{ "cells": [ { "cell_type": "markdown", "metadata": {}, "source": [ "# freud.diffraction.StaticStructureFactorDirect and freud.diffraction.StaticStructureFactorDebye\n", "\n", "The `freud.diffraction` module provides two methods for calculating a one-dimensional [static structure factor](https://en.wikipedia.org/wiki/Structure_factor) $S(k)$ which can be used to characterize structure of crystals, liquids or amorphous phases.\n", "\n", "The `freud.diffraction.StaticStructureFactorDirect` class implements a \"direct\" $S(k)$ method. First, the following expression is computed over a $k$-space (reciprocal space) grid:\n", "\n", "$$S(\\vec{k}) = {\\frac{1}{N}}\\sum_{i=1}^{N}\\sum_{j=1}^{N}\\mathrm{e}^{-i\\vec{k}\\cdot(\\vec{r}_{i} - \\vec{r}_{j})}$$\n", "\n", "Then, the angular dependence is integrated out, resulting in $S(|\\vec{k}|)$, otherwise denoted $S(k)$. For an excellent introduction to the theory of scattering and $S(k)$, please refer to the documentation of the [dynasor package](https://dynasor.materialsmodeling.org/), which performs a number of calculations related to scattering. The **freud** library implements the core method of static structure factor calculation based on the dynasor package, with some additional performance optimizations in parallelized C++ code, as well as an interface to compute $S(k)$ that aligns with the APIs and conventions of the **freud** library.\n", "\n", "The `freud.diffraction.StaticStructureFactorDebye` class computes static structure factor based on the Debye scattering equation:\n", "\n", "$$ S(k) = {\\frac{1}{N}} \\sum_{i=1}^{N}\\sum_{j=1}^{N}{\\frac{\\sin(kr_{ij})}{kr_{ij}}} $$\n", "\n", "which is obtained by integrating out the angular dependence from the original formula. This implementation provides a much faster algorithm, but gives worse results than the \"direct\" method at low $k$ values.\n", "\n", "Note that freud employs the usual physics convention, as opposed to the crystallographic convention, with the following expression linking the two: $k = 2\\pi q$. The static structure factor is related to the radial distribution function, $g(r)$, by a Fourier Transform:\n", "\n", "$$S(k) = 1 + \\rho \\int_{V}\\mathrm{d}\\vec{r}e^{-i\\vec{k}\\cdot\\vec{r}}g(r). $$" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Lennard-Jones Liquid Example\n", "\n", "One of the use cases for $S(k)$ is to characterize structure of liquids. The example shown here uses data generated by a HOOMD-blue simulation of a 1000 particle system subject to the Lennard-Jones potential. See the HOOMD-blue [documentation](https://hoomd-blue.readthedocs.io/en/latest/) and [examples](https://github.com/glotzerlab/hoomd-examples) for more information." ] }, { "cell_type": "code", "execution_count": 1, "metadata": {}, "outputs": [ { "data": { "image/png": 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", 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" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "import freud\n", "import gsd.hoomd\n", "import matplotlib.pyplot as plt\n", "import numpy as np\n", "\n", "bins = 100\n", "k_max = 30\n", "k_min = 3\n", "sfDirect = freud.diffraction.StaticStructureFactorDirect(\n", " bins=bins, k_max=k_max, k_min=k_min\n", ")\n", "sfDebye = freud.diffraction.StaticStructureFactorDebye(\n", " num_k_values=bins, k_max=k_max, k_min=k_min\n", ")\n", "\n", "with gsd.hoomd.open(\"data/LJsampletraj.gsd\", \"r\") as traj:\n", " for frame in traj:\n", " sfDebye.compute(frame, reset=False)\n", " sfDirect.compute(frame, reset=False)\n", "\n", "plt.plot(sfDebye.k_values, sfDebye.S_k, label=\"Debye\")\n", "plt.plot(sfDirect.bin_centers, sfDirect.S_k, label=\"Direct\")\n", "plt.title(\"Static Structure Factor\")\n", "plt.xlabel(\"$k$\")\n", "plt.ylabel(\"$S(k)$\")\n", "plt.legend()\n", "plt.show()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Crystal Comparison Example\n", "\n", "The static structure factor $S(k)$ can also be used to characterize and compare crystal structures. In the below example we compare the computed static structure factors $S(k)$ of a face-centered cubic (fcc) crystal and simple cubic (sc) crystal." ] }, { "cell_type": "code", "execution_count": 2, "metadata": {}, "outputs": [ { "data": { "image/png": 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qiIiIQkzLU04d6anng6GGiIiIVIGhhoiIiE5KCIHf/OY3SEhIgCRJKCwslHtI7bBRmIiIiE7q888/x2uvvYb169ejf//+SEpKkntI7TDUkLoIATibABOb8IiIetL+/fuRlpaGcePGyT2UTnH6idTl87nAov5A5X65R0JEpBq33XYb7r33Xhw+fBiSJKFfv37weDx44oknMHDgQJjNZvTt2xePPfaY/2eOHDmCG2+8EQkJCYiKisKoUaOwZcuWXh0nKzWkLke/A1xNQPkuIHGA3KMhIuqSEAJNTrcs9x1h1Hd71dGzzz6LAQMG4MUXX0RBQQH0ej3mzp2LZcuW4emnn8ZFF12E0tJS/Pe//wUA1NfXY/z48ejTpw8+/vhj2Gw2/Oc//4HH4+nNh8RQQyojRPBnIiIFa3K6MeSRL2S5712PXo5IU/digNVqRUxMDPR6PWw2G+rq6vDss89iyZIlmDFjBgBgwIABuOiiiwAAK1aswPHjx1FQUICEhAQAwMCBA3vngQTg9BOpi/AEfyYioh63e/du2O12XHrppR1eXlhYiJEjR/oDTaiwUkPqwlBDRGEkwqjHrkcvl+2+T/tnW05tcLqX9xaGGlIXhhoiCiOSJHV7CkhJcnJyEBERgTVr1uCOO+5od/k555yDl156CSdOnAhptYbTT6Qy7KUhIuptFosFv//97/HQQw/h9ddfx/79+7F582a8/PLLAICbbroJNpsN11xzDTZu3IgDBw7g/fffx7ffftur4wq/eEjUFX+jMCs1RES96eGHH4bBYMAjjzyCkpISpKWl4e677wYAmEwmrFq1Cvfffz9+9rOfweVyYciQIXjuued6dUySENpYJlJbWwur1YqamhrExsbKPRzqLUvHepdzX/t3YPiNco+GiChIc3MzioqKkJ2dDYvFIvdwFKOr5+VU3r85/UTqwp4aIiLNYqghdeE+NUREmsVQQ+rCSg0RkWYx1JC6MNQQEWkWQw2pDFc/ERFplSJCTX5+PiRJCvqw2Wz+y4UQyM/PR3p6OiIiIjBhwgTs3LlTxhGTYvnDDHtqiIi0RhGhBgCGDh2K0tJS/8eOHTv8ly1atAiLFy/GkiVLUFBQAJvNhsmTJ6Ourk7GEZMicfqJiEizFBNqDAYDbDab/yM5ORmAt0rzzDPPYN68eZg2bRqGDRuG5cuXo7GxEStWrJB51KQ4XP1ERKRZigk1+/btQ3p6OrKzs3HjjTfiwIEDAICioiKUlZVhypQp/uuazWaMHz8emzZt6vT27HY7amtrgz5IAxhqiIg0SxGhZsyYMXj99dfxxRdfYNmyZSgrK8O4ceNQWVmJsrIyAEBqamrQz6Smpvov68jChQthtVr9H5mZmb36GEghOP1ERKRZigg1eXl5uO6665Cbm4vLLrsMn3zyCQBg+fLl/utIkhT0M0KIdscCzZ07FzU1Nf6P4uLi3hk8KQtDDRGRZiki1LQVFRWF3Nxc7Nu3z78Kqm1Vpry8vF31JpDZbEZsbGzQB2kAQw0RkWYpMtTY7Xbs3r0baWlpyM7Ohs1mw+rVq/2XOxwObNiwAePGjZNxlKRMos1nIiLqCe+99x5yc3MRERGBxMREXHbZZWhoaAAAvPLKKxg6dCjMZjPS0tJwzz33yDJGgyz32sYDDzyAqVOnom/fvigvL8ef//xn1NbWYsaMGZAkCbNnz8aCBQuQk5ODnJwcLFiwAJGRkbj55pvlHjopDSs1RBROhACcjfLctzES6KKNI1BpaSluuukmLFq0CNdeey3q6urw9ddfQwiB559/HnPmzMHjjz+OvLw81NTUYOPGjb08+I4pItQcOXIEN910EyoqKpCcnIwLLrgAmzdvRlZWFgDgoYceQlNTE2bOnImqqiqMGTMGq1atQkxMjMwjJ8VhqCGicOJsBBaky3PffygBTFHdumppaSlcLhemTZvmf2/Ozc0FAPz5z3/G/fffj/vuu89//dGjR/f8eLtBEaHm7bff7vJySZKQn5+P/Pz80AyIwhdDDRFRjxs+fDguvfRS5Obm4vLLL8eUKVMwffp0OJ1OlJSU4NJLL5V7iAAUEmqIeoy/pYY9NUQUBoyR3oqJXPfdTXq9HqtXr8amTZuwatUq/O1vf8O8efOwZs2aXhzgqWOoIXXxV2oYaogoDEhSt6eA5CZJEi688EJceOGFeOSRR5CVlYXVq1ejX79+WLNmDSZOnCj3EBlqSGU4/URE1OO2bNmCNWvWYMqUKUhJScGWLVtw/PhxDB48GPn5+bj77ruRkpKCvLw81NXVYePGjbj33ntDPk6GGlIXhhoioh4XGxuLr776Cs888wxqa2uRlZWFp556Cnl5eQCA5uZmPP3003jggQeQlJSE6dOnyzJOhhpSGe5TQ0TU0wYPHozPP/+808vvuusu3HXXXSEcUccUufke0WljpYaISLMYakhdGGqIiDSLoYbUxbfqiaGGiEhzGGpIXbikm4hIsxhqSD2EgL9BmJUaIlIwwT+8gvTU88FQQ+oR+I+CoYaIFMhoNAIAGhtlOomlQvmeD9/zc7q4pJtUhH/5EJGy6fV6xMXFoby8HAAQGRkJqZtnylYjIQQaGxtRXl6OuLg46PX6M7o9hhpSj8DqDCs1RKRQNpsNAPzBhoC4uDj/83ImGGpIPRhqiCgMSJKEtLQ0pKSkwOl0yj0c2RmNxjOu0Pgw1JB6MNQQURjR6/U99mZOXmwUJvUIahRmfw0RkdYw1JB6sFJDRKRpDDWkHgw1RESaxlBD6sFQQ0SkaQw1pCKik6+JiEgLGGpIPbijMBGRpjHUkHoETT+xUkNEpDUMNaQerNQQEWkaQw2pBys1RESaxlBD6sHVT0REmsZQQ+rBUENEpGkMNaQi7KkhItIyhhpSj6Agw54aIiKtYagh9eD0ExGRpjHUkHow1BARaRpDDalH0D41nH4iItIahhpSD4YaIiJNY6gh9eD0ExGRpjHUkHow1BARaRpDDamI6ORrIiLSAoYaUg9WaoiINI2hhtSDoYaISNMYakg9GGqIiDSNoYbUg0u6iYg0jaGG1IOVGiIiTWOoIfVgpYaISNMYakhFAkMNKzVERFrDUEPqERRkWKkhItIahhpSD/bUEBFpGkMNqQdDDRGRpjHUkHoI9tQQEWkZQw2pR1Clhj01RERaw1BD6sHpJyIiTWOoIfVgqCEi0jSGGlIRbr5HRKRlDDWkHtynhohI0xhqSD24+omISNMYakg92FNDRKRpigs1CxcuhCRJmD17tv+YEAL5+flIT09HREQEJkyYgJ07d8o3SFImVmqIiDRNUaGmoKAAL774Is4555yg44sWLcLixYuxZMkSFBQUwGazYfLkyairq5NppKRI3KeGiEjTFBNq6uvrccstt2DZsmWIj4/3HxdC4JlnnsG8efMwbdo0DBs2DMuXL0djYyNWrFgh44hJcTj9RESkaYoJNbNmzcKVV16Jyy67LOh4UVERysrKMGXKFP8xs9mM8ePHY9OmTZ3ent1uR21tbdAHqR2nn4iItMwg9wAA4O2338Z//vMfFBQUtLusrKwMAJCamhp0PDU1FYcOHer0NhcuXIg//vGPPTtQUjYu6SYi0jTZKzXFxcW477778Oabb8JisXR6PUmSgr4XQrQ7Fmju3LmoqanxfxQXF/fYmEmhOP1ERKRpsldqtm3bhvLycpx33nn+Y263G1999RWWLFmCPXv2APBWbNLS0vzXKS8vb1e9CWQ2m2E2m3tv4KQ8bBQmItI02Ss1l156KXbs2IHCwkL/x6hRo3DLLbegsLAQ/fv3h81mw+rVq/0/43A4sGHDBowbN07GkZPicEk3EZGmyV6piYmJwbBhw4KORUVFITEx0X989uzZWLBgAXJycpCTk4MFCxYgMjISN998sxxDJqUSPPcTEZGWyR5quuOhhx5CU1MTZs6ciaqqKowZMwarVq1CTEyM3EMjJWFPDRGRpklCaONP2traWlitVtTU1CA2Nlbu4VBvKPwH8OHd3q+jUoAH98k7HiIiOmOn8v4te08NUc9hTw0RkZYx1JB6cJ8aIiJNY6gh9WBPDRGRpjHUkHow1BARaRpDDakHl3QTEWkaQw2pB3cUJiLSNIYaUg9OPxERaRpDDakHT5NARKRpDDWkIgw1RERaxlBD6sF9aoiINI2hhtSDPTVERJrGUEPqwZ4aIiJNY6gh9eCSbiIiTWOoIfVo21PDYENEpCkMNaQebaecGGqIiDSFoYZUpE2IYV8NEZGmMNSQerQLMazUEBFpCUMNqUfb6SZWaoiINIWhhtSjXU8NQw0RkZYw1JB6sFJDRKRpDDWkHlz9RESkaQw1pB6cfiIi0jSGGlIPhhoiIk1jqCEVYU8NEZGWMdSQejDEEBFpGkMNqQenn4iINI2hhtSDS7qJiDSNoYbUg6GGiEjTGGpIPbhPDRGRpjHUkHqwp4aISNMYakhFOP1ERKRlDDWkHqzUEBFpGkMNqUe7EMOeGiIiLWGoIfVgpYaISNMYakg92i3pZqWGiEhLGGpIPbikm4hI0xhqSD24+R4RkaYx1JB6sKeGiEjTGGpIRVipISLSMoYaUg8u6SYi0jSGGlIPTj8REWkaQw2pB0MNEZGmMdSQenD1ExGRpjHUkHpwnxoiIk1jqCH1YKghItI0hhpSEU4/ERFpGUMNqQd7aoiINI2hhtSD+9QQEWkaQw2pB5d0ExFpGkMNqQenn4iINI2hhtSDlRoiIk1jqCH14JJuIiJNU0Soef7553HOOecgNjYWsbGxGDt2LD777DP/5UII5OfnIz09HREREZgwYQJ27twp44hJkVipISLSNEWEmoyMDDz++OP47rvv8N1332HSpEm4+uqr/cFl0aJFWLx4MZYsWYKCggLYbDZMnjwZdXV1Mo+clIU9NUREWqaIUDN16lT87Gc/w6BBgzBo0CA89thjiI6OxubNmyGEwDPPPIN58+Zh2rRpGDZsGJYvX47GxkasWLFC7qGTknD6iYhI0xQRagK53W68/fbbaGhowNixY1FUVISysjJMmTLFfx2z2Yzx48dj06ZNMo6UFKddiGGoISLSEoPcA/DZsWMHxo4di+bmZkRHR+ODDz7AkCFD/MElNTU16Pqpqak4dOhQp7dnt9tht9v939fW1vbOwEk52FNDRKRpiqnUnHXWWSgsLMTmzZvx29/+FjNmzMCuXbv8l0uSFHR9IUS7Y4EWLlwIq9Xq/8jMzOy1sZNCcJ8aIiJNU0yoMZlMGDhwIEaNGoWFCxdi+PDhePbZZ2Gz2QAAZWVlQdcvLy9vV70JNHfuXNTU1Pg/iouLe3X8pADsqSEi0jTFhJq2hBCw2+3Izs6GzWbD6tWr/Zc5HA5s2LAB48aN6/TnzWazf4m474NUjtNPRESapoiemj/84Q/Iy8tDZmYm6urq8Pbbb2P9+vX4/PPPIUkSZs+ejQULFiAnJwc5OTlYsGABIiMjcfPNN8s9dFIUTj8REWmZIkLNsWPHcOutt6K0tBRWqxXnnHMOPv/8c0yePBkA8NBDD6GpqQkzZ85EVVUVxowZg1WrViEmJkbmkZOisFJDRKRpkhDaaDyora2F1WpFTU0Np6LU6sUJQMn3rd//4jVg6LVyjYaIiHrAqbx/K7anhuiUsVJDRKRpDDWkHu2WdGuiCElERC0Yakg9uE8NEZGmMdSQevhCjNTysmalhohIU85o9ZPT6URZWRkaGxuRnJyMhISEnhoX0anzhRqdAXA7WKkhItKYU67U1NfX4+9//zsmTJgAq9WKfv36YciQIUhOTkZWVhbuvPNOFBQU9MZYiU6ipTKja8nqDDVERJpySqHm6aefRr9+/bBs2TJMmjQJK1euRGFhIfbs2YNvv/0W8+fPh8vlwuTJk3HFFVdg3759vTVuovb800/64O+JiEgTTmn6adOmTVi3bh1yc3M7vPz888/H7bffjhdeeAEvv/wyNmzYgJycnB4ZKNFJ+aeffFmdPTVERFpySqHm3Xff9X997NixTk8oaTabMXPmzDMbGdGpCuypCfyeiIg04bRXP1133XVwuVwdXtbZcaJe5VvtxOknIiJNOu1QEx8fj3vvvbfd8crKSlx22WVnNCii0+Kv1DDUEBFp0WmHmjfeeANr1qzBSy+95D+2e/dunH/++Ty3EslDtF39xJ4aIiItOe19auLi4vD+++9j/PjxyM3NRVVVFW688Ub85je/wRNPPNGTYyTqnnaVGoYaIiItOaVQc/XVV2PEiBEYOXIkRowYgdzcXDz33HO48sor0dzcjOeeew4zZszorbESnQR7aoiItOyUQk1OTg42btyIpUuXorKyEnFxcRg+fDiEELjlllswYsQIOJ1OGI3G3hovUefaVmq4pJuISFNOKdT85S9/8X995MgRFBYWorCwEImJif7+GoPBgLPPPhvbt2/v8cESdYlLuomINO20e2oyMjKQkZGBq666yn+svr4e33//PX744YceGRzRKfE3CnP6iYhIi87ohJZtRUdH4+KLL8bFF1/ckzdL1D08TQIRkaad0pLuw4cPn9KNHz169JSuT3RGuPqJiEjTTinUjB49GnfeeSe2bt3a6XVqamqwbNkyDBs2DCtXrjzjARJ1G3tqiIg07ZSmn3bv3o0FCxbgiiuugNFoxKhRo5Ceng6LxYKqqirs2rULO3fuxKhRo/Dkk08iLy+vt8ZN1IG2m+8x1BARackpVWoSEhLwl7/8BSUlJXj++ecxaNAgVFRUYN++fQCAW265Bdu2bcPGjRsZaCj0/Od+0gV/T0REmnDKjcI7d+6E2WzGtGnTMG3atN4YE9Hp4T41RESadsrnfpozZw6WLl0adOyjjz7CDTfcgHvvvRcHDhzoscERnRL21BARadoph5rt27fjuuuu83+/e/du/OIXv8DGjRvx9ttvY8yYMSgpKenRQRJ1S7sTWjLUEBFpySmHmpqaGmRmZvq/f/3119G/f38cOnQIR44cwYgRI/D444/36CCJuoX71BARadoph5qMjAyUlpb6v//yyy9x/fXXQ6/Xw2w2Y+7cuVi1alWPDpKoW/zTT2wUJiLSolMONZMnT8bixYsBAIcOHcL333+PyZMn+y8fMGAAiouLe26ERN3FnhoiIk075dVP8+bNw8iRI9G/f380NzcjMzMTF110kf/yY8eOITo6ukcHSdQ9viXdnH4iItKiUw41ffr0QUFBAf7617+iuroa99xzDyRJ8l++du1aDBo0qEcHSdQt7U6TwFBDRKQlp3VCy6ysLDz11FMdXrZr1y5Mnz79jAZFdMoC+2d800/cp4aISFN69CzdgHc1FFHIBYUantCSiEiLTrlRmEiRAqea2FNDRKRJDDWkDoEBhj01RESaxFBD6hAUanxLujn9RESkJQw1pBIdNAqzUkNEpCkMNaQOQT01uvbHiIhI9RhqSB066qnhkm4iIk1hqCF16LCnhpUaIiItYaghdeho8z2GGiIiTWGoIXXgPjVERJrHUEPqEFSp8TUKyzMUIiKSB0MNqQMrNUREmsdQQyrhK8tI3FGYiEijGGpIHXwBRpIASMHHiIhIExhqSB38oUbXuvkem2qIiDSFoYbUoaNQw0oNEZGmMNSQOvhWP0m6likoMNQQEWkMQw2pgz/ASOFbqfG4gffvBLb8Xe6REBGFJYYaUoeg6SdfpSbMemrKdwE7/gl887TcIyEiCksMNaQSgdNPYVqpcTm8n90OecdBRBSmGGpIHfw9NYFLusOsUuNxej+7XfKOg4goTDHUkDoE7lMTrpUajyv4M/m9+10xFq/aI/cwiEjhFBFqFi5ciNGjRyMmJgYpKSm45pprsGdP8H9gQgjk5+cjPT0dERERmDBhAnbu3CnTiElx1LBPDUNNp/78yW78de1PKD7RKPdQiEjBFBFqNmzYgFmzZmHz5s1YvXo1XC4XpkyZgoaGBv91Fi1ahMWLF2PJkiUoKCiAzWbD5MmTUVdXJ+PISTGECnpqfNNOvmko8mtyugEAdpdb5pEQkZIZ5B4AAHz++edB37/66qtISUnBtm3bcMkll0AIgWeeeQbz5s3DtGnTAADLly9HamoqVqxYgbvuukuOYZOSBC3pDtN9anwVGuEBPJ7Ws40TXG7v79LpDrPqGxGFlCL/16ypqQEAJCQkAACKiopQVlaGKVOm+K9jNpsxfvx4bNq0qcPbsNvtqK2tDfogFVPDjsKB006cgvLzeAQ8LVnG7WGoIaLOKS7UCCEwZ84cXHTRRRg2bBgAoKysDACQmpoadN3U1FT/ZW0tXLgQVqvV/5GZmdm7Ayd5dRhqwuwNMHDaiaHGzxUQZJzuMAuqRBRSigs199xzD3744Qf84x//aHeZ5JtWaCGEaHfMZ+7cuaipqfF/FBcX98p4SSlU0FPjCegXYajxc3k8AV+HWVAlopBSRE+Nz7333ouPP/4YX331FTIyMvzHbTYbAG/FJi0tzX+8vLy8XfXGx2w2w2w29+6ASTkCl3S3PRYu3KzUdCQwyLjYU0NEXVBEpUYIgXvuuQcrV67E2rVrkZ2dHXR5dnY2bDYbVq9e7T/mcDiwYcMGjBs3LtTDJSXqcEl3mGFPTYcCg0xg1YaIqC1FVGpmzZqFFStW4KOPPkJMTIy/T8ZqtSIiIgKSJGH27NlYsGABcnJykJOTgwULFiAyMhI333yzzKMnRQjcUThsp58YajrC6Sci6i5FhJrnn38eADBhwoSg46+++ipuu+02AMBDDz2EpqYmzJw5E1VVVRgzZgxWrVqFmJiYEI+WFClon5owX9INBE9FaVxQpYbTT0TUBUWEGtGNVSqSJCE/Px/5+fm9PyAKP0H71LBSoyaBQcbN6Sci6kKYNh8QtaGKJd2BoYY75/oETj9x8z0i6gpDDamECpZ0B61+4vSTT9DqJ1ZqiKgLDDWkDoGVGoRrTw33qekIe2qIqLsYakgdAvepCddKTWB1xs1Q48PVT0TUXQw1pA4d7lMTZm+AbBTukDNon5ow+50SUUgx1JA6qG1JN0ONnztoR+Ew+50SUUgx1JA6BC3p9oWaMPurPnDKiY3CfoFBhj01RNQVhhpSB+4orFrBq58Yaoiocww1pA7cp0a1ghqFOf1ERF1gqCGVUME+NUGrnzj95ONiozARdRNDDalD4JJu7lPT445WN+GNzYfQ7Ax9BYmb7xFRdyni3E9EZ6zD6acwewNUcE/NM6v34t1tRxBp1OO68zJCet9ON/epIaLuYaWG1EEN+9QEnSZBWaGmqtE7tuqm0E+LBS/pDrPfKRGFFEMNqYNQQ0+Ncis1vmqJU4ZG3eDTJITZ75SIQoqhhtShw31qwuwNMDDIKKxR2NfL4nTJEGq4pJuIuomhhtQhaPrJF2rkG85pUXKlxuV9Mp0yhIrgJd3h9kslolBiqCF1UMUJLZW7T43TI9/0E8/9RETdxVBD6iLpELZLuoMahZU1/eQLM3L0tLiDztIdZr9TIgophhpSB1VUapS7T41v2scpw/RPUKWG009E1AWGGlIHNSzpDmoUVlaocbRUaByyVGq4+R4RdQ9DDamDKpZ0K3efGl+FRI7pJ56lm4i6i6GG1KHD1U/hFmoUvPrJv0+NDNNPXNJNRN3EUEPqELRPTZhWagKnnBTXKOzrqeH0ExEpF0MNqUOH534Ks7/qlbykW8YdhZ2cfiKibmKoIZXoqKcmzN4AFTz95JJx+snN6Sci6iaGGlKHwCXdbY+FCwWfJkHO6Scnz/1ERN3EUEPqoIp9apRZqRFCyLqjcNDqJ1ZqiKgLDDWkDh0t6Q7nfWoUFGrcHuF/euXoaQmafmJPDRF1gaGG1EEN+9S4lblPTWB1RJbpJ65+IqJuYqghdQha0h2u+9Qo8zQJgbsIO2Sp1HD6iYi6h6GG1KHDJd3hFmqU2SjskrlRl+d+IqLuYqghdVDFPjWB00/K2acmcMpJ/kbhMAuqRBRSDDWkEmHeUyOEYhuFg0NN6IOii43CRNRNDDWkDkH71Pj2qhHhU61pW5lR0GkSAoOMPJUabr5HRN3DUEPq0NH0ExBGocbV9fcycsk8/RS8pDuMqm9EFHIMNaQO/iXdUvCuwuGyV027UKOcnhqHzOdecnL1ExF1E0MNqUNQpSYMT5XQdrpJoaufHHJXahhqiKgLDDWkDv5pJqnN9FO4hJq2PTXKmX6Se/VTYE+Pd3djBhsi6hhDDamD6npqlFOpCQwVHhFcOQmFtn00rNYQUWcYakglOjr3E8KnUtN2uklBPTVtqzOhrta0DVFc1k1EnWGoIXUIrNQgHHtqFLz6ySNvpcTZ7v7D5HdKRCHHUEPqELhPTThWatqGGAU1CjtcwSHG6QpxpcbNSg0RdQ9DDalDZz01XNJ9xtpWRkI9/eRsUxlqW7khIvJhqCF1EGHeU6Pg6ad2PTUyNwqHulGZiMIHQw2pQ6f71ITJG2C7RmHlTD+1Pd9TqKef2vbwcPqJiDrDUEPqEFiRCctKTXjsUwOEvlG3bYjhkm4i6gxDDalDuFdq/CGmZexu5YSatqGibeNwb2u/pDtMgioRhRxDDamLr0rj+xw2lZqW6SZjRMv3ygk1cu9T035Jd5gEVSIKOYYaUofAJd3eL4KPK50vxBgswd8rQNuemlBOP3lPi+D92mL0/nfFnhoi6gxDDalD0OZ7CMNKTUtPjb9S41TM1Fnbykwop58CA5TFqPeOh0u6iagTDDWkDp2FmnDZp8a3+slgbj2mkEDW/txLoRtXYFXGYvCGGi7pJqLOMNSQOgTuUwO0TkMpJBiclH/6KaL9MZk52i7pDmFPTWD/TIRJH/L7J6LwwlBD6uAPLy1hJuymn3yNwpbWYwo5VULbSk1Ip58C7tts8P5OWakhos4oItR89dVXmDp1KtLT0yFJEj788MOgy4UQyM/PR3p6OiIiIjBhwgTs3LlTnsGSMqmlp0aBlRo596nxVWp0EmDUs1GYiLqmiFDT0NCA4cOHY8mSJR1evmjRIixevBhLlixBQUEBbDYbJk+ejLq6uhCPlJSr7fSTL9SEyRugf/rJ3P6YzNqde0mG6SeDXgeDXgr5/RNReDHIPQAAyMvLQ15eXoeXCSHwzDPPYN68eZg2bRoAYPny5UhNTcWKFStw1113hXKopFSdLukOk1Djm2rSm7yBTHiUE2pcbfepCf30k1EnwaDz/k45/UREnVFEpaYrRUVFKCsrw5QpU/zHzGYzxo8fj02bNnX6c3a7HbW1tUEfpGJtQ024Ngrr9IDOEHxMZm03u5OjUqPXSTDovP9dhfqEmkQUPhQfasrKygAAqampQcdTU1P9l3Vk4cKFsFqt/o/MzMxeHSfJrN3qpzDtqdEbAZ3R+7VCGoUdbXcUDuEJLX39M8aA6Sc396khok4oPtT4SIHn84F3WqrtsUBz585FTU2N/6O4uLi3h0hy6izUhMs+Nb7VTzpDQKXG3fn1Q6j9PjWhe059VSF9wPRTKKe/iCi8KKKnpis2mw2At2KTlpbmP15eXt6uehPIbDbDbDZ3ejmpTLvVT+E6/WTwTkEFHpNZ2xDRtnLTm3z9M95KDZd0E1HXFF+pyc7Ohs1mw+rVq/3HHA4HNmzYgHHjxsk4MlKUcN+nxh1QqdG3TD95lDH95KuWRPhOUyDDaRIM+tZKDc/STUSdUUSlpr6+Hj/99JP/+6KiIhQWFiIhIQF9+/bF7NmzsWDBAuTk5CAnJwcLFixAZGQkbr75ZhlHTYrS6T41YfJXvW+qKWj6SSmVGu9zG2nSo8npluU0CXqd5K/UcPqJiDqjiFDz3XffYeLEif7v58yZAwCYMWMGXnvtNTz00ENoamrCzJkzUVVVhTFjxmDVqlWIiYmRa8ikOOHeKNwSYPTG1lDjVkao8QWLCJMeaAjt9JOvf8eo03FJNxGdlCJCzYQJEyC6+ItakiTk5+cjPz8/dIOi8NK2UoNw66npqFFYGaEmsFIDhHZH3+Al3S2Nwlz9RESdUHxPDVG3tNunJtymn5S7T43TX6kxtHwfyumnls339K3TT25OPxFRJxhqSB0623wvbJZ0+3pqjIptFI40hv4s2b5AZdDrAio1YfI7JaKQY6ghdQj3zfcCVz/5l3QrZJ+alhARZfaFmtCFCnfg9JOeq5+IqGsMNaQO/mmmcD9NgvJ6ahwtOwjLMv3kCZh+YqMwEZ0EQw2pQ6dLusMs1OgNijtNgi9Y+KafQtoo7F/SreOSbiI6KYYaUonOpp/C5A1QwZUaZ+CSboR6SXdHZ+kOk6BKRCHHUEPqEPZLun2hxuit1gCK6alpu6RbnkZhnqWbiE6OoYbUodMl3WESatwd7VOjjOknOfep8fXPGHQBZ+nm9BMRdYKhhtRBLT01CtynxtVmn5pQTj/5AlXguZ+4+R4RdYahhtShsyXd4bZPTdBpEuSv1Agh/Eu6Wys1oT9Ld+C5n0JZKSKi8MJQQ+rQrlLT5rjSdXiaBPl7agJXGrX21IT+NAk89xMRdQdDDalD2/DC1U89IrApOEKWHYUDpp9aempCef9EFF4Yakgdwn1HYf9pEgyKOk1C4FRPlDn0m++1NgpLMLasfmKlhog6w1BDKhHm+9R0eJoE+Ss1gU3BFmPoN78LPPeTnud+IqKTYKghdVDLPjV6Y+uOwgroqfFtfmfS62D07+gbykpN++knnvuJiDrDUEPqEO771HTUKKyA1U9OV+vmd0YZTlPgr9ToWjffc7FSQ0SdYKghdehsn5pwW9KtsH1qnP4TSupglKFR11cpCtx8j5UaIuqMQe4BEPWIsG8U7ug0CQqo1Lhbz5Jt9O8TE/pG4QsP/x1Zh49Cwi2haRT2eAAd/+YjCjf8V0vq0K5SE2Y9NR2eJkEBPTUt0z9GvTxnyfbel8C5R15HavFn6C+V9v79r1sIPNkfOHGgd++HiHocQw2pgz+8hGtPjTL3qXEE7BPjm35yuD0QIVpV5vYIWOCAQTgAAHGo7/1Kzb4vgKYq4PCW3r0fIupxDDWkDp1WasKsp0ZvaF39pIBG4cBKjUnf+t9FqPaKcbo9iEO9/3ur1ND7535qqgr+TERhg6GGVMLXU9O2UhMuoUaZ+9T4e2p0rdNP3uOheV5dbgGr1OD/3oqG3j/3E0MNUdhiqCF1EG1CTbjuU6MzBuwoLH9PjT/UGFqnn4DQnSnb5RGIQ0CokRp6t0rkcQPNNd6vGWqIwg5DDalDZ0u6wy7UBPbUyD/91LpPjM5/mgIAcLpCFWo8iJNap5/ipPreXVLuCzQAQw1RGGKoIXXobEl3uOxT4/aFGmXtU+Nbvm3S66DTSa2nKgjR9JPbIxDbZvqpVys1gUGGoYYo7DDUkDqE+5LuoNMkKGdH4cDVTwBCvgFf20bhWKmhd++boYYorDHUkDqE/ZJuZe9TM9q+BXglD9m64wBCF2rcHhE0/WRFQ++eJoGhhiisMdSQOoRzT43H0zpOhe1T4wsvkxo+AQ5vwmRdAYDQnX/J6RawBjQKx0kMNUTUOYYaUonOTpMQBj01IqAiozMErH6Sf/rJ2RIgrJ5qAECy5G2kdYS0Ubjtku4QTT811yiiWkZE3cdQQ+rQtlLT9riSBfbOBO1TI/8bqm+VU6zb+2afBG+oCdX0k8stYG2z+Z5HAJ7eqtYEVWdE8GooIlI8hhpSB3+oCcOemsBpJr2xdUdhBUw/ec+SLVpDjVTdcjxEm+952m++B4jeu/+2U06cgiIKKww1pA5tN98Lp+mnwPAS2FOjgNVPTrdALBphEN6xJIiWSk2Ipp/cHhG0+sksOWGBo/eWdbcLNdW9cz9E1CsYakgdwnmfmsBQI+kU1yicJLVOwcSLau/xUJ77KaBSA3irNb22ozErNURhjaGG1CGc96kJPEWCJHlPahl4XEZOt8ffRwMAVlEDCZ6QVWo8LhdipUYAgJC8vUZWqRfP/8RQQxTWGGpIHcJ5n5rAUyQEflZAqHG5RVClRg8P4tHLpyoIEOFprdJI1j4AfHvV9HKlJio5+HsiCgsMNaQO4bxPjTtg473AzwoINY42008AkCTVhGz6KcpTCwDwGKOBqBQAIarUJPQP/p6IwgJDDalEGO9T41u67Zt28q1+UkSjcCehJkTTT1Eeb5Owx2IFIuIAeE9q2SuNwh4PQw1RmGOoIXVot09NOPXUtK3UKGefGpdbIAm1QceSUBOy6Sd/pcYSD1jiALQ0CvfG/TvqWl8vDDXtbDtUhQlPrsPX+47LPRSiTjHUkDqoYZ8aX4VGr5x9ajqafkoO4fRTjPBWaoQlzl+pie2tUyX4AowhAohJCz5GePe7YhysbMTbW4vlHgpRpxhqSB06W/0UTku62/XUyD/9FNQobM0EELrpJyEEoltCDSxxQES8dxjopZ4aX4CJiPffF0NNq/+W1QEAdpfVnuSaRPJhqCF18L3HhWWjsC/UtEw7KahROGhJd+pQAN7pp15bfRQgaOO9iNbppzipvnfuP5Sh5uungFeuCJvQ5PEI7DvmDTUHKxrQ5JB/apSoIww1pA7tpp98PTVhVKnxTTv5dxRWQqgRSJJa/jL3hRqpBs7eWn0UwOUR/o33pMh4//STd0l3GFdqPB7gm2eAw98Cez7r+dvvBUerm9DQEmQ8AthXXifziIg6xlBD6sB9anqFztmASMnu/SYg1ITiLN2B532SAio1vbak2x9q4oJDTU8H4+P/BewtQfHwtz17273EN/Xk/76UoYaUiaGGVCKcl3T7Vj8pb/opylUJAHDpLUB8NgAgSaoNyfSTy+3xn6Fb165S09vTT977gnC3BpCeUryl9evDWzq/noLsadNHw74aUiqGGlKHsF7S3dKf0Hb1k3DLHsqiHN43eoc5EYj2bn6XiBo4Xb3fU+GdfgoMNS2Nwr1Wqan2fo6IB4wR3lVQQM9PQRVvbf26Yg/QUNmzt98L9hzz/h4GpkQDYKWGlIuhhtQhnJd0t9tRWN96mczVmmj3CQCAw5LkP3WASXLD4Kjp6sd6hMstYEUH009ogMvdC6EqsFIT+LnHQ01Ldcb3Gi1WfrXGV6m5ZkQ6AG+lRoRDFZQ0h6GG1CGcT5PQrlHY2P4ymcS4vKHGGZEEGMxo1scAAMz2il6/b5cn4AzdAVNCRskN4Wjo/AdPVyhCTUMFcGK/9+uzr/J+Lt7cc7ffCxwuDw4c9z7fV56TDr1OQnWjE8dq7Wd+4z+uBPavO/PbIWrBUEPqIDrpqQmrfWra9NQAsp8qIdZd7R1GRBIAoMmUAACwNJ/o9ft2uVp7arxTQpFwwfvcSM29UCkKRag5UuD9nHw2cFae9+vDyg41+4/Xw+URGGM5hH7rZmFa3E8AeqCv5sf3gfd+Bbw1HSj5/swHKgSw5lHg2RFAccEZ3IzA8+v346In1uLLXcfOfFwUUgw1pA6dbb4XTpWatqufAi+TSYzb+4buivBOPTWZEgEAEc7e7wNxOxphlloef0QcIEmo13krRTp7dc/fYbtQExd8vCf4ppoyRgN9L/B+XfI94GzuufvoYXuP1WGIdBAvS49B2vkBHm/MxzW6b86sr6bmKPDv33m/9riAlb8BnE1nNtCCl7z7/1QVecNSYzeDt8ftbdgu+xFCCDz2yW488fl/caSqCbPfKcSB4/WA24XyowdRuP8o9pTVobI+uErl8YgOp+Nqmpz4YmcZik80ntljCwUhuvwjyuX2hMWUo+HkVyFSOCEQsPtey6dwDDW+6afAnhp5NzmL81R7hxHpDTXNZm+oiXT2fqVGtIQJF/QwmLwNqg26aMR5qqBrru75O+xOpaZiH1BfDthy0SBFotHhhtPtgS3WAp1OCr49IQBHPapcZvyj4DDsTg9u3PkV0gB8Yx+Akv0GXBeZAn1jOXD0O6DfRR2Pq3w3sPdzABJgimr9cDYD1YcAZxOcZ1+NguYMVB/+EWn7VsAelY6mEbfDIZmw+UAlTpyowm+SfsCQ2q8hRSaiOWU4iiPOxl70xYkGB5Irv0Ni3W40x52F5vTzcbBOj/+WVCNVqkTUid14w7TIu7tzRDz0TVV4xrQUa7cVozbjXsT2GwnUHoFoqsEh2LDrBDDY6kQ/xz402+3YXOJBXUM9hhlLkSqdwHERh8j9nyCluQaNicNgaCyHqWIv9r7yG8SfOw3J+no0HPgWjkNbIZx2NAsD6s02iKxxSM0ciMhj/4Guaj+q0y/GvvRroDNFoW/FV7B98XtIABz6KJhqilH6xh34ts+vYC7ZgniDA32SE5AUqYezvgKe5jroTVEw6ARMez+BsaEEAFBkGICE5qFYYKhDP1MdYlwVsC6tgUfUIAUeRAsz/uUei3WeERid0IgR0TWoratFdV0D3IZIxCbakJSQgEiLGeWNHny6rwllDgtqEI2crEwMSjRAqi9HvKMEmc6DsLpPoNSUhUP6LES5a5HqPIJkRzGSHcUwe5rQGNkHzTH9UBI1GAcsQxCl9yANx5Gga0SMwQW9wYRyUwaO6dMRaxKIkZqx93AJdh0sQZKnHBdZK5FlrIbeYIIwRqAxKhPVkdlobGqAOHEQkQ3FsDYdQURzGYyOOuiEE3WxOThmuwTlqZegIn4Efqqwo/jHr5FQ+T2MkhtGnYSkaCP6WM2I0zXB2FgGCRIsZ01C9thrYLSm9dS/yNPCUEPhL/Cvh7Bc0t2mUiNJ3q89LtlPleALNaKlSdhh8YYae3UZjlQ1IiM+EnA5gMZK73glHRBjA3R6NDvdWLp+P/Yfr0dqjAX9kiJxxVAbUsxOwBgF6HSAyw6U7wJM0UBSDoQQkISAKNqAqA3LAAC1iEZCS0ht0scALkAq+Q8q99hQZuyLA3U69BFlGHHoNXgq9mKnpx9+aEzABZFH0d9dhJqYHLzvuQSN1gG47SyBaOcJbNh9BN8dPIEm60Ak9z8HOY3bMamhEnoAO6p0iDTUw1FjwGAAZRvfwo6dJchp2o5+tdsAAB5IKPZkYKNnGAo9A3CJaQ+u0G+FBzp87xmIRphxseG/iHFWoAEpSHcPRBSakajbDkjA/O+jsP8/OxBt7Ief6cvhee0qVJgzUWfpgyZzImrdZlTWNyPDvh8j8d+T/p6M3yxGqicN43Sl/mPFe9/ER55xuEg6jDG63Yguaq0GWfAGcgBkCiOcMCBGaq2SuIUEF/StVTIAkIDK2CFI/O1nOPzho+i752VMqvsX8Oa/Aq+CfgDiRJS/FyoCwMQ2Y41q+dwozLiy5FfoK5VjuekJDCr9GPjkY/91ogJ/yH4A2LEJ2NF6KOnAGljE4xCQ/ON/330xXrVfjpWm+UgrXYNppWtaf+Bw589frYiEGQ70d+3HTENLz5MH3rmMlv9CPEJCpGTHDYb1uAHrgXrANzsKXcv1j7d8ADgbwCUAYGq5TmnLRxuDOh8WompOADU7kIl/YUwn10kEMDjg+xwAV/q+qQ++bmzLR1diavchpnYfBu59GbUiEqNgQbp0Agho9UNjy0egzauAzf+L7X1uxPA7/36Se+k9DDWkAoGhpu3qpzAINe42+9QAraHG7QTs9d6/zCWp458P1FDprSw4GyGcjaiurUFzYwNSzG7oXQ3eKkNDBUT6SJRlXYVVuyuxtmA70qu24rKUegy3NmI/MvDBib6I0btwh6fM+24V5e2pSUjJAA4DE+zrUPTMFYiIqkd80yHoROsboFMywhWbhYMNRoy1SxiEWOzz9EGV5MGJz75Diq4YLsmIOkMCYlyVMLT87DbdMHzjGIRpho3IxDH4/t77wZCLCS1fN+m9/yVffPBvwMG/IU5IMIp09JdKoZM80AEYjm8xHABaCiwJZdtxJ97zfvMf76dJLR9oADxHJegk7+ukXlgw/fV9sOMQrtZF4FkTYLMXwXasyPurEhKOIR7p0gmcrSvG2bqAkzu2FNUmoKWfo+XXmoFyZOjL/Vc7ZszA4JxzEVfrwJvFkzFS9xPSpBNIsR9Gir39O69L6LDBMxzViEYE7IhCMyKlZjiFAUdEMiKlZlyu+w4DdKXwQMKemLGwNe1Fpus47tF95L+dg8KG91wXwyI5MFzaj+H6IsRKDbDAiVp9PA5EDEN60z6kuMugh6vlIelxGGkoFAMx+vrngIg42H7xF7z61mD0PfwRxrm2IEJyoEmYUA8LkqVaf6A54LGhARYk6ptgMBiw152O/Y449DXVI91Yj4/NU9HQ1A8HTQPwvukOjKpfiyq7hAZhwQ7RHzVJ5yIlOQWJFgFD5R5Yy7ciylGB7Z7+KBFJuN6wAQMkb4WlARask87HhxkP4uwEK94tm4VbKv+KJl0USqwjUeqJR01tDZpdAnU6Kxz6KOjczdC7m7HHNBT74i/G4AQ9rjFsxFmGMsQk9gFiUrGnIQoPr62ENTkTv8k7H6MN+4Ftr8FZuhNHpVT85ExCnDUeWSlWNDXUouJYCeyNdXC4nDAJJwbEupFsaIS7oQruxiq4JBOaTIlosKSi1NQPJ3QJyHAeQoq9CE2mBFRZ+qLSnIkKcyZq3CboaooR13AAg9170M+xF3bJgnJdMirc0ah1G2D02JGjL0OaKIcdRjQIC5yGaETEWNFoTMTGmmQU1sdCDw+i0YT++mM4W18Kj8GCanMfnDCl46hkwxGRhAZdDDySHkOdO3CufStG2r9DrKcWsWiEUx8Jd7/xEJZYuNwCVY0uVDY40CBFwh1lg6upDrbyrzAU+1EbmdXR/0whI4lwmCTrAbW1tbBaraipqUFs7MmyKoUVtxP4k/dNF78/5O2F+PKPwDeLgTG/BfIe7/ZN1R87ANfuT2At+xZSbSkw6lfAiP8BdDp4PAKSqwlSfRlQWwrUlQLORmBQHhCdDCEE9h+vx+ETjTjR4ERZTRMOlpbDdfwnDDSUY6DhOGwmO5IiAIPHjvqGBjS7JaQaGpF8dDVqB16NDbmPY195PX67aTwiRCPqLGmIaS6FSzLgBOLQZE5CbFIfOIQepZVVaHC44TLHI9JsQv/mnUhs7uLP0TYOeVJwSKTiQt2P0Etd/zdw6NbNyBowGNj1EfDPX7a73CV0cEMPHTwwSqc2ZVYlohGDRhik1qnCGhGJz8Q4HEr/GcZP/jkuGOCtFO3b8DYiv/4zhMsBg3DAJrVODa1zD8dnnvMxNqoUw6OqsKnOhi2NabjYsAs/N2yGydOEEpGIMpEAt86EvnFmJNTvgdlVj0ZdNP5jnYx/W67El8fjUdPkwMjMeFyVXIb+DduRVLcb5YY0rLJcAXtkGiZnSbjQuBeRxV8BR7ehMuZsbIyYAMkYhXN1e2FvasA75Rn4V1kc5gxrwrWp5TBExgNJOUCf8wCztzeoptGJ/xRXobr8CFC2A8aGMpjslYjWOZAcG4GYuGSU981DpZSI2mYnapuc0OkkRJkMqGp04MejtahudGDaIAOmRO6FMeM8IGkg4GgAtrzgnS5LGw5kno/SqMH4oLAEydFmjBuYhD5WC3DiAOCoB1JzvZUzAKgr8/6bMkYAFis8kvdv33bTawBq62pRXlGJGskKSBKGJgCWhiOoj+iDraVOJESZMTzDCqklkDvdHhj1nbdyHq+z48eSGuT2sSIp2tzuco9HwOH2wO0RiDRKkEq+BwwWIGVw8B8FAFB3DIhMBPTe8Qsh4PYIGALuXwjhH1tnunMdJWtyuOERApIERBj13X8sHre336u5Bsga5309dMHtESjcvQeZyfFISUntgZG3OpX377AKNUuXLsWTTz6J0tJSDB06FM888wwuvvjibv0sQ418PB4Bjwj+z8RPCO+28Xs+81YmzrvNu8lbbSmav38bJnMkdEkDgLSRQFRi8M+6HEDlPtglC8xLzwUArL3mO5ii4mH+6jGMLn4FFaY+0Ol0qDGn4dvkX2Bf7FhYDU6kSjUYbDqGvtIxOCQLKp1GOHd8iNzar9q9wf8o5aDCE4PBOIBUqbrdQ2iWzPgy+moU1scjzlmGTOk4MqTj6CuVI9l3hutuWOm+CHOcMwEA/zH/BglS/Ul+oj2PkFCHCDTBjCZhQjPMsEtmNHhMaIIJFcKKRlhwtX4jEqXWRs/axOHY7uiD7dUWnB9xBOeIPXDpIrBbn4P98Rfhhjt+7/3P0OMGfloDd30FNhdVYNtxPb6sTEKpSMCN5/fFhf3j8f66LSgt2omcOAmzLs5EkqfCu8mcswmVtkuwzn0OXPZGmJqOoUafiEqDDWm6Skyo+RCJTYdQkzUZ5VlXYWB6CiJM+s4fq0dA13AMOLoN7ph0FLr6weHyYEx2AnQ6CW6PwI9Ha9AnPgJJETq43W68/8Nx7DtWhzsv6Y+UGIv3PEy1R7178BgtwbfdwZv4qQr3N0QiJVBlqHnnnXdw6623YunSpbjwwgvx97//HS+99BJ27dqFvn37nvTntRhqnC1/0ViMnb8xQAhvmNAbIYRARVUNqo/uRUS0Fcl9+sFsMnv/43c1eVcnuJ3e0KHTAy4HXEe/x5Hj1djWmIJiRxQGpkQjJ9EC09FNMP70BY5XHEdRlRPVLjN01j5ITE6BzdCARFEFa0MRomv2wNxY5h9Os2TBdvMojGjeAjNa+0nckgF74sfjQNRIRFbvQUbjf5HtPggjgntOhja/jAZE4HeG93CfYWW7h+sW0kmrEps9g7HBPRwAMMvwIaKl4JUpTcKEMhGPcsQjFo0YrOu6OuIwxaM2si/Kjekoc0ahrBFoFkbERkfDqmtGStU2pLuP4nHcjgOpkzEoJQbTmlcitboQ66TR+MIxHOdnRmJMsgs/HdiPn4r2I0IPjMi2YXBaNBqqytFQX4uDphzsNg1DbFwSBqbGICclGtlJUTDpdThQUY99x+ohSYBRr0OfKIEBJR/D6GoAhlwNJPTv8jGcquITjbBZLV3+VU5E1B2qDDVjxozBueeei+eff95/bPDgwbjmmmuwcOHCk/58KEPNkW2fw+l0wikkONyAQwAONxAdn4phw0cDADZ//haEvR56SUAHAbvThWaHE5FGHeIi9DDqAIfTBU9zLUx1xYhoOIrYpiOIbi6FwxCNWksfVEZm40jUUJwwZyJO1CDGVYmm+jrUN9ajpMmIvU0xaBJG5EQ7MTCyAenOw0h2HgVMUdBFJ8PQWI642j2IEg2oQizqhRnpqPC/6buFBCcMsEjBwcEBI6qMNsQ7j8EEh/94vbDAAQNMcLULAl2xCyM2eoYiUarFcN0B//FtnhxUilgMkEowQNdBhx2AWhGBSNhhkDyo1ifhl9aXUWMXyEs8htur/orj0YOwM/J8ZNb/gHMrPobZ7Z3vd0hmFEvp+MmVDIvOjSR9A+piBiJ24r3oN3gUth2qwt5j9cgyVmPIsY9hiY6Drs+5cCWchQYpEvUONxodbtQ3OxF96Etk/LQCEWYjYlL7Q5+QBcRlAXF9vWHBtzS4C40OV7dLwy63B5IkQd8DlQQiIqVTXahxOByIjIzEu+++i2uvvdZ//L777kNhYSE2bNjQ7mfsdjvs9ta9BGpra5GZmRmSUFM7Pw2xUvt9Cb6PuggjH/wEAFCWPxA2X5u8wtQhEmbhgElqv0dK20pHpYhBIyLRRyqHLqBh9wRi8a3xAnjiszHUFokEXSNqyw/DUX8CJ0QMjrljcQg2/CQyUBs/BOf074OByVFIPvI5Uo5thHvodKSccxkOVTZh26ETkI7twJDSD5HoOILmhLPhTB2Bffoc7G5OwIj0CFxhq4MxLqP9FFUgZ7N3lU5EHGCM7F7jLRERyepUQk1YrH6qqKiA2+1Gampw81FqairKyso6/JmFCxfij3/8YyiG184hQxYsnkboIaCThL8aI6Jt/uuUWofjhL0SHgF4oINOp4dOr4PTDTS5BNxCgk6vg0dvQY0pDTWWPqgwpuG4PgXRaESquxSZ9v3IatqFOEcZavUJqDYkQmeJQWREJOL1jYh1HAdczajTxaAKVtRGZaMmsi+qauvQVFUGj9mK2Oxzkdm3P+I8VYhGA+IyBiPGaoMQHpwoP4qGxiY49WZ49BEwR0RBeASKD+5BZfFemBL6YODgkeifHAOdq8nbONuykichcSCu1Ae/vOK68+QN/zWAX/u/zc0wITfDCiAbwM+Dr3qqvxijBbD2OdWfIiKiMBEWlZqSkhL06dMHmzZtwtixY/3HH3vsMbzxxhv473/b7+MgZ6WGiIiIeobqKjVJSUnQ6/XtqjLl5eXtqjc+ZrMZZnP7JYFERESkTmGxNMFkMuG8887D6tWrg46vXr0a48aNk2lUREREpCRhUakBgDlz5uDWW2/FqFGjMHbsWLz44os4fPgw7r77brmHRkRERAoQNqHmhhtuQGVlJR599FGUlpZi2LBh+PTTT5GVJe+WzERERKQMYdEo3BO0uPkeERFRuDuV9++w6KkhIiIiOhmGGiIiIlIFhhoiIiJSBYYaIiIiUgWGGiIiIlIFhhoiIiJSBYYaIiIiUgWGGiIiIlIFhhoiIiJShbA5TcKZ8m2cXFtbK/NIiIiIqLt879vdOQGCZkJNXV0dACAzM1PmkRAREdGpqqurg9Vq7fI6mjn3k8fjQUlJCWJiYlBXV4fMzEwUFxfzPFAhVFtby+ddBnze5cPnXh583uXTG8+9EAJ1dXVIT0+HTtd114xmKjU6nQ4ZGRkAAEmSAACxsbF8wcuAz7s8+LzLh8+9PPi8y6enn/uTVWh82ChMREREqsBQQ0RERKqgyVBjNpsxf/58mM1muYeiKXze5cHnXT587uXB510+cj/3mmkUJiIiInXTZKWGiIiI1IehhoiIiFSBoYaIiIhUgaGGiIiIVEFzoWbp0qXIzs6GxWLBeeedh6+//lruIalefn4+JEkK+rDZbHIPS3W++uorTJ06Fenp6ZAkCR9++GHQ5UII5OfnIz09HREREZgwYQJ27twpz2BV5GTP+2233dbu9X/BBRfIM1gVWbhwIUaPHo2YmBikpKTgmmuuwZ49e4Kuw9d87+jOcy/X615Toeadd97B7NmzMW/ePHz//fe4+OKLkZeXh8OHD8s9NNUbOnQoSktL/R87duyQe0iq09DQgOHDh2PJkiUdXr5o0SIsXrwYS5YsQUFBAWw2GyZPnuw/LxqdnpM97wBwxRVXBL3+P/300xCOUJ02bNiAWbNmYfPmzVi9ejVcLhemTJmChoYG/3X4mu8d3XnuAZle90JDzj//fHH33XcHHTv77LPF//7v/8o0Im2YP3++GD58uNzD0BQA4oMPPvB/7/F4hM1mE48//rj/WHNzs7BareKFF16QYYTq1PZ5F0KIGTNmiKuvvlqW8WhJeXm5ACA2bNgghOBrPpTaPvdCyPe610ylxuFwYNu2bZgyZUrQ8SlTpmDTpk0yjUo79u3bh/T0dGRnZ+PGG2/EgQMH5B6SphQVFaGsrCzo9W82mzF+/Hi+/kNg/fr1SElJwaBBg3DnnXeivLxc7iGpTk1NDQAgISEBAF/zodT2ufeR43WvmVBTUVEBt9uN1NTUoOOpqakoKyuTaVTaMGbMGLz++uv44osvsGzZMpSVlWHcuHGorKyUe2ia4XuN8/Ufenl5eXjrrbewdu1aPPXUUygoKMCkSZNgt9vlHppqCCEwZ84cXHTRRRg2bBgAvuZDpaPnHpDvda+Zs3T7+M7Q7SOEaHeMelZeXp7/69zcXIwdOxYDBgzA8uXLMWfOHBlHpj18/YfeDTfc4P962LBhGDVqFLKysvDJJ59g2rRpMo5MPe655x788MMP+Oabb9pdxtd87+rsuZfrda+ZSk1SUhL0en27hF5eXt4uyVPvioqKQm5uLvbt2yf3UDTDt9qMr3/5paWlISsri6//HnLvvffi448/xrp165CRkeE/ztd87+vsue9IqF73mgk1JpMJ5513HlavXh10fPXq1Rg3bpxMo9Imu92O3bt3Iy0tTe6haEZ2djZsNlvQ69/hcGDDhg18/YdYZWUliouL+fo/Q0II3HPPPVi5ciXWrl2L7OzsoMv5mu89J3vuOxKq172mpp/mzJmDW2+9FaNGjcLYsWPx4osv4vDhw7j77rvlHpqqPfDAA5g6dSr69u2L8vJy/PnPf0ZtbS1mzJgh99BUpb6+Hj/99JP/+6KiIhQWFiIhIQF9+/bF7NmzsWDBAuTk5CAnJwcLFixAZGQkbr75ZhlHHf66et4TEhKQn5+P6667DmlpaTh48CD+8Ic/ICkpCddee62Mow5/s2bNwooVK/DRRx8hJibGX5GxWq2IiIiAJEl8zfeSkz339fX18r3uQ77eSmbPPfecyMrKEiaTSZx77rlBS9Cod9xwww0iLS1NGI1GkZ6eLqZNmyZ27twp97BUZ926dQJAu48ZM2YIIbxLXOfPny9sNpswm83ikksuETt27JB30CrQ1fPe2NgopkyZIpKTk4XRaBR9+/YVM2bMEIcPH5Z72GGvo+ccgHj11Vf91+Frvnec7LmX83UvtQyQiIiIKKxppqeGiIiI1I2hhoiIiFSBoYaIiIhUgaGGiIiIVIGhhoiIiFSBoYaIiIhUgaGGiIiIVIGhhoiIiFSBoYaIwtr999+PqVOnyj0MIlIAhhoiCmuFhYUYMWKE3MMgIgVgqCGisLZ9+3aMHDlS7mEQkQIw1BBR2CouLkZlZaW/UlNdXY2pU6di3LhxKC0tlXdwRBRyDDVEFLYKCwthtVqRnZ2NHTt2YPTo0UhLS8P69euRlpYm9/CIKMQYaogobBUWFmL48OH4xz/+gUsuuQQPPPAAXnzxRZhMJrmHRkQykIQQQu5BEBGdjuuuuw7r1q0DAPz73//GuHHjZB4REcmJlRoiCluFhYW47rrr0NzcjOrqarmHQ0QyY6WGiMJSXV0drFYrtm3bhu3bt+O+++7Dpk2bMHToULmHRkQyMcg9ACKi01FYWAi9Xo8hQ4Zg5MiR2LlzJ6ZOnYqtW7ciKSlJ7uERkQw4/UREYWn79u04++yzYTabAQBPPPEEhgwZgmnTpsHhcMg8OiKSA6efiIiISBVYqSEiIiJVYKghIiIiVWCoISIiIlVgqCEiIiJVYKghIiIiVWCoISIiIlVgqCEiIiJVYKghIiIiVWCoISIiIlVgqCEiIiJVYKghIiIiVWCoISIiIlX4/zrR78bfU74iAAAAAElFTkSuQmCC", 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" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "sf = freud.diffraction.StaticStructureFactorDirect(bins=200, k_max=25, k_min=1)\n", "fcc_system = freud.data.UnitCell.fcc().generate_system(10, sigma_noise=0.10)\n", "sf.compute(fcc_system)\n", "plt.plot(sf.bin_centers, sf.S_k, label=\"fcc\")\n", "\n", "sc_system = freud.data.UnitCell.sc().generate_system(10, sigma_noise=0.10)\n", "sf.compute(sc_system)\n", "plt.plot(sf.bin_centers, sf.S_k, label=\"sc\")\n", "\n", "plt.title(\"Static Structure Factor\")\n", "plt.xlabel(\"$k$\")\n", "plt.ylabel(\"$S(k)$\")\n", "plt.legend()\n", "plt.show()" ] }, { "cell_type": "markdown", "metadata": { "tags": [] }, "source": [ "## Calculation of Partial Structure Factors\n", "\n", "Both methods support calculation of partial structure factors according to [Faber-Ziman decomposition](https://freud.readthedocs.io/en/latest/modules/diffraction.html#freud.diffraction.StaticStructureFactorDirect). In the conventions adopted in **freud**, the summation of partials reproduces the total scattering. In this example we load a simulation trajectory of $\\text{GeS}_2$ and calculate the Ge-Ge partial, the S-S partial and the mixed Ge-S partial (which is the same as S-Ge partial). The calculation of the partials requires the usage of `query_points` and `N_total` parameters for the compute method." ] }, { "cell_type": "code", "execution_count": 3, "metadata": {}, "outputs": [ { "data": { "image/png": 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" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "import freud\n", "import matplotlib.pyplot as plt\n", "import numpy as np\n", "\n", "# read in xyz file\n", "# read number of particles\n", "N_particles = int(np.genfromtxt(\"data/ges2.xyz\", max_rows=1, dtype=int))\n", "cleaned_data = []\n", "# remove lines that don't contain particle data\n", "with open(\"data/ges2.xyz\") as f:\n", " for line in f:\n", " if line[0] != \"\\n\" and line[0] != \" \":\n", " cleaned_data.append(line)\n", "\n", "positions = np.genfromtxt(cleaned_data)[:, 1:4].reshape(-1, N_particles, 3)\n", "particle_types = np.genfromtxt(cleaned_data, dtype=str)[:, 0].reshape(-1, N_particles)\n", "\n", "box = freud.Box.cube(19.21)\n", "\n", "# max_k_points is the number of k-points used in the calculation,\n", "# higher values give better S(k) but takes longer\n", "k_max = 15\n", "k_min = 1\n", "bins = 50\n", "sfGe_Ge = freud.diffraction.StaticStructureFactorDirect(\n", " bins=bins, k_max=k_max, k_min=k_min\n", ")\n", "sfGe_S = freud.diffraction.StaticStructureFactorDirect(\n", " bins=bins, k_max=k_max, k_min=k_min\n", ")\n", "sfS_S = freud.diffraction.StaticStructureFactorDirect(\n", " bins=bins, k_max=k_max, k_min=k_min\n", ")\n", "sfTotal = freud.diffraction.StaticStructureFactorDirect(\n", " bins=bins, k_max=k_max, k_min=k_min\n", ")\n", "\n", "for frame_positions, frame_types in zip(positions, particle_types):\n", " Ge_positions = frame_positions[frame_types == \"Ge\"]\n", " S_positions = frame_positions[frame_types == \"S\"]\n", " sfGe_Ge.compute(\n", " (box, Ge_positions),\n", " query_points=Ge_positions,\n", " N_total=N_particles,\n", " reset=False,\n", " )\n", " sfGe_S.compute(\n", " (box, S_positions),\n", " query_points=Ge_positions,\n", " N_total=N_particles,\n", " reset=False,\n", " )\n", " sfS_S.compute(\n", " (box, S_positions),\n", " query_points=S_positions,\n", " N_total=N_particles,\n", " reset=False,\n", " )\n", " sfTotal.compute(\n", " (box, frame_positions),\n", " reset=False,\n", " )\n", "\n", "plt.plot(sfS_S.bin_centers, sfS_S.S_k, label=\"S-S partial\")\n", "plt.plot(sfGe_S.bin_centers, sfGe_S.S_k, label=\"Ge-S partial\")\n", "plt.plot(sfGe_Ge.bin_centers, sfGe_Ge.S_k, label=\"Ge-Ge partial\")\n", "\n", "# Note that the Ge-S partial must be included twice\n", "S_tot = sfS_S.S_k + 2 * sfGe_S.S_k + sfGe_Ge.S_k\n", "assert np.allclose(S_tot, sfTotal.S_k, atol=1e-5, rtol=1e-5)\n", "\n", "plt.plot(sfGe_Ge.bin_centers, S_tot, label=\"Total\")\n", "plt.title(\"Static Structure Factor\")\n", "plt.xlabel(\"$k$\")\n", "plt.ylabel(\"$S(k)$\")\n", "plt.legend(loc=\"upper right\")\n", "plt.show()" ] } ], "metadata": { "interpreter": { "hash": "1c5ea5ec1f260001eb9a4e66a3ab43a0f997dbe5fe2d97f8292a6d25178f0968" }, "kernelspec": { "display_name": "Python 3 (ipykernel)", "language": "python", "name": "python3" }, "language_info": { "codemirror_mode": { "name": "ipython", "version": 3 }, "file_extension": ".py", "mimetype": "text/x-python", "name": "python", "nbconvert_exporter": "python", "pygments_lexer": "ipython3", "version": "3.10.13" } }, "nbformat": 4, "nbformat_minor": 4 }