cell_type": "code",
"execution_count": 6,
"id": "d01bf60c-7544-47f5-a4b0-3c7d4293d885",
"metadata": {},
"outputs": [
{
"data": {
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DZnZFtu9j7n5NdvmyJGX7rpf0I5Kuk/RxMzuvRL9gKN3jG0ssfPFN1Tdfut+4caOgeEpL9O5+0N13Ztefl/SEpMHTPGS9pHvc/Qfu3pS0R9IbyvIrAkr3+MYSC198U/ZlMl65LMnyOjNbKelrkl4v6cOSfkHStKQdan/qf9bM/lTSg+7+Z9lj7pT0FXf/3EnHGpU0KkmvfOUrh5566qnS/U9Hq9VST0+PZmZmzmopyWL7lvIY+OKLL74xxOowMDBQ+bx7ltedA2b2Ukmfl/Sr7j5tZrdJ+m1Jnv38Q0m/2O3x3H1c0rjUXkdfvPHZ0Ww2tX37dk1NTbF8Bl988Y0iVkq+jcb88rqDBw9W/Be9npR6qqOZna92kv+Uu39Bktz9aXefdfc5SVs0X57fL+my3MMvzbZFCz16fGOJhS++qfoyArd8yjzr3iTdKekJd/+j3Pb8Fw6/S9Jj2fWtkq43swvM7NWSVkn6ell+RUCPHt9YYuGLb8q+nR796tWrBcVTZun+zZLeK+lRM9uVbfv3kn7OzK5Ru3S/V9KNkuTuj5vZZyV9U+0z9j/o7tGvv2B5Hb4xxMIX31R980xOTi7YBuGUedb9dnc3d78qv5TO3d/r7ldm29e5+8HcY37H3V/r7q9z96+U5VYUlO7xjSUWvvim6psv3Y+OjgqKh3FEAVC6xzeWWPjim7Jvp3S/ZcsWQfGQ6AOhdI9vDLHwxTdVXygfEn0AlO7xjSUWvvim6stZ9+VDog+A0j2+scTCF9+UfTul+/37o15RnSxLMhmvLIaHh33Hjh2VOrRaLV1++eXau3evWi0mX+GLL77Vx0rRV5ImJiY0MjKiKqnjZDwSfSC7d+/W9PS0enuZfIUvvvjGESsl30ZjfjKemanqnFTHRE/pPgB69PjGEgtffFP1pUdfPiT6AOjR4xtLLHzxTdm306OHcuDVDYTldfjGEAtffFP1zbN58+YF2yAcEn0AlO7xjSUWvvim6stkvPIh0QdA6R7fWGLhi2/Kvp3Sffu70KBoOOs+kFarpZ6eHs3MzJzVUpLF9i3lMfDFF198Y4jVgbPuy6HMb697QdBsNrV9+3ZNTU2xfAZffPGNIlZKvo3G/PI6KAdK9wHQo8c3llj44puqb75Hv3btWkHxkOgDoEePbyyx8MU3Zd9Oj35iYkJQPCT6QFheh28MsfDFN1XfPFWPv60rJPoAKN3jG0ssfPFN1Tdfut+2bZugeEj0AVC6xzeWWPjim7Ivk/HKhVc3EEr3+MYQC198U/WF8iHRB0DpHt9YYuGLb6q++dK9e7pzXWKGRB8ApXt8Y4mFL74p+3ZK9+Pj44LiYTJeIK0Wk/HwrT4Wvvim7isxGa8smIwXCJPx8I0hFr74purbaDAZr2wo3QdAjx7fWGLhi2+qvvkePZQDiT4AevT4xhILX3xT9u306Ldu3SooHhJ9ICyvwzeGWPjim6pvnqGhoQXbIBwSfQCU7vGNJRa++Kbqmy/dDw4OCoqHRB8ApXt8Y4mFL74p+zIZr1x4dQOhdI9vDLHwxTdVXygfEn0AlO7xjSUWvvim6psv3W/YsEFQPCT6ACjd4xtLLHzxTdmXyXjlwmS8QFotJuPhW30sfPFN3Vdqn3U/OTmpKmEyHiyAyXj4xhALX3xT9W005ifj7dy5s+K/6PWE0n0A9OjxjSUWvvim6stkvPIh0QdAjx7fWGLhi2/Kvp0efX9/v6B4SPSBsLwO3xhi4Ytvqr55Dhw4sGAbhEOiD4DSPb6xxMIX31R986X7sbExQfGQ6AOgdI9vLLHwxTdl307pftOmTYLiYXldIK0Wy+vwrT4Wvvim7itJZqaqcxLL684CM7tM0iclvUKSSxp39z82s5dL+oyklZL2SvoZd3/WzEzSH0t6h6S/k/QL7h79WguW1+EbQyx88U3Vt9GYX14H5VBm6b4l6d+4+xWS3iTpg2Z2haSbJd3v7qsk3Z/dlqS3S1qVXUYl3VaiWyHQo8c3llj44puqb75HX3WFtq6Ulujd/WDnE7m7Py/pCUmDktZLuju7292S3pldXy/pk97mQUm9Zhb1Wgt69PjGEgtffFP25dvrymVJXl0zWynpRyU9JOkV7n4w23VI7dK+1P4n4Du5h+3LtkUNy+vwjSEWvvim6ptneLhWrfFoKD3Rm9lLJX1e0q+6+3R+n7fPujirMy/MbNTMdpjZjiNHjhRoevZQusc3llj44puqL5PxyqfURG9m56ud5D/l7l/INj/dKclnPw9n2/dLuiz38EuzbSfg7uPuPuzuw319feXJdwGle3xjiYUvvin7Urovl9Je3ews+jslPeHuf5TbtVXSDdn1GyR9Kbf9fdbmTZKey5X4o4XSPb4xxMIX31R982zcuHHBNginzH+j3izpvZLeama7sss7JH1U0k+Z2W5JP5ndlqQvS3pS0h5JWyR9oES3QqB0j28ssfDFN1VfJuOVT5ln3W93d3P3q9z9muzyZXd/xt3f5u6r3P0n3f172f3d3T/o7q919yvdPfp1FpTu8Y0lFr74puzbKd0PDAwIiofJeIG0WkzGw7f6WPjim7qvxGS8suh6Mp6ZvUTS37v7wsbKCxgm4+EbQyx88U3Vt9FgMl7ZLFq6N7NlZvbzZvbfzeywpL+VdNDMvmlm/8nMLl86zTihR49vLLHwxTdV33yPfvXq1YLiOV2P/gFJr5V0i6RL3P0yd/9hSW+R9KCk3zezf7EEjtFCjx7fWGLhi2/Kvp0e/eTkpKB4Tpfof9Ldf9vdH3H349MM3P177v55d3+32l9O84KG5XX4xhALX3xT9c0zOjq6YBuEs2iid/djZ3pwN/epM5Tu8Y0lFr74puqbL91v2bJFUDzntLzOzLYVLZIilO7xjSUWvvim7MtkvHI5p+V1ZtbvEUyti2V53a233qqxsbGzWkqy2L6lPAa++OKLbwyxOrC8rhy6Xl6XJ4YkHwvNZlMjIyMsr8MXX3yjiZWSb6Mxv7xu//4FX28CBXDGeomZPWpmj5x0+V9m9jEzu2gpJGOFHj2+scTCF99UffM9es66L4duPtF/RdKspE9nt6+X9ENqf5f8XZJGSjFLgE6P/ujRo2o0GnL349c7/aiz3beUx8AXX3zxjSFWp0e/bt26ykv3p2JycvKHly9ffoek12sJvt79HJiT9Fir1frloaGhwyfv7CbR/6S756cYPGpmO9199Qt9Hb3E8jp844iFL76p+qbA8uXL77jkkkv+cV9f37PLli2L7j+Rubk5O3LkyBWHDh26Q9K6k/d385/JeWb2hs4NM7tW0nnZzVYxmmlC6R7fWGLhi2+qvvnSfcS8vq+vbzrGJC9Jy5Yt876+vufUrjgs3N/FMX5Z0p1m1jSzvWp/x/yGbPb97xVmmiAsr8M3llj44puyb6d0v3nzZkXKsliTfIfM75Q5/Yyle3f/hqQrzexl2e3ncrs/W4hhwlC6xzeGWPjim6pvHibjlcMZE72ZXSDp3ZJWSlpuZpIkd/+tUs0S4OTSfYejR49qcHDwhDJVt/uW8hj44osvvlXH6pTuly1bFsU6+jrSTen+S5LWq92P/3+5ywseSvf4xhILX3xT9mUy3pmZnp5e9uM//uOXv+51r7ti1apVP7Jly5ZGt48942Q8M3vM3U/Z4K+aWCbj9fT0aGZmRq0Wk6/wxRff6mOl6CvFOxnv4Ycf3nv11Vd/92yPNTc3Z0X19u+6667ee++992X33HPPU5L0zDPPnHfRRRed0P94+OGHL7766qtXnvzYbpbX/W8zu9LdHy1Ctm40m01t376dyXj44otvNLFS8m005ifjrV27tuK/6MWxe/fu10xPTzcuvPDCZ1etWvVk6PFWr14985GPfOSyX/mVXxlcv379c9ddd933u31sN/WSt0iaNLNvZVPxHjWzR85dtz6wvA7fWGLhi2+qvvnldRMTE6oDc3NzNj093ZCk6enpxtzcnIUe86qrrvrBzp07v3nllVfO/OZv/ubgr//6r/d3+9huEv3bJa2S9NNqT8FbqxfwNLw89OjxjSUWvvim7Nvp0Y+M1CO1LFu2zC+88MJnJenCCy8sZMjO3r17z+/p6Zn7wAc+8L0Pf/jDh3bt2vVD3T62m+V1T0mSmf2wpBVnuPsLDpbX4RtDLHzxTdU3z7Zt9fkG9FWrVj1ZZI9+cnLyxbfccsuly5Yt0/Lly/3jH//4U90+tpvldesk/aGkAUmHJb1K0hOSfuRchesCy+vwjSUWvvim6ptfXlc3ihyy8+53v3v63e9+9zfPyaOL+/y2pDdJ+ra7v1rS2yQ9eC7B6gale3xjiYUvvin71jHJx0Q3r+4xd39G0jIzW+buD0gaPtODXihQusc3hlj44puqbx53huWUQTeJ/qiZvVTS1yR9ysz+WAzMkcRZ9/jGEwtffFP1zZ91Pz4+LiiebhL9ekl/J+nXJN0raUqcdS+J0j2+8cTCF9+UfTul+xtvvFGRMlfEErkyyfxO+TWAi07GMzPzM9RRurlPmTAZL63JV/jGfQx88a3SV4p6Mt7WSy655Iq+vr7nYvwWu+z76F926NChb1599dULvo/+dGfdP2Bmn5f0JXf/v52NZvYitYfo3CDpAUl3FeycFEzGwzeGWPjim6pvozE/GS9WWq3WLx86dOiOQ4cOvV7dVcKXmjlJj7VarV8+1c7TJfrrJP2ipD83s1dLOirpxWo/yb+S9J/d/f8U65oWLK/DN5ZY+OKbqm9+ed3WrVsVI0NDQ4clLfiknAqL/mfi7n/v7h939zervXb+bZJ+1N1f5e4bXuhJXqJHj288sfDFN2XfTo9+aGhIUDzdfKmN3P2YpIMluyQJy+vwjSEWvvim6ptncHCw8h59HYmx15AMLK/DN5ZY+OKbqm9+eR2UA4k+AEr3+MYSC198U/ZlMl65LLq87vgdzP6VpD9z92eXRql7Yllex/IZfKuOhS++qftK0ujoaOVDc061vC51uunRv0LSN8xsp6RPSLqvyrXzsdFsNjU9Pa3eXpbP4IsvvnHESsm30ZhfXld1kq8rZ6yXuPt/UPv76O+U9AuSdpvZ75rZa0t2ix569PjGEgtffFP1zffoOeu+HLpqjGSf4A9ll5akhqTPmdkflOgWPfTo8Y0lFr74puzb6dHv3LlTUDzdfB/9hyS9T9J3Jd0h6d+6+zEzWyZpt6R/V65i3LC8Dt8YYuGLb6q+UD7dfKJ/uaR/5u5r3P0vvL2mXu4+J2ntYg8ys0+Y2WEzeyy3bczM9pvZruzyjty+W8xsj5l9y8zWBDynJYPSPb6xxMIX31R986X7/v5+QfF006Pf6O5PLbLvidM89C61x+iezMfc/Zrs8mVJMrMrJF0v6Ueyx3zczM47k1vVULrHN5ZY+OKbsm+ndH/gwAFB8ZS2eNHdvybpe13efb2ke9z9B+7elLRH0hvKcisSSvf4xhALX3xT9c0zNja2YBuEU8WUgpvM7JGstN/Itg1K+k7uPvuybVFD6R7fWGLhi2+qvvnS/aZNmwTFs9SJ/jZJr5V0jdqz8//wbA9gZqNmtsPMdhw5cqRgvbOD0j2+scTCF9+UfZmMVzLuXtpF0kpJj51pn6RbJN2S23efpB870/GHhoa8ao4dO+Y33njj8eszMzMn7Ovc7nbfUh4DX3zxxTeGWB3aKalaJO3wEvNiFZeuvr2uKMys390734L3LkmdM/K3Svq0mf2RpAG1B/R8fSndzpVms6kNGzZoampKs7NMvsIXX3yrj5WSb6MxPxmv6pHmdaW0eomZ/bmkv5H0OjPbZ2a/JOkPzOxRM3tE0k9I+jVJcvfHJX1W0jcl3Svpg+4e/SJLevT4xhILX3xT9eXb68qnzLPuf87d+939fHe/1N3vdPf3uvuV7n6Vu6/LfbqXu/+Ou7/W3V/n7l8py6tI6NHjG0ssfPFN2bfTox8ertV3yUQDZ0AEwvI6fGOIhS++qfpC+ZDoA6B0j28ssfDFN1VfSvflQ6IPgNI9vrHEwhfflH07pfuNGzcKisfc0/1q+eHhYa/6LM1Wq6Vbb71VY2NjarVaarVaWrFixfF9ndvd7lvKY+CLL774xhArJsxs0t1rdbLAki6vqyPNZlMjIyMsr8MXX3yjiZWSb6Mxv7xuYGCAefclQOk+AHr0+MYSC198U/XN9+gPHjy+EAsKhEQfAD16fGOJhS++KfsyArdceHUDYXkdvjHEwhffVH3zrF69esE2CIdEHwCle3xjiYUvvqn65kv3k5OTguIh0QdA6R7fWGLhi2/Kvp3S/ejoqKB4SPSBULrHN4ZY+OKbqm+eLVu2LNgG4ZDoA6B0j28ssfDFN1VfJuOVD4k+AEr3+MYSC198U/blrPtyYTJeIK0Wk6/wrT4Wvvim7itJBw4c0MDAgKqEyXiwgGazqenpafX2MvkKX3zxjSNWSr6NxvxkvMnJycoTfR2hXhIAPXp8Y4mFL76p+uZ79OvWrRMUD4k+AHr0+MYSC198U/alR18uvLqBsLwO3xhi4Ytvqr5QPiT6ACjd4xtLLHzxTdU3X7rfvHmzoHhI9AFQusc3llj44puyL5PxyoVEHwile3xjiIUvvqn65jGzBdsgHBJ9AJTu8Y0lFr74purLZLzyIdEHQOke31hi4Ytvyr6cdV8uTMYLpNVqad++fVq5cqVaLSZf4YsvvtXHStFXkkZGRjQxMaEqYTIeLKAzGW92dlazs0y+whdffKuPlZJvozE/Ga/qJF9XqJcEQI8e31hi4Ytvqr75Hv3IyIigeEj0AdCjxzeWWPjim7Jvp0e/bds2QfGQ6ANheR2+McTCF99UfaF8SPQBULrHN5ZY+OKbqi/L68qHRB8ApXt8Y4mFL74p+3ZK9ymvAosZltcF0mq11NPTo5mZmbNaSrLYvqU8Br744otvDLE6jI+PVz4Gt47L60j0gezevVvT09Pq7WX5DL744htHrJR8G4355XVmVvmn+jomekr3AdCjxzeWWPjim6ovPfryIdEHQI8e31hi4Ytvyr6MwC0XXt1AWF6Hbwyx8MU3Vd88W7duXbANwiHRB0DpHt9YYuGLb6q++dL90NCQoHhI9AFQusc3llj44puyb6d0Pzg4KCgeEn0glO7xjSEWvvim6gvlQ6IPgNI9vrHEwhffVH056758SPQBULrHN5ZY+OKbsm+ndL9hwwZBCbh7KRdJn5B0WNJjuW0vl/RVSbuzn41su0n6E0l7JD0iaXU3MYaGhrxqjh075rfddtvx6zMzMyfs69zudt9SHgNffPHFN4ZYMSFph5eUF6u6LC/xf4i7JP2ppE/mtt0s6X53/6iZ3Zzd/g1Jb5e0Kru8UdJt2c/oaTabuvbaazU1NaXZWSZf4YsvvtXHSsm30ZifjDc0NKTJycmK/6rXj9JK9+7+NUnfO2nzekl3Z9fvlvTO3PZPZv9QPSip18z6y3IrCnr0+MYSC198U/XN9+h37twpKJ6l7tG/wt0PZtcPSXpFdn1Q0ndy99uXbVuAmY2a2Q4z23HkyJHyTLuAHj2+scTCF9+UfZmMVy6VvbpZL+Ssv73A3cfdfdjdh/v6+kowOztYXodvDLHwxTdV3zz9/dEXcpNkqRP9052SfPbzcLZ9v6TLcve7NNsWNZTu8Y0lFr74puqbL90fOHBAUDxLnei3Srohu36DpC/ltr/P2rxJ0nO5En+0ULrHN5ZY+OKbsm+ndD82NiYontK+j97M/lzSj0u6WNLTkjZK+qKkz0p6paSnJP2Mu3/PzEztM/Svk/R3kv6lu5/xi+Zj+D76Vqulnp4ezczMqNVqqdVqacWKFcf3dW53u28pj4EvvvjiG0OsDnwffTmUluiXghgS/e7duzU9Pa3eXpbP4IsvvnHESsm30ZhfXkeiLwdOdQyAHj2+scTCF99UfRmBWz4k+gDo0eMbSyx88U3Zt9Ojr7pCW1dI9IGwvA7fGGLhi2+qvlA+JPoAKN3jG0ssfPFN1Tdfuh8erlVrPBpI9AFQusc3llj44puyL5PxyoVXNxBK9/jGEAtffFP1hfIh0QdA6R7fWGLhi2+qvvnS/caNGwXFQ6IPgNI9vrHEwhfflH2ZjFcuDMwJpNViMh6+1cfCF9/UfSVpYGCg8nn3dRyYs7xqgdRpNpvavn27pqamNDvL5Ct88cW3+lgp+TYa85PxDh6M/itOkoTSfQD06PGNJRa++Kbqy2S88iHRB0CPHt9YYuGLb8q+nR796tWrBcVDog+E5XX4xhALX3xT9c0zOTm5YBuEQ6IPgNI9vrHEwhffVH3zpfvR0VFB8ZDoA6B0j28ssfDFN2XfTul+y5YtguIh0QdC6R7fGGLhi2+qvlA+JPoAKN3jG0ssfPFN1Zez7suHRB8ApXt8Y4mFL74p+3ZK9/v37xcUD5PxAmm1Wrr88su1d+9etVpMvsIXX3yrj5WiryRNTExoZGREVVLHyXgk+kB2796t6elp9fYy+QpffPGNI1ZKvo3G/GQ8M1PVOamOiZ7SfQD06PGNJRa++KbqS4++fEj0AdCjxzeWWPjim7Jvp0cP5cCrGwjL6/CNIRa++Kbqm2fz5s0LtkE4JPoAKN3jG0ssfPFN1ZfJeOVDog+A0j2+scTCF9+UfTulezMTFA9n3QfSarXU09OjmZmZs1pKsti+pTwGvvjii28MsTpw1n05LK9aIHWazaa2b9+uqakpls/giy++UcRKybfRmF9eB+VA6T4AevT4xhILX3xT9c336NeuXSsoHhJ9APTo8Y0lFr74puzb6dFPTEwIiodEHwjL6/CNIRa++Kbqm6fq8bd1hUQfAKV7fGOJhS++qfrmS/fbtm0TFA+JPgBK9/jGEgtffFP2ZTJeufDqBkLpHt8YYuGLb6q+UD4k+gAo3eMbSyx88U3VN1+6d093rkvMkOgDoHSPbyyx8MU3Zd9O6X58fFxQPEzGC6TVYjIevtXHwhff1H0lJuOVBZPxAmEyHr4xxMIX31R9Gw0m45UNpfsA6NHjG0ssfPFN1Tffo4dyINEHQI8e31hi4Ytvyr6dHv3WrVsFxVNJ6d7M9kp6XtKspJa7D5vZyyV9RtJKSXsl/Yy7P1uF39nA8jp8Y4iFL76p+uYZGhpasA3CqfIT/U+4+zW5kx5ulnS/u6+SdH92O2oo3eMbSyx88U3VN1+6HxwcFBRPTKX79ZLuzq7fLemd1al0B6V7fGOJhS++KfsyGa9cKlleZ2ZNSc9Kckmb3X3czI66e2+23yQ927m9GCyvS2v5DL5xHwNffKv0lVheVxZVLa97i7vvN7MflvRVM/vb/E53dzM75bttZqOSRiXpla98ZfmmZ4DldfjGEAtffFP1bTTml9dt2LCh4r/o9aSSeom7789+Hpb0l5LeIOlpM+uXpOzn4UUeO+7uw+4+3NfXt1TKp4QePb6xxMIX31R98z16JuOVw5InejN7iZn1dK5L+mlJj0naKumG7G43SPrSUrudLfTo8Y0lFr74puzb6dFz1n05VFG6f4Wkv2y34bVc0qfd/V4z+4akz5rZL0l6StLPVOB21rC8Dt8YYuGLb6q+eXbu3LlgG4Sz5Ine3Z+UdPUptj8j6W1L7RPCyaX7DkePHtXg4OAJZapu9y3lMfDFF198q47VKd1z5n158MoGQOke31hi4Ytvyr6dJN/f3y8oHhJ9IJTu8Y0hFr74puqb58CBAwu2QTgk+gA46x7fWGLhi2+qvvmz7sfGxgTFQ6IPgNI9vrHEwhfflH07pftNmzYJiqeSyXhFwWS8tCZf4Rv3MfDFt0pficl4ZVHVZLzawGQ8fGOIhS++qfo2GvOT8aAcKN0HQI8e31hi4Ytvqr75Hn3VFdq6QqIPgB49vrHEwhfflH1ZQ18uvLqBsLwO3xhi4Ytvqr55hodr1RqPBhJ9AJTu8Y0lFr74puqbL91DOZDoA6B0j28ssfDFN2VfSvflwqsbCKV7fGOIhS++qfrm2bhx44JtEA6JPgBK9/jGEgtffFP1ZTJe+ZDoA6B0j28ssfDFN2XfTul+YGBAUDxMxguk1WIyHr7Vx8IX39R9JSbjlQWT8QJhMh6+McTCF99UfRsNJuOVDaX7AOjR4xtLLHzxTdU336NfvXq1oHhI9AHQo8c3llj44puyb6dHPzk5KSgeEn0gLK/DN4ZY+OKbqm+e0dHRBdsgHBJ9AJTu8Y0lFr74puqbL91v2bJFUDwk+gAo3eMbSyx88U3Zl8l45cLyukBarZZuvfVWjY2NndVSksX2LeUx8MUXX3xjiNWB5XXlwPK6QJrNpkZGRlhehy+++EYTKyXfRmN+ed3+/fsr/oteT6iXBECPHt9YYuGLb6q++R49Z92XA4k+AHr0+MYSC198U/bt9OjXrVsnKB4SfSAsr8M3hlj44puqL5QPiT4ASvf4xhILX3xT9c2X7qEcSPQBULrHN5ZY+OKbsm+ndL9582ZB8ZDoA6F0j28MsfDFN1XfPEzGKwcSfQCU7vGNJRa++Kbqmy/dm5mgeEj0AVC6xzeWWPjim7Ivk/HKhcl4gbRaLfX09GhmZkatFpOv8MUX3+pjpegrMRmvLJiMF0iz2dT27duZjIcvvvhGEysl30ZjfjLe2rVrK/6LXk+olwRAjx7fWGLhi2+qvvke/cTEhKB4SPQB0KPHN5ZY+OKbsm+nRz8yMiIoHhJ9ICyvwzeGWPjim6pvnm3bti3YBuGQ6AOgdI9vLLHwxTdVXybjlQ+JPgBK9/jGEgtffFP2ZXldubC8LpBzXUqy2L6lPAa++OKLbwyxYoLldbCAe++9V/39/brvvvskSWvWrNGhQ4e0Zs0als/giy+++J7hfo3G/PK68fFxxuCWQHT1EjO7zsy+ZWZ7zOzmqn1Ox9zcnPr7+yW1E/yaNWskSZdccolaLXpw+OKLL75nul++R3/jjTcKiieqRG9m50n6L5LeLukKST9nZldUa7U4y5YtO/5J/r777jvhOj04fPHFF9/u7kePvlxie3XfIGmPuz/p7v8g6R5J6yt2OidaLZbP4Isvvvgudj/OtF86Ykv0g5K+k7u9L9t2HDMbNbMdZrbjyJEjSyp3MnNzc8fL9fnS/Zo1azQ5ObloCaunp6erUtfp7lfEMZYy1r59+7o6xnve857gWN2WEk/3Hl1++eVdHWNiYiK49Nnt6/vmN7+5Nr8PN91005L5FvG7d8cddxRaCi/7d6/o34cyfvc6S5OfffZZnX/++Tpw4IC2bt0qKJ7YEv0Zcfdxdx929+G+vr5KXRYr3T/99NN64xvfqEajIaldmspfn5mZWXRft/cr4hhLGWvlypVdHeOLX/xicKwVK1Z0dYzTvUd79+7t6hjvete7urrf6Zy6fX0feuih2vw+3H777UvmW8Tv3vvf//7g93kpf/eK/n0o+3fv2LFjGhgYYDJeSUS1vM7MfkzSmLuvyW7fIknu/nunun8My+uk9if7To8pf/1c9y3lMfDFF198Y4gVC3VcXhdbol8u6duS3iZpv6RvSPp5d3/8VPePJdEDAEA9qGOij2odvbu3zOwmSfdJOk/SJxZL8gAAAHBmokr0kuTuX5b05ao9AAAA6kBczREAAAAoFBI9AABAjSHRAwAA1BgSPQAAQI0h0QMAANQYEj0AAECNIdEDAADUGBI9AABAjSHRAwAA1BgSPQAAQI0h0QMAANQYEj0AAECNIdEDAADUGBI9AABAjSHRAwAA1BgSPQAAQI0h0QMAANQYEj0AAECNIdEDAADUGBI9AABAjSHRAwAA1BgSPQAAQI0h0QMAANQYEj0AAECNIdEDAADUGBI9AABAjSHRAwAA1BgSPQAAQI0xd6/a4ZwxsyOSnqraQ9LFkr5btUQAqftL6T8H/Ksn9eeQur8Ux3N4lbv3VexQKEkn+lgwsx3uPly1x7mSur+U/nPAv3pSfw6p+0v1eA4xQukeAACgxpDoAQAAagyJvhjGqxYIJHV/Kf3ngH/1pP4cUveX6vEcooMePQAAQI3hEz0AAECNIdEHYmbXmdm3zGyPmd1ctU83mNleM3vUzHaZ2Y5s28vN7Ktmtjv72ajas4OZfcLMDpvZY7ltp/S1Nn+SvR+PmNnq6sznWeQ5jJnZ/ux92GVm78jtuyV7Dt8yszXVWM9jZpeZ2QNm9k0ze9zMPpRtT+J9OI1/Su/BCjP7upk9nD2HTdn2V5vZQ5nrZ8zsRdn2C7Lbe7L9KyP1v8vMmrn34Jpse1S/Q0nj7lzO8SLpPElTkl4j6UWSHpZ0RdVeXXjvlXTxSdv+QNLN2fWbJf1+1Z45t38iabWkx87kK+kdkr4iySS9SdJDVfuf5jmMSfr1U9z3iux36QJJr85+x86r2L9f0urseo+kb2eeSbwPp/FP6T0wSS/Nrp8v6aHstf2spOuz7bdL+pXs+gck3Z5dv17SZyL1v0vSe05x/6h+h1K+8Ik+jDdI2uPuT7r7P0i6R9L6ip3OlfWS7s6u3y3pndWpnIi7f03S907avJjvekmf9DYPSuo1s/4lET0NizyHxVgv6R53/4G7NyXtUft3rTLc/aC778yuPy/pCUmDSuR9OI3/YsT4Hri7fz+7eX52cUlvlfS5bPvJ70HnvfmcpLeZmS2N7UJO478YUf0OpQyJPoxBSd/J3d6n0//xiAWX9FdmNmlmo9m2V7j7wez6IUmvqEataxbzTe09uSkrS34i1y6J+jlkJeAfVfsTWXLvw0n+UkLvgZmdZ2a7JB2W9FW1Kw1H3b2V3SXvefw5ZPufk3TRkgqfxMn+7t55D34new8+ZmYXZNuifA9ShET/wuQt7r5a0tslfdDM/kl+p7frZsksx0jNN8dtkl4r6RpJByX9YaU2XWBmL5X0eUm/6u7T+X0pvA+n8E/qPXD3WXe/RtKlalcY/lG1RmfHyf5m9npJt6j9PK6V9HJJv1GdYT0h0YexX9JluduXZtuixt33Zz8PS/pLtf9gPN0pi2U/D1dn2BWL+Sbznrj709kfvjlJWzRfGo7yOZjZ+WonyU+5+xeyzcm8D6fyT+096ODuRyU9IOnH1C5pL8925T2PP4ds/8skPbO0pqcm539d1lZxd/+BpP+qRN6DlCDRh/ENSauys15fpPYJL1srdjotZvYSM+vpXJf005IeU9v7huxuN0j6UjWGXbOY71ZJ78vO2H2TpOdypeWoOKnf+C613wep/Ryuz86afrWkVZK+vtR+ebLe7p2SnnD3P8rtSuJ9WMw/sfegz8x6s+svlvRTap9r8ICk92R3O/k96Lw375H011nVpRIW8f/b3D+Kpvb5Bfn3IJrfoaSp+mzA1C9qnxn6bbV7ZR+p2qcL39eofTbxw5Ie7zir3bu7X9JuSf9D0surds05/7naZdVjavfpfmkxX7XP0P0v2fvxqKThqv1P8xz+W+b4iNp/1Ppz9/9I9hy+JentEfi/Re2y/COSdmWXd6TyPpzGP6X34CpJ/ydzfUzSf8y2v0btf0L2SPoLSRdk21dkt/dk+18Tqf9fZ+/BY5L+TPNn5kf1O5Tyhcl4AAAANYbSPQAAQI0h0QMAANQYEj0AAECNIdEDAADUGBI9AABAjSHRAySOmb3YzP6nmZ1XYowXmdnXcoNZACARSPQA6fOLkr7g7rNlBfD2lzbdL+lny4oBAOVAogeIFDO7NvuijxXZRMPHs9ngJ/PPlU1DM7OXmtn9ZrbTzB41s/XZ9pVm9oSZbcmO81fZdLJ8nF1m9p/M7LFTxJCkL2axACAhGJgDEDFmdqvaE85eLGmfu//eSftfJOn/uvsl2e3lkn7I3afN7GJJD6o9vvVVak9IG3b3XWb2WUlb3f3PssS+wd3/xsw+Kmmtuy/4hyJrDRxy977ynjEAFA39NoC4+S21v1Ph7yX961Psv1jS0dxtk/S72TcSzqn9tZ6dr45tuvuu7PqkpJXZ7PEed/+bbPunJa09lYi7z5rZP5hZj7e/0x0AEoBEDxA3F0l6qaTz1f5k//9O2j+Tbe/wzyX1SRpy92Nmtje3/we5+82qXSU4Wy5Q+58OAEgEevQAcbNZ0m9K+pSk3z95p7s/K+k8M+sk85dJOpwl+Z9Qu2S/KN7+utDnzeyN2abrF7uvmV0k6bvufuysnwUAVAaJHiBSzOx9ko65+6clfVTStWb21lPc9a/U/nY2qf0PwbCZPSrpfZL+totQvyRpi5ntkvQSSc9l8QfM7Mu5+/2EpP9+Ls8FAKqDk/EAEsfMVkv6NXd/7zk+/qXu/v3s+s1qf1Xrh05xvy9Iutndvx0kDABLCj16gMRx951m9oCZnXeOa+n/qZndovbfg6ck/cLJd8jO7v8iSR4gPfhEDwAAUGPo0QMAANQYEj0AAECNIdEDAADUGBI9AABAjSHRAwAA1BgSPQAAQI35/xlxb9D6vLTbAAAAAElFTkSuQmCC\n",
"text/plain": [
""
]
},
"metadata": {
"needs_background": "light"
},
"output_type": "display_data"
}
],
"source": [
"a = 3.5 # Lattice constant in ang\n",
"\n",
"lattice = pz.Lattice(\n",
" cell_vectors=[[a, 0.0], [0.0, a]],\n",
" repeat_cell=[100, 100],\n",
" site_types=[\"s\"],\n",
" site_coordinates=[[0.000000, 0.000000]],\n",
" neighboring_structure=[[(0, 0), pz.Lattice.EAST], [(0, 0), pz.Lattice.NORTH]],\n",
")\n",
"\n",
"lattice.plot(marker_size=1, markers=[\"o\"], colors=[\"0.8\"]);"
]
},
{
"cell_type": "markdown",
"id": "54dca68b-6b69-43c4-9430-6432036da299",
"metadata": {},
"source": [
"The Initial State\n",
"-----------------\n",
"Once the lattice is built, we need to set up our initial \"experimental\" conditions. First, we create a Growth Front. We seed a horizontal line of `M` atoms along the bottom and top edges of the lattice. This acts as our initial conductive electrode surface where deposition will begin. Next, we add the electrolyte by randomly filling 20% of the remaining lattice sites with `M+` ions. This specific 20% concentration provides a sufficient ionic flux to trigger visible competition between the two key processes, the rate at which ions reduce onto the surface, and the rate at which they diffuse along it."
]
},
{
"cell_type": "code",
"execution_count": 7,
"id": "33908940-40d0-4c01-8f84-c967d54abb92",
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"0.2"
]
},
"execution_count": 7,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"initial_state = pz.LatticeState(lattice, [M, Mp, s], initial=True)\n",
"\n",
"for sid in range(0, 100 * 100, 100):\n",
" initial_state.fill_site(sid, M)\n",
" initial_state.fill_site(sid - 1, M)\n",
"\n",
"initial_state.fill_sites_random(\"s\", Mp, 0.2)"
]
},
{
"cell_type": "markdown",
"id": "25620097-1af4-465f-9f5a-4ea92dc4c738",
"metadata": {},
"source": [
"To verify that our initial state is configured correctly, we can visualize it using the following code:"
]
},
{
"cell_type": "code",
"execution_count": 8,
"id": "c6c97bcf-611f-4f40-9ed5-3453cfc3e725",
"metadata": {},
"outputs": [
{
"data": {
"image/png": 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\n",
"text/plain": [
""
]
},
"metadata": {
"needs_background": "light"
},
"output_type": "display_data"
}
],
"source": [
"initial_state.plot(marker_size=2.5, markers=[\"o\", \"o\"], colors=[\"#98dbff\", \"#0053b6\"], lattice_color=\"0.95\");"
]
},
{
"cell_type": "markdown",
"id": "92bc405f-8802-4726-be93-5a5be6a7961c",
"metadata": {},
"source": [
"Elemental Reactions & Bulk Diffusion\n",
"------------------------------------\n",
"\n",
"The core of any KMC simulation is its reaction network. In our model, the electrodeposition dynamics are driven by four different elementary events:\n",
"\n",
"1. **Bulk Diffusion**: `M+` ions swap places with neighboring empty sites (`*`) to simulate random walk transport through the liquid electrolyte.\n",
"2. **Electrochemical Reduction**: An `M+` ion adjacent to a solid `M` atom receives an electron and is reduced into a newly deposited `M` atom.\n",
"3. **Surface Diffusion**: Deposited `M` atoms hop across the surface. We explicitly track two pathways: terrace diffusion (moving along a flat plane) and step-detachment (moving away from a step edge).\n",
"4. **Ion Replenishment**: A background source term acts as an infinite reservoir, continuously introducing new `M+` ions to maintain a steady concentration.\n",
"\n",
"Now, let's translate each of these physical steps into pyZacros elementary reactions."
]
},
{
"cell_type": "markdown",
"id": "dfd4a45f-6daa-4856-b10e-902b9cb7ddb5",
"metadata": {},
"source": [
"**Electrolyte Diffusion**\n",
"\n",
"First, let's model how ions move through the liquid. We define ionic electrolyte diffusion as a reversible two-site hop where an solvated `M+` ion swaps places with an adjacent empty site (`*`). On the left side of the image below, there is a representation of this process using graphs, as needed for pyZacros, which in this specific case consists of only two nodes. On the right side is the enumeration of the graph's nodes. This graph is trivial, but it will be very useful later for more complex reactions."
]
},
{
"cell_type": "markdown",
"id": "64894f0f-d83c-464d-b883-091435026554",
"metadata": {
"tags": [
"html_base64_image"
]
},
"source": [
""
]
},
{
"cell_type": "markdown",
"id": "3029603c-5626-4d94-a3a1-1078e65fb66c",
"metadata": {},
"source": [
"Because diffusion in a liquid is faster compared to solid-state surface reactions, inputting raw physical rates introduces a computational \"stiffness\" problem into our KMC model. The solver would get bogged down simulating millions of fast ion hops without any actual deposition happening. To fix this, we apply a diffusion scaling factor (`sf`). This trick artificially slows down diffusion just enough to keep the simulation efficient, while maintaining the physical rule that bulk transport must remain at faster than the surface processes. For our setup, a scaling factor of 0.1 preserves this physical hierarchy.\n",
"\n",
"We derive our diffusion coefficient from Valoen and Reimers [J. Electrochem. Soc. 152 A882](https://iopscience.iop.org/article/10.1149/1.1872737). Their fitted data for LiPF$_6$ electrolytes suggests that at high concentrations (>4M, as in our case) and around 300 K, a reasonable order-of-magnitude estimate is $D = 5 \\cdot 10^{-7}$ cm$^2$/s.\n",
"\n",
"Finally, when translating this into the pyZacros elementary reaction, notice that we set the activation energy to zero (`activation_energy = 0`). Because Zacros calculates rates using the Arrhenius equation, a zero activation barrier forces the exponential term to 1. This ensures that the prefactor we supply becomes equal to our rate constant."
]
},
{
"cell_type": "code",
"execution_count": 9,
"id": "d77921c9-c3da-4329-abb7-a8f2713d7fa1",
"metadata": {},
"outputs": [],
"source": [
"D = 5.0e-7 # Diffusion coefficient of M+ in the electrolyte in cm^2/s\n",
"sf = 0.1 # Scaling diffusion factor\n",
"k_T = (D / a**2) * (1e16) # Ion diffusion rate in 1/s\n",
"\n",
"MpDiffusion = pz.ElementaryReaction(\n",
" label=\"MpDiffusion\",\n",
" site_types=[\"s\", \"s\"],\n",
" initial=[Mp, s],\n",
" final=[s, Mp],\n",
" initial_entity_number=[0, 1],\n",
" final_entity_number=[0, 1],\n",
" neighboring=[(0, 1)],\n",
" reversible=True,\n",
" pre_expon=sf * k_T,\n",
" pe_ratio=1.0,\n",
" activation_energy=0.0,\n",
")"
]
},
{
"cell_type": "markdown",
"id": "b238edd2-49da-4c0d-a0d5-72492688af25",
"metadata": {},
"source": [
"**Electrochemical Reduction**\n",
"\n",
"In this step, a local pair consisting of a solvated ion and a solid metal atom (`[Mp, M]`) transforms into two solid metal atoms (`[M, M]`). This represents the critical electron transfer event at the metal/electrolyte interface. Just as we did for bulk diffusion, the image below breaks down this process. On the left side, we see the graph representation of the physical reduction event. On the right side, we have the corresponding node enumeration."
]
},
{
"cell_type": "markdown",
"id": "de121761-c957-4c00-97fe-07ce14905d08",
"metadata": {
"tags": [
"html_base64_image"
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},
"source": [
""
]
},
{
"cell_type": "markdown",
"id": "292c73e6-6c29-4305-9bdb-4e74e49b0010",
"metadata": {},
"source": [
"We start by calculating the overall reaction current density ($J$) using the classic Butler-Volmer equation. You will likely recognize the standard experimental parameters used here, such as the applied overpotential ($\\eta$, eta), the exchange current density ($i_0$), and the operating temperature ($T$). However, pyZacros does not work with macroscopic currents, it requires a specific event frequency for a single atom! Therefore, we take $J$ and scale it down to the area of just one lattice site ($a^2$). After applying standard unit conversions using Faraday's constant ($F$) and Avogadro's number ($N_a$), we finally arrive at $k_R$, the per-site reaction rate in events per second. Finally, just as we did for bulk diffusion, we set `activation_energy = 0`, so our calculated $k_R$ plugs directly in as the `pre_expon` parameter."
]
},
{
"cell_type": "code",
"execution_count": 10,
"id": "45f8cfc6-4f35-44d5-9c5a-43893a2d490a",
"metadata": {},
"outputs": [],
"source": [
"eta = 0.6 # Local overpotential in eV\n",
"i_0 = 5.0 # Exchange current density in mA/cm^2\n",
"alpha = 0.7 # Charge transfer coefficient alpha\n",
"beta = 1.0 - alpha # Charge transfer coefficient beta\n",
"T = 300.0 # Operating temperature in K\n",
"J = i_0 * (\n",
" math.exp(alpha * F * eta / R / T) - math.exp(-beta * F * eta / R / T)\n",
") # Faradaic reaction current density in mA/cm^2\n",
"k_R = J * a**2 * (N_a / F) * (1.0 / 1e3) * (1.0 / 1e16) # Electrochemical reaction rate in 1/s\n",
"\n",
"MpReduction = pz.ElementaryReaction(\n",
" label=\"MpReduction\",\n",
" site_types=[\"s\", \"s\"],\n",
" initial=[Mp, M],\n",
" final=[M, M],\n",
" initial_entity_number=[0, 1],\n",
" final_entity_number=[0, 1],\n",
" neighboring=[(0, 1)],\n",
" reversible=False,\n",
" pre_expon=k_R,\n",
" activation_energy=0.0,\n",
")"
]
},
{
"cell_type": "markdown",
"id": "0a7c20ef-f6b1-4d19-a5dd-5633495e4c2f",
"metadata": {},
"source": [
"**Surface Diffusion**\n",
"\n",
"Once an atom is reduced onto the electrode, it does not necessarily stay where it landed. It can hop to neighboring sites. We model this surface self-diffusion using standard Arrhenius hopping rates:\n",
"\n",
"$$\n",
"k_T = \\nu e^{-E_a / (k_B T)}\n",
"$$\n",
"\n",
"Here, $\\nu$ represents the attempt frequency—how often an atom vibrates and \"tries\" to jump to a new site (typically $10^{12} - 10^{13}$ s$^{-1}$). For this example, we set $\\nu = 2 \\cdot 10^{12}$ s$^{-1}$ (nu)"
]
},
{
"cell_type": "code",
"execution_count": 11,
"id": "49ab609e-2888-43f6-b5a9-10a2061165e6",
"metadata": {},
"outputs": [],
"source": [
"nu = 2e12 # surface self-diffusion hopping frequency in 1/s"
]
},
{
"cell_type": "markdown",
"id": "018f9230-337d-4de2-88c1-3c3a33d3b1ec",
"metadata": {},
"source": [
"The activation barrier $E_a$ will change depending on the local geometry of the hop. We use the values from the reference paper, but you can find inspiration on how to calculate such parameters from scratch using a quantum chemistry package (like the Amsterdam Modeling Suite) in this reference: Jäckle M. et al. **Self-diffusion barriers: possible descriptors for dendrite growth in batteries?** [Energy Environ. Sci., 2018,11, 3400-3407](https://pubs.rsc.org/en/content/articlelanding/2018/ee/c8ee01448e).\n",
"\n",
"To connect our model with the mechanistic discussion in the Vishnugopi et al. paper, we divide surface mobility into two distinct pathways.\n",
"\n",
"1. Terrace diffusion: An atom hops laterally across a flat layer (intralayer hopping).\n",
"2. Diffusion away from a step: An atom escapes from a highly coordinated step-edge environment to a less coordinated site.\n",
"\n",
"The original paper also studies a third pathway: interlayer (across-step) diffusion, where an atom descends from an upper terrace to a lower one. The authors identified this as the predominant mechanism for smoothing the surface and suppressing dendrites. To keep our tutorial model minimal and computationally fast, we have intentionally omitted this descending pathway."
]
},
{
"cell_type": "markdown",
"id": "c1c08a5e-b17d-4500-be24-7d60e8414356",
"metadata": {},
"source": [
"First up is **terrace diffusion**. To implement this, we must translate the physical mechanism into a graph-based representation. The goal is to keep this representation as small as possible without losing the underlying physics (for instance, we need enough surrounding nodes to guarantee the atom is actually on a flat terrace and not perched on a step). The image below illustrates the diffusion process for our proposed graph representation and the corresponding node enumeration:"
]
},
{
"cell_type": "markdown",
"id": "636418a3-4fc5-4864-b43f-57e28a9a3d24",
"metadata": {
"tags": [
"html_base64_image"
]
},
"source": [
""
]
},
{
"cell_type": "markdown",
"id": "3df4b45d-f5fb-40f0-9f24-28782d8b9b1a",
"metadata": {},
"source": [
"Based on the reference paper, we use $E_a = 0.15$ eV for this reaction. The following code demonstrates how to translate the graph above into a pyZacros elementary reaction:"
]
},
{
"cell_type": "code",
"execution_count": 12,
"id": "4f6f0af9-5ac5-4557-9fd9-afe9d47a349c",
"metadata": {},
"outputs": [],
"source": [
"E_a1 = 0.15\n",
"\n",
"MTerraceDiffusion = pz.ElementaryReaction(\n",
" label=\"MTerraceDiffusion\",\n",
" # 0 , 1 , 2 , 3 , 4 , 5 , 6 , 7\n",
" site_types=[\"s\", \"s\", \"s\", \"s\", \"s\", \"s\", \"s\", \"s\"],\n",
" initial=[s, s, s, M, s, s, M, M],\n",
" final=[s, s, s, s, M, s, M, M],\n",
" neighboring=[(0, 1), (0, 3), (1, 4), (2, 3), (3, 4), (3, 6), (4, 5), (4, 7), (6, 7)],\n",
" reversible=False,\n",
" pre_expon=nu,\n",
" activation_energy=E_a1,\n",
")"
]
},
{
"cell_type": "markdown",
"id": "1f002b54-8220-4652-a36b-fcb645a739c8",
"metadata": {},
"source": [
"Next, we define **diffusion away** from a step. Just as before, we translate this physical process into a graph. Notice that this specific mechanism requires a slightly larger 9-node cluster to properly capture the local geometry of the step and ensure the atom is moving away from it."
]
},
{
"cell_type": "markdown",
"id": "9cd8ca09-394c-40c8-ba86-68b426e131a1",
"metadata": {
"tags": [
"html_base64_image"
]
},
"source": [
""
]
},
{
"cell_type": "markdown",
"id": "61ec7977-e57c-449c-970f-11a851d1221e",
"metadata": {},
"source": [
"Following the reference paper, we assign this reaction an activation barrier of $0.30$ eV. Notice that this is twice as high as the terrace diffusion barrier ($0.15$ eV)! This energy penalty physically represents the difficulty of breaking the extra atomic bonds associated with a step-edge environment, capturing the reduced mobility of these trapped atoms.\n",
"\n",
"Here is how we translate this graph into our final surface diffusion pyZacros reaction:"
]
},
{
"cell_type": "code",
"execution_count": 13,
"id": "3e7dc0d4-ccff-4f3e-ab56-f172186119de",
"metadata": {},
"outputs": [],
"source": [
"E_a2 = 0.30\n",
"\n",
"MDiffusionAwayFromStep = pz.ElementaryReaction(\n",
" label=\"MDiffusionAwayFromStep\",\n",
" # 0 , 1 , 2 , 3 , 4 , 5 , 6 , 7 , 8\n",
" site_types=[\"s\", \"s\", \"s\", \"s\", \"s\", \"s\", \"s\", \"s\", \"s\"],\n",
" initial=[s, s, M, M, s, s, M, M, M],\n",
" final=[s, s, M, s, M, s, M, M, M],\n",
" neighboring=[(0, 1), (0, 3), (1, 4), (2, 3), (2, 6), (3, 4), (3, 7), (4, 5), (4, 8), (6, 7), (7, 8)],\n",
" reversible=False,\n",
" pre_expon=nu,\n",
" activation_energy=E_a2,\n",
")"
]
},
{
"cell_type": "markdown",
"id": "6cc0e849-c338-479d-9d6f-af52586e11b7",
"metadata": {},
"source": [
"**Using a \"Fictitious Gas\" Strategy to Keep Ions Constant**\n",
"\n",
"To avoid the rapid depletion of M+ ions during deposition, we introduce a numerical replenishment event. We use a fictitious gas species (`Mg`) that continuously produces new `M+` ions on empty sites at a constant rate $k_A$."
]
},
{
"cell_type": "markdown",
"id": "6cead3a4-5d38-46a0-bbee-f97da6738756",
"metadata": {
"tags": [
"html_base64_image"
]
},
"source": [
""
]
},
{
"cell_type": "markdown",
"id": "5b73780d-3ecc-4946-8e7c-fa6c36b3fdfb",
"metadata": {},
"source": [
"Assuming a scenario where diffusion in the electrolyte is much faster than the interfacial reduction step, the ion addition rate should depend directly on the surface reduction rate\n",
"\n",
"$$\n",
"k_A=f_A k_R\n",
"$$\n",
"\n",
"Here, $f_A$ can be physically interpreted as the probability fraction of having an `M+` ion sitting directly against the electrode, ready to react. In practice, it serves as an empirical tuning parameter adjusted by trial and error to keep the overall ion concentration approximately constant. For our specific setup, we achieved this balance by setting $f_A = 0.0005$.\n",
"\n",
"The following code adds this fictitious gas species and the replenishment mechanism to our simulation:"
]
},
{
"cell_type": "code",
"execution_count": 14,
"id": "456c48dd-b7c8-4f18-b354-763d4dcfb6cd",
"metadata": {},
"outputs": [],
"source": [
"Mg = pz.Species(\"Mg\", gas_energy=0.0, mass=1.0)\n",
"\n",
"f_A = 0.0005\n",
"k_A = f_A * k_R\n",
"\n",
"MpAddIons = pz.ElementaryReaction(\n",
" label=\"MpAddIons\",\n",
" site_types=[\"s\"],\n",
" initial=[s, Mg],\n",
" final=[Mp],\n",
" reversible=False,\n",
" pre_expon=k_A,\n",
" activation_energy=0.0,\n",
")"
]
},
{
"cell_type": "markdown",
"id": "4105e3cd-ffbe-48b9-a818-89f12f25dc98",
"metadata": {},
"source": [
"Setting up the ZacrosJob and Running the Calculation\n",
"----------------------------------------------------\n",
"\n",
"Now that we have all that we need, we are ready to configure the calculation. We do this using a `Settings` object, which controls the macroscopic conditions (temperature, pressure), simulation stopping criteria, and sampling time for different properties. Notice that we set the molar fraction of our fictitious gas (`Mg`) to 1.0. We also define an output sampling interval ($\\Delta t = 3 \\cdot 10^{-8}$ s) to ensure we capture enough frames to properly resolve both the transient growth dynamics and the final surface morphology."
]
},
{
"cell_type": "code",
"execution_count": 15,
"id": "cb0a492d-1b37-4ca3-bfc8-16af82ace116",
"metadata": {},
"outputs": [],
"source": [
"sett = pz.Settings()\n",
"sett.temperature = T\n",
"sett.pressure = 1.0\n",
"sett.molar_fraction.Mg = 1.0\n",
"sett.random_seed = random_seed\n",
"\n",
"dt = 3e-8\n",
"sett.max_time = 15 * dt\n",
"sett.snapshots = (\"time\", dt)\n",
"sett.process_statistics = (\"time\", dt)\n",
"sett.species_numbers = (\"time\", 0.25 * dt)"
]
},
{
"cell_type": "markdown",
"id": "0c590465-95f2-4797-a084-b68915fa6f82",
"metadata": {
"tags": [
"hide"
]
},
"source": [
"The following commands store important objects to Electrodeposition.ipynb, allowing them to be restored by other notebooks, such as Electrodeposition-inlet.ipynb."
]
},
{
"cell_type": "code",
"execution_count": 16,
"id": "ccf1f54b-dad9-45b8-95fe-a1260d066870",
"metadata": {
"tags": [
"hide"
]
},
"outputs": [],
"source": [
"import dill\n",
"\n",
"nombres = [\n",
" \"M\",\n",
" \"Mp\",\n",
" \"s\",\n",
" \"lattice\",\n",
" \"M_cluster\",\n",
" \"Mp_cluster\",\n",
" \"MpDiffusion\",\n",
" \"k_R\",\n",
" \"MpReduction\",\n",
" \"MTerraceDiffusion\",\n",
" \"MDiffusionAwayFromStep\",\n",
" \"sett\",\n",
"]\n",
"data = {n: globals()[n] for n in nombres}\n",
"with open(\"Electrodeposition_data.pkl\", \"wb\") as f:\n",
" dill.dump(data, f)"
]
},
{
"cell_type": "markdown",
"id": "64b0b90d-09ae-42ac-852b-a3d10f05ed97",
"metadata": {},
"source": [
"Finally, we pack all components into a single ZacrosJob and execute it. Grab a coffee! On a typical laptop, this simulation should take about 20 minutes to complete!"
]
},
{
"cell_type": "code",
"execution_count": 17,
"id": "4e8f4ee8-55d0-4e9e-aa9b-b768838566f5",
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"[31.03|10:47:07] JOB plamsjob STARTED\n",
"[31.03|10:47:09] JOB plamsjob RUNNING\n",
"[31.03|11:06:04] JOB plamsjob FINISHED\n",
"[31.03|11:06:04] JOB plamsjob SUCCESSFUL\n"
]
}
],
"source": [
"cluster_expansion = [M_cluster, Mp_cluster]\n",
"mechanism = [MpDiffusion, MpReduction, MTerraceDiffusion, MDiffusionAwayFromStep, MpAddIons]\n",
"\n",
"job = pz.ZacrosJob(\n",
" settings=sett,\n",
" lattice=lattice,\n",
" mechanism=mechanism,\n",
" cluster_expansion=cluster_expansion,\n",
" initial_state=initial_state,\n",
")\n",
"\n",
"results = job.run()"
]
},
{
"cell_type": "markdown",
"id": "99092fd3-487f-4b4b-9380-e2ad8f8cd27d",
"metadata": {},
"source": [
"Analyzing the Results\n",
"---------------------\n",
"\n",
"First, let's look at how the species populations evolve over time. By plotting the molecule numbers, we can verify that our fictitious gas trick worked! The concentration of solvated `M+` ions (the green line) remains approximately constant throughout the entire simulation. Notice the gradual deposition of solid `M` atoms (the red line), steadily growing from the initial seed surface up to a total of about 1000 atoms."
]
},
{
"cell_type": "code",
"execution_count": 18,
"id": "021bbd53-58c7-4b37-84e2-960de77fe86b",
"metadata": {},
"outputs": [
{
"data": {
"image/png": 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\n",
"text/plain": [
""
]
},
"metadata": {
"needs_background": "light"
},
"output_type": "display_data"
}
],
"source": [
"results.plot_molecule_numbers([\"M\", \"M+\"]);"
]
},
{
"cell_type": "markdown",
"id": "afda1d55-d7cb-4054-9b6c-58002a2d23c9",
"metadata": {},
"source": [
"To inspect the final spatial distribution of our deposited film, we can plot the last frame of the `lattice_states` trajectory (using index `[-1]`):"
]
},
{
"cell_type": "code",
"execution_count": 19,
"id": "25fb92fa-e12d-49dc-9421-cd2d89da4b96",
"metadata": {},
"outputs": [
{
"data": {
"image/png": 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cVrP3OqnPdUQxl4GOU1kUczH/t913qIve5Oa27L6h/3SdVUVRp55jSu1rxqZs/RTg1pwEun7o/FPau0BZm3T86TqR9iwdM25vUftw/5ZR2Ddee05U/6U9pzmOo1H0Zf5L7RefgSdPnsTs7Gypf4b+w/iPBEi0UQodp7HXUJOSb1o6VxPFrm1TC0oHaiLHtYVcJJvuKOby9im0kfsUHLWqpVPDyGHuQcvRqeFYcn2ka046quDbL4+o1kKz5uhYSEco2n3S7X81HU1pZinyX3MEE1LYEtVd156rOrbQfDaUtU+V0gyDh30DrxkpdJzGXkNNtm/NUW46OlcTxa5tUwtKB2oixyUKnF4n2dC+cO339JE5zqCR+xQctaqlU8PIYaD8GyRHp9K+SHNJ15x0VMG1n0J799gv96U68l06QtHuE8340deUZpYi/zVHMCGFrY3Q58ZMA+nYQvvZYBg9DEROtF8YVi30EydOYGmpvI7w6z6yA1/53qHKe7zi0g2lNKNkz9nEImyjrvvWDe1Y5I55nb5obSjCutTF/QY1T3Wv2X74KfnIjV8/25dqiZe1rx2jYe9NbftTU1NYtWqV1UIfMoxCT4Ckf7v94rjoUK29lg7UaPNKdGqKtm+uHjBnLxV/oT7njnnsmIX3LaQWtTah/UsEOlVzhJE7/nWuWe06pcgdf278+tV+2KZmnEJ7zZrp55xr9pymfQtiGy6MQk/A1NQUlpaW0Gw2l88/vfeYnJzEO647D19/4DC+8dARXHn+qXjpheuW6bhvPHQU39p5FC++YN0ybRXa/8KrngWgrbtLba48/1QA7b+Qr962gbVvNBpYWFjo8Q1o05C33XcIL3/eOmy/eH3PfbdffNpy+6E99zpsE3B4aG4Ke+YnsXmmiQtWLwHQ29PfFfm+t913aPmDpKAAqc9vf+Uzs8aca5/zhd73JReswzuuO690Pbx1+2Z846Gj+Kbg10suWIfPvPMS/ORH7ln2v+gbnadc/6Xxp2v2R55zCpxz+NbOo12vqV90LsrGv2qdpvjPjWXR/us//L1a2qf7hPaTzsVLLliHz77rUvzBTY/27FNunuj6KfbZ4uKiuGbqnHPar+0Xn4Z3XHcePnrzLtx67xNsP6X2p6baj45Wq2WpZEOEUegJWFhYwPz8fOnvPn7bXrz3cz/A3EILqxsTeP+PPxNvu2ZL1zkjfT/E5OTk8gcJtQn1eDX2FNy9wvt+4HXPwg1Xl6dFcaBtPnh8Gncfm0ETDpPwuGztPC5cIwe6cD5zCMeSahvnjnlK+9yYce1L/ktzU5f/IeiarVNbWvI51n9pLjn/U9pP2Sfadabp86DWbO6am5mZQaPRMAp9yLA/nRIgbZxb732iJyUI6K2ExFXvovemNlIlLY1v3L3C+9567xNs3zjQNvcuTKKJ9l/rTTjsW6im+mIfPuFYfoNUIssd85T2uTHj2pf8l+amLv9D0DXLtS/5xfkv+RzrvzSXnP8p7afsE+0649rU9lNjz2HU1pyhHtgDPAESZSSlRGnOlgadRiZVFdOmMdE2NzWamOzkXk/C4+xG9UZ3bgIPHp/GVw/N4sHj06gihbTCDlphDwCqfnLtS5XYYoUpJhwwRXzOmXMtuEp4KdrYKXEbGv+l/aNJo9O2z521h33WCLBo29T2U2PPQaqeyOmZ15nGZugP7Ay8ZnApSdqUrEGnkfXed4UK1qYx0TYvWN2my/ctTOLsRnP5ZwkPHp9cpt0fW2gvSYl21wo7aIU9aEpQSiU0rhJbijCFA3DxRRux1PR43nNOwzmzTezY+Xhf0/i4Sngp2tjJlfgqIO0fTRqdtn1OdKcy9TKlelxkPzX2HKTqiZyeuaYvJic6XNgZeAKkNLJcjFIa2aBSWr56aBZ7FqaXf97SWMSPbjipttemQXHoVxpS6jhffNFG/PxPt4/1YseiTj9j338qQ+rzuI9HymdOkUY2bDzdz8DtG3gCqsRMpFKrIbz3y38JX7V1Pa7auh633XcYi00PB2BiAmi24qi5on16766iFB1qebHpu6jlq7auXw6ykq4Lv+XceO05Wd8CN8+28NiCXw5809DuFFdvOw1fu799pjc10S5h2Wy1ad/JiRX/i/fDcb3y/FOXv52nVhIrm3M6l7IwxYbl66YmHZ53fltrWTsWXPveAw/NTWPvwiQ2ddiQsqJxdPzCYx/N+9wRghaxe2YY9r1jsSF6n7x1++blaO46feb2uVQjndvndG+Enw2h/wCGHsT2dIc9wGtG7INM1OlFHJ0Vts9Vr5KqgqVoS3OVyLS4YNUifMtH0e4UlEJV0b4oGdeaKon1vK+tqtX5nfMe5zQWsaWxqB4L7r4PzU2rjiZij320Rwha1HIE0Gf7sM+Ar6yyl6LBnuIzt8+lqnrcPm/fu7cvmqMlw+BhkQgJ0IqZaCDp9HrwGsaa9rmIWk4zOlVbmmqIp8HjwjVtqvjCNeXfEqtQpsdMhTXo++G4Uj1w7Th3ec/MuVbPPdSG3vHwE1FjwbUfkxFQprXNaXBLGvYpGIcHeNhnTmtc2icaDfYUnzWR86Ev3D6neyP8bKD+57AHhvpgD/AEaPXANZCiQ+uMqOUiisM2uPalCl11UKg54CL3OW1orbBErv/a6GSNmIr3YCP1ufa1GQG5458/f+VZCFKf62xfYx9mZHACKtpKdnX6zIn+0NeSAJBWgKXM/9yKcIY8GIVeM+qMDq0zopajlsvaiD1PGzaFykXuc9rQWmGJXP9TtJ259iU6nLuvNiNg2N+AuSwE7RHAIPyXjrq4/STt3zp95kR/6Osw24RmPnD+a4RNVq9endUPQx4sCj0B/YxC7xfGPVJWQqwYx7BEQnLayY3UH2VwfRulPleJmQxzP6WI0WjWpnRNEYU+Nzc31Ie4RaEbolFQtsVf1i+78pnYtziFTY0mLlrbhPf9jYjlok7D6FJt5HludOwgooDDaH3qM43ippHntCwk1XOmY1FQg2VjFraj8Z/6WeeYb2o08djCVGmkvnMTeODYZGW0+cpYdken92vNaqPguSwEqc+a9nP9pwij0K88fx1uuvuJqMjzfvlMfZPKonYXv9lQmSFBsyjC9fuO684DYBXZhg17gCfgozfvWqbTvnr/EfzYkzN42UuehccWpuDcPC5Ynb4xY+k8KbpUG3kO5EXHDoPCBAKfK+hMqufcFXXrPb7+4JHl32k1sDn/tRrgPf5XQKLDYwvhhNR0v9aslgLnshBG6QhAWzwoSkO9Jp+54jOVFH7F8Q69Jly/U1NTeNdrnpPVB0M+LIgtAbfc8/hyBOfJhRZ27Gxv5CYc9s7nBXVoNrZUI/2bTI1jKfI8Nzp2EB+gUo1oGsVNI89vvPac5cjhhSVfGnW72AK+tfNoVi1tLiK4zjF3Dmyk/p75uPrzYXR6v9asPgq+PAtB6rOm/Vz/KcIodJphoI0875fP1De65ulrmkUA9GY+lGVIcH2cW2jhlnsfz/LfUA/sAZ6Aay45YzlqeLYxga2k8Mbm2byNWac2sjaKfFT1wCmkGtEaPeqUMUvRYNdqgOeOOcWWWR9Vfz6MTu/XmtVGwQ9i/dRtPwgNegl1asCn7JlrLj4DAKyIy5BhFHoC3nHdM/G17z/e0R9eh39/7Vl4bHERm2c9Lt4wgcXFyWRt5rq1kYvfhZq/ZfrFKTrDdehR52qYUz1qTsOYjhnVuS7T4y7GLEVPWqMBnjvmYfsXb5gAsIg9Jx02LWuw8z5fuGYJzgF75yfVa5bqvG/qPIj3Lkxiy6zHtvUTeOBYC7tPuq7fbWo0cdnaeexbmGT9mpycxPR0o9Se6slzOvODWn9VGuhl+4xbP/30OUUDXqNhHmrYv+O6ZwJoSys3Gg0YhgOLQk/Ah7/0j3jPZx8u1ezN1WauUxuZ0/OV7FP871eftdrMnB645l5ae63/Wg3wQa+ZXHuq8+7QLrnZ6gSXbZ5pLtP44e80evA7T8zgu0enRXtJZ37Q66/uNVOnz1poPicowvX7wdc/B+96zbOHXkr16R6FbhR6Am655yB7HpsblVmnNjJ3BifZp/jfrz5rtZk5PXDNvbT2Wv+1GuCDXjO59vQ828OhRc62DyxMsL/T6MHvPukq7aXz9EGvv7rXTArq1IDX+B+u31vuPZjVvqEe2AM8Addccjp7fqSr6hRfVYuiSht5lpzPc2dbZdXKPnbL7sqUqTL0qxIWV+0qrBB15fmnVlY8k87z6qzEdtXW9aXjL1Vlo/ba6mNc+xT0Xg8cm8YDGWuOnmc7eEyQs+2Njebyz+1HcJER4HGWQoxl82yLvTdNKePO02PXXzjGzlVrc4drhlYySxXAyUG+Bnz3Gfi2808X11y4frdnVl801AM7A0/Ajdeeg6WlpeQKSylVtSgkzeCXXfkM/NjRaezY+Ti2nn86Xnbl2QC6i85I6SEpwiT9igLm0sNKK0RVpMRwqTZh9bncSmwvu/KZ+LEnZ3rGX/KRvtamXnHtU9B77V2YWqamU9YcTek6a7oJOOCxTnqX98Cu+ZWPEk//r1gaNI0svLcmpSx2/WnT6KQ1Q9PIuDUnYdjV72j1v23nn44LXvBs7FmYYNdcuH4LjIKk6NMZdgaegNxKbP2sMKW59yA0x+uAVo96lKpiceOvrcpW59oI70XRzzXXr3bqQh1j/FSqbJjymfHKy0/Dl3/9RWi1WtlsQA6e7mfg9g08AYX4QlmFqdyqWrkVmjTa2rTCEq1clipMwlUC01bi0uhpdwmTBJXU+qXnnWLPzS2nrS3ZT8BjAu0PWGn8uPGn9wqDw/q15qR2OAy6klw4R5tmV2y5KofhN3BubaZUYtPuE84+BZo1SxGu32subqfOHj9+3FLJhgh7gCfg/mMTuPvYVDIFXicd2HNvhbY2R02nCpP0S4yCo/rDSmpa0RAOddKZ3NxKxx6c/QSAPQvl64yCG3+J9u7XmpPa4TDoSnI9c7Rqhb3RaGuHYia5ldjqPDbRQrNmKcL1e+O152S1b6gH9gBPwJ6TEz0RsTEP8KLCVD+UlYqqVtIHAK2wRCuXpaKsEtiFaxZLI4dj+hxWgmqRqnIFOD3vmA+Yeqtilc9tUS2r6sOc2n/10Kxq/LjxL/PlogGtubJ2OHD+cyirJKf5Q6GAtP/CyPPiEJ++nlto4Vs7j5auzfC623ccrpxz7T7h7FOgWbMU4fod56PXpxL6dnjhnJt1zv2dc+57zrkdzrn/0Hn/Wc657zjnHnbO/aVzrtF5f6bz88Od35/XL99yQaNmcyNiQwzCPowo3UoiULmIXAnceOTqUWv0zOuOCPa+W/dZ80HVrznjxi+Mot7UaC1HbmsjvymGrcfNrR+u/XBcKAWeglht7VBDntPQptT6R2/e1bWuKK2u3Seczymoa86np8tjHwyDQT+/gc8DuMp7f8w5Nw3g6865mwD8ewAf9t5/1jn3MQBvBvDRzv8Pee+f45x7PYDfBvATffQvGc9d20Jzab4vFPgg7Cnl7L3HrpOT2LMwnSxs0S8xCo2eed0RwZJoisY+BZw9N34h5bqpsRQd+U0xbD1ubv1w7UsUeAp6MgK6fkbva9+tIc9paEvUOs320O4TzucU5M55gdnZ2Sw/DHno2zdw38axzo/TnX8ewFUAPt95/9MAfqzz+vrOz+j8/mqXkpQ8AHjfYkUWxuEB3kWht4DvP/wEgBxhi/6IUVCRhsUmSmn/UFiCE2YQvSftSwVXNPYp4PtfPn4h5XpwcbITOtbOwn5sMW4OOTEUrRhJXRR8VT+L9sNxif6LJWyd+E/XkseKGA19XayxMtEQuk4lkZPb7luJ6NbuE87nFOTOeREAd/z48Sw/DHno6xm4c24SwF0AngPgDwH8I4DD3vviT+ZdAIqvN1sA/DMAeO+XnHNHAJwO4GBwzxsA3AAA5557bj/dZxEW3qARpBeuaeLB4/VH1OZGdFNctXU9vnr/EZxcaGFmuluMJYWO5KPQdRG9N157TuUHEo36DWnyq7edxkZ4axBqK1fpJEv2KYjV0w6jhjc2mtgz7yp1sznE6nFLazY3opraT6K9JmPaTwGnrT010X5wN1ttCn1iov16etLh6m0blu3pOqcZEjTDg94rtM/1OQW5c75tfXtSc3ww5KOvD3DvfRPAZc659QD+GsBFNdzz4wA+DrTzwHPvl4uQctq/uIQ989WRw5w9R2HXSWfSYiPPO/90/NuXbYF3i8l0JEfHaSN6NcVjpEhzWpQitxBLSkR7v76Bqynk1Ut4aK4ZRcFSxB6BSGs2N6Ka2k/AY0tjCS1A3X4KutdS+bFN+7qVF9yxC82QqCw+lIF+HVto53xyagmXG3s+dAwkA997fxjAHQCuBLDeOVf84XAOgN2d17sBPAMAOr9fB2AkRWfpX50h5XRArYFcbs9R2HXSmfsWp/CylzwLP//TV+DlL3kWvHNZdCRHx2lrmVM6kUMVTc7pHmvAUahaOr5fH8ZaCtm5cgo6woOoIxBpzeo1wMv7T+1bcGgBUe2noDsiu/zYJqTQQz36Mg14etRD7xXa5/qceIesOd9zcqJz/Uiecj5t0M8o9I2db95wzq0CcA2A+9F+kP9457I3Afhi5/WXOj+j8/vb/YjmKlAt3jCCdGODj1Avg1abuU5tZeleKTrDnB61Vht7+8XVxWOk+u91aitL7Wjsc9unGFU9bWnNpkRUS/upzH5QeuZSLXS6ZqXraC18uq40az7F537Zh2O+pTPma9euzfLDkId+UuibAHy6cw4+AeBz3vu/cc59H8BnnXMfBPAPAD7Zuf6TAP6rc+5hAE8AeH0ffcvC1NQUlpaW0Gy26cv9i5PYvzCJMxstXH0msONI/drM3e3w2sq8tnG3nnOZTnNoz2kw0/cLPegyPWqqJ8zpkbe1hc9bHk+NBrqkpw2saDhTPWb6fqjt/I7rzsNHb96FW+99gtUdpzah/S+86lkAULu2M10bkp72oLWlpTXLrVNJT7ytZ95uX9PnFD3zlP5z2u7FnC8uLqLZbLLrnK4/ek1or/Ez3HN0zDQ2koa6Zp/Tz4z2mLcfHfPz85iZmYFhOLBa6AlYWFjA/Pw8APToFD//1EWcv2o++d6czq+kh9wve84mt8+htvAHXvcs3HC1XAFOq6et0eOWtJ053XFJj1zjv4Rha0PXaa9ZM2G51X7tmVz7UdJwT9lzWg117T6n9jMzM2g0GqYHPmSYnGgC6MbrPRvKOxPiNrX2bLFOe84mt89hqtat9z4RbcPpaWv0uCVtZ+6sXjrD1/gvYdja0HXaa9ZMqPndrz2Taz9KGu4pe06roa7d53VqsBvqgZVSTQBNIzu70cS+hSm0OlGzm2byq0KVpWZoBAfqtueENcL0ntjUs7JUrY/dsltMN6PpObTC1VVb1y9/w5au49J7Cj3wWyK+gUspQTSlSBKzoMgV8+BSF+tMPaT3OrtT73xfSftc6pckrFJHJbWYNDzJnksJC9ecJvVRAp3zcDzL/OzZvzOtUkElTRpe2OfwM6yo5Me9X9gbhg97gOfCr8Rtewy+Klc/7TlhjZ70nsjUszBV6+sPHsGt9x4W081oek6oYf6Nh44uP4C567j0nlAPnPsDgqu2JaUUaSu55Yp5cKmLdaYeStritH0u9UsUVqmxkhrns7b/XEpYuOY0qY8S6JxLWu0Fwv0Lj8pKatxchH0OP8PoD6XvE6xevTp5DAz5sAd4Auhf+/uCKlgaIQIJVVW5UkUOUuw5YQ2a3pOCMFXrWzuPVgpIUAETKh4xt9DCNwkFzl1H3y8TcAmFRqTXr/vIjp6UoOKaMtq16gGeK+ZRlrpYh5gM16aHW/4sD9vn1oZWWCUFMWl4Vf0PU8IKhGvutvsOZT3A6ZyH41nmZzh+nNANl4Yn9Tn8DHtscRIXYZF9H7ACLqMC40ESQIUACpoKkCuZeb8iEvDAsWk8wAgGcNRUrr0WscIa2japSEhBTQJY1vMuE5CgoiWcYIRkz72mdGgoLJHif3EEwP2u917dghGbZ+JSD89uNLvESzZON0vFTMLrivfD9jUCNnT+HfzyfYtKcFViKmGbdM1ywhpapKxZzp5LCQvXHJ1zregNBRVwCcdTk3qnERCix17S5wQ3Tpo9Pzc3F9VvQ72wb+AJoHrgWjpZoiCBaj3xXHstUih4TZscNblMQXdVQ2v/n1LdlRR2iT33OoUOlfynRwClfQsQUruXrZ1fTtFRVVLrObaJo0BTKplJFLj3wK75qd72hT4DK2s29gihZzhqPDaildikNUfnXHtU0uVbpoa6ppKapCfPHZWliBEZhgd7gCeA6oFr6WSJgtToiefaa5FCwWva5KjJUM+7eCAV15VR3SGFzdlzr1PoUMl/egQQ/q5Mm7yM2l2phFeNkNo8uBRHgaboaUsU+FcPzbJUq9Tn4l6xRwgh6j026tVtL1tzdM61RyVBq5lHCr32bf91evLcURl3rxBGoY8GjEJPwOYZXn+Zo/MonQmBMuPoxNDeRbZPIdHxlE6VaE+KWA3yUM+baitzesqUpgyrWlE9cA3tHrZ/9TZdJbgymj6k8MN7l1HouXrWPRR6JAXa834nojmVwqb7oYgwD9fWhAe7Zzg6WIvYY6NwXQOcNjZ/bELXbKqATg40xw4Sna45NpFQ+N9oNLLuY8iDfQNPgAcfncl+G/Vdl2Hz9BK8640OZenEwD66fQKJjk8RplALfvjiw4SPAuf0lClNSWnOUA9cQ7v3tl9dhIWl6QMKv6xvIbL1rANqfONUE2dO94qZaKlRLqJZ7Y73Xf7s6aQe0bVFF2m4Zjk6OKb9GGij+KVjE6oHniugkwLNsYNEp+cKwBSwKmzDhT3AE7B3foKlDLmNSelMwMG7ctqdoxND+wLa9rv8F+h4SqfWGcXcpUHOUOMhVRlS3QVNGdKc1EZDu5ddE+M/peNDCl9zby21y6GMGi+j4LXUqES1arB3oXttFo8FurakNcvRwVrEPgy1UfzSsckd3z+yLJ4zCJ9DaI4dJDpdc2wioaDQjx07ZvXQhwh7gCdg80wLe05OsAUOYgqphMUmNs+s6PRyxVNoIQx6jVYbWSqqQQtESIUgKLQa5Jxmt0aPmUZ0h8VSNBre0jVa/wt7h25t6CvPP3WZKdBqiFPweuo6PXA6Z5qiICGoNnS4njRFYag9XU/ca6moCAep/dhCOFo99aq1WFV8iHsdFh/iCv5ox5ybM6nPXCEYrv1wXRV64ONcivupAHuAJyCFQtfq7NKIZK54Co1aTaHGpIhiSqdKhSC6xkOxiUPam1KOKj1mEtEdFkvZfvF6Eq1WHvkt6XzHHgF0btF9r4r2JXB0qFYPnM6ZpihICEphc5HL0nEKF1HNvU7JYqgzil2rpy6tRU3xIe51WHyIi2LXjrkUbc71WXNsIh21mR74aMCC2BJQRqEXqIqIrdLZLaiwH91wEs3Oe0B3tPtFaxdxUck1BTVWBeoLvZdUCELSmdZ8AFOd5VCzW6PHTLW5w2Ip39p5tFLDW9L5jj0C8OjWhqYUulZDnILTU9fqgUt1xjV63AWFXbaeNHWxqT1dT9zrcC3FHvuE7XPjx0Grpy6txbD4UGz9fFp8KKyzrumzZs6kPmu0EeT69e1Hh5VUHS5s9BPA6V8Dg9dWrlsbWeobh35pE3Pa3OH7L1FEBOfqiUuaz5r2JXBjri1EQu1TioJo9Ljr1pDn2ucgtZ+yZmPbl9Ycp3XPvdauGe2Yp2iwa8ZMKt5T6IGvWbOmsi1D/2AUegIu3jCBVqtX/7pubWVOG1nW6Y3TRpa0vYtN/dVDs106wYPSo+Y0wENt5Xdcdx5+/8uP4NZ7n+jSYKb36tZs3oCXv/hcfPXQlFpbmdqHeuafeecl+MmP3INvdHSjAVlDvFeP/FnLY07nmc4/nYtQT7tszkKtd+34S21yGvLT0w08cKyF3Scdu05y9cg5vyQ9+hRt7G6bFQ15qhP/kgvW4bPvuhR/cNOjuPXeJ1TzLK0ZurY1evDhmNO54fZsuM+3rpvAvvkm9i9MdOm2c+2fNd3EgcVJ7F+cxJmNVmfMgZMnT2J21rj0YcH0wBNA9cBDDEInWKvzq4GkM5yrQa5Fih5zTvt165kPQk98GHra2vnfeWIG3z06XXldbPsc+qmNTSFpyMdqwEtrRlrbHLgx12p7b55pLh89aOYstL9ifROXnTFleuBDhlHoCZA+bAahE1ynTq+kM5yrQa5Fih5zTvt165kPQk98GHra2vnffdJFnUFr2+fQT21sCklDPlYDXloz0trmwI25Vtv7wMJE1JyF9rsz15yhHtgDPAFS4Ab9nbaSGUVshSWpkpskelIgrOpF9cxTxCDq7DN3bh22EVtVKqUSWq4YS24lOOozzbCegMfZjbxKarliIFxlQqniH/UxtnpgKCCkqSSXIsYjVd+jGvAahGtZU8lN2ku0el1ZumnYT231Pg69sTZWSnUUYGfgNYMeSWgrmVHEVliSKrmpUop8d0qcRuRgUH3mUs9SxDgoUiqh5Yqx5FaCoz47D+xeXBEP2b8wUZlGJKEOMZCytMo6BXgknWtNSlSKGE9l6mAEytYyrWVQVsktJY2MTf0M9jlXvY9DOH7PXdv+w8aC2IYLe4AnQCo6QTe2tpIZRWyFJcleozMs6ZmniEHU2ecyYYmyNmKrSqVUQssVY8mtBBdW1aJzdmBxuGIgtBIbJ5qSK8Aj6VxrKsmliPFI1fdixUs4kRTpHvJe8l3rgRubAtrqfbz/3ePnffvR0Wq1LJVsiLAHeAKkBUurQhUCDmHFNqnCEa3ExlVsozah/aZGC/sW/HL96Qn0Vr+i9wp9LOhYbVWrYjyKP2rObjSxr1MLm9OGDrF5ZsVnjU1YVUpHgfNVrbhKYNRm2/mnL1flCgOarjx/HW66+wksNj0mHDA5sfI7mvqmqUSn8T+skMdVEpP6TEHb166zrqpgzPyJFf+CY5+qSnS0z2HlMW7PaMH1X5pzzbGHtk0OdPykiouaPZdSva9qzwDAiRMnhhrE9nSHPcBrBqWDaYk2LbXIaUNzNqH9psYS6PeJMtEUeq/QxxQ6tusbTEDVofrLFUvBckihwCU6UqPBfsELno2fA3Dfzsd7ymJyYiqUGtVWotP430uTllcSSxGj0a6zcPzK5k+q+KcR8OH6HFYei9ZTV/ZfmnPNsYe2TQ5qMRLFnkup3pdyHGYYLOwBngDpL2dKB3MCDlXUYhm1xdmE9gcVoin0XqGPKXQs/TDiNKglcBQshxQKXKIjNRrsLTeBH33xeXjvq85e/r1WTKXtc/lxgNQ+60sJTVo2HiliNNp1Ru/FzZ+kIU7BHaFwfS6jzGPoYG3/pTnPha56oU6MRLPnJAEbbm6l9WN64KMBO7xIgESh04jcNoUtR4T2XMNE1HI2YUQyjS4NNYCLe0kVljaSdqi2sxTdTKPIuShYbURtnXrQYuSyIgpZG4V99bYNXdHmZRrmKf5ThFHEsRr00tEEN390bUgV3mLnL1wLm2fKI6o5DXFtFoE2Cl6zfkPERs5LbWoyB6Q+p1Rio3PGza0mct/kRIcL+wZeMyidCDC63x7sNZTakvTAC5swIplGl3IiBxK16T2wa37lfoW2s0ShUQqUi4LVRtTWqQct087VUchRUfide3Aa5in+d1/E06QaDXrpaIKbP60YSez8aQV8uCMo7RGKNgpes357hnbYAiykz9p12nU/RoBGoydP0Wg0Ktsy9A/2AE+ARB+F2shlFLakDc5F1HI2YUQyjS7l7iVRm/R+VNtZomApBcpFwWojalOgosAZvyR7LVV/+47DlRrmKf5TSDSpRoNeOpqomr+LKijw2PkrWwtla5Y7goqJjtdEwWvWb0+PEwVYytrUHFVJfU7Tl++ds3BupfsWn4HDrsT2dIdR6AmQxA9iRQK0wgxakYlYMRTJf60wRm6f+yWGoe1/bvvbLz6NFTrRCJvkinnk9n8QYiCSX9ya1a4/Tf+le/VLwGfYAiyjbG+oB/YNPAFTU1NYWlrqET+YnJzsCGP0CitwAiShSAG114hJXLB6CfsXJ7F/YUVkYGlJFkORhCXK2peEMaQ+a4UZ+iWG0j02vP+57f/Cq54FAD3CFpywSq6Yh3b8OAGQUMxDM3+5/qcI+ND1J4m5cGI03L3C8du2vlzYI0UARbP+pDb7NeaSPddPyX5qyh4dowATM0lAiphJijCIxiZXmEPrf902g7AfthjLKNnXKYCT0n6ufT/FXGKFQVJ8Du0HLQAj2Wv3CcXMzAwajQbm5uawevXqZD9yYWImhmikiJmkCINobHKFObT+120zCPthi7GMkn2dAjgp7efa91PMJVYYJMXn0H7QAjCSvXaflNkP8+FtMAo9CVViJmVVnaRKUrTCEa1KFVbc4s6WuapkUsU3TVUuipRKZlpwY8b5GV5Dq1JJY8NVKLtwTRMPHu+tBJbivwaS/9rqabHtc2OR4r+2/dxKcNSG+o/ON3Df2UtUgIdDSvVDWuGMplRKa06qmNeVekeq19F7p+zT3DWjqeQWtrFtfbuBYX8Df7rDHuA1g6vqJFWSAtJTWqT0Em0aDec/RUolMy1ixVC0YiZcGkxov39xCXvm6xcD4SD5n1L9KraqlzaNTouUNcPZczaSmEtsSpe2+mGYhkdTKrk1F5O6WHbvlH2avWYU6YZhG5NTS7h8Np8JMOTBKPQEpIiZ0PSUJsBSVlxKS5H+FaJI9VipRFXefkg7cjSZJiUrtK/zAZBybLB3vrwv4dgU49erjRxPIXL+ayD5n0JnxlT1KltL/XqAa/uimX/qf8sV38Hb/9eMUdVeKBubMHWzpVhz3J4PxzxMN20JvqWOmYSq6olSv9rHFvboGAXYLCRAqqJE6XVN6ldYLY1WpcqtSiZWfIusMJWip5ziM9eOVFUtPDaoqr4VtqGpXqf1XwOtBrvWF00lOmofvg+Ur2dtJTNODz6lqhlXPU47/xzqrH4o2WjWb7jPaYobzViXKiFq9gxF2L5z5faa6o3t1D8rpToKMAo9Afcfm8Ddx8opV42etiRSUKcwA6XGAKYqnGRPMCgKVkN791CTkccGvW2siIFIxxsa/3Ud7qYsuf5rfYmlsLVHCCl63loKmfWfoXO1889C2AvwcdUPJRvtsQ3d57QSWng8wFVC1OwZCunYRrPmOD1wK+IyXNg38ATsOTmhopM52pK+X0anc1SnBhw1Rqu3SfetqkrWbwpWQ3uH1GTssUFvG16cjxj/NSjTYC/rv9aXWApbe4SgPYLRHBtp1xxH52rnn4O0F7hxSrHRHtvQfX7R2kVcVHI8ENL2sZ8zFNKxjWbNhW0UAXwLCwuVY2/oH+wBngBJvCGWTpVECrQUaA61FiKWjg1tpOs4aIQdJJqPowO1lbxo+5yAhoTY/mvFOLTzF3vsIR0hhFHYmiOYFDEQCs34p4i5UFD7kJre1GhVthnaaI66Umh/7fqt89iGa1+z5rh6GIbBoG8UunPuGQD+DMBZaP+J/HHv/X92zr0fwFsAHOhc+mve+y93bH4VwJsBNAH8gvf+b/vlXw6eu7aF5lI5zR37bUwbRa7V6Y2l1kLkRqGnRMRqhB202shaDWquffptjlK4EmL7rxXjiBJTibCXjhC0ojucnreWNqdQjT9DrUv970JgT6npTY2l8nsLNpqjrhTaX7t+6zy24dpPOcIzDBb9PANfAvB/eO+/65w7BcBdzrlbOr/7sPf+d+jFzrnnAXg9gK0ANgO41Tl3gfd+5PIUvG/hwjVLUeeRHCTBAI5202pbp4gcxNCxZW1qNagpNMIOWm1krQY11z4noCEhtv/aedFeFyvGUvZ+2XWS6A5FihgIZ8+Nf4qYi9QXKtJzkLm3ZKPRINeK6VBo128dxzY5wiimBz4a6BuF7r3f673/buf1kwDuByDJMl0P4LPe+3nv/Q8APAzghf3yLwcSZUrp3Nx7aynQOiPCOTo7hcLWRsRyFCYHLQWtBT0SoVHAKRS6NgqZfv5qjhC09lK0uMZ/Cq2eOHekpD1OydWmjj2CCeeYO0KQ6GyNBjk9DggpeLpnNOOU+zmTclSnaX/VqlVRfhjqxUCi0J1z5wG4HMB3ALwEwNudc28EcCfa39IPof1w/zYx24WSB75z7gYANwDAueee21/HFdAWFdEiNoq97ohwjs5OobC1EbEshclAS0FrQbWRwyjgWApdG4UMxGlDa+21hUA4/7t/wdPWFJweuPY4JVebOvYIJpzjjVNNnDnde4Qg0tkKDfLwOIArBFNn8SIOKUd1UvtFIZfcLwyGPPR99J1zawF8AcA7vfdHAXwUwLMBXAZgL4Dfjbmf9/7j3vsrvPdXbNy4sW53VaD0kbaoiBaxUex1R4SX0dlhm2GkKhfRqo2ILaMwJUjFa9KwEoUeFgmp8gWIj6IPI4q5MafQ2msLgXD+U2gKfHTuEN1nzp5GZGvXvGb8pEIwjy2WZ35Qm9Avbs3RPrePA8ojymOL9+R+zmgLPmnbLwq5HD9+PMoPQ73o6wPcOTeN9sP7z733fwUA3vvHvPdN385D+ARWaPLdAJ5BzM/pvDdyoFq4krZx7r2HYZ+i7R3b594o6LziNXWOWUrk/iC0obX22sh7jf+5euqD0mOP1dauY8/GapCH88JpoPdrz0n+p7S/JbN9Qz3oZxS6A/BJAPd773+PvL/Je7+38+O/BnBf5/WXAPyFc+730A5iOx/A3/XLvxxMTk5h54m2ohDV6Q61jUMNcKD9lyynuTs5OYnp6QYeONbC7pOOvU7SKY61D7WVt66r1imW9Jw1esShhvnVZwI7jsh61LnazJK2MR0zTnc9RZs5RQM+RU+daktvnG7izEYTj0X4H/a/WA+cz7RfW2Y9tq2fiLJPGT9pz5Rp2Ie65ynrV9onnAY5Xdt0LqgeuaSBzo1TuGe2rZ/A0pJ+z4VzRv1Pbd8wfPRND9w591IA/wvAvcByAOevAfhJtOlzD+ARAG8tHujOuV8H8O/QjmB/p/f+JqmNYemB331wCXceblNKk+B1giUNY05zV6MTnKszLPm1eaa5TElKflLEahOnaJj3U8+6X9rMg9Ijz/Wf2mvWadgvuma065yizvFL0bbWtK/VIO/XnKfsmX7aX7G+icvOmMLJkycxOzurvk/dMD3wPsF7/3XvvfPeX+K9v6zz78ve+zd47y/uvP8a8m0c3vsPee+f7b2/sOrhPUxIWr6czq72bFKjE5yrMyz5dWCBrzLHIfbhk6Jh3k89635pMw9KjzzXf2qvWae9ldwmotc5RZ3jl6NtLbWv1SDv15yn7Jl+2u/u2A/z4W2wWuhJ2Dzbwt5OOdWyNK4iyI1qGId/wXPndJtny7WJvVfqDBN7Tnec6v8W4TyFtvLG6SZ2L7goneJYbWKthjmnBx32i+p5Uz+12spUm1mbOkZBNdxpmxo993D8NAjHiOpZS1rzGnvNOg3nb2OjiT3zTrSnbYbzEqvnLo2/ZszD/nN68OE+maD96oiZaOc8bJPrM4dQs/vsRnn71H/pM0Oz5yT7tpjJJI4fP441a9ao+2GoF/YAT4C2EltKVTBNSo5U7Yras2IYJD0ICCs0df+s0SmusxKZRg867BcV46B+xmgrx6SxheDSuJLEPBSQhDE0AihaYQ21Bj2p5MbZS8IosXruIWIrwan14IN9womZaOY8O9002Jf7FyaW55lb5ykCQFr7QszECroMF/YAT4C2EltKVbAipSa8t76q04p9WLGsqL4UVphasXQ4uFRefWql9EV+JbaU6nNSJTYqxkH9lHwO2+SqfGkQpnEVbWqrb8U+wMvGqEgP4uZca19AWqeaSm6hfUhH03mhlfSq2ilDbCU4jZhL2T6hlejoOGvmvCwNLKZMaZjSd2CRH8+yio3SuGgqPob23tujYxRgs5AAqXgBR4dKFCJHR1NwdKJEB3J0nkTtUzqU0us9FCJzbBBSfWcxfnJ95uylsdjYaGL3fHFGueKnhs7d1GhiU2OFQqfHBnVS0FL/KQXMUZjccUJI52oo5HCMOWELrs/h+uUoaG7OwmMbSgdr+i/Nn7aSH3cEQI8gikpqZfelR1Upxw6x1QO1a57b5+HRCqXwuc8WaS8Wn4Gu7EzKMDDYA7xmaMRAtHQ0hbbCF6UDOTpPpvZX6FBasQrgxSxi9ZzFPiuqf4Vj4T2wa77XTw2dW1YJjtNgLpBCQadUYtMcJ4R0roq2D8ZYwwBI65eloJk5CyuhUTpY0//aK/kxevD0RuF9NdXjxDYjqwdq1zy3z5OqJyr24tq1a6P6YagX9gBPgHTuoxED0dLRFBydKNGBHG1WRe1TqlojZlGl53wR9AIskmgF53+VnxKd20R3Jbgy0Yo6KGip/5yYi+Y4oeh/DIWsFbbg/A/XL0dBU4RHIBwdrOm/ppKfdAQiHQHQsZSFbXqPumKPHWIQu+ZDm1gBIEDei8Vn4Pz8PGZmZpL6ZMiHZeMnQBJP0AhDtCmv8spHudrSnDCDVlgiRRtbY6MVYEkRA5H02csgjRl9PIVHAFwfNRS01H/qP6U6qYZ0KCCj6T83ZqFISUFha9dZWFVsY0MnesKNhUaPXFpLtP1QNEQjzAGUr19pn3KfAdyYS2Ik2r1JsXmmPgEgrn3Nnl1YWKh21tA32DfwBNx/bAJ3HyunDDXCEICOjk6K6Ga0nbXCEina2BobrQBLihgIF7nPQRozTsxEEqnQUNBS/7nMAUqHS9Hl0WIiATXKUdic/yFlTOncXApbQ+FKdHLKEQg9Agid12igp9D+sWImIWIzJ3IzP0wbfDRhD/AE7DnZW+yk6gGu1VauI6JbQ7VztGmKNrbGRqIQNRrmsv/lkfscqijUqiOAsI8aClqmUMszBygdLkeXV2cucNHVEoVd5X9BGXNjFjMWMRRuFZ0cewRygJlbrQZ6Cu1PKWzt3gz7kDvm3HhwRzUUlj42GrAHeAKkQi5cRLEmuhqIj8jWFojQRrHTiF4a3SoVCKERuTTCmCsEIxXyUEdeM1HwmkIyKWMuRe5rimLU2b62/5osBCkKO7cQjnYsuD0jRVFz60+TBRCOC5d5IWUkcAWX6PxRe6mQirZgTdeYMwWbtHPGFb/hxjmcy23r2zddvXp1pa+G/sEe4AmQCrmw2sSKiE4gPiJbWyBCS03TiF5ghULUUrghBV1WCEYq5JFC58UeO6SMuVYbehDta/uvyUKQorBzC+GkHNtoi/fQe2kiwuVx4Y9QODqePbYJ5m8P+WOMK6SSQlVzxy7aOeOK33DjzOmBG4YLC2JLQLuQS5w2sVZbuSoiO4RWJ1irUx1GZBcUYqgB3l3juVxPm2oge+Z16DNXS1qrgZ5SC1sz5lpt6EG0r+0/peCpTe+9VuaPzrO2rnkZnRszFika9Nz64/TE5XGpXr9Sm7Sd8KisxbRJ14w0tzzy5owrfsONM6cHPjc3p3HW0CfYAzwBkn4xp02coo08CJ1grTa35AvnM6eHnKuNHKJOPW+z56PNuXvlrvlcPfRcPfaU/sfqgaf4LGHQc2Z64KMJo9ATMDU1haWlpR4tXkmbmGojh+8D5TrDnE4vpzOt1TamOsmhNvK29RO473CvNrWkR031nOl1Z003cWBxEvsXu7WR6fuhtrFGm1irbUzHWavBzs2TZM/1P0WP++zpJjY3ljpjE69Hrlkzkp562fjtW6jWAy/TM+/WkOb1wGP10Om8SHrk3DpPXb+etMnpgWvGL2yT0x2n/ktrno7zGVNNOAccCHwO55z7nOLWX6+Guj06RgF90wMfBIalB76wsID5+XItXY02cYrOMEWKNnY/talj2xyUtrG2z5ye9jD0vOvU06aoU0+97vHPbX8QeuQp+1TbptSOZs9w9tJYxLYfYmZmBo1GY+iFXEwP3BAN6cNGo02cojNMkaKN3U9t6tg2B6VtrO0zp6c9DD3vOvW0KerUU697/HPbH4Qeeco+1bYptaPZM5y9NBax7XP+WxW24cJ4kARIYiaa9AwqkkBTtcL0Eg7alCKNjZSGlpIGpNFGTtED12obp/SZE8PQpjHVqeddpxiKZiy09uK9ZsrFSLTCNpwYCtfn8L5Uw55LfUwREKLt0PSysPqeVqiIgksd5PyX1jxnH/ocipEU7UtCM1K6KwAcO3bM6qEPEfYArxma9IwwH6yr2pNC5ECbUqSxqaNCVKwedkpVKK22cUqfOTEMbRpTnXredYqhaMZCay/dCx7l9kxKnFaPW1tJjmrYA+WpjykCQgju291meepeTOod106Z/+KaZ+y5qoJh+5LQDCqW9jgfwT4VYBR6AqRvW5r0jHa1p5XXRapWmF7CQZtSpLGR0tBS0oAoBadNY9KkYUlpQNyYpaTOcalbUhpTHXreMWlQYftcGpZmLLT20r0437iUOI0et9Tn8L6hhn1Z6qNEDWurJ4Lci9qnUNBc6iDnv7TmOXuaEhemoZZVP6yyobBKbKMB+waeAIlC56pSaWkqDZ2p1WbW0HkSna2tEMVVYkupHsfR1lK1qNw+00pcXD+lqnjcEYKaziYUNGcvtZ9bCY2rKsZBOgKQjkrKqpVNCOPPrYVQp1tjL2l2ayrB9dgzGuwabXCAp7C1euS51ftyq98Vn4HSZ6Gh/7AHeM3gqlJpaSoNnanVZtbQeRKdra0QJVViK/tyLNH2HG0tVYvK7jMnpkHB0MEAf4SgbZ9S0Ky90H5uJbRYMRjpCECu+FZerWzjVBNnTveOP7cWaOe19pJmt6YSXGhP54yuTY02eDFny+Ov7CdHgXNrI+XYRHtsVGDNmjWl/TMMBvYAT4BEH3EiA5IeMhUi4EQSwjYoZVds3pCOlHTHC0iCBXoNY6/qW5n/BW1fpk2sFfaoo89V/ZS0kcMjhNj2aX84e6l9bs3pRTLixGA0euhl/ZTGssq+Sqdb236ZZje356oEXMrWptQOBSfgo9Ujr6reVyUgpOmzJKBTfAaePHkSs7NWU3VYMP4jAZIeONXppWIGDxybxgMKnW1OG5rT6S3TZo6tykTBUWKSZjEdD6phHUZRc9dwUeQxetBlfZY0tLk+azS0Q83pTY2VOUfCmNM55+aM9jns1+aZ6up50lho+p8yfxS59rQv9M8crZ65BE5bO1eDntrT/R/qgWv7GVLoZTbaNa/RkJf06Av/Fxd1f/QZ+gP7Bp6AKj1wSmeViXlI1BgnUqCl9igdrKXzKLiAHm0UNBd5nhJFrqcGy/usoQDDPmsjn6nIBScAkyJMwc2ZRG1qKGxtFH2dWQAUufbSEZRGz1xCyhGE5thBOurSiA6lRJFr17xGQ146tjIxk9GAPcATIOmBUzqTahNTalTW2S7XhtZSe4CONuTAPcAlOpaLvOfsuWtCxFCDZX2WNbTL+6zR0A41pzkBGD16KexwzqqozRgKOhwLTf9T5o8i1146gtLomVf5Fn8EUX3sIB110WMjbT85Cl07z92o1pCXjq32nJzA5WzPDYOCPcATQPXAw0hNGpFLI7LD/9LiLVwhFk0hkhRtbQmxhWCK8SjTJtZGUccWgsn1WRsFr41o1kSxp4w5RUohG81YhO1r+q8tHpTSfkohn42NJnbPO3UUvjaKntP2DteMZp60GvLa9a9Z89riQyka8ptnWwAmLYhtyLAHeAKoHrhEZ1IKDOgOyOZoVo4a42iuFG1tCbGFYAAd7c/R4UB8IZhcn7VR8PqIZkUUuwBNHnmdFHTKmkspHpTSfgqF7z2wa76XatbcSzqCkI5NOAqc81OrIa9d/5o1n3Jsoi2+9Ny1nW/prZalkg0R9gBPQFsPfKmSzqQUGKXNJZqVo8YotNScPgq5vH0KOSK9mvZPieLWUq2xPmuj4KvuJR1bxEDzAKyTgpbaj+l/jP9a+xQKn6OaNfeSjiCkYxOOAq+ap7LjLG4/S/OsWfMpxyZcm+H8ed9+dJw4cQKnnHJKqS+G/sP+dEqApL/MaVtrI8JjtY37qa2thUaPWvKFahOnRM7H+pyroZ7bfop9rh52bvuDss9dPxob7fxr9xlno93ng/ickNbMoD4nDPXDvoEnYHJyCjtPoES/uVvbmtPplbSRqU4wp4FN26Q626EeOKfHLGlDU21qTo841DCnesycnjD1JdRWpnrSnIaypAeu0YOWNNTbGugzor1Wz5vaa+4ljTm9jptLrb1WT51bG1o9cm6dcGOh1TOX9Lw5PXFOQ1yaf05DnK5Lac3Qe3PrN+xzuDeK/ay15+ZGq6Eefp54Mk7cnE1N2aNjFGB64Am4++AS7jxcrj+s0emdRLw2svZesXrkob1GGztsX6PHXKe2cooetLbPKXrSnL32XtyYS33WzJl2/Lg1q+2/Rltau2ZTkKuHHjt+oU2uBnnumGug3TPaOSv0wBcWFtBoNNR+1A3TAzdEQ9Jv1uj0FudRZUjRJtbo/NLrJGEMjTZ22L5Gj7lObeUUPWhtn1P0pDl77b24MZf6rJkzDlptaW3/NdrS2jWbglw99NjxC21S1oxmn2rtNdDumdg5G+bD22AP8CTQyk007CTUCU452+IiOnMrNGnPE7kKTVXV36oqkUn+0zGj4CphaSuxhSlBmup3KWfwnD03T2G/aCU37jqpKhZnz6Fn/mdape1wFbqkqmJnB2vBoXddcFW9UiFVRizrs7aSnQTNmpEqueVWUtP0meu/tGe419ycPfnkk5VjZegf7CAjAR7dKWE01YRLyUkROaDIrdCkTQniKjRJfaFpPEB5ipzkf2z1N20lNikliI6ZphKaBM6emyetHrm2KhZnz/oriKloKumJVcV8+d4AynWupZQsLWL10LWV7CRo1oyUxplbSS1Xw53bM9xrq8Q2mrAz8AT8z11N7DpZTnNtaSxGVuGKx1cPzWLPwvRA26zTH+31dfZzGGPGtRm+P+taOOknKq+Ltc/1U7qGgl6vua7uuejX+stFSjvD2BsahO2dM9vEq86ZxJNPPjnUNDI7AzdEQ6LPuKpYEp1GoSmKIAlrAHHUWgiOmtMKO2gowJDOC6tSFe1Q0ZewnxwdyUE6NtDYa+lQTZtldKZGtCXWXuu/RtiCzoX22Ig7QgiPM6gYSUjPa9Zv7PoL2+eOcCjC8eNo/1gxkBBaOl0jpiIhds2HRyubO3vW0smGC6PQE0ArsUkVlii0VdFUjEhAB9MKUVQbO0XYgaPmtMIOGgpQ0iCn7VACNuwnvW+dlcA4aOlQTZvh+1wlsVx7rf8aYYvwpppjI/aoJ1i/VIxEo6ceInb9he2nzH9sJTbtsYGWTo/VcA+RW/2vqMS2evXqqHYN9aJv38Cdc89wzt3hnPu+c26Hc+4XO++f5py7xTm3s/P/DZ33nXPuvzjnHnbO3eOce36/fMtFuxJbm7K6aO0iLuq8bm+u8o2hjTTVbKzeClE0ujQ+opWiTCe42n+/PB7Nzu+l9ouqTmVjRttpV68r7ye9b0wlsKJNWhM+thKatn2uzfD9sip1ddhr/afzR9uR5gKkPXov6lvLodSv0F8qRpIS0R27/sL2NW2UVe+ruo5WNQv94uzp+Ml9KZ8zLXKq/124ZnG5Dvzc3Fxcw4Za0c9v4EsA/g/v/Xedc6cAuMs5dwuAnwZwm/f+t5xz7wbwbgC/AuCVAM7v/HsRgI92/j9ykOinWGEOSViDQiuSkCusQYVJQto2VgyDUoCh6AoVVqBjxvWteBR4yGIoGtGWcMwvXNPEg8d754zeK1eMI2XMtdCIyaSIkVAbOv5AtxiPpOdeJmAT+kLFSMJ7azXsC/+5Num8FMcBxTVSFgQr8tGJ3A/nWS0Gw9hrxk+aM04YJVzXdM2ntg/kpwAa8tC3B7j3fi+AvZ3XTzrn7gewBcD1AF7WuezTAL6K9gP8egB/5tt/Gn7bObfeObepc5+xQawwRy41V7ewhiYKXSuGQSlAiRrl9MQ1Ed2hvYZ2DcecHjtwfuaKcaSMuRaxGvIpwhihME9XpkGmnrsmi0FCl/9Mm9LRjCYLIty/IJH7mnGWIv+1VD9d8xqf6VoO17XqqE1of5Rx1113nTk1NfUnALZh/OO8WgDuW1pa+tkXvOAF+8NfDuQM3Dl3HoDLAXwHwFnkobwPwFmd11sA/DMx29V5r+sB7py7AcANAHDuuef2z2kBknRirDCHJKzBXVclkpAjrFFQc6liFpyYQii6EqMnXmh7a8RQwnuXobeoBS8OI2mwl/U/RUCGG3M90jTky/yn4LSptZrnWj33lHtz/nNt9h4HYPkabo6qBFRixrmsz1XrRBIA4uaME0YJ13XZUVtM+1XyscPE1NTUn5x99tnP3bhx46GJiYkx+bOjHK1Wyx04cOB5+/bt+xMArwl/3/cHuHNuLYAvAHin9/6oIzyN994756IG2Hv/cQAfB9ppZHX6qoVEoVM6M6S3y+jAkKbi6DwNNViHHjh3BCDZc3Qe9VmiwDUUslaPnLPX6klrKFxpzCXakUPsmOe2rz1CSNGm1mhLh9g808K+BV+5tjk9b+q/Rs9a0uam0K457tiCo7MlDXLt+MXuuXBda47aqo5dAIyqEtm2p8LDGwAmJib8xo0bj+zbt29b2e/7+gB3zk2j/fD+c+/9X3Xefqygxp1zmwAUtMBuAM8g5ud03hsrRBcF0UbEKqjBOvTAuSOApMh54jNxuYeO01DIKcVnKLR60kA1hSseeyTQjrFjntu+9gghRZtaoy0dwnuvWtvFWEj+a/SstZkj2jXHHVtIxW+44jHa8Yvdc0C4rquP2qT+Fxh2LXQGE0+Fh3eBTl9KvzX27QHu2l+1Pwngfu/975FffQnAmwD8Vuf/XyTvv90591m0g9eOjOr5t0wf9dKhZRrABcoiYssekhpqMKTgU+hc7ghAsuc+TMJo+eXrAzpOQyFr9cg5aPWkNRSuNOYS7cghdsxz29ceIaRoU6folu9d0K1tTs/7gKLNKj33MmjXHEeHc3R2cU2ZBrl2/GL3XNm6ztlzxWfg/Pz8KD7Anzbo5wH/SwC8AcBVzrm7O/+uQ/vBfY1zbieA7Z2fAeDLAP43gIcBfALAz/XRtyxIxQv6pU2dom2covObos3N9VlbC37YetqcnrT2XoMe89z2ewvBlBcmSpn/3P5La5svZJNX1CRl/cVqmPdTT5yzH/aeM/Qf6m/gzrk1AE5671W7w3v/dXT/CUhxdcn1HsDPa/0ZJqamprC0tNSjfxxqK3M6vZxmb6jnzWmAUz1oyZ7TkJa0nam2MqfNrdWT5nTLQz1nTk+6bj3qMp1mSU86Zc443eo6xzzUs45tP/S/rW3d2z7nizT+nAa1pIfOjT+3fiX/NWOu3bPcWkzRMD9ruokDi5Od/dvC1nUT2HFE1iBP2XN0bXS3ye85TZ/D9i9dbTXAOBw9enTiNa95zQ/t3bu30Wq13C//8i/vectb3nKoH22xtdBdu9bf6wH8FIAfBjAPYAbAQQD/E8Afe+8f7odTWgyrFvrCwgLm58v1k2O1rUNotJUnodMT75fOsFZPehg+16nBrsWw9axH1X/tXPbLnoN2z9Y55pIet2adp2i4p/ivvdcV65u47Iz2F5mpqeE9zMtqoX/ve9975NJLLz2ovYf3HgsLC2c0m81TJycnjzYajYM02DoWn/rUp9Z/5StfWffZz372UQB4/PHHJ08//fSshPnvfe97Z1x66aXnhe9LFPodAJ4N4FcBnO29f4b3/kwALwXwbQC/7Zz7tzlOjSskLd9YbWvtvVP0xPulM6zVkx6Gz3VqsGsxbD3rUfVfO5f9sueg3bN1jrmkx61Z5yka7in+a++1u9O+pqb6qGNhYeGMhYWFZzSbzQ0LCwvPWFhYOCPnfs9//vNP/K//9b9OvfHGG7d85StfWZv78JYg/em03Xvf8yeh9/4JtCPLv9CJMn/agS5abRqYFlxVMi4NS0opktJApL5V5XhKVaWkKnGa6nMpPmsquXGpPmGfpdQfLo1OkwYmpfRxleS0KUUpqX8UsVW9JP/pdWHFM82apdCm5MWOfziWoZgOV7GNq4SmSXcrS10s0rg0FQulzxlunLSV3DR9DvdlW8xkEsePHx/VVDI1ms3mqVj5MjvR+Vn9DT7EJZdcMv/d7373+1/4whfW/cZv/MaWW2+99ejv/M7v9CUgm32Alz28U655ykObBqYEV5VMqy1NU4o0aSA93UkQBoEv15PW6iTn+qyp5CYJQ3BpUNo0Ok0amJTSpxGQkVKKUlL/KGKrekn+0+toEpN2zXY7pkvJix3/nrFUiunQ9jXV9+T5W0njUlUslD5nuHESxo/zn+tzuC8LMZOnAiYnJ482m811aD/EW5OTk0dz7vfII49Mn3nmmUs/93M/98SGDRuan/zkJ7O+0UtI4j+cc39TtyPjBPptJUUYQQJXlYwThpBEFiQBDw4pwiBc6kso9FImklGHz9yY0fab4IUhuDQoLQUfpoGV2Uh0pkZAJhSToOOiaV+CtqoXd1+u/VD0RLNmKTQiLdr+S2NJH1qcgEvYflX1vao2nSsXYOH8lz5nuHGSxo/zn+tzuC/LGJNxRaPRONhoNP55cnLyUKPR+OdGo5H87RsA7rrrrlWXXXbZcy+66KLnfehDH9r83ve+t2/p0KnRB2+p1YsxA6XQQ2qJo+NyhS04almi1lLoYA2FrvWZg9ZnLQUdW8ktpNO5SmbaYwtaVYs7NqD3pdrmmxpNbGqUVyLTHifQSmZAnhiIVjSnqyoZ0z5nI+0Zbs5i+l82Z9L4c0c43L3CMVMLmCjstWNGj60o7U37pj0C0LQfrvlt69ubb3p6/E9RnXOYmZk5iAzanOK1r33t0de+9rXfr+NeVUh6gI9qgZVhQKttnStswVLLArWWQgenHAFEi3EofU7RI9dUlRK1mYlvhX/L/2coYFpVi62+F/SZaptvaiyVtqM9TqCVzIA8MRC9aE53VbCy9jkbac9QpPZfQyfT8eeOcCQBHU7AJ1cASDtm9NgqpL33kD9Au8ZE4b/22GtyagmXzwKzs7MwDA+VD3Dn3L3oPX06AuBOAB/03j/eD8dGGfQbqlStqE5hC64dqZJbVSWouh7gnM8ctD5TP+WxjKvkFlbO4iqZcdXjynwJq2qFVb56NdyxbH9QKfrBgVYyyxUDiRHN0bYf2mj7ldr/5X6RsZTGn84/J+AiiYloBUwoquyrxoyu4bDiGvl0Kh2LlPZ7o+AncDmA48ePY82aNT39MwwGmm/gNwFoAviLzs+vB7AabSWxTwH4V33xbITh3MQyfRVS03VGVGsoZImO1FBjITQRydoobo6q10axU6qbe1+KYuYgjVlIoRd0MOeLRAFzbZZpuBdiKhxVLx2BaIQ1JGjoYArpCEFro4nC5+wlYRANBR1S42c3qrW9U9acds+kQHNsIe15LnKfW2dcFPooq5I9HaB5gG/33j+f/Hyvc+673vvnP13zwO8/NoG7j5VHjdYZUa2hkCU6UkONhdBEJGujuDmqXhvFTqlu7n0xipmBSOEGFHpBB3O+iHrYTJvhXFAxFY6ql45ANMIaEjR0MIV0hKC1oX5p9Ny1wiAaCjqkxvcvTFRqqKesOe2eSYHm2ELa81zkPrfOnspR6OMMzQN80jn3Qu/93wGAc+6HARThjNWfXE9B7Dm5UoQhpKY5Ok59b0bbmqOQpTZSBBw0EckhhR2rhy3RgZS21bwfjrkG0piFVGtBB3O+5LR5Eel/lZiHfARSLawhQUMHU2iOEDQ2xfUaPfdYYRCJgg7H+8Bi9d5KWXPaPZOCmGOLsj3PCehw6yxcF963Hx05FcsM+dA8wH8WwJ92dL0dgKMAfrZTG/0/9dO5UcXm2Rb2dh7iWm3hmHvHRKGHiC0wkVuUI7ThCo6kRJFro3tzI//rjCim0I4/R0FztK82ilpTIETyn0PK+EtFRTg9cK7N3D0X+rJxuondC71HGNo+U+TqeWvXb+yxibTm6NqS1lm4ZgBg7dq1VcNt6CMqH+De+78HcLFzbl3n5yPk15/rl2OjjOeubaG5xFB2CjpVQnQUeoDciO7YohyhDVdwJCWKXB3dmxn5X2dEMYV2/DkKWqJ9NVHUqgIhgv8cksa/oqgI97uyNrP3XE8WBO+bps8UuXre2vUbe2wirTm6tmj3w3VWdt/5+XnMzMyU9uXpDOfcC17zmtc88cUvfvEHALC4uIgzzzzz0ssuu+z4HXfcUZuGiCYKfQbAawGcB2CKKNd8oC4nxg3et3DhmqUoajri7tERrd2+VdPZWjqT0mlSRCtXSIUiJYo8Jbo3JfK/zohijS9aCpqjfWOiqDUUfOwDPGX8JZ1yTg+8qs3UPRf6cnAprf0y5Op569dv3LGJtObCtUV63bXO6H0L9mBhYcEe4CVYtWpV68EHH1x17Ngxt3btWv/Xf/3Xp5511lmli+e1r33teT/zMz/z+Ktf/eonY9vRVGL7IoDr0T7vPk7+PW1Rpx54P+21esqcNrZWG1qjpy21OYg+a+1z26dI0XDnkKstPSht6Nw1p50zrn0N6tATj53zftqnaMBzGvLaPW964NXYvn37kf/+3//7egD4zGc+c9prX/vaJ+puQ3MGfo73/hV1NzzOmJycws4T6NHylXR2Na+12taStrJGm1mrja3RhtbqaXM6x3WM2fR0Aw8ca2H3Scf2TWuv0SCvar+YJ84XrQY8pxNN5yK0p75RPW2tHrtGQztc85rxl+Z/2/oJ7JtvYv/CBDZON+E76zRXD56z1+ihV2mYc2smHPOyvkhjzmmga/d5roY81RCX1swwJUTrhvfAPxzCmbvmcOo5q3H08g3YX0ds3hve8IYn3ve+9236iZ/4icP333//6je/+c2Pf/Ob36w1aIDVA1++wLmPA/h97/29dTZcB4alB373wSXcebhcy7dObeU6ta37pa2calOn/c4TM/ju0enKvg3CXjtPFP3ScK9zzqV7PZXGT2vP9Vm7Z4c9Z7ntz8zMoNFooNlsDvXbeB164N99Amd+9xC2ND0mJh1az9+A3c8/Dftz/Fq9evXlc3Nz/7Bt27bnvuUtb9m/c+fO2Ve84hVHf/d3f/esO+644+EvfOELp/76r//6OQCwd+/exrp165ZWr17dajQarXvuueeB8H4peuAFXgrgLufcg865e5xz9zrn7snp3Lhj90nXc55UoE5t5Tq1rfulrZxqU6e9NB+Dtk8RE+mXhnudcy7d66k0flp7rs/aPTvsORvG58SoYtccTm22A/nR9JjYPYdT67r3K17xisPve9/7nvHGN76xiz5/7Wtfe/SBBx74/gMPPPD97du3H/6jP/qjRx944IHvlz28JWh4kFdGefw0AE0jkyo01ZnSlFJJTZvSwtlz0Oo5a1FnVSqa+qLV5qZiIin2XCUwLo2r7up93PjVmXooVSXTVGIT52+2upKaVIlNk0anFfBRC6gwaVxaARjNnEn+a6rXaSvJafTAOTGTubm5sdcDP2c1ju6fxynFN/Atq5ElJ0px4403Hly/fn3zhS984Ym/+Zu/qX2gNGlkjwKAc+5MAFa5Ht1pZFKFpjpTmlIqqWlTWjh7Dmo9ZyXqrEpFU1+02tyhmEisPVcJjEvjqrt6Hzd+daYeSlXJNJXYJNCUKI2Yhnb8tFXpYivRhT5zVfqqBGBK76v0X1O9TltJTqMHzomZPBVw+YY2Xb57Dqdu6ZyB13XvZz/72Yvvec97artfCE0a2WsA/C6AzQD2A3gmgPsBbO2XU6MOmkYmVWjqR0pTTCU1bUoLZ8+hTM859kM7ts0qf8pSrLjUqdD/g4zQhdaeqwTGpXHVXb2PG786Uw+lqmSaSmwVPahc51IlNk0anbT/YivRhT5XVekr27OaOZP811Sv01aS69UDL3rIC/gUYiZPBTgHPP807M8996aYm5v7h/C9V7/61U+WpYp94QtfeCS1HQ2F/h8B/AiAW733lzvnXg7gaVkDvYCkB87p9HIVnsruHUNh59KxKXS41GdtJShNJTB1VSpGDxoo18YO/adiItSGo8N7jiOY/nNHIFIlMY2AST+PMDRrRluVTAuNsIZETcfqiYfjd+GaJh48rhcQShkzbZ8lAZEuDXameiGHsPocFXDR0P6cmEmj0ajsq6F/0DzAF733jzvnJpxzE977O5xzH+m3Y+OCGJ1eKL5oxlLYuXRsCh0u9VlbCYpek1uVitODBsq1sUP/qZgIteHo8PA4gus/dwQiVRLTCJj08whDs2a0Vcm00AhriNR0pJ54OH77F5ewZ76Xqtau2VzRIq2ACL0vV72QRVBtjgq4aGh/TszEirgMF5oH+OFOHfSvAfhz59x+PM0LuUh64JxOL1fhKUQshZ1Lx6bQ4VKfOTovRdhBewTB6UFz2thl/lcJQ0g0Kdf/qiMQTlubm1uOwq/zCEOzZlJofgkaYQ0tNa3xMxy/A8w6067ZXNEirYBIN8qrF3IIq89RARfN2HJiJseOHbN66EOE5gF+PYATAN4F4KcArAPwtC2jCnRT6CEotUXpXCmiM1ZYQoxOV9DZ3L1S6VCNGAWl8EKRBI7ClAQwuPY52lwrpsJFjktR/LF0ZojYzIMUYQ1pLcRq0Ev+a9rXRvFrMy9i9cTDo62NjSb2zLue+ZPWbKweeEiT08wH+jkhCYjk9Dlcv1yftSg+A3PjVwx5YB/gzjnn2yi+bbcAfLrsmn46OG6g1FYoQMFFdAJxwhJSdLqGzubulUqHasQoQgqPiiRwFGZowx1BcNrIKWIqXOS4FMUfTWeW+L98L0XmQYqwhrQWYjXoJf817Wuj+LWZF7F64uHR1sapJs6cbvbOn7BmY/XAQ5qcZj4U9y9rp6wvKX3uXb9LeGiupM+GsYL0DfwO59wXAHzRe/9PxZvOuQbaxV3eBOAOAJ/qq4cjCPkbcnd0apXOs5ZOpqjSlo6JfK+DDtWIUYQ621QkgaMwJQEMrn2ONteKqXCR43IUfxyd2WMdmXmQIqwhrYVYDXrJf0372ih+rv9a/zlfyo62yqLopTUbqwce0uRh5sMKeAGRnD6Xrd+cNVt8BkpspKH/kEb/FQCaAD7jnNvjnPu+c+4HAHYC+EkAH/Hef2oAPo4cpEUbRqjHCjs4N4EHj0/jq4dm8cCxaTzQef3g8WmUfU56j+XrHzw+jc0z8cIM2r5x2Dy70ialoKnPkrDGRsU4cfcF2hQ6FWAoKEg6fgVtGl7z4PFpACtjTq8DeDEHzZiFc8P9bUbnnF6ntefaTxk/elTBrdPQL+eq2xfXf+fYJ7X/seuPPk4n4LFpho9i59as5qhJanMjc29JQITrM3fd2Y1m6bwC+Wu2sF+zZg3X/ac1nHMvuP76659V/Ly4uIgNGzZc+vKXv/w5dbbDfgP33p8E8EcA/sg5Nw3gDAAnvPeH63TgqYZcbWlNdCqFVls6xX8tNNrEMjVcTudpi1poCrmEtClH4Yc8fRkdrx2zYVPYqeNX/KCN4uboZO3654596tTGlrTVNeOXokEutUlp+5RjA9WxjXAElbtmC5w8eRKzs0+Rii41IkZONAeqr1ve+0Xv/V57eLchUehldGhBz62UQSx/H+iNTq2qC83RlGX31iAtpMEvt9ns+BH6TPt80dpFXNTlo68cJ+6+xRh0U52949emKXuvCSn88LqCjpfGMoZCLkMZHRpjX1UUJGb8Cko5tKf9L4uCr2pfWv9cP/V1zePWX8uhq7/cfaU1q8kJldp8bHGy9N69e4O7e/meoSg7glq2zlyzxWfg4qKdnXMYhJyoHWAkoJ964Jwed4rObwpS/B+EHneuhrlEU1I9aC2FqfFfOxacHnautrTWl1g97rrXXJ39z9XG1iJXg3wQ+1Qai37pmY8jWt7jg59/+MyXv+87z/ng5x8+s1VTXPYb3vCGJ/7yL/9yw9zcnLv//vtXX3nllbWnXz91RF0HiBQ9cI1OcaitTbV5OW3gbv3gFratn8DSUq82tLZ9jTY2vdeWjrYwUK1BDvTqmWvHTKthzukZc9rmm2c9tq6bwG37V/SoyzSQtXrUGm3ncPy2re/VYJd027Xta/XYyzTgJT1sSc88Rc+d05PnfE7Rxq7WA5/p0XOX9kmshnqox03b1OieS3uOu+7s6SY2N5Z6Pj/q0DN/KumB/+YX/vHMD33hH7ecXGxNfPuhw6cAwHt+/DnZZVVf9KIXndi1a9fMJz7xidO2b99+JN/TXmhqob8DwH/z3h/qhwPjiHsPtZa1gB9bmIL3baqs2Wwub2qgm6Z68PhU19lSYUOvadst4PxVTZy/qh1MUpzn7Zl3eGiu2WPT3qwr19x3eBHnr0pv/4Fj5X3j7+UBrLTZ/hBonzlSbeHwPD9lzC5bO98TBS6N2d4Fh7MazZ7I2/D1jiMz2DM/zdqEfoVjxvkfzk0xf+XjN7/sf1Wfte1306Qr81I1flXrJLxX8fCW2pfGj7bfjXKfpf5rbMJr7ju8ou3NrdOUMZfWL22Ta0e757jraF/o+pP2OV2zuxdcV6wI3bNLS0toNBpPiSC22+59/NSTi60JADi52Jq4/d7HT63jAQ6syInefPPND+7fv7/2v3o0FPpZAP7eOfc559wrXPHn3tMYKXrgKTq7GptekYHy6cnVOc5tc1DayCl60Ll61rH+S+NXpx54iv/Dbn8Y9il65IPWUK97z9WlZ54jAzwquPri04/OTk+0AGB2eqJ11cWn1yon+ku/9Et7XvjCF56o654UGjnR9zjnfgPAtQB+BsAfOOc+B+CT3vt/7IdTow6qB16WBlYmUpCix12nsIRUVYqrSpbbJr2uCOEpqzbFVbXSVmKjY6a1oYitpKYVE+H0mMNKYJywRK4euOQzpy3NtZ9bPVCqSsZpU6cIi6S0TyvB0XUqVU9MEv0hcxm75lL2OdcXgK+eqKkECKykkZ04cWLs9cB/7bXP3g8At9/7+KlXXXz60eLnOjB0OVEA8N5759w+APsALAHYAODzzrlbvPe/3C/nRhVUD1ybBpaix12rsESQUsJVe9Kkp2jblNJoVFWthDSYrssoPaq06fIzspJaShoVTW+iTnnwwhK5euCSz0C5tjTXfm71QK0Aj7Z6W53t09RLbfXEFNGfnOp9KfucuN+zFzSpg9qUtnHHhHN4z48/Z39dtDkQJyeaA80Z+C8CeCOAgwD+BMD/6b1fdO3qDTsBlD7AnXN/CuDVAPZ777d13ns/gLcAONC57Ne891/u/O5XAbwZ7eIxv+C9/9uMfvUVVA88BCdSkKLHXaewhFRViqtKlttmqEccW9VKW4mNjpnWJrhDVFUqrZgIp8ccVgKrEpaoQoqGO6ctzbWfWz1QK8ATU72trvZpJTht9cQU0Z9uxK251H2+0lr3XuCqJ2oqAQJPDer8qQDNN/DTAPy/vfeP0je99y3n3KsFu08B+AMAfxa8/2Hv/e/QN5xzzwPwegBbAWwGcKtz7gLvfd7hVp9AqxhphRlS6FCJNuTa19C5nM61JCyi9ZnzLVfPOfSzX9rMKWIYtJIXN2fccYIkpsHRvhIFzSGXzpXsYwV4wv7T8ePa0QqLcGMmal4TAaBwbsuo5RTRoBCxAjAhuDWr3ef0c4oT8JGOMLatbztlcqLDheYM/H3C7+4Xfvc159x5Sj+uB/BZ7/08gB845x4G8EIA31LaDw1aYYYUOlRTFSmFzuV0rkVhEaXPnG+5es5VlcTKbFK0mVPEMDRzpq3KxdHWnE72oOhcyT5WgEeqhMa2IxwBcRS8Vk8cHuzcllHLKaJBIfpVvU+7z+nnFCfgIx1hTE4t4fJZoNFoqPtsqB/DKOTydufcPc65P3XObei8twXAP5NrdnXe64Fz7gbn3J3OuTsPHDhQdknfQf9yliqh6asqrYBu7JQodE1VLOpXWLmqTFgkxmfON0rNaqtaaSuJaarfSeAqoXF9odXawkpe3Jxpq3JxFc9oRHAYHczNOYU8LtVVvST7GAGeqkpoXDu9R0Dl/efGTFp/0txyVelSovUp+lW9T7vP6ecU/R0Xed4bBd9+dDz5ZK1HunWh1Wq1IviQ0UanL6V/oQ86G/+jAP4j2p/Y/xHA7wL4dzE38N5/HMDHAeCKK65QhCjVj1CwJFabWaJDKYXN0XkUudrQob2GztVGAXMR4SkRvVJ0uYbClRBLIUtHABoKP+wLjULX0O5At+Z5ioY7RZ1R7Cna1FphEDY6eqY8il8bUa6JQg/BRXFzfdYee2iPgDQa9lIWDLdmOdo9tN882wIwstXY7jtw4MDzNm7ceGRiYmIoz4i60Gq13IEDB9YBuK/s9wN9gHvvHyteO+c+AeBvOj/uBvAMcuk5nfdGHinazBIdyglrcBHVudrQvZRlubBIUhQwExGeEtHL3UtsX4lYClk6AlBR+EFfaBS6hnYHApGVBA33LndqjGJP0qaOFAaRKHB6b21EuSYKvWzMqrIdtJH3XD+1YiYcBS5mwTBrlqPdQ/vnrh3dL7hLS0s/u2/fvj/Zt2/fNox/ufAWgPuWlpZ+tuyXA32AO+c2ee/3dn7811j5q+JLAP7COfd7aAexnQ/g7wbpWwzot5UUbWYaBRtGxPYKa6xcVxZRnasNXWZfdr+UKGAuIjwloleKLs99gKdG3pdF52rmI+wLjULn5iaM4i/TPE9FnVHs4e/K7FMi7aXxpxH+9N7aiHJNFHrZeFRdp428r+pnOao17LVZMNzYcuMKAN63Hx2jWBP9BS94wX4Arxm2H4NA3x7gzrnPAHgZgDOcc7sAvA/Ay5xzl6H99+ojAN4KAN77HZ3iMN9HO8/850c1Ah1Y0W+OoZM5mqonInm6id0Lbvl3lCoto9Nyi4rk0uHaPociFRztr6X6ueI5KRHBnH3KsQcXxSuNJZ1zjuqlxynaQjhaaCKipfa5iGZu/sJrcv3XFCWR1h8XhS4WPCJtcteFRVVijz20FDz32SJlwWj2TFXmAQCsXr06YcYMdaFvD3Dv/U+WvP1J4foPAfhQv/ypE/cfm8Ddx6ojoik4mqo3IrebjavSo84tKpJLh2v7LOqhEzpPT/WXF89JiQjW6HFrjz00Gu7hWHpmbKXId1UhHCU0EdFS+1xEMzd/4TV1+F82fil65FI/i76UtVl6nbSXFccGWgqe+2yRsmA0e0ZD58/NzdlDfIgY9/OBoWBPp4wqIEdEU3DRoWFE7sGl7mjbKj3qlCh0bUQ3RYq2sFYPmn7MaaK4w7HQRJFL0OhxS1HgB5jrOF/CsaRzTseWi46WorBToImIltrnIpq5+QuvyfU/Vs9ciiiv6mdZm9x1YeQ83cvs4XrQL25d0THjPlukLBjNnpH2XMHY5NahN+TBHuAJkPSTc3WCqTZ1v7SZ69YJzj0Hy9UTj9Wz1tpTX+rUE9fOubb9fmlLp7Q/KD1uijrnX+qnRoNeq2ceq+dd95znjtkonn0/HfHUEXUdILatn8CeEyv60R7t8y9Jp1ej07yiE9yrjRxnL+sMczrVks4xp/Ot7XOojQy0v2FIeuJaPW5OT7pOPWpOZzycszLd8VBPOdRwv/pMYMeR3Pbr0ZbmNKwlPXWqB87NX4o2NrWRtLlz53/b+gnsm2/v5zOmmnAOOLA42fU63OdUw53ODd1Pkga7Rk881Oamcx6rwR7OOfWfmyduLrbMely62h4dowCXH8E7PFxxxRX+zjvvHHi7dx9cwp2HJ0tzUp9/alvbORWTk5NZtNTOEys6w5PwuGztfM/ZFtV8Dq/RtB/aa/pMbUZtzFL6rBkzziZ3/ML2NXMu3Yu2L7XTr/Hj/Nf6Uuee4YLApDU7jDGL7bN2zWnX7BXrm7jsjOE/xJ1zd3nvrxi2H8OCUegJkPSDOZ1eLerUNubOtqRqTyk6x5o+S+d5wx6zXG3nOvXAU9qvU1u6X3rgKf6n6MGngNvPUtzDsMcsts8peuLSXOzu2C8sLET5YagXw/8TagyxeaaFPScnakkPSdE2Fn1jqopJlbBihSnCNCgqRsFBW0lLK6bAjVm/9KRT0thS0phSUno0leS0ldByxWC4+RP9Z1KytNromjRA6X1OgEhK99QIsOSuuTqrD2orNmrXbFGJbX5+3uqhDxH2AE+AR33pISnaxhK4qmJiJaxIYQr0pEFV22graWnFFIr3Q5/7pSedksaWksaUktKjqSSnrYSWKwbDzV+VGEpZSpZWG12TBii9zwkQyemeK2uG61v2Pk9I3eSgrdioXbOjXInt6QR7gCdg7/wEcqpi5WobyyivKqathKVpP0yDKqu8FUJbSatMq5kTjygbs37pSUsVsrhKZJxN+D7tf+ibpn1uzim086+vBLYC2n9u/qT79qZkodJPrn3NnEuV2ApcFLwOK7TROeL6lrvm6qw+qJ1X7ZotKrEZhgubhQRsnm1hbycXXKJTNXRiSlWqXGERqcJUbFUuiULXVjLTaKhLdCIdc66SlraSWYoGO/U/JSVHc+whVZiL1WNPOTaRqoJtaqxQ4OGRkmYsaP+l6mFlvkiV4Lg+13GEoRENksSIco9tNMdGEmKPHUIUldhWrVolN2ToK+wBnoDnrm2huTRfSgfG0okpVanqEBaRKkxVtRlWq9LYSJXMVBrqAp1Ixzz0regn976kJ63VYKf+a2lnCs2xh1RhLlaPPeXYRKoKtqmxxB8pKcaC9l+qHlbmi1QJjutzLUcYCtGgcM3FUuBaDXbtOqGIPXbgQJUZDYOHPcAT4H0LF65ZqqRTNXRiSJ9qhD1yhUUoTam1761WheU+chS6VsClisIM/Q/pRDrm1DfaT+79cMylsS3rF+d/HKqPPThfAN2c5R6bSMIcB5mKY3r09r9MKKbMl3D8JQGOAvUfYZT7JokR5R7baI6NJMQeO4Qovv0fP34cp5xySmVfDP2B/fmUAOmvzs2z5VW5KLX34PFpFPsvrNakiWI/u9Hsum9IJz94fLqnHWoD8BWmuL5JVaE4n7k2eypXdSjM0Geu/bIo7KpKWtyfEFSPm1Ltxe84DfbYOfMebB+5MafjR2n/B45N4wFyL+eq7SVta823KGn+NyrakfrPrVkOYb/CiPBJ8rtiz4VjRtug6yc8woidM2mcwqO2mD6HoO2nVC/k+szdKxwLbs0ZBgv7Bl4zODpQI/Kg1nZW0slqYQUFnarVw+b8pG1KUei5UdiaKGI6ZB7detwS7cn60q/MA+bYQ6stLa2Trssyswi8B3bNyxrauXriUr+4iHBOJztsI+UII2mf1CjAo4mCl8D1WRtRPzm1hMtn1e4a+gR7gCdADj4ppwM5mi4l6ldLJ9N2OGGFHu8rhEm0NGfoZ1mbZVHodUVhS1HEIbVJ9bgl2lPnSznqPPbQaktL64Qilc6l8xejjR32X6MnLvWLiwjXZDd0RqC2KHLtPontcwjafsp65Pqsjajfc3IClwOYnp6OaNNQN+wBngCqBy7p9FJoiz1ootC1RT0ohShFxFJoIppTNNClPudGcWsiamlEMiBrsBf/pbS1FEWfO2exGvJSIRxOj1qa81w9dU0UvVZPnLOnYy4VouHmnI5ZmPlB9dy1xWdyo8A1xXcopM+JlPZjC8GEa2nzTLuQy+ysfQ0fJuwBngCqB66lM7XUlCYKXUsnUwpRQw0DuojmFDpR6nNuFLcmopZGJFdpsFfR1moKWzEWQDwdqz6CUFLouXSuhoKWsgC4+eci36VCNNycS8dZVM89pvhMWZva8dMU36GQPidS2o+uNxEeW3ReHz9+HGvWrIm7l6E22AM8AVQPXEtnaqkpTRS6lk6mFKKGGgZ0Ec05dCJ3r5wobk1ELY1IDinfUIOd9KCUttbOOYU2orjKJjwaAPgjCC2FnkvnaihoKQuAm38u8l2KqK+KvC87zjrArO1+RoFzY8ZB+pxIaT/2AR6upb3z7SC2nLLPhnxYKGECJC3gWJ3eurWROW1tjU51aC/5WacGer+0jTmfJT1uLop9GHrcWsT2X2uvRZ164hp7af2l6JFzeuzaPqdEgde5Z4bR/pbMNW+oB/YNPAGhHnisTm+d2siStnOZhve+BV5nW6sHnqJtLGmYx44Z7X+o50x1m8v0rMP3JT1vToO7W/+5hW3rJ7C01Ou/Vs+ajh+nmy7NOaftrNFWD8eP6lnHaEs/cKzVs2a59acdP0kPvZjjFD35cP1tXTeB2/br+z85OYnp6cZyn+l60mrY5+4Z+jlx9nQTmxtLPWOTsuY4m1DDvr3mVvpoGA5MDzwBVA98Evl62jnayCna0hJStJWHrcfN6Tlrxk9qP3fMU/SsJd30fs15rp745pnmMg2fYj9sPfnY/qfaUAxCwzxlzXE2pgc+mjAKPQGS/vKgtZFTtKUlpHyoDFuPW9Jn12hL90vPO0XPWtJN79ec5+qJH1iYyLIftp58bP9TbSgGoWGesuY4G04PfH4+/Q8nQz6G/yfUGIKKmWhTUrTCErHayCnCDBJS9Mg1Ai7aNrmUGEkARiOGkpvGRW0kPXRt6hQdF06MBVgRBpFEOjSV4Ci0aXyauSgqse2Zd6Vzo9I2jxQTCeeYSyPrV0qXZCOJvnBzrhXNodfQ9mnqI10zUl/omtdowHN64AsLC5iZmakcL0N/YA/wBFAxE21KSoywRFkaU53CDBJSjlQ0Ai7aNrmUGEkARiOGkpvGJQmrcP5LqVN0XDgxFmClep0o0qGp3kegTePTzMXZnTPjh+aapXND+8mNq2bNaisBDiKlS7KRRF+oL5rUPakvtP2wyqBGTCa2kpvpgY8m7AGeACpmok1J0QpLxGojpwgzyH2Lf4BrBFy0bXIpMZIAjEYMpa40LkCuBBaTOlVWiSy0KarXaUQ6tNCm8WnmooA0N1XVvlIr8ZVVOBtESpdkI4m+xFafk/vSnS4aKyYTW8nN9MBHEzYLCaCV2MIKZ7SqF61+xVHAtWsrEwqetq+l9lIqseXqOdOqUho6L6SwCzESLR0Z9p879uAgaUOrq6cxxyZa2pzToM/1X7pOQ8dqq79RcNUDuSMoqRKetvoft+Zz9wk3/9KxD/d5oNUTl46XNBry3NhUjRkArF69unJ+Df2DPcATQCuxhTSpD+jV4getyEKutnJIwRc/aKm9lEpsuXrOtKqUSpghGGMqRqKhI8P+c8ceHCQxE231NO7YBFDS5hnCGFoxFq1IRteaUVZ/62qHqR7IHUFJlfC01f+K+4b+5+4Tbv6lYx/u8yD8bKFjqRFw0WrIc2OTchxhGCzsAZ4AWoktrHBGq3rR6ldakYVcbWVKwdP2tdReSiW2MjoxRs+ZVpXS0HkhhU3FSDR0ZNh/7tiDg+Sjtnpa6FvZnGtp89hKalrxC+11dM1oq78Fd6ik4KX506wfbSXB3H3Czb907MN9Hmj1xKuOl1IryUljVnx7n5ubMz3wIcLSyBJAtXTplpvoROROkp+rNMDLtJVjqiqFOr2bGq1SDWmqcw3SZugjsKJTTDWUCwq3zC+NnjT1M7xXGEVcpZMc6kHHjrk0ZymVyDT9l8BpM2v1vDfPtFTXFQjHmM55v7SptdraXJ/FqmwKPXlpLLn2EbYTHFuU7RO1nv1MuQY9bVOqPqfRI+f2QmjP2eTueUP/Yd/AE0Cj0ENhjI1TTZw5LUfkyprBKxG9KSIHlIKnkc+a6OaQThYFJBRR3JyfWjEKlrYLaNrYMZfmLEVMJbcYEhsFraSjuWMTDuEYxx4hlLW/3JdMCpvrs7Rn4BWZF8JYcu0D/BFWbOaFFHnP7c2qY5cyaOl0DQUv7XnDaMAe4AkIo9BDyrCMGquK4qXUakxEbEhzhRT8ynfb6ujmkE7WCkhoHmAxUfhVFGAZTRsz5tKcpSC/mmF5RLOWjuaOTTj0FmLpvza1lsLm+lylR56yZsro6CoN+wKxmRdS5D23N8N+UmgofGlcNBS8tE8LCr3RaJT6YRgM7AGeABqF3hMdTIpSSJHD0r1jCjyEbdCiGkB1gQepKIcmohzQRa5TP8NI2dgo4jA6lxZS0dinFELJjWJOKeqRq6fO+RxGinOZE1poiv9oC+loI98pNIVYpEhtmoXARX5LY073mWSjydyQMlRi15xUSIjTsNeuuW3r245YEZfhwh7gCaBR6CHNRKmxFAoqtsBDbxsrFLymwINUlEMTUQ7oItepnyG1FxtF3Bv5H0fhphRCyY1iTinqkaunzvoc0Mlc5oQWGgZCW0hHG/nedW9FIRaJWqZHCFzktzTm4ZEMZwNUZ25IGSrUXrPmwr7QQkKchr12zU1OLeHyWeDYsWNYu3Zt5RwZ+gN7gCeARqGHNFNuwY3YAg9lbcQUeJCKchSQIsoBXeR6qMcdG4XOFUgJC6lo7FPmJTeKOaWoR66eOudzSCdzmRNaaB7g2kI62sj34A5RhUikYyMu8lsa87IjGc6mKnNDylCJXXNSISFOw1675vacnMDl0M29oX+wUMIESPrJudrKGnutNvcgdIIlG60et0ZPW4pCjrWXxizXXquBnbNmtOOXooeesmZz9cwHba/Vg9euWe04a9ZcrgZ6vzTsTQ98NGHfwBNw8YYJtFq9+suStrJWG7qtbdx7b16bl9fm1mgjSzrHnJ9abWPqJ6fTrdUD57SlU+wlPXNunrT2nJ+cHrt2zlP01Dmfy7Wlu/XQi3kCqvXIqR63Rts6d82laGuHOuucHny3VnnVmM2IeuBla6FMw1zaM4UGfbhmOD1y6v8ZU004BxwI9OxD/7kxl8bs4g3tR4elkw0XpgeegIWFBVZGL1bPO0SuNnadOsOSnxqfNdrWdfhcp712nvrV/rDtx0GPXPKfg3bPaOc/V0M9V0Ne8zkj7TmN/5IvMzMzIxGBbnrghmhIHxaxet4x9y6Qom2tRYrOsUZPW9IpHoSeuNZeO0/9an/Y9uOgRy75z0G7Z7Tzn6uhnqshr/mckfacxn/NmJ08mSaoY6gHfaPQnXN/CuDVAPZ777d13jsNwF8COA/AIwBe570/5Nq8zX8GcB2AOQA/7b3/br98y4VEG3F63ina0FwaiZRqw9lrdbpTtJFzhR1oSotGzzm8JlaMRPKfpljReZLGss72OWjFPKRx0ghb0P5z6VFaPW9t+5wAT8r4pejJc2mMkjBI7D7Rjpk2jY5rX9JN7xLQiUy94yqxLS4uYnZ2VjNNhj6gn2fgnwLwBwD+jLz3bgC3ee9/yzn37s7PvwLglQDO7/x7EYCPdv4/duD0vKWUDqA8pYhLI5FSbTh7rU53ijZyrrADTWnRVGLrZyUxBClVxTxJY1lr+wy0Yh6cjVbYgva/GIPl/3d+0Op5x7RfVxpbip48l8YoVTKL3SfaMdOm0XHty1UeFyvtJZ+tEtvooW8Uuvf+awCeCN6+HsCnO68/DeDHyPt/5tv4NoD1zrlN/fItF9K3pV49b5qe0vt+SE2FFZ7KritSPYo0FvqthrOX6LRuePbeHKqqQv3ohpO4aO0iLuq8bnZ8KHzZO7/ii4ZC1FQSi4FUiats/MKxrLN9DhI1SsePs5H8kvoP0uZji+Xrj2tH235ZJbkYVAlzhD5L60+6rtv/uH2iHTNpbwe9Lr2O23O996r2X/KlijEyDAaDjkI/y3u/t/N6H4CzOq+3APhnct2uznt7EcA5dwOAGwDg3HPP7Z+nAmglNm2FpVxtaK4qUkinchWi6H+1FL6WDtZQmBRhJTBNJTUKqXpcShoU7TOt0qadv42NJnbP91YyS9GW1lDAYfu5et5c/7Vrhjs24qrvSWuWu047fhoKXKuHLmmba449JAzi2EBrz0GjB75mzZoovw31YmhpZN5775yLDoH33n8cwMeBdhR67Y4pQCuxaSss5WpDc1WRQjqVqxAFlFPD2qpgEjQUZrdBty+xlbik6nEpVB/tM63Spp0/74Fd83IlrpSqWmoBnEw9b67/YYUxbs1wx0Zc9T1pzXLXacdPQ4Fr9dDDdUo3Zm72ziCODbT2HDT3bbValko2RAz6Af6Yc26T935vhyLf33l/N4BnkOvO6bw3kqCV2Ar6q6rCUtXrApw2dHgNpVPDak1lFaKkqkyaqmASNNrCFGElME0lNQpN9bgY0D6XVWmrmj9NJa6Uqlr0uioBnDJoq5px/Q/XD7dmeo+NUHov7Zotu047fhoxD+24aAVQUhArQBMids9J9pKP3H2Lb+8nTpwwPfAhYtB/On0JwJs6r98E4Ivk/Te6Nn4EwBFCtY8cqH5zqLnrXH+0oTk97bDCEqUDOW1jahP6v3mmuv1Q/5jqSUsawgXCqk4chanRBge6tZnpdZx9+D7XZy04Pe5w/F3JNYBOT1sC13+1/wo9coCvCkbtuX5KFcbo/KdUsqtTG5uzL8v2yFlzmxqtrr4Vxw7a+dPoeUv34vpM/aQ65dKaNQwP/Uwj+wyAlwE4wzm3C8D7APwWgM85594M4FEAr+tc/mW0U8geRjuN7Gf65VcdoHrgUkRrCrjoUE6MQ6RTg4jiMp3h0H+NMIYUha0RcNFSmFpqkKP9OXutGIgWLB2qiOgu7AukRP6mHHtQaPTIAV4bm9pzwh7aIwDuukFpY3P2UrZHyprb1FhSHWlxiD02kOwpJNGgWJrf0H/07QHuvf9J5ldXl1zrAfx8v3ypG6EeeBjRmpduUS7MUCXGUUanVmkbh+IJIZ3JtR/SmQcqfAuhpTC11CBH+3P2WjEQLTg6tDeiGz3XADwFrEXKsUc3qvXIJW1sas8dJ2iPAKqu67c2dpUvBXLX3MGebAeU+sYh9thAsqeQRIPomi0odJMTHS6sFnoCKH0kRVRrEEZ6ckU5pIhYChpRrNE21mpjhwU+aHQ8F4WtBRcRq+0zV5SCs0+ZM23kP6UwuYh2qfiOpnhN2P6mRn0RzRRabehYPXcpijwFGvuUiHKtnjdXSIVbC2HmBI325+ZP+zmhzTzQzLnkV/EZOArlVJ/OsAd4LoSIag1Cao2l4IWIWApK7XEUWJI2tkCnclHYWrBjpuyzhgLmqG3tnGkj/ymFKR51KOhYbfshHVvX+Gu1oWP13LUUdq7/3RfFR5Rr9by5QircWggzJ7hjB8mXWD3vnuFQzLnGryeffNKC2IYIi0RIAP3LtSyiOgYhtcYV5SiLiC0Dpfa4QhwcHd/+cCrf2BydeuGaXn3pnEIcKX0uKNyw4ARnnzJnVTWmy4p/0LGVimqU0bEx7R/s0/hzhTykNau1oX0cxANcWksaOrl3XqoLqXBroX39in3LoXL+tJ8T2kIwmjmX/LJCLqMBe4AnQNLcztXZjdV2DkG1pbXaxrE6xaFNrgZ6Sps59v3UI0+JIo/VgA/bH7Sed+74adecFnXquefapNhr1kzu50yIfo2ZYbAwCj0Bk5NT2HkCPVq8Wm1qrbYzp8dLtYWplm+oLc1pUGv1xDXtb+loC4dthr5xOttSm2dPN7G5sdSjzazVg+b0sLv738LWdRPYcUTWRtbqkadosJfNWTh+1Geq83xmo4WrNgK3H9Br0OfqeWv1yLn1I+mpc/bcvGjtU9rX7pNcDXrNmon5nAB6NdxTxozbf5OTk5iamlp+bRgeTA88AXcfXMKdhyeXA0X6pW3N6fHm6oHnaiNL2sa5Pmv1jLkx0yD0ZfNMc5nGltrhMOg5D8eF8z9l/nL9p9BqW4+j/bhpuGvb197L9MBHA0ahJ0DS0h2ENnWuHniuNrKkbZzrs1bPmCJ2zHvFUHor68Vg0HPeK6ZS7n/K/OX6T6EVMxlH+3HTcNe2r71XYT83N5fVD0MejEJPwObZFvZ2yqmmpARJ4IQZuFSVsqpUdaXUqNsn2sZhukxVek2YEiOlq2nSmDQoE0Mp0uA40Y6UNKhcPW5OGKRMTKVISZJSlzTzp9WN5/ynfebSGENwGvac/7n2daRk5aa+cZ8TKQI4mj0TIjaNLNwX29Z3HuyZf4gY8mAP8ATQSmwpKUESNFW5pFSROlNqtO3Dg09Lq0iv6UmJEdLVNGlMGoT+h2lwZVWxUtKgcvW4qS9yStpKSpKculQ9f1rdeM7/lEpenIa9pqpfin0dKVm5R4+aSm5aARfNngmRkkZG98Xk1BIun03vv6Ee2AM8AbQSW4jcqliaqlxShajUlJqYqmDh+7T6E1eJTaoWRavXaap/laXUxFS/K/O/qiqWVBUuJg2pas569cjbqKq+Vza2mrko+k9p08Ib7frlhDWkSl4UoYZ9cTdNVb8Ue+36yd1nWp+5daYVcNFXzKv2P9yn3L7Yc3ICl8d22lA77AGeAK0eeEpKTyy1FtJsHB2opTZTdII1es5aPeYUPXBJDEVDYXMa7ilHACkUMndsQSlMrpKedAQh2XBrlmtTAue/VH0udvwlcPYpeuApxx4U6jXH6IFr6XDNsYvWf40GfbguNs+0AExaEZchwx7gCdDqgedqU2uotZBm4+hALbWZohOs0XPW6jEn6YFniqFwGu4pRwApFDJ3bMFVwhIpYOZ4RFtVTFN9S+u/VH2OQjP+Ejj7FD3wpGMPghj70mMsJR2uOXbR+q/RoA/XRWG9sLAwEtHoT1fYAzwBsXrgUfeOpNZCmo2jA7XUZqpOcJWeM+2LRE2m6oFr/Sy3kTXcwzalI4AUClkSpqjSGZeOICQbbs1ybUqoOnap0i3XjH+KfYoeeMqxR4q9VgCHo8M1xy5a/zUa9OG62DvfTmCan5+3B/gQYQ/wBEhR6LHRqSF9xQlTcHRWD83GRBRrhTU01GBIDVMxkDojYqVx0kSBp4hxaCBFcdOx0dLRsf6nHEFImQf02EYb+a3xn0Pu+Gvb1wp7cP2XjoNyxURiBXi0AjLaI4hYCj70q6DQDcOFPcATIEWh54qZcMIUHJ0FdNNsYCKKtcIaKTrB/YqIlcYJSNdzrjuKnY55yDlz0f5d10T6n3QEIWQe0GMbbeS3xn8OueOvbV8r7MH1XzoOyhUTiRXg0QrIaI8goin44Jq8ED5DXbAHeAKkKPTYDzNJJ5jTUw6jQynNxlHYWg3xFJ1gStPVGRHLta+NAueo0n5EsZeNTQqFrvE/5QhCyjygxzbayG+N/xxyx1/bvvaoheu/dByUErkeeB01T9KYpRxbxFLwoV8Fhb5q1aqKfhr6CXuAJ4DqgfejqEhZUQ6ODg8jbSkFr6GwU4pahDRdbBR52XhWUbB1FtWQ9MC1UcQUXBQ3N/7aMdcW9eAKmXARxeGaoVkEkp9cUZsL1zTx4HG9nrlWg14LTeaGNgtBq+eeErmu8Tnl2ISD5Bd3bMBF8Ydztnm2TaHTz0LD4GEP8EzUTcdyRTk4OjyMtKUUPFBNYacUteih6SKjyENovsHVWlQjpAMVEbmib0wUN5BXiEZb1IMrZMJFFIdrhmYRaDS8w/f3Ly5hz3x5VkZZX9Qa9EpoMje0WQhqPfeEyHWNzynHJhwkv7hjAy6KP5yz565t/yVw/PhxSyUbIuwBngD6ba9uOhYoj3bm6PAw0vZgJIWdU9SijKbTU4gr0DyA6yyqUaYHXtxXH7ne5YHqeKOAdsy1RT24QiZSRDGXRSD5yRW1OaAYM06Dvg5oMje0WQhVhXDK1nzKmuF8Tjk24SD5VXVsEkbxh9d4b4+OUYDxHwmoUw9ce2+ttnesNnQd/g9Cz7lOe6nPKXre/dJ21sw/oNOAz20/d831U1ua01NP0ZPvp43GZy1y9bxjNejrnjNDPbA/oxJA9cC7NXNb2LZ+AktLej1wSaeX06CmmsGhTvC29RO473BbW5rTFuZ0klP0zLXayIOy12hIS3rgnG50ypylaDtrNMhDbelt6yewb76tB75xuokzG008JvivbZ/Tw05Zc2V9KfTkqR45p23N6VyH/ef85PxKmb8Um9Ce87nOPSPpmWval+bs0tXtR8f09DQMw4PpgSeA6oGHwS390lau075uneNR1UYO+1ZglPXAU7DzxAy+e3S6dv9z9bQ5aPXk6d6StKn71f+6bSgG4bM0f7Hth/e6Yn0Tl50x/O9/pgduiAbVAw81c/ulrVynfd06x6OqjRz2jbtmlPTAUyDp0+e0n6unzUGrJ0/3lqRN3a/+121DMQifpfmLbT+81+6TK0FshuHBHuAJ2Dy7cuZHw4bClKQU5KZlcPbet/+KpikhQO/ZVkr7YVpd0c4Dx6bxQOf1g8enUZA99JoHj0/Dufr6rDmPPLvRXD4nnkA7dS/nPLLOOQvHRkOQ0fVIU3+09oU4T2ijPdvl7DmE9w3TEMvO86Wz/c0zra75LKt4J41ryvzF9jlEnXPG7bNwndNxoe1r1nx4r82dz7kcTXRDPobPgYwhaCW2niL/mUcS/bIX03gydY65NCwupamflbhUaWxBGtnGqSbOnG4mC9DUOWe5aWycgIeE2JQmrT3rr7KSHE1pqqoeWFa9jCKlkp+E2D6HqHPO2BRDpqpb2L5qzVsltpGEPcATQCuxhUX+Y/W/e+/dnwe4No0n9wGuSX3qZyUuTbpNWbWrsjSqlPZz7etIY+t3SpPWnkNsJbmLmNcFOGGQ8BrOx5T5i+1zL+qbM26fSdX3uEpwHLhKbEXQm2E4sAd4AijlllvVK6UqV4rOr1akIkXnOLeqEyfA0q8xS6lqJd2XViLL9V+qmKaZ85RKeLka9rn23WvW449v3YPbdxzGVVvX463bN1c+JKi2NifGIY2LppKd1KZWN53rMzfnki+5Gvaxa5YTM1m7dm1Uvw31wh7gucis6pVSlStF51crUpGic5xb1Qm+XIClX2OWUtVKui+tRJbrv1QxrexeQMIRQoBcDftce+r/H9+6B+///KOYW2jha/cfAQC87ZotlfZ0D5aJcUjjoqKjK9qM5ZS5OZMEVKgvuRr2sWuWo9Dn5+cxMzMT13lDbbAgtgTQb6hlVb0KpERE750vjwbVRgRzdCylzQt6tMpe2z5X1emitYu4aM0ifnTDSTQ7dmW+cJHH/RqzgqZdoc3jPn2lSmS5/lPf6Jhp5zzsm47h9Ak29dlT/2/fcRhzC+39NbfQwu07DlfaUwodzPhL4xLS0VXzF7ZZ0NMx4OaMzrnsy8qY031G+yatpdg1y1HoCwsLUf021At7gCeARoCGEd2UjqWRm5Tae+DYFD52y2687iM78LVvPoKJDn0q0bkpEcFStLmmb9qIZE1ErdaeizYWo+g7FPygoqilKPYwK6GMWu3xS+G/FKncr8wFCimKOzcim7Z/1db1mJ5sPyimJx2u2rq+0p5bP9yYhX3Z1FiJYgez/qQ268xc2KRcS7Fz3ls9rxnV597qfRZ9PgowCj0B9x+bwN3HyungLjo2oJ0Kau8v7tiF//G3j+Jkhyb8OQA/+uLzRDo3V9tYS22mRCRrImq19hwdKB0HUAp+EFHU4bzSKPYwK6Hsy72kJ64VIKE+DiLzQXuEkhKRTdv33oM+aVVCN8z64cYs7EusAFDYZp2ZC3TOpbUUO+fhmvMe2DUvi+5I9oWYiWG4sAd4AvacXCn8IUV0czq7O3Y+jpOEJrxv5+N476vOFtvM1TbWIi0iuTqiVmtfIIw2lqLo09qs7jMHKYo9zEooi4iW9MQ5/6VI5UE8wLXCGCkR2bT9O75/BIudjbLYav9847XnVN2hdP1wYxb2JVYAiGszBhoNc2ktxc552ZqL6XNoX4iZrF69OsoPQ70wCj0BkhCARoxk6/mnY7bRHvrVjYkumrBfwg79tM8VdhiEMIOEWPu6xVCGLSwx7PGn7V+1dT1WM3tDY6/xOVcASGpTi9wxH/bnhImZjAbsG3gCLt4wgVarV7xBK0by7689C3N7DuBbO4/gxResw1u3by611wgbUPGHLR1hCUAWlkgRWeBEQjR9/uqhWVZYRNtnSViB9lnTptTnjdNNeKyk2wC9AhqSGEhK/7n2uTbDNTc93cADx1rYfdKp+pwiBiO13xYjSV9z09PT+OjNu3DrvU/g5c9bh+0Xr8e3dh7t2hspwh65YizaNc9dxwmzFGu2mDNOtIUT1pH6rBHz0a45acynptqPjrm5OdMDHyJMzCQBCwsLmJ8vFyzRiAx87Jbdy6kyqxsTeP+PP3M5VaZOYYgUcCIHKQIowxbD0IpE0D5rBTQ0/mt94dpP8T9XGCNl/HKFPT5+216893M/wNxCC9MTAJzDYtP37I3Y9nPXn3bNc9dxwiyT6BbQGcc1NzMzg0ajgSeffHKoD3ATMzFEQ/qw0nyQSakydQpDpIATOUgRQBm2GIbUJgUnTqNNKcrtvySOE+u/1obzP2X8coU9br33ieX9sNgCFpvtLxXaNLJ+rT/tmueuk9IjqYDOOK653Dk31AN7gCdASuHQpHfQVJmpCaAx5fC6j+zAx27ZHV2aUBKGoNCKZHDpMVxKnCRGoj0Pzk2J0aTuSWlEm2fK05A0KWGh/1rRGApNGp0EKubB9ZnCe7+cxhiuOS51jRPMkPqvTSm7ettpy+feUxPAZOd22jQybv1IYh6cvXb+aOrchEdpO7T9MFWLph5yoi3a1MFBrDlOgKjRaJTe3zAYDOUM3Dn3CIAnATQBLHnvr3DOnQbgLwGcB+ARAK/z3h8ahn850BxJ0FSZVgu46e5DWGx6fO3+I3DOLZ/7aaCtKqat5MamxzApcVIlNG0aV25KjCZ1T0ojumzt/PJZI01D0qSEhf6nVL/TpNFJ0FQiowirndE1l1IVLFeM5a3bN8H79rft6UngK3cfQrN9Y/1+Kv1F91qoc/5o6hy9cVc7vrvJ7lStJTw01xRFW7Spg4NYc+G8Tk4t4fJZWBW2IWOY38Bf7r2/jJxfvBvAbd778wHc1vl5JCFJ6Gk+cGiqTAvdlOFt98X9zaKtKqanRsuravWmxK3ci6uEpq0KlpoSU9ZnyU/pOKCsqlXLYfleUrWt3Op3dMy5qloSNJXIKMIjHLrmUqqCVYmxaPC2a7bgc+/cisUmetLIqsCtn7J0vyp77fzR1DnAdf51txOuxSJVq32v8jnnqhdqx7xfa6732Kr96Dh27BjXgGEAGCUK/XoAn+68/jSAHxueKzKkylOxFLpDL2VI6c3YhxtHrXE0n2RPIdGBubR9nZXEuNS9MjGVMv9T6EhN9TtpLHL7H0uHhtXOrt62ofS+3FhKdDLtv1bnWlOJLaUSnOY4JWxfe+yjqf4mrR/NnEuV+OixlbZiHwXXPjfOXCW2cQ6CfipgWGlkHsDNzjkP4I+99x8HcJb3fm/n9/sAnFVm6Jy7AcANAHDuuecOwtce0EpsKVWxuqpNgbz0Hl9/8AhuvfdwlJhDz707oLQXS/MJ9t2/EOjATNq+zkIknJ60JKZC/U+hIzXV7+rWo6aIpUO11c64sZToZNr/FDEWzrekSnCK45Swfe2xj6b6m7R+VBXmhEp8dQrgUGgFgKwS22hgWN/AX+q9fz6AVwL4eefcv6C/9O3VVbrCvPcf995f4b2/YuPGjQNwtRe0EptEbXGgFLoH0OqYLLaAb+08Gi3mQMFRaxzNJ9lTSHRgLm1f5wOcUsBaMRXqfwodyVW/ozbSWOR/i4mjQ8NqZ9wa48ZSopNp/1PEWMoqsQF6MR36O81xSti+XgymfMyldUbvpZlzSYykTgEcCq0AUCF/m8seGfIwlNH33u/u/H8/gL8G8EIAjznnNgFA5//7h+GbBpKQgXNumQL/6M27SulwShNOOCy/Xt2YwIsvWFdZiUpLJ1LaPKS9YyPCJWox1oaLaI3pp8bnFP+1PlNfaBQ4PZ7Q0vH9EiMJo83L1p9EoWvB7YeULASOQteK4XDtS0cAKeOfsk809hR0/nJFj7R7Ltb/NWvWVPbD0D8MnEJ3zq0BMOG9f7Lz+loAHwDwJQBvAvBbnf9/cdC+afHctS00l+ZLaTZapOW2ew8tF6WgdDilCScAvPLSDVhoely1dT3eun0z/vjWPbh9x+Hln0No6cTwm7FGpEFDp2rpQM6mnxroHLT+a32mvnDa0Fo6vl+1zDlt7RTBEAlc5kJKFgLnm1YMh2tfOgJI6X/KPtHYU4TzlyN6pN1zsXryJ0+exOzsbGVfDP3BMM7AzwLw153c0ykAf+G9/4pz7u8BfM4592YAjwJ43RB8U8H7Fi5cs1T6MLntvkNdRSmKT/OCDn/bNVu6aMIlDyw0PT73zq3L93jbNVvEc2+tsARA+T+dSINGZCHXpkwPu+yDQuqnpv0U/7U+U1/KtKEvwiJLx6f4L4GzLysYFK6/gkKPibMo8aB0zLRiMhoxk1gxHK79UCQnbF+LlH0S22Y4fzmiR9o9p/W/yMRZXFy0B/gQMfAHuPf+fwO4tOT9xwFcPWh/UiDRX1dvOw1fu/8I5hZamJpoP76bre6CLY1Jh+nJ9jfzsFjFxMTE8ubwvv2Xc1EX+YLV7XO0TY0mHusEqpTRiY8teJSVSNQUBaHtx4xHjE3ov0QHPkYCgoroWjoWqT7H+q8d85DCrct/730PM1MUYOHsr9q6HrfddxiLTS+uv1wKPdb/lz9vHZxzy3152zVb8LFbduP2HYfFvZHTPufLVVvX48Zrz0nK9uh3m3T+pM8JDbR7Tgs7+x4NmJhJzeCKUtCCLVMOy9KiIYWpKYqRq60toc5vIxy0xWdGSQ87l8LN9Z+jwyV7rmCQtP5SEOt/eLT0jYeO4pZ72sxVim+x/kuFbLQYRJvSUUe/9pxhvGB/RiWg6i/fsqIUtGDLku+OPKfFKjRFMeRI2byiIIN4gGuLz2ijawfxANKOOf1dnf5L9fM5e65gULj+YjMdQsT6H9Y7/+ZDR5Z/J+2NnPY5X1KKJw2qTS4iP6V97Z7TovgMtCC24cIe4AmQtHA5bePpiZVoc/pa0gPvl7Z23fbjro08Dv5LOtmcvXb9bb/4tMr2JcT6H7b/EpJ5Ie2NnPY5X1L7P4g2U+Zci7rsc46uDPkwCj0BU1NTWFpa6tHiDXV637p9M77x0FF886EjuPL8U/HSC9ctn4EB7b/Kr962gdUD5zSYU7SRtXribW3nMp3hNg14232HRJ+563J9lvSoY/ucO2bD8J+upVBDnupp0zGnNj/ynFPgnMO3dh7tev2SC9bh7a98Jv7gpkd77Ovs/9uu2QLnHG6771DX+t9+8Wl4+yufidd/+Hv4RuDnleefCgB43Ud2dPmlX7Pletwvu/JcbH/wKL618whecsE6vOO680r3c51rhs6FNOZ0/3Da6HWvWY2GOKcHfuLECdMDHyJMDzwBWj1wSfebQ662cr/0xLUa5uPQ53G0l8aV6mnT31EbqrMdam5fe8kG3Nw5g9bOWZ395/TAOW1w7Zrl9Li/+o0f4H/87UM42envB173LNxw9aYon2P7HM4fN+bcnEl7LgW5GvCmBz4aMAo9AVo9cOncMuXeub6VQasnrtUwH4c+j6O9NK5UT5v+jjt3Ds+gv0HOoFOq//VLD5zTBteuWU6Pe8fOx3GS9PfWe5+I9jm2z+H8cWMuxQpwey4Fw9aAN9QDe4AnQKsHLul+c8xHtxhJeSWtVN/KoNUT5ypkhW1q+qytCsVBa0/Hj1bFCyvkAahNQCYFuRry3O+KlCygWzSHvp6edLjy/FPZua3Lf4pwXXOVCbnzcO2a5SqxPe/80zHFVKLT7jlOQEWqfkfPs688f13lnIVVGrk9l4IUAZcye5MTHS7sDLxmcFWlQt1voFykhNpLqUOa9jXQppdoU1o0fdZWheKgtedSl6Q0plwBmRSoU6WYcd1+8frqdDGsTF/X62Iumbmty3+KcF1T/2llwjBfvEyzXJuGSFMqz2kswjH91e45TkCFsy98L/rivcdN//A4AH7Oyqo0FqhzzcVWX6NoNBpZfhjyYN/AE6DVA5d0vzmaktqn0NH9Si/RprRo+lxWFSoGWnsthfzNTAp5EA9waVy/tfNoZbqYR/nrxRbw7YefjNbgjvWfIlzX1H9amfDGa89ZTsksguCAtDREmlK54+EnWDEX7Z7jBFQ4e+dcV180KX50LGj/gXrXnF7AZQXFZ+CTTz6Z5YchD/YAT0AKhc7RYSHlBqzQuZRO01KbklZ5Tt8kCpd+sGj6rKVAOcTQ/gVtOTWho5C1Rx0UddKZGgqW9iX0n6OgqU04L5TOHQSFrqWT+zX+ZcdBsXuOE1CRjpoort52mmptcvaDOLbpp72hHhiFXjM4Opmjw0LKLbcqFauNnOB/z/sMhUurSmn6nFsVSmtPaUtaFa/t58qLlKOOnrHJgIbCZfsS+M9R0NQmnBdK5w6CQtfSyf0a//DI4OsPHsGt9x6O2nNc9T3tcQRXsbFjVmk/CNbHMPqwP6MSkEKhc3RYSLnlVqXiqD0tYqt6hVWlNH3OrQqlp1BdaVU8iULWHnVQ1PlhqqFgaV9C/zkKmtqE8yIdj8T6r4GWTu7X+If9/dbOowl7rrz6XsxYatYmZz/sB3jxGZhbEMaQB3uAJyCFQufosJBOpHrgIVXK0e50M0pa5Tl9kyhcjoKkdCinjS61qQXVYOdoV6kSGKVwpchfTftStLsm84A7qqD3CmleTRS5VNWL0rnaPnP+p+DqbRuyxj+XwtfsOW2bWgo9nPOy9qX945iD6jBDg3tO8xrycfarV68uv8AwEBiFXjM4Cp2jw0I6keqBl1KlkCNlOWovxX/Oz9AvjoKkdCinjS61qQUtfsHRrtT/MLqZUrhS5K+mfSnavcwvQBfFT+9VSvMmrLOV363Qudo+c/6nQHPsUmf7KXtO26aWQqfvc3tL2j+cGIqkW6/xX2tfYG5uzh7iQ4R9A09ACoXO0WEhnShRpYW9HClbTu1pwee98n5xFCSlQ6WiFLkPAKrBztGu1P8wullD+2vb1xQiCaGJ4qf3CmleTRR52TqjkH5Xhdz5u33H4azxz6XwNXtO26aWQu+OAi9vX9o/nBiKtigL57/WvvgMtIIuw4V9A0+ARNk55/DRm3f1aBtTOizUcw7vXWwOTg+4Tp1gqX3vyzWcQ83mK88/dfmbwoQDJidW+uzR1kN3ACYm2q/r9vnqbRtKda/L8oidc139umrrenE8de2vaMDT8pe0/1V0Kp3zqnvRMS6OAG66+4modca1nwLOnls/4bxwuuXc/NXtP7dntXNGwa2lcM1xeuB0/qX9w2m4c7r12vYl3fuw/4bhwx7gNYPSqRydnEKnUjpOW1QlBVxEtJbCpRSoNrq2TgpWQ9tLhURSorApBc1FfqfQqSlR5MOOoqfQFtLhCtGkHEGkgNuzdVLoWj3wqMyJEnBFWbTt5xR1MQwe9mdUAqS/9imdytHJKXQqpePq1AmW2ucKoUgULqVAtdG1dVKwGtpeKiSSEoUNoJSeT6FjOapfG0U+7Ch6Cm0hHa4QTcoRRAq4PVsnha7VA9dmTnBjwRVl0bevK+pSfAaaEtlwYQ/wBEipE9svPq002lmrc8zpiVObQekEa/WkqZ4z56dWAz0FsWMejh/nvxYaPW7tnHOQ7sX1v1962lr7lPWTu2dSkDJ+sXOeqweeq+FehwY6RdH/hYWFrPsY8mAUegIkPfBfeNWzALQVll7+vHX4xkNHl7WNCz1wTnO5Sk8cwPLZ4CB0gqmGM+1LqCf92XddWqptzNnX7XPsmFO/Qj1qOs5Ut1qr4Q5U6znL2szleurcWij8//oDh3v0tLk2B6WHzumR03nZfvFpeMd15+H3v/xIz/xp+qL1n45rqEf+juvOK10/KW1q9qxWgzy8FzdmnJ447WfYPtUj59Y2N37bLz4N7/xXzwYAzM/PWz30IcL0wBMwKD1wrZ5zv3SCKSSdYo2eslZPPNfnlDHX6FFrx1yr5xzrv3Rfqi2tbZNrPwUpa6Zf48dBu3616ye2z3XvmTo14DXjHPrywdc/B+96zbNND3zIMAo9AYPSA9eeIfZLJ5hC0inW6Clr9cRzfU4Zc40etXbMtXrOsf5L96Xa0to2ufZTkLJm+jV+HLTrV7t+Yvtc956pUwNeM86hL7fce7DSf0P/YQ/wBEiVv+jvuKpk3drYnq2wRKs6UZEDSfBAk94hVXLjhDUkneKrt8Wd5/VT2zhFg52rBCYJgGj00LVVxTT+S+NPK8lJa4NDPwVwNGfLXP9pX1KqknG+aCsJplZiK2undy1sKN2D3J4LfaFrVrNOwj6/mIk74NZpWGFue2fPr1q1qnQcDIOBnYEn4KM372Irf8WmkUnpHV0pKeh6mZWSJVVy49LIZJ1imQoE5EpgdUZBcylllWlIFWlwUoUwrn1tVTGN/9L40zSy9j1WXmjGtl8COFL1O8340b6kVCXjfNFWEkxJI+PaCecM8KV7kNtzpfs8Yp2EfX7x+afgJRecWjk3Ze3R+bF88OHCRj8Bt9zzOEttxaaRSekdNCWFppHkpmRJ1ByXRibpFGsgVQKr8wGeklLFVQKTUrc4/1Oqumn8l8afWyfDFsCRqt9pxo/2RUov41KiOF+0lQRT0si4dsI50xyVSL5wqZPcOilLadTMTYEwPe7W+9pHAMePHy8dB8NgYA/wBGy/+DSB2ipPSeFEEkJqilZY4uhYSXBB8xexJLgQK7KgpTAl1E2ha3ymH8CcmEeqMEUsha/xX6LjuTWnTSPjBHAonTsoMZrGlKvsf7j+uapkHMJ55fTUtccemnbCtZByVJL7OUPXuObYK+wLtb/m4tOj7A39gVHoqWAqd8VW5aqsqlZB7aZQ6NpKbhqRBS2FWelPBlJ8BlbodE7MQxonrv1kCr/Cf4mO59acVgyEE8DhKqn1U4xm1bTDNZdswMISf4ShrXDHoXReM449NO2Ea4GrPicfVVXPOTc2vUdY1cdeFKH9jdeeE2Vv6A/sG3gCbr33CbHCVkxVrpCaojQvR8dKFb40HyzaSm4akQUthSmhzge41ueQTi+jEFOEKVIofI3/VXR8DB1a4kFl9a5BidGcWPRYWJKPMML1r4m0pwjnlaskqD320LQTrgWu+px0VKKZc+6zITzCikVoX/R/eno6+l6G+mAP8ARIFLpGJ5ijzLTa2lJ0O4BK2lNLoXP+S1HoUoQ7By7ynbOXIvc1kfOrph07ZtpxouAyDzgKNPS/zva1Y06RqgFfZc8h7H/M3gj9SqWDNXrq2mwNqR1u/LgocO2xT+znTErkvoSi/dnZ2az7GPJgFHoqFBR09+XVUaNSRCxnE1Jz33joKG7pFGjgaE8thc75L0WhSxHu/FCutKmxlyL3NZHzjSm3PMbhmGnHiYLLPOAo0ND/OtvXjjlFbER1yrENhSQmI+2NuuhgiUKn7WizNThI48dFgWuPfWI/Z1Ii9zU4fvw41qxZk30fQxrsG3gCJAqd21ia6GKttrYU3f5NRYGGFDEUKbqaIqWQChf5ri0qQSl8TeT8wpLvsqdjph0nCi7zgKNAQ//rbF875hSxEdW5YjSSmIy0N+qigyUKXRIgiT02qBq/KgpcOoKJ/ZxJidyXUIiZ5Mi4GvJhD/AEUApdorBDOlQj2KCh1qSIXE1EbS6FLkWhc/eWIpo5e45CLGsjhsIOKVhaCEV7VMFFsUtUM+0j176UocBR6LSoh7Z4CwWl4Onc0NfSWHBHGBydH/Y/lk7OpYNT5l/aJ9o+c2tW8zkhFb/RHBuF94o9dghh+d+jAaPQU8FEl3J0KFfUoixq+I9v3aPWgy6lNisianMpdCkKXUNHSnSeJoo7bIM7duD6H1KwtBCK9qii8KV9v5WIYE2EtNQ+tYmKgldcx4FS8JxutzQW3BEGR+eXFfWpWvN10sEp8y/tE02fpTWr+ZyQit9ojo167xV37MAh9yzdkAd7gCeAUugtAC2Gwi5or4I+fds1W7o2tvQ6/Pl1H9lRSmHT96WIWooyarZIC9FSc62Ajis+XLh7hxHNQLV92E4xlmEb4bFDAa7/4VzQMaRt0ntxvhQo7hfOBx1bTfvURponClrUQ7qOA6Xg6dzQ19JY0Pkro53Dhxm3F6Q1T9uU1o8GKfMv7RNNn6U1G/M5UUAquFSgbP2nHDmUoaDO165dW8v9DGkwHiQB11xyBktzDVpbOnxf075UlzxW2znUFtb4qbVP0fNOKWSi0RPX6plLY6tpX+ondy/OXovY/qfMv4RcPfFcbetYPfnQZ02fU/apBK79QWmoF/acKqNhMLBv4An4hVedh1ar2aMf/JIL1uEz77wEP/mRe/CNh46o9JiBbp3dQtta0hmm95W0rbn2uXtJOsectneobazxM7Sn2sRUt1ir583pSWv1sDV64sUHYZUeONd/qf13XHfesp43tdHcS7LXrjlOD5v2n3u/WLOLi4ti/2mb4fhNT0/jozfv6tG2TtET57SxufdDPXWuz+E+oT6HaxZof6vn+vKSC9bhs++6tEePO7TRfk5weytXQ11as1NT7UfHwsICZmZmYBgOTA88AVQPPNTJpTq7Gj3m0J7TCdbqFHM6wdp7xWorp+gpS2OWq2ddpwb7oOw12s65c06RMn/aNZNiH6ttnWIvvc/tWa3PGt34uvdM7udErgb8zMwMGo2G6YEPGSNHoTvnXuGce9A597Bz7t3D9qcMkn7zN5iUIA6hPacTrE3P4nSCtfeK1VYOfU5JA6tTzzoljW3Y9hpt59w5p0iZP+2aSbGP1bZOsZfe5/as1meNbnzdeyb3c6JfGvCGwWKkKHTn3CSAPwRwDYBdAP7eOfcl7/33h+tZN4q0m9t3HF5O21hs+uU0ruUoVpKSwkWeh/ZFeol0HXffq7aux1Vb1+O2+w6L13H3umrr+uVvC1K0vOSzxk9pzByAiQmg2YJq/EKfNe2Pmj03Z3XOee78addMir2m/9y6SBk/7Z7V+kx94/yse8/kfk5o9rm0Zotjl9WrVw/vg9gwWhS6c+5KAO/33v/Lzs+/CgDe+/9Udv2wKPQPf+lhvOez/9iVttHy7QCSV1y2AV+5+xAWW216Y3Kyl1qjr0P7V15+2nJ6CXcdd992QM963PQPT4jtc/da3ZjANZdsWE6DS/FZ46c0Zq59mWgf9pn6rGl/1Oy5OatzznPnT7tmUuw1/efWRcr4afes1mfqG+dn3Xsm93NCs8+lNfvB1z8b73rNc9BsNrMD4nLwdKfQR+0B/uMAXuG9/9nOz28A8CLv/dvJNTcAuAEAzj333Bc8+uijA/fzug9+BzfdXU5hbTx1CgeOLiXfexztx9Fnszf7HPtx9LlO+1dcumE5Pc3OwIeHkTsDr4L3/uPe+yu891ds3LhxKD5o08hSUnLGzX4cfTZ7s7c1n2d/7aUbccoppwz14W0YsTNwALsBPIP8fE7nvZHCL766ncJxy70Hsb1TkvDW+57ANRefgXdc90z8/pcf7fmd5vU42o+jz2Zv9jn24+hz3fbFZ6BhuBg1Cn0KwEMArkb7wf33AP6N935H2fXDOgM3GAwGw/DxdKfQR+obuPd+yTn3dgB/C2ASwJ9yD2+DwWAwGJ7OGKkHOAB4778M4MvD9sNgMBgMhlHGxLAdMBgMBoPBEA97gBsMBoPBMIawB7jBYDAYDGMIe4AbDAaDwTCGsAe4wWAwGAxjCHuAGwwGg8EwhrAHuMFgMBgMYwh7gBsMBoPBMIawB7jBYDAYDGMIe4AbDAaDwTCGsAe4wWAwGAxjCHuAGwwGg8EwhrAHuMFgMBgMYwh7gBsMBoPBMIawB7jBYDAYDGMIe4AbDAaDwTCGsAe4wWAwGAxjCHuAGwwGg8EwhrAHuMFgMBgMYwh7gBsMBoPBMIawB7jBYDAYDGMIe4AbDAaDwTCGsAe4wWAwGAxjCHuAGwwGg8EwhrAHuMFgMBgMYwh7gBsMBoPBMIZw3vth+5AM59wBAI8O0YUzABwcYvupML8Hi3H0exx9BszvQWPYfj/Te79xiO0PFWP9AB82nHN3eu+vGLYfsTC/B4tx9HscfQbM70FjXP1+qsAodIPBYDAYxhD2ADcYDAaDYQxhD/A8fHzYDiTC/B4sxtHvcfQZML8HjXH1+ykBOwM3GAwGg2EMYd/ADQaDwWAYQ9gD3GAwGAyGMYQ9wBPhnHuFc+5B59zDzrl3D9sfDs65R5xz9zrn7nbO3dl57zTn3C3OuZ2d/28YAT//1Dm33zl3H3mv1E/Xxn/pjP09zrnnj5jf73fO7e6M+d3OuevI73614/eDzrl/ORyvAefcM5xzdzjnvu+c2+Gc+8XO+yM75oLPIz3ezrlZ59zfOee+1/H7P3Tef5Zz7jsd//7SOdfovD/T+fnhzu/PGzG/P+Wc+wEZ78s67w99jTzt4L23f5H/AEwC+EcAPwSgAeB7AJ43bL8YXx8BcEbw3v8F4N2d1+8G8Nsj4Oe/APB8APdV+QngOgA3AXAAfgTAd0bM7/cD+KWSa5/XWSszAJ7VWUOTQ/J7E4Dnd16fAuChjn8jO+aCzyM93p0xW9t5PQ3gO50x/ByA13fe/xiAGzuvfw7AxzqvXw/gL4e0Rji/PwXgx0uuH/oaebr9s2/gaXghgIe99//be78A4LMArh+yTzG4HsCnO68/DeDHhudKG977rwF4Inib8/N6AH/m2/g2gPXOuU0DcTQA4zeH6wF81ns/773/AYCH0V5LA4f3fq/3/rud108CuB/AFozwmAs+cxiJ8e6M2bHOj9Odfx7AVQA+33k/HOtiDj4P4GrnnBuMtysQ/OYw9DXydIM9wNOwBcA/k593Qf4gGSY8gJudc3c5527ovHeW935v5/U+AGcNx7VKcH6Ow/i/vUMj/ik5ohhJvzsU7eVof8MaizEPfAZGfLydc5POubsB7AdwC9pswGHv/VKJb8t+d35/BMDpA3W4g9Bv730x3h/qjPeHnXMznfdGZryfLrAH+FMfL/XePx/AKwH8vHPuX9Bfeu895L+qRwLj4mcHHwXwbACXAdgL4HeH6o0A59xaAF8A8E7v/VH6u1Ed8xKfR368vfdN7/1lAM5BmwW4aLge6RD67ZzbBuBX0fb/hwGcBuBXhufh0xv2AE/DbgDPID+f03lv5OC93935/34Af432h8djBbXV+f/+4XkogvNzpMffe/9Y54OvBeATWKFtR8pv59w02g/CP/fe/1Xn7ZEe8zKfx2W8AcB7fxjAHQCuRJtinur8ivq27Hfn9+sAPD5YT7tB/H5F5yjDe+/nAfw/GOHxfqrDHuBp+HsA53eiSBtoB5p8acg+9cA5t8Y5d0rxGsC1AO5D29c3dS57E4AvDsfDSnB+fgnAGztRrz8C4AihfYeO4NzvX6M95kDb79d3ooyfBeB8AH83aP+AdsQwgE8CuN97/3vkVyM75pzPoz7ezrmNzrn1nderAFyD9vn9HQB+vHNZONbFHPw4gNs7bMhAwfj9APkDz6F9bk/He2T35VMSw46iG9d/aEdcPoT2WdavD9sfxscfQjsK93sAdhR+on2edhuAnQBuBXDaCPj6GbTpz0W0z87ezPmJdpTrH3bG/l4AV4yY3/+149c9aH+obSLX/3rH7wcBvHKIfr8UbXr8HgB3d/5dN8pjLvg80uMN4BIA/9Dx7z4A7+28/0No/0HxMID/DmCm8/5s5+eHO7//oRHz+/bOeN8H4L9hJVJ96Gvk6fbPSqkaDAaDwTCGMArdYDAYDIYxhD3ADQaDwWAYQ9gD3GAwGAyGMYQ9wA0Gg8FgGEPYA9xgMBgMhjGEPcANhhGEc26Vc+7/55yb7GMbDefc10gxEYPBMEawB7jBMJr4dwD+ynvf7FcDvi3EcxuAn+hXGwaDoX+wB7jBMEA45364IwIx26mUt6NTXzrET6FTmcs5t9Y5d5tz7ruure1+fef985xz9zvnPtG5z82dilm0nbudc/+3I3rlAf5Hpy2DwTBmsEIuBsOA4Zz7INrVtlYB2OW9/0/B7xsA/sl7f3bn5ykAq733R51zZwD4NtplQZ+JdrWuK7z3dzvnPgfgS977/9Z5YL/Fe/8t59xvAXi1977nD4UORb/Pe7+xfz02GAz9gJ19GQyDxwfQrqd/EsAvlPz+DACHyc8OwG92lORaaEs0FjKfP/De3915fReA8zr1q0/x3n+r8/5fAHh1mSPe+6ZzbsE5d4pva2wbDIYxgT3ADYbB43QAawFMo/1N/Hjw+xOd9wv8FICNAF7gvV90zj1Cfj9Prmui/a0+FjNo/zFhMBjGCHYGbjAMHn8M4DcA/DmA3w5/6b0/BGDSOVc8pNcB2N95eL8cbeqchW9LPz7pnHtR563Xc9c6504HcNB7vxjdC4PBMFTYA9xgGCCcc28EsOi9/wsAvwXgh51zV5VcejPa6ltA+0F/hXPuXgBvBPCAoqk3A/iEc+5uAGsAHOm0v9k592Vy3csB/M+UvhgMhuHCgtgMhhGEc+75AN7lvX9Dov1a7/2xzut3oy2x+Ysl1/0VgHd77x/KcthgMAwcdgZuMIwgvPffdc7d4ZybTMwFf5Vz7lfR3uOPAvjp8IJOtPv/sIe3wTCesG/gBoPBYDCMIewM3GAwGAyGMYQ9wA0Gg8FgGEPYA9xgMBgMhjGEPcANBoPBYBhD2APcYDAYDIYxxP8fevRR1rKyjQQAAAAASUVORK5CYII=\n",
"text/plain": [
""
]
},
"metadata": {
"needs_background": "light"
},
"output_type": "display_data"
}
],
"source": [
"results.plot_lattice_states(\n",
" results.lattice_states()[-1],\n",
" marker_size=2.5,\n",
" markers=[\"o\", \"o\"],\n",
" colors=[\"#98dbff\", \"#0053b6\"],\n",
" lattice_color=\"0.95\",\n",
");"
]
},
{
"cell_type": "markdown",
"id": "bc75322c-8b10-406a-b374-d9cb8bc11515",
"metadata": {},
"source": [
"The resulting plot reveals the macroscopic morphology of the electrodeposited metal (`M`, dark blue). As expected from our kinetic parameters, the growth fronts have advanced inward from the boundaries, but the resulting deposit is highly uneven, exhibiting severe roughening and dendritic branching. This morphology is a direct consequence of our chosen reaction network. The fast electrochemical reduction rate outpaces the lateral surface diffusion (terrace diffusion and step-detachment). Furthermore, because we intentionally excluded interlayer (descending) diffusion from this minimal model, deposited atoms cannot easily relax into lower layers. This forces the system to grow outward into peaks and branches rather than forming a dense, conformal film.\n",
"\n",
"As a final step, we can visualize the entire deposition process as a continuous animation. This dynamic view is often much more informative than a single final snapshot when trying to diagnose which kinetic step limits morphology evolution. The following cell uses `matplotlib.animation.ArtistAnimation` to compile our sequence of lattice states into a movie. We then use the `to_jshtml()` method to render an interactive HTML5 video player."
]
},
{
"cell_type": "code",
"execution_count": 20,
"id": "9c1b089d-d764-40b3-b86f-4a5e32ea5cf3",
"metadata": {},
"outputs": [
{
"data": {
"text/html": [
"\n",
"\n",
"\n",
"\n",
"\n",
"\n",
"
\n",
"\n",
"\n",
"\n"
],
"text/plain": [
""
]
},
"execution_count": 20,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"fig, ax = plt.subplots()\n",
"\n",
"frames = []\n",
"results.plot_lattice_states(\n",
" results.lattice_states(),\n",
" show=False,\n",
" marker_size=2.5,\n",
" markers=[\"o\", \"o\"],\n",
" colors=[\"#98dbff\", \"#0053b6\"],\n",
" lattice_color=\"0.95\",\n",
" frames=frames,\n",
")\n",
"\n",
"ani = animation.ArtistAnimation(fig, frames, interval=500, blit=True)\n",
"plt.close(fig) # prevent extra static figure display in notebook\n",
"\n",
"HTML(ani.to_jshtml())"
]
},
{
"cell_type": "markdown",
"id": "19f5f7b5-fd2c-4bd6-b75a-10dfa1fabbd8",
"metadata": {},
"source": [
"Controlling Morphology: The Low Overpotential Regime\n",
"----------------------------------------------------\n",
"\n",
"You can easily alter the final morphology by shifting the kinetic balance of the simulation. If you adjust the initial parameters to a lower overpotential (`eta = 0.4`) and a longer time step (`dt = 1e-6`) to account for the slower reactions, the simulation will produce a dense, conformal film rather than dendritic branches."
]
},
{
"cell_type": "markdown",
"id": "c1a221da-54ae-4a12-9875-71ba65d0e53c",
"metadata": {
"tags": [
"html_base64_image"
]
},
"source": [
""
]
},
{
"cell_type": "markdown",
"id": "8da02cf1-aed4-4cf1-a8a2-629ff097799b",
"metadata": {},
"source": [
"Achieving this film-type deposition is the ultimate goal in metal anode engineering. A flat, uniform morphology minimizes localized current density \"hot spots\", extends battery cycle life, and eliminates the safety hazards associated with dendrite-induced short circuits.\n",
"\n",
"This shift in growth mode happens because lowering the overpotential exponentially decreases the rate of electrochemical reduction. With a much slower influx of new solid atoms, the system is no longer diffusion-limited. The deposited atoms have ample time to undergo lateral surface diffusion, allowing them to reorganize and relax into highly coordinated, tightly packed configurations before subsequent layers are formed."
]
}
],
"metadata": {
"kernelspec": {
"display_name": "Python 3",
"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": "3.8.12"
}
},
"nbformat": 4,
"nbformat_minor": 5
}