{ "cells": [ { "cell_type": "markdown", "id": "9b7b0fd4", "metadata": { "tags": [] }, "source": [ "# 熱膨張率の理論計算\n", "\n", " これまでの説明では、原子間ポテンシャルの温度変化が無視されていたが、実際には温度によって変化する。\n", " \n", " より精密に熱膨張を計算するには、この温度変化を考慮する必要がある。\n", " \n", "\n", "\n", " \n", " この温度変化した原子間ポテンシャルの極小値から、平衡原子間距離$r(T)$と **ヘルムホルツ自由エネルギー $F(T)$** が求められる。\n", " \n", " 原子間ポテンシャルの温度変化は格子振動の効果によって現れる。格子振動の効果を計算によって求めるには、\n", " \n", "* 原子間に働く力 ``ダイナミカルマトリックス``を求める。\n", "* ``ダイナミカルマトリックス``を対角化し、固有値 $\\omega(k)$ (``フォノン分散``)を得る。\n", "* ``フォノン分散``を波数空間で積分し、 ``フォノンDOS`` を得る。\n", "* ``フォノンDOS`` とボース分布関数から、有限温度における格子振動状態を見積もる。\n", "\n", "\n", " このようにさまざまな段階を踏んで計算を行わなければならず、まともに計算をするのはかなり大変である。\n", " \n", " ここではMoruzziらが考案したデバイ-グリュナイゼン近似により、熱膨張について考えてみる。デバイ-グリュナイゼン近似は、**原子間ポテンシャルから、ヘルムホルツ自由エネルギーを計算**する方法である。\n", " " ] }, { "cell_type": "markdown", "id": "357d9be4", "metadata": { "tags": [] }, "source": [ "## 課題\n", "\n", "- 下記の例に倣い、熱膨張を計算するpythonコードを完成させて提出してください。\n", " \n", "- 提出ファイルはJupyter notebookを推奨するが、それ以外でも可。ただし実行できる形で提出すること。" ] }, { "cell_type": "markdown", "id": "32e75184", "metadata": {}, "source": [ "## デバイ-グリュナイゼン近似\n", "\n", " 熱膨張を電子論的に計算する手法として,デバイ-グリュナイゼン近似[[1](#anchor1)],[[2](#anchor2)]による方法を説明する." ] }, { "cell_type": "markdown", "id": "dfb2db99", "metadata": {}, "source": [ " この方法としてはまず,電子状態計算により基底状態における化合物の体積と全エネルギーの関係を計算する.このときエネルギーが極小値をとる体積 $V_0$ を含む範囲で体積を変化させる.\n", " \n", " 化合物の体積と全エネルギーのフィッティングを以下のモース型ポテンシャルにより行う.\n", "\n", "$$\n", "E_{\\text{total}}(r) = A + D\\exp\\lbrack - 2\\lambda(r - r_{0})\\rbrack - 2D\\exp\\lbrack - \\lambda(r - r_{0})\\rbrack\n", "$$\n", "\n", " $r$ は原子間距離,$r_0$ は平衡原子間距離,$A$, $D$, $\\lambda$はフィッティングパラメータである." ] }, { "cell_type": "markdown", "id": "7dfe15fe", "metadata": {}, "source": [ " これらのパラメータを用いると、以下の式により体積弾性率$B(r_0)$が求められる.\n", "\n", "$$\n", "B(r_{0}) = - \\frac{D\\lambda^{3}}{6\\pi\\ln\\lbrack\\exp( - \\lambda \\cdot r_{0})\\rbrack}\n", "$$" ] }, { "cell_type": "markdown", "id": "325705a5", "metadata": {}, "source": [ " つぎにこの式を平衡体積におけるデバイ温度の式に導入する.\n", "\n", "$$\n", "\\Theta_{\\text{D0}} = \\frac{h\\omega_{D0}}{2\\pi k_{B}} = (6\\pi^{2})^{1/3}\\frac{\\hslash}{k_{B}}(\\frac{4\\pi}{3})^{1/6} \\times k(\\nu)(\\frac{B(r_{0})}{m_{A_{x}B_{y}}})^{1/2}\n", "$$" ] }, { "cell_type": "markdown", "id": "74754787", "metadata": {}, "source": [ " $h$はプランク定数,$\\omega_{D0}$ はデバイ振動数,$k_B$ はボルツマン定数,$\\hslash$ はディラック定数,$m$は化合物A$_x$B$_y$ の有効原子質量であり全質量の対数平均で定義される.\n", "\n", "$$\n", "\\ln(m_{A_{x}B_{y}}) = \\frac{x}{x + y}\\ln(m_{A}) + \\frac{y}{x + y}\\ln(m_{B})\n", "$$ " ] }, { "cell_type": "markdown", "id": "e36a46d3", "metadata": {}, "source": [ " ここで$k(v)$ はポアソン比$\\nu$を用いて以下の式で表される.\n", "\n", "$$\n", "k(\\nu) = \\left\\{ \\frac{2}{3}\\left\\lbrack \\frac{2(1 + \\nu)}{3(1 - 2\\nu)} \\right\\rbrack^{3/2} + \\frac{1}{3}\\left\\lbrack \\frac{1 + \\nu}{3(1 - \\nu)} \\right\\rbrack^{3/2} \\right\\}^{- 1/3}\n", "$$\n", "\n", " 大抵の固体はポアソン比が0.2~0.3であるため,ここでは$\\nu$ =0.2として取り扱うこととする." ] }, { "cell_type": "markdown", "id": "9802bd95", "metadata": {}, "source": [ " デバイ温度体積の関係はグリュナイゼン定数$\\gamma$用いて以下の式のように定義した.\n", "\n", "$$\n", "\\Theta_{D}/\\Theta_{\\text{D0}} = (V_{0}/V)^{\\gamma} = (r_{0}/r)^{3\\gamma}\n", "$$\n", "\n", "また,グリュナイゼン定数は\n", "\n", "$$\n", "\\gamma = \\frac{\\lambda r_{0}}{2}\n", "$$\n", "\n", "で表される.グリュナイゼン定数の定義としてはSlater 近似[[3](#anchor3)]、Dugdale-MacDonald 近似 [[4](#anchor4)] などがあるが,ここでは広い温度域での再現性が良好な後者を使用している." ] }, { "cell_type": "markdown", "id": "f65d7839", "metadata": {}, "source": [ " 次に各体積でのヘルムホルツ自由エネルギーを算出する.\n", "\n", "$$\n", "\\begin{align}\n", " F(r,T) &= E(r) + E_{D}(r,T) - T \\cdot S_D(r,T)\\\\\n", " &= E(r)-k_B T \\left[f_D\\left(\\frac{\\Theta_D}{T}\\right)-3\\ln \\left(1-\\exp \\left(-\\frac{\\Theta_D}{T}\\right)\\right)\\right]+\\frac{9}{8} k_B \\Theta_D\n", "\\end{align}\n", "$$" ] }, { "cell_type": "markdown", "id": "60e2ab42", "metadata": {}, "source": [ " デバイ関数 $f_D$ は以下の様に定義される。\n", "\n", "$$\n", "f_{D}\\left( \\frac{\\Theta_{D}}{T} \\right) = 3\\left( \\frac{T}{\\Theta_{D}} \\right)^{3}\\int_{0}^{\\frac{\\Theta_{D}}{T}}{\\frac{x^{3}}{e^{x} - 1}dx}\n", "$$\n", "\n", " 各温度についてエネルギーの底 $r_0$ を取り,線膨張係数$\\alpha$を以下の式を用いて算出する.\n", "\n", "$$\n", "\\alpha(T) = \\frac{1}{r_{0}}\\frac{dr_{0}}{dT}\n", "$$\n", "\n", "\n", "[1] X. -G. Lu, M. Selleby and B. Sudman, Acta Materialia, 55(2007), 1215\n", "\n", "\n", "[2] X. -G. Lu, Ma. Selleby and B. Sudman, Acta Materialia, 53(2005), 2259\n", "\n", "\n", "[3] J.C.Slater, Introduction to chemical physics. New York (NY): McGraw-Hill; 1939\n", "\n", "\n", "[4] J.S.Dugdale, D. K. C. MacDonald, Phys. Rev., 89(1953), 832\n", "" ] }, { "cell_type": "markdown", "id": "5834ac2f", "metadata": { "tags": [] }, "source": [ "## エネルギーの体積依存性\n", "\n", " 物質の全エネルギーの体積依存性について見てみよう。2つの原子を近づけていくと、ある距離までエネルギーが減少する。これは2つの原子に電子が共有されることが原因である。一方で近づきすぎると、電子同士の反発する力が強くなるためエネルギーは急上昇する。\n", " \n", " このような全エネルギーの体積依存性は、第一原理計算と呼ばれる計算手法によって求めることが可能である。ここでは、[Materials Project](https://next-gen.materialsproject.org)に収録されている計算データを利用する。FCC構造のCuについて、全エネルギーと体積との関係を図示してみる。\n", " \n", " \n" ] }, { "cell_type": "code", "execution_count": 1, "id": "c53d3a0e", "metadata": { "tags": [] }, "outputs": [], "source": [ "from pylab import * #this includes numpy as np!\n", "from scipy.optimize import leastsq\n", "\n", "plt.rcParams[\"figure.figsize\"] = (5,4)" ] }, { "cell_type": "markdown", "id": "2fa6344a", "metadata": {}, "source": [ " 必要なライブラリをインポートする。" ] }, { "cell_type": "code", "execution_count": 2, "id": "e8fc9386", "metadata": { "tags": [] }, "outputs": [ { "data": { "text/plain": [ "Text(0, 0.5, 'Energy (eV)')" ] }, "execution_count": 2, "metadata": {}, "output_type": "execute_result" }, { "data": { "image/png": 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KiIhQZmamhg8frp49e2rGjBnq06ePtm3bVq3bNi8vTzabzfV8woQJeu655/Twww/rsssu01//+letX7/e7VAFAMBTbg9eatWqlfr166eZM2dqypQpio6O9nZtAYEzVgCA5IX7WHfs2KFf/epXWrhwoSwWi2666SZt3brVkGIBAGgu3A7WQYMG6cUXX9TRo0f17LPP6siRIxoxYoTi4+P1wAMP6MiRI96sE0aprJSys6WMDOfXykp/VwQAzYrHE0RERETo5ptvVnZ2tvbv36/Jkyfr+eef18UXX6yxY8d6o0YYJTNTiouTEhOlKVOcX+PinNsBAIZo8lzBp0+f1urVq3XPPffo5MmTqmxmZ0DN5hprZqaUkiL9/H931eQab7whJSf7vi4ACBJenyt427Ztuvnmm9W5c2fNnz9fycnJ2rFjR2NfDt5UWSndcUfNUJX+s23OHLqFAcAAbk0QUaWwsFCvvPKKXnnlFR06dEiDBw/WihUrdMMNNygyMtJbNaKptm+X6rsG7nBIhYXOdsOG+awsAGiO3A7WkSNHauvWrerYsaOmTZumGTNmqGfPnt6sDUYpKTG2HQCgTm4Ha0REhNavX6/f/va3CgkJ8WZNMJrFYmw7AECdGj146dtvv9WBAwd09dVXKyIiQg6Ho9ZVZoJdsxi8VFnpHP1bVFT7dVaTSYqNlQ4dkvijCQBq5bXBS8ePH9fw4cPVo0cPjR07ViX/7j6cOXOm7rrrrsZXDO8JCZGeeML53z//46fq+fLlhCoAGMDjYJ07d65CQ0NVUFCgtm3burZPnDhR7733nqHFwUDJyc5bai66qPr22FhutQEAA3k0KliSsrKytGXLFsXGxlbb3r17d+Xn5xtWGLwgOVkaN845+rekxHlNdehQzlQBwEAeB2tFRUW1M9UqpaWlLBAeDEJCuKUGALzI467gq6++WqtWrXI9N5lMOnfunB555BElJiYaWhwAAMHG4zPWRx55RMOGDdPu3bt19uxZzZ8/X/v27VNZWRkzLwEAWjyPz1h79eqlL774QldeeaVGjhypiooKJScna8+ePYqPj/dGjQAABI0mT8Lf3DWL+1gBAE1m6H2sBQUFHr15UVGRR+0BAGgu3ArWAQMGaNasWcrJyamzjc1m04svvqg+ffook/U9AQAtlFuDl7766is9+OCDGjNmjEJDQ9W/f3/FxMQoPDxcJ06c0Jdffql9+/apf//+euSRR3Tttdd6u24AAAKSR9dY//Wvf+mdd97R9u3bdfjwYZ05c0Zms1n9+vXT6NGj1adPH2/W6hdcYwUASO7nAYOXGkCwAgAkL07CDwAA6kawAgBgIIIVAAADBU2wJiUlqUuXLgoPD5fFYtHUqVNVXFxc7z4mk6nWxyOPPOKjqgEALY3HwVpRUeGNOhqUmJiodevWKS8vT+vXr9eBAweUkpJS7z4lJSXVHv/7v/8rk8mk//7v//ZR1QCAlsbjUcEXXHCBbrjhBs2YMUNDhgzxVl0N2rRpk8aPHy+73a7Q0FC39hk/frxOnTqlDz74wO33YVQwAEDy4qjgjIwM2Ww2DR8+XD169NBDDz3UYJes0crKyrR69WoNHjzY7VA9duyY3n77bf3+97+vt53dbld5eXm1BwAA7vI4WK+//nqtX79excXF+p//+R9lZGSoa9eu+u1vf6vMzEz99NNP3qhTkrRgwQJFRkaqQ4cOKigo0MaNG93ed+XKlWrXrp2Sk5PrbZeenq7o6GjXw2q1NrVsAEALYsgEEStWrNC8efN09uxZmc1m3XrrrVq4cKHatm1b735paWlasmRJvW127dql/v37S5JKS0tVVlam/Px8LVmyRNHR0dq8ebNMJlODNSYkJGjkyJFasWJFve3sdrvsdrvreXl5uaxWK13BANDCeX3mpaNHj2rVqlV6+eWXVVBQoAkTJuj3v/+9iouL9dBDD8lisSgrK6ve1ygtLVVpaWm9beLi4hQeHl5j+5EjR2S1WrVz504NGjSo3tfYvn27rr76auXm5uryyy9v+MOdh2usAADJ/TxwaxL+82VmZurll1/Wli1b1KtXL91+++266aabdOGFF7ra9O3bV/369Wvwtcxms8xms6clSJKq/h44/+yyLi+99JKuuOIKj0MVAABPeXyN9ZZbblFMTIx27Nih3NxczZ49u1qoSlK3bt107733GlWjcnJy9NRTTyk3N1f5+fnaunWrpkyZovj4+GpnqwkJCdqwYUO1fcvLy/X6669r5syZhtUDAEBdPD5jLSkpafDaaUREhBYvXtzoomp7vczMTC1evFgVFRWyWCwaM2aM1q5dq7CwMFe7vLw82Wy2avuuXbtWDodDkydPNqweAADq4vE11rpuPzGZTAoLC1ObNm0MKSxQcI0VACB58RrrhRdeWO8o3NjYWE2fPl2LFy9Wq1ZBM2MiAACG8DhYX3nlFd17772aPn26rrzySjkcDu3atUsrV67Ufffdp++//17Lli1TWFiY7rnnHm/UDABAwPI4WFeuXKlHH31UN9xwg2tbUlKSLrvsMj3//PP64IMP1KVLFz3wwAMEKwCgxfG4r/aTTz6p9Vaafv366ZNPPpEkDRkyRAUFBU2vDgCAIONxsMbGxuqll16qsf2ll15yTf93/PhxtW/fvunVAQAQZDzuCl62bJl+97vf6d1339WAAQNkMpm0a9cuff3113rjjTckOachnDhxouHFAgAQ6Bo1pWF+fr6ee+455eXlyeFwKCEhQX/4wx8UFxfnhRL9i9ttAACSl263+fHHHzVq1Cg9//zzSk9Pb3KRAAA0Nx5dYw0NDdXevXvdWk0GAICWyOPBS9OmTat18BJakMpKKTtbyshwfq2s9HdFABAwPB68dPbsWf31r3/V+++/r/79+ysyMrLa9x977DHDikMAysyU7rhDOnLkP9tiY6UnnpAaWEQeAFoCj4N17969+tWvfiVJ2r9/f7Xv0UXczGVmSikp0s/HuxUVObe/8QbhCqDFa/RC5y0Fo4L/rbJSiourfqZ6PpPJeeZ66JAUEuLT0gDAF9zNg0bPkv/tt99qy5YtOnPmjKT/LDyOZmr79rpDVXKexRYWOtsBQAvmcbAeP35cw4cPV48ePTR27FiVlJRIkmbOnKm77rrL8AIRIP79/9mwdgDQTHkcrHPnzlVoaKgKCgqqLXg+ceJEvffee4YWhwBisRjbDgCaKY8HL2VlZWnLli2KjY2ttr179+7Kz883rDAEmKFDnddQi4pqDl6S/nONdehQ39cGAAHE4zPWioqKameqVUpLSxUWFmZIUQhAISHOW2okZ4ier+r58uUMXALQ4nkcrFdffbVWrVrlem4ymXTu3Dk98sgjSkxMNLQ4BJjkZOctNRddVH17bCy32gDAv3l8u82XX36pYcOG6YorrtCHH36opKQk7du3T2VlZdqxY4fi4+O9VatfcLtNLSornaN/S0qc11SHDuVMFUCz55VJ+CWpV69e+uKLL/Tss88qJCREFRUVSk5O1u233y4LA1dahpAQadgwf1cBAAGJCSIawBkrAEDy4hmrJJ08eVI5OTn67rvvdO7cuWrfmzZtWmNeEgCAZsHjYH3rrbd04403qqKiQu3atas2P7DJZCJYAQCBww9jQjweFXzXXXdpxowZOnXqlE6ePKkTJ064HmVlZd6oEQAAz2VmOuc4T0yUpkxxfo2Lc273Io+DtaioSH/6059qvZcVAICAULUa18/nOK9ajcuL4epxsI4ePVq7d+/2Ri31SkpKUpcuXRQeHi6LxaKpU6equLi43n1Onz6t2bNnKzY2VhEREbr00kv17LPP+qhiAIBfVFY6142ubWxu1bY5c5ztvMDja6zXXXed5s2bpy+//FKXXXaZQkNDq30/KSnJsOLOl5iYqHvuuUcWi0VFRUW6++67lZKSop07d9a5z9y5c7V161a99tpriouLU1ZWlm677TbFxMRo3LhxXqkTAOBnnqzG5YVbBz2+3aZVq7pPck0mkyq99BfAz23atEnjx4+X3W6vEe5V+vTpo4kTJ+rPf/6za9sVV1yhsWPH6v777691H7vdLrvd7npeXl4uq9XK7TYAECwyMpzXVBuyZo00ebLbL+u19VjPnTtX58NXoVpWVqbVq1dr8ODBdYaqJA0ZMkSbNm1SUVGRHA6Htm7dqv3792v06NF17pOenq7o6GjXw2q1euMjAAC8xc+rcTV6oXN/WLBggSIjI9WhQwcVFBRo48aN9bZ/8skn1atXL8XGxqpNmzYaM2aMnnnmGQ0ZMqTOfVJTU2Wz2VyPwsJCoz8GAMCbqlbj+vmCIVVMJslq9dpqXG4H69ixY2Wz2VzPH3jgAZ08edL1/Pjx4+rVq5dHb56WliaTyVTv4/yBUvPmzdOePXuUlZWlkJAQTZs2TfX1ZD/55JP69NNPtWnTJn322Wd69NFHddttt+nvf/97nfuEhYUpKiqq2gMAEET8vBqX29dYQ0JCVFJSok6dOkmSoqKilJubq27dukmSjh07ppiYGI+6g0tLS1VaWlpvm7i4OIWHh9fYfuTIEVmtVu3cuVODBg2q8f0zZ84oOjpaGzZs0HXXXefaPnPmTB05csTtRdmZ0hAAglRmpnN08PkDmaxWZ6g2YjUuw6c0/Hn+GjHFsNlsltlsbtS+Ve9//kCj8/3444/68ccfawy2CgkJqTENIwCgGUpOlsaN8/nMS42aK9jXcnJylJOToyFDhqh9+/Y6ePCgFi1apPj4+GpnqwkJCUpPT9eECRMUFRWla665RvPmzVNERIS6du2qbdu2adWqVXrsscf8+GkAAD7jh9W43A7WqmueP9/mCxEREcrMzNTixYtVUVEhi8WiMWPGaO3atQoLC3O1y8vLq3YdeO3atUpNTdWNN96osrIyde3aVQ888IBuvfVWn9QNAGh53L7G2qpVK1177bWuIHvrrbf0m9/8RpGRkZKcXbLvvfeez2658RWusQIAJC9cY7355purPb/ppptqtGFlGwBAS+d2sL788sverAMAgGYhqCaIAAAg0BGsAAAYKChutwEAtDCVlT6//9QoBCsAILDUNmNSbKxzmsJGzJjka3QFAwACR2amlJJScz3VoiLn9sxM/9TlAYIV/lNZKWVnO9dOzM52PgfQclVWOs9Ua5teoWrbnDkB/7uCYIV/ZGZKcXFSYqJzQeLEROfzIPhrFICXbN9e80z1fA6HVFjobBfACFb4XjPo6gHgBSUlxrbzE4IVvtVMunoAeIHFYmw7PyFY4VvNpKsHgBcMHeoc/VvXAi8mk3M91aFDfVuXhwhW+FYz6eoB4AUhIc5baqSa4Vr1fPnygL+flWCFbzWTrh4AXpKcLL3xhnTRRdW3x8Y6twfBfaxuLxvXUrFsnMEqK52jf4uKar/OajI5/wEdOhTwf5UC8KIAnHnJ8GXjAENUdfWkpDhD9PxwDaKuHgBeFhIiDRvm7yoaha5g+F4z6OoBgLpwxgr/SE6Wxo0LuK4eAGgqghX+E8RdPQBQF7qCAQAwEMEKAICB6AoGABgrAG+V8SWCFQBgnCBfpNwIdAUDAIzBylWSCFYAgBFYucolaII1KSlJXbp0UXh4uCwWi6ZOnari4uJ69zl27JimT5+umJgYtW3bVmPGjNE333zjo4oBoAVh5SqXoAnWxMRErVu3Tnl5eVq/fr0OHDiglJSUOts7HA6NHz9eBw8e1MaNG7Vnzx517dpVI0aMUEVFhQ8rB4AWgJWrXIJ2Ev5NmzZp/PjxstvtCg0NrfH9/fv3q2fPntq7d6969+4tSaqsrFSnTp20dOlSzZw50633YRJ+AHBDdraUmNhwu61bg3ZiGHfzIGjOWM9XVlam1atXa/DgwbWGqiTZ7XZJUnh4uGtbSEiI2rRpo48//rjO17bb7SovL6/2AAA0oJksUm6EoArWBQsWKDIyUh06dFBBQYE2btxYZ9uEhAR17dpVqampOnHihM6ePauHHnpIR48eVUk9XRHp6emKjo52PaxWqzc+CgA0L81kkXIj+DVY09LSZDKZ6n3s3r3b1X7evHnas2ePsrKyFBISomnTpqmunuzQ0FCtX79e+/fv1y9+8Qu1bdtW2dnZuvbaaxVSz//Y1NRU2Ww216OwsNDwzw0AzRIrV0ny8zXW0tJSlZaW1tsmLi6uWndulSNHjshqtWrnzp0aNGhQva9hs9l09uxZdezYUQMHDlT//v319NNPu1Uj11gBwEPNdOaloFjo3Gw2y2w2N2rfqr8Hqq6l1ic6OlqS9M0332j37t26//77G/WeAAA3tPCVq4LiGmtOTo6eeuop5ebmKj8/X1u3btWUKVMUHx9f7Ww1ISFBGzZscD1//fXXlZ2d7brlZuTIkRo/frxGjRrlj48BAGgBgmKu4IiICGVmZmrx4sWqqKiQxWLRmDFjtHbtWoWFhbna5eXlyWazuZ6XlJTozjvv1LFjx2SxWDRt2jT9+c9/9sdHAAC0EEF7H6uvcI01CDTT6zkAAktQXGMFmoyVNAAEmKC4xgrUipU0AGNVVjpnUMrIcH5tARPmewPBiuDEShqAsTIzpbg457SEU6Y4v8bF8QdqIxCsCE6spAEYh94fQxGsCE6spAEYg94fwxGsCE4Wi7HtgJaK3h/DEawITqykARiD3h/DEawITqykARiD3h/DEawIXqykATQdvT+GY4IIBLfkZGncOGZeAhqrqvcnJcUZoucPYqL3p1EIVgS/Fr6SBtBkVb0/tc1itnw5vT8eIlgBAPT+GIhgBQA40ftjCAYvAQBgIIIVAAAD0RUMAMGONYkDCsEKAMGMNYkDDl3BABCsWJUmIBGsABCMWJUmYBGsABCMWJUmYBGsABCMWJUmYDF4CZAYVYngw6o0AYszViAzU4qLkxITpSlTnF/j4hj4gcDGqjQBi2BFy8aoSgQr1iQOWAQrWi5GVSLYsSZxQAq6YLXb7erbt69MJpNyc3PrbetwOJSWlqaYmBhFRERo2LBh2rdvn28KReBjVCWag+Rk6fBhaetWac0a59dDhwhVPwq6YJ0/f75iYmLcavvwww/rscce01NPPaVdu3apc+fOGjlypE6dOuXlKhEUGFWJ5qJqVZrJk51f6f71q6AK1nfffVdZWVlatmxZg20dDoeWL1+ue++9V8nJyerTp49WrlypH374QWvWrPFBtQh4jKoE4AVBE6zHjh3TrFmz9Oqrr6pt27YNtj906JCOHj2qUaNGubaFhYXpmmuu0c6dO+vcz263q7y8vNoDzRSjKhEIKiul7GwpI8P5lWv6QS8ogtXhcGj69Om69dZb1b9/f7f2OXr0qCTpl7/8ZbXtv/zlL13fq016erqio6NdD6vV2vjCEdgYVQl/41avZsmvwZqWliaTyVTvY/fu3VqxYoXKy8uVmprq8XuYfvYL0+Fw1Nh2vtTUVNlsNtejsLDQ4/dEEGFUJfyFW72aLZPDUdu9Br5RWlqq0tLSetvExcVp0qRJeuutt6oFYmVlpUJCQnTjjTdq5cqVNfY7ePCg4uPj9Y9//EP9+vVzbR83bpwuvPDCWvepTXl5uaKjo2Wz2RQVFeXmJ0PQYeYl+FJlpfPMtK5R6SaT84+7Q4f4OQwg7uaBX6c0NJvNMpvNDbZ78skn9Ze//MX1vLi4WKNHj9bf/vY3DRw4sNZ9Lr74YnXu3Fnvv/++K1jPnj2rbdu2aenSpcZ8ADQfVaMqAV/w5FYvfi6DTlDMFdylS5dqzy+44AJJUnx8vGJjY13bExISlJ6ergkTJshkMmnOnDl68MEH1b17d3Xv3l0PPvig2rZtqylTpvi0fgCohlu9mrWgCFZ35eXlyWazuZ7Pnz9fZ86c0W233aYTJ05o4MCBysrKUrt27fxYJYAWj1u9mjW/XmMNBlxjBWC4qmusRUW1T6nJNdaA5G4eBMXtNgDQrHCrV7NGsAJG4mZ/uItbvZqtZnWNFfCrzEznajnnj/aMjXWemfBLErVJTpbGjeNWr2aGa6wN4Bor3FJ1s//P/zlVdetxBtL8cO9zi8M1VsBXWNe15WEqQtSDYAWainVdWxamIkQDCFagqbjZv+WgdwJuIFiBpuJm/5aD3gm4gWAFmop1XVsOeifgBoIVaCpu9m856J2AGwhWwAjc7N8y0DsBNzBBBGAUbvZv/qp6J1JSnCF6/iAmeifwbwQrYCTWdQ0OTZncoap3orZZtpYvp3cCBCsQkJjVx3uMmHqS3gnUgykNG8CUhvA55hz2HqaeRBMwpSEQjJjVx3uY3AE+QrACgYJf/N7F5A7wEYIVCBT84vcuJneAjzB4CQgU/OJvWFMGdTG5A3yEM1YgUPCLv35NXaqNyR3gIwQrECiM/sVfWSllZ0sZGc6vwXxt1ohBXUw9CR8hWIFAYeQv/ua0ELeRg7qYehI+wH2sDeA+VvhcbfexWq3uz+oTiPdqNuXaaHa28w+Dhmzd6v6sV0zAgUZwNw8YvAQEmqbM6tPQ2Z3J5Dy7GzfO/SBpagg1dcILbwzqYupJeBHBCgSixv7i9+SWHXdev6mhWNfZc9W1UXfOnhnUhSATdNdY7Xa7+vbtK5PJpNzc3HrbZmZmavTo0TKbzW61B4KekWd3TR0wZNS1UUbzIsgEXbDOnz9fMTExbrWtqKjQr3/9az300ENergoIEEad3RkRikZNeMFoXgSZoArWd999V1lZWVq2bJlb7adOnapFixZpxIgRXq4MCBBGnd0ZEYpGnj0zmhdBJGiusR47dkyzZs3Sm2++qbZt23rtfex2u+x2u+t5eXm5194LMJxRC3EbEYpGXxtlqTYEiaA4Y3U4HJo+fbpuvfVW9e/f36vvlZ6erujoaNfDarV69f0AwxlxdmdEKHrj2mjVoK7Jk51fCVUEIL8Ga1pamkwmU72P3bt3a8WKFSovL1dqaqrXa0pNTZXNZnM9CgsLvf6egOGSk6XDh533dq5Z4/x66JD7XaZGhCLXRtFC+XWCiNLSUpWWltbbJi4uTpMmTdJbb70l03n/OCsrKxUSEqIbb7xRK1eurPc1Dh8+rIsvvlh79uxR3759PaqRCSLQYlWNCpZq71J29+y3qRNeAAHC3TwIipmXCgoKql3rLC4u1ujRo/XGG29o4MCBio2NrXd/ghVoJKNCkZmO0Aw0q5mXunTpUu35BRdcIEmKj4+vFqoJCQlKT0/XhAkTJEllZWUqKChQcXGxJCkvL0+S1LlzZ3Xu3NkXpQPBzagBQ8x0hBYkKILVXXl5ebLZbK7nmzZt0i233OJ6PmnSJEnS4sWLlZaW5uvygOBEKAIeCYquYH+iKxgAILmfB0Fxuw0AAMGCYAUAwEAEKwAABiJYAQAwEMEKAICBmtXtNt5QNWiayfgBoGWryoGGbqYhWBtw6tQpSWIyfgCAJGcuREdH1/l97mNtwLlz51RcXKx27dpVm6s4mJWXl8tqtaqwsJB7c93EMfMcx6xxOG6e89UxczgcOnXqlGJiYtSqVd1XUjljbUCrVq0anIs4WEVFRfEP10McM89xzBqH4+Y5Xxyz+s5UqzB4CQAAAxGsAAAYiGBtgcLCwrR48WKFhYX5u5SgwTHzHMescThungu0Y8bgJQAADMQZKwAABiJYAQAwEMEKAICBCFYAAAxEsDYz6enpGjBggNq1a6dOnTpp/PjxysvLq3efkpISTZkyRT179lSrVq00Z84c3xQbIBpzzDIzMzVy5Eh17NhRUVFRGjRokLZs2eKjiv2vMcfs448/1q9//Wt16NBBERERSkhI0OOPP+6jigNDY47b+Xbs2KHWrVurb9++3isywDTmmGVnZ8tkMtV4fP311z6pmWBtZrZt26bbb79dn376qd5//3399NNPGjVqlCoqKurcx263q2PHjrr33nt1+eWX+7DawNCYY/bRRx9p5MiReuedd/TZZ58pMTFR119/vfbs2ePDyv2nMccsMjJSs2fP1kcffaSvvvpK9913n+677z698MILPqzcvxpz3KrYbDZNmzZNw4cP90GlgaMpxywvL08lJSWuR/fu3X1QMbfbNHvff/+9OnXqpG3btunqq69usP2wYcPUt29fLV++3PvFBShPj1mV3r17a+LEiVq0aJEXqwtMjT1mycnJioyM1KuvvurF6gKXJ8dt0qRJ6t69u0JCQvTmm28qNzfXN0UGGHeOWXZ2thITE3XixAldeOGFvi1QnLE2ezabTZL0i1/8ws+VBI/GHLNz587p1KlTLfY4N+aY7dmzRzt37tQ111zjrbICnrvH7eWXX9aBAwe0ePFiX5QV0Dz5WevXr58sFouGDx+urVu3ers0Fybhb8YcDofuvPNODRkyRH369PF3OUGhscfs0UcfVUVFhW644QYvVheYPD1msbGx+v777/XTTz8pLS1NM2fO9EGVgcfd4/bNN99o4cKF2r59u1q3btm/st09ZhaLRS+88IKuuOIK2e12vfrqqxo+fLiys7M96lFprJb9f6mZmz17tr744gt9/PHH/i4laDTmmGVkZCgtLU0bN25Up06dvFhdYPL0mG3fvl2nT5/Wp59+qoULF+qSSy7R5MmTvVxl4HHnuFVWVmrKlClasmSJevTo4cPqApO7P2s9e/ZUz549Xc8HDRqkwsJCLVu2zCfBKgeapdmzZztiY2MdBw8e9Gi/a665xnHHHXd4p6gA15hjtnbtWkdERIRj8+bNXqwscDX256zK/fff7+jRo4fBVQU+d4/biRMnHJIcISEhrofJZHJt++CDD3xUsf819WftL3/5iyMhIcHgqmrHGWsz43A49Mc//lEbNmxQdna2Lr74Yn+XFPAae8wyMjI0Y8YMZWRk6LrrrvNylYHFqJ8zh8Mhu91ucHWBy9PjFhUVpX/+85/Vtj3zzDP68MMP9cYbb7SIf99G/azt2bNHFovF4OpqR7A2M7fffrvWrFmjjRs3ql27djp69Kgk5+K8ERERkqTU1FQVFRVp1apVrv2qRhiePn1a33//vXJzc9WmTRv16tXL55/B1xpzzDIyMjRt2jQ98cQTuuqqq1z7REREuLUQcrBrzDF7+umn1aVLFyUkJEhy3te6bNky/fGPf/TPh/ADT49bq1atalxL7NSpk8LDw1vMuInG/KwtX75ccXFx6t27t86ePavXXntN69ev1/r1631TtE/Oi+Ezkmp9vPzyy642N998s+Oaa65pcL+uXbv6tHZ/acwxu+aaa2rd5+abb/Z5/f7QmGP25JNPOnr37u1o27atIyoqytGvXz/HM88846isrPT9B/CTxv77PN/ixYsdl19+uddrDRSNOWZLly51xMfHO8LDwx3t27d3DBkyxPH222/7rGbuYwUAwEDcxwoAgIEIVgAADESwAgBgIIIVAAADEawAABiIYAUAwEAEKwAABiJYAQAwEMEKAICBCFYAAAxEsAJolM2bN6tbt24aMGCA9u/f7+9ygIDBXMEAGqVHjx565plntG/fPn3yySdau3atv0sCAgJnrADqdPz4cXXq1EmHDx+u8T2z2axLLrlE3bp1q7FUXkpKih577DEfVQkEFs5YAdTp7rvv1okTJ/TSSy/V+N6LL76oW2+9VR07dtS+ffvUoUMH1/e++OILJSYm6tChQ4qKivJlyYDfccYKtHBnz56tdfuZM2f00ksvaebMmTW+99NPP+mJJ57Q/PnzderUKbVv377a9//rv/5LcXFxWr16tVdqBgIZwQq0MMOGDdPs2bN15513ymw2a+TIkbW2e/fdd9W6dWsNGjSoxveee+45devWTbfffrt++OEHffPNNzXaJCUlKSMjw/D6gUBHsAIt0MqVK9W6dWvt2LFDzz//fK1tPvroI/Xv37/G9hMnTuj+++/X0qVLFRsbq+joaOXm5tZod+WVVyonJ0d2u93o8oGARrACLdAll1yihx9+WD179lRCQkKtbQ4fPqyYmJga2xctWqQJEybo0ksvlST16tVLn3/+eY12F110kex2u44ePWps8UCAa+3vAgD4Xm1noj935swZhYeHV9v25Zdf6rXXXtNXX33l2tanT59az1gjIiIkST/88EPTigWCDMEKtECRkZENtjGbzTpx4kS1bXPnztXJkycVGxvr2nbu3DlZLJYa+5eVlUmSOnbs2MRqgeBCsAKoVb9+/fTaa6+5nm/evFmfffaZ9uzZo9at//OrY9euXZoxY4a+//77aiG6d+9excbGymw2+7RuwN8IVgC1Gj16tFJTU3XixAldcMEFuuuuuzRv3jz17du3Wruq+1Q///xzjRgxwrV9+/btGjVqlC9LBgICwQqgVpdddpn69++vdevWqaKiQidPntTs2bNrtLNarWrbtq1yc3Ndwfqvf/1LGzZs0JYtW3xdNuB3zLwEoE7vvPOO7r77bu3du1etWrl/E8HTTz+tjRs3Kisry4vVAYGJM1YAdRo7dqy++eYbFRUVyWq1ur1faGioVqxY4cXKgMDFGSsAAAZigggAAAxEsAIAYCCCFQAAAxGsAAAYiGAFAMBABCsAAAYiWAEAMBDBCgCAgQhWAAAM9P+yyexwkads2wAAAABJRU5ErkJggg==", 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" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "#Cu(mp-30)\n", "v = np.array([8.6664, 8.9586, 9.5623, 9.8741, 10.5179, 9.2571, 10.8500, 11.5351, 12.9905, 12.2484, 13.7620, 12.6158, 14.5635, 11.1890, 14.9757, 15.8231, 10.1926, 15.3955, 11.8882, 14.1590, 13.3726])\n", "r = np.cbrt(v)\n", "e = np.array([-3.3243, -3.4941, -3.7562, -3.8536, -3.9921, -3.6372, -4.0371, -4.0873, -4.0660, -4.0937, -4.0115, -4.0836, -3.9364, -4.0681, -3.8927, -3.7961, -3.9314, -3.8457, -4.0956, -3.9763, -4.0416])\n", "\n", "\n", "plot(r,e,'ro')\n", "xlabel('r ($\\AA$)')\n", "ylabel('Energy (eV)')" ] }, { "cell_type": "markdown", "id": "f7bdf1cb", "metadata": { "tags": [] }, "source": [ " エネルギーが最安定となる$r_0 \\sim 2.3$ の周りで原子間距離を変化させたエネルギーの変化を示している" ] }, { "cell_type": "markdown", "id": "25a76c3c", "metadata": { "tags": [] }, "source": [ "## Morse ポテンシャルでフィッティング\n", "\n", " この様な固体のミクロの振舞いを記述するモデルを考える。\n", " \n", " 固体の原子間に働く力を数学的に記述する2体間ポテンシャル (pair potential) にはさまざまなものがあるが,簡単なものとしてモース (Morse) 型がある。\n", " \n", " Morseポテンシャルは,2原子分子の原子間距離$r$に依存するポテンシャルである.\n", "\n", "$$\n", "E_{\\text{total}}(r) = A + D\\exp\\lbrack - 2\\lambda(r - r_{0})\\rbrack - 2D\\exp\\lbrack - \\lambda(r - r_{0})\\rbrack\n", "$$\n", "\n", " ここで$r$は原子間距離。$r_0$は平衡原子間距離。$A$、$D$、$\\lambda$はフィッティングパラメータである。\n", "\n", " Cuのエネルギーと体積の関係に、モース型ポテンシャルをフィッティングしてみよう。\n", "\n", "```\n", "*****here*****\n", "```\n", "に正しい式を記入して実行してください。" ] }, { "cell_type": "code", "execution_count": 4, "id": "289089ac", "metadata": { "tags": [] }, "outputs": [], "source": [ "#difinition of the functions\n", "def Morse(parameters,r):\n", "\n", " A = parameters[0]\n", " D = parameters[1]\n", " r0 = parameters[2]\n", " la = parameters[3]\n", " \n", " #*****here*****\n", "\n", " return E\n", "\n", "def objective(pars,y,x):\n", " #we will minimize this function\n", " err = y - Morse(pars,x)\n", " return err" ] }, { "cell_type": "code", "execution_count": 7, "id": "3055ab02", "metadata": { "tags": [] }, "outputs": [ { "name": "stderr", "output_type": "stream", "text": [ "/var/folders/qx/bp1cy1rx2g3b3fqmxf9knzph0000gn/T/ipykernel_14877/2984365570.py:10: RuntimeWarning: overflow encountered in exp\n", " E = A + D*np.exp(-2*la*(r-r0)) -2*D*np.exp(-la*(r-r0))\n", "/var/folders/qx/bp1cy1rx2g3b3fqmxf9knzph0000gn/T/ipykernel_14877/2984365570.py:10: RuntimeWarning: invalid value encountered in subtract\n", " E = A + D*np.exp(-2*la*(r-r0)) -2*D*np.exp(-la*(r-r0))\n" ] }, { "data": { "image/png": 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", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "#now here are our initial guesses.\n", "A = -4.1\n", "D = 1\n", "r0 = 2.3\n", "la = 0.1\n", "\n", "x0 = [A, D, r0, la] \n", "\n", "rfit = np.linspace(min(r),max(r),100)\n", "morpars, ier = leastsq(objective, x0, args=(e,r)) #this is from scipy\n", "\n", "plot(r,e,'ro')\n", "plot(rfit, Morse(morpars,rfit), label='Morse fit')\n", "xlabel('r ($\\AA$)')\n", "ylabel('Energy (eV)')\n", "legend(loc='best')\n", "\n", "#add some text to the figure in figure coordinates\n", "ax = gca()\n", "text(0.4,0.5,'A = %1.2f eV' % morpars[0],transform = ax.transAxes)\n", "text(0.4,0.4,'D = %1.2f eV' % morpars[1],transform = ax.transAxes)\n", "text(0.4,0.3,'r0 = %1.2f $\\AA$' % morpars[2],transform = ax.transAxes)\n", "text(0.4,0.2,'lambda = %1.2f $\\AA^{-1}$' % morpars[3],transform = ax.transAxes)\n", "savefig('a-eos.png')\n", "show()\n" ] }, { "cell_type": "markdown", "id": "8d4e64e8", "metadata": {}, "source": [ "二次関数の時よりもフィッティング結果が良好であることがわかる。ここで、\n", "\n", "* $r_0$の平衡原子間距離は2.29 Å\n", "\n", "* $A$=-1.31 eV、$D$=2.79 eV、$\\lambda$=1.80 Å$^{-1}$\n", "\n", "である。\n" ] }, { "cell_type": "markdown", "id": "a8083f70", "metadata": { "tags": [] }, "source": [ "## 体積弾性率B\n", " これらのパラメータを使うことで、熱膨張を求める際に必要な **体積弾性率B(bulk modulus)** を計算することができる。体積弾性率とは、物体に圧力を加えたときの変形のしにくさを示す指標である。体積弾性率$B(r_0)$は以下の式で表される。\n", "\n", "$$\n", "B(r_{0}) = -\\frac{D \\cdot r_0^2 \\cdot \\lambda^{3}}{6\\pi \\cdot \\ln x_0}\n", "$$\n", "\n", "$$\n", "x_0 = \\exp(-\\lambda \\cdot r_0)\n", "$$\n", "\n", "\n", "```\n", "*****here*****\n", "```\n", "\n", "に正しい式を記入して実行してください。\n", "\n", "なお、得られた体積弾性率の単位は eV/Å$^3$ なのでkbarへ単位変換をしてください(eVA3_to_kbar)。" ] }, { "cell_type": "code", "execution_count": 8, "id": "8afde509", "metadata": { "tags": [] }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "B(r_0)= 1749.9896494141262 kbar\n" ] } ], "source": [ "D = morpars[1]\n", "r0 = morpars[2]\n", "la = morpars[3]\n", "\n", "#transformation\n", "eVA3_to_kbar=160.218*10\n", "\n", "x0=np.exp(-la*r0)\n", "#*****here*****\n", "\n", "print(\"B(r_0)=\",B0,\"kbar\")\n" ] }, { "cell_type": "markdown", "id": "5689c55f", "metadata": { "tags": [] }, "source": [ "## デバイ温度\n", " 次に**デバイ温度** $\\Theta_D$を求める。デバイ温度とは格子振動や原子間力と深くかかわり合いを持つ温度のことを指し、物質の硬さの指標となる。一般的に物質のデバイ温度は、硬い物質ほど高く、逆に柔らかい物質ほど低い値を取る。\n", " \n", " 平衡体積におけるデバイ温度は以下の式で表される。\n", "\n", "$$\n", "\\Theta_{\\text{D0}} = 41.63 \\left( \\frac{r_0 \\cdot B}{M} \\right)^{1/2}\n", "$$\n", "\n", "$r_0$は平衡原子間距離、Bは体積弾性率、Mは原子質量である。\n", "\n", " デバイ温度体積の関係はグリュナイゼン定数$\\gamma$用いて以下の式のように定義した.\n", "\n", "$$\n", "\\Theta_{D}/\\Theta_{\\text{D0}} = (V_{0}/V)^{\\gamma} = (r_{0}/r)^{3\\gamma}\n", "$$\n", "\n", "\n", " またグリュナイゼン定数は\n", "\n", "$$\n", "\\gamma = \\frac{\\lambda r_{0}}{2}\n", "$$\n", "\n", "で表される。グリュナイゼン定数はSlater近似やDugdale-MacDonald近似などがあるが、ここでは広い温度域での再現性が良好なDugdale-MacDonald近似を利用している。\n", "\n", "```\n", "*****here*****\n", "```\n", "\n", "に平衡体積におけるデバイ温度の式を記入して実行してください。" ] }, { "cell_type": "code", "execution_count": 9, "id": "657828b2", "metadata": { "tags": [] }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "ThetaD0= 330.55437406219244 K\n", "Gru= 2.0548457352477607\n" ] } ], "source": [ "mass=63.546 #Cu\n", "\n", "#*****here*****\n", "\n", "Gru=la*r0/2\n", "\n", "print(\"ThetaD0=\",TD0,\"K\")\n", "print(\"Gru=\",Gru)\n", "\n", "\n", "def DebyeTemp(r): \n", " #return 67.48*sqrt(r*B/mass)\n", " return TD0*(r0/r)**(3*Gru)\n", "\n", "\n" ] }, { "cell_type": "markdown", "id": "258f29aa", "metadata": { "tags": [] }, "source": [ "## ヘルムホルツ自由エネルギーの体積依存性\n", "\n", " これらの結果を利用して、次式で表されるヘルムホルツ(Helmholtz)の自由エネルギーの体積依存性を0~3000 Kまでの範囲で算出する。\n", " \n", "$$\n", " \\begin{align}\n", " F(r,T) &= E(r) + E_{D}(r,T) - T \\cdot S_D(r,T)\\\\\n", " &= E(r)-k_B T \\left[f_D\\left(\\frac{\\Theta_D}{T}\\right)-3\\ln \\left(1-\\exp \\left(-\\frac{\\Theta_D}{T}\\right)\\right)\\right]+\\frac{9}{8} k_B \\Theta_D\n", " \\end{align}\n", "$$\n", "\n", "デバイ関数$f_D$は以下の様に定義される。\n", "\n", "$$\n", "f_{D}\\left( \\frac{\\Theta_{D}}{T} \\right) = 3\\left( \\frac{T}{\\Theta_{D}} \\right)^{3}\\int_{0}^{\\frac{\\Theta_{D}}{T}}{\\frac{x^{3}}{e^{x} - 1}dx}\n", "$$\n" ] }, { "cell_type": "code", "execution_count": 10, "id": "356c144e", "metadata": { "tags": [] }, "outputs": [], "source": [ "from scipy import integrate\n", "\n", "def integrand(T):\n", " if T==0:\n", " return 0\n", " return (TD/T)**3/(np.exp(TD/T)-1)\n", "\n", "def Debye(T):\n", " if T==0:\n", " return 0\n", " y, err = integrate.quad(integrand, 0, TD/T)\n", " return (3.)*T * (T/TD)**3 * y\n", "\n", "def FreeEnergy(r,T):\n", " #kB=1.380662e-23 #J/K\n", " kB=1/1.16048e4 #eV/K\n", " F = Morse(morpars,r) - kB*T*(Debye(T)-3*np.log(1-np.exp(-TD/T))) + 9/8*kB*TD\n", " #print(Debye(T))\n", "\n", " return F\n" ] }, { "cell_type": "code", "execution_count": 12, "id": "5e4e08a7", "metadata": { "tags": [] }, "outputs": [ { "name": "stderr", "output_type": "stream", "text": [ "/var/folders/qx/bp1cy1rx2g3b3fqmxf9knzph0000gn/T/ipykernel_14877/2017970456.py:17: RuntimeWarning: divide by zero encountered in scalar divide\n", " F = Morse(morpars,r) - kB*T*(Debye(T)-3*np.log(1-np.exp(-TD/T))) + 9/8*kB*TD\n", "/var/folders/qx/bp1cy1rx2g3b3fqmxf9knzph0000gn/T/ipykernel_14877/2017970456.py:6: RuntimeWarning: overflow encountered in exp\n", " return (TD/T)**3/(np.exp(TD/T)-1)\n" ] }, { "data": { "image/png": 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", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "#make a vector to evaluate fits on with a lot of points so it looks smooth\n", "T_list = np.linspace(0,3000,7)\n", "Nr=rfit.shape[0]\n", "NT=T_list.shape[0]\n", "\n", "def BulkModulus(r): \n", " x=np.exp(-la*r)\n", " return -D*r*la**3/(6*np.pi*np.log(x))*eVA3_to_kbar\n", "\n", "with open('out.csv', 'a') as f:\n", " for T in T_list:\n", " F=[]\n", " for r in rfit:\n", " #print(T)\n", " #F = Debye(T)\n", " #plt.scatter(T,F)\n", "\n", " B=BulkModulus(r)\n", " TD=DebyeTemp(r)\n", " #print(TD)\n", " Tfit=np.full(Nr,T)\n", " F.append(FreeEnergy(r,T))\n", "\n", " #print(F)\n", " #csvファイルとして保存\n", " data = np.c_[Tfit,rfit,F]\n", " np.savetxt(f,data,delimiter='\\t')\n", "\n", " #plt.figure(figsize=(16,10))\n", " plt.scatter(rfit,F, label=T)\n", "\n", " #plt.plot(x,F_model,label=PlotT); # 折れ線グラフのプロット\n", "\n", " #plt.title(PlotT) # x軸ラベルの設定\n", " plt.xlabel('r ($\\AA$)') # x軸ラベルの設定\n", " plt.ylabel('Free energy (eV/atom)'); # y軸ラベルの設定\n", " plt.legend()\n", "\n", "\n", "plt.show()\n", "\n", "\n", " " ] }, { "cell_type": "markdown", "id": "2395926f", "metadata": {}, "source": [ "## 熱膨張\n", "\n", " ここまでで求めたヘルムホルツ自由エネルギーから、各温度における自由エネルギーの最小値をとる原子間距離$r_0$を求めることができる。これをつなげていくと、$r_0$を$T$の関数で表すことができる。つまり、各温度における平衡原子間距離$r_0$を求めることができれば、熱膨張係数が計算できることになる。\n", "\n", " 各温度におけるヘルムホルツ自由エネルギーの最小値をとるには、pandasで最大値・最小値の行名・列名を取得するidxmax, idxminを使います。\n", "\n", "https://pandas.pydata.org/pandas-docs/stable/reference/api/pandas.DataFrame.idxmin.html" ] }, { "cell_type": "code", "execution_count": 13, "id": "02efb35e", "metadata": { "tags": [] }, "outputs": [ { "name": "stderr", "output_type": "stream", "text": [ "/var/folders/qx/bp1cy1rx2g3b3fqmxf9knzph0000gn/T/ipykernel_14877/2585520366.py:3: ParserWarning: Falling back to the 'python' engine because the 'c' engine does not support regex separators (separators > 1 char and different from '\\s+' are interpreted as regex); you can avoid this warning by specifying engine='python'.\n", " df = pd.read_csv('out.csv', delimiter='\\\\t', dtype='float', names=('T', 'r', 'F'))\n", "No artists with labels found to put in legend. Note that artists whose label start with an underscore are ignored when legend() is called with no argument.\n" ] }, { "name": "stdout", "output_type": "stream", "text": [ "Temperature list\n", "[ 0. 500. 1000. 1500. 2000. 2500. 3000.]\n" ] }, { "data": { "image/png": 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EijKIiIigEEKIgR5ET1paWqDT6VBcXIykpKQe2z766KO46aaboFQqUVhYiOrqave6OXPmwOFw4IMPPnAvS01NRVhYGLZs2eLTWBwOB7RaLex2O0JDQ/tUDxERDW69yQLZHcn+nN1uBwCEh4f32C4/Px9ff/01srOzu11/+PBhpKSkeCx74IEHUF5e7rXP9vZ2OBwOjw8REZGvZB2yQgikp6cjMTERRqPRa7v6+npkZGTg3XffRWBgYLdtbDYbxowZ47FszJgxsNlsXvvNzc2FVqt1f6KiovpWCBERDUuyDlmz2YyampoeT+c6nU489thjyMnJwcSJE3vsT6FQeHwXQnRZdrnMzEzY7Xb3p7GxsXcFEBHRsNb9YZ8MWCwW7N69GyUlJYiMjPTarrW1FZ9++imqqqpgNpsBAC6XC0IIBAYGYv/+/bj33nsRERHR5ai1ubm5y9Ht5VQqFVQqlX8KIiKiYUd2R7JCCJjNZuzYsQMHDx6EwWDosX1oaCiOHj2K6upq9+eZZ57BzTffjOrqatx1110AgISEBBw4cMBj2/3792PatGmS1UJERMOb7I5kTSYTCgoKsGvXLmg0GvfRp1arRUhICICLp3GbmpqwceNGBAQEdLleq9PpEBwc7LF8yZIlSEpKwssvv4xHHnkEu3btwkcffYSysrL+K46IiIYV2R3J5uXlwW63Izk5GXq93v3Ztm2bu43VasWJEyd61e+0adOwdetW5OfnY/LkyfiP//gPbNu2zX2kS0RE5G+ynycrJ5wnS0REQ2qeLBER0WDFkCUiIpIIQ5aIiEgiDFkiIiKJMGSJiIgkwpAlIiKSCEOWiIhIIgxZIiIiiTBkiYiIJMKQJSIikghDloiISCIMWSIiIokwZImIiCQiu/fJEhENNKdLoLLhNJpb26DTBCPeEA5lgGKgh0WDEEOWiOgy+45ZkbOnFlZ7m3uZXhuM7FmxSDXqB3BkNBjxdDER0f/Zd8yKxZuPeAQsANjsbVi8+Qj2HbMO0MhosGLIEhHh4ininD21EN2su7QsZ08tnK7uWhB1jyFLRASgsuF0lyPYywkAVnsbKhtO99+gaNBjyBIRAWhu9R6wfWlHBDBkiYgAADpNsF/bEQEMWSIiAEC8IRx6bTC8TdRR4OJdxvGG8P4cFg1yDFkiIgDKAAWyZ8UCQJegvfQ9e1Ys58tSrzBkiYj+T6pRj7x5UxCh9TwlHKENRt68KZwnS7121Q+juHDhAmw2G86fP4/Ro0cjPJynUoho8Eo16nF/bASf+ER+0acj2bNnz+Lf//3fkZycDK1Wi+uvvx6xsbEYPXo0JkyYgKeeegp/+ctf+jSg3NxcxMXFQaPRQKfTIS0tDXV1dT1uU1ZWhunTp2PUqFEICQlBTEwM1qxZ06Xd66+/jptvvhkhISGIiorCs88+i7Y23ilIRJ6UAQokRI/CI7ePQ0L0KAYs9Vmvj2TXrFmDl156Cddffz0efvhhZGRkYNy4cQgJCcHp06dx7NgxlJaW4v7778fdd9+NP/3pT7jpppt87r+4uBgmkwlxcXHo7OzE0qVLkZKSgtraWqjV6m63UavVMJvNmDx5MtRqNcrKyrBo0SKo1Wo8/fTTAIB3330XGRkZeOeddzBt2jR89dVXWLhwobsmIiIif1MIIXr1+JJf/vKX+MMf/oBJkyb12K69vR0bNmzAiBEj8OSTT/Z5gC0tLdDpdCguLkZSUpLP282ePRtqtRqbNm0CAJjNZnzxxRf4n//5H3eb5557DpWVlSgtLfWpT4fDAa1WC7vdjtDQ0N4VQkREQ0JvsqDXR7L/9V//5VM7lUqF3/72t73tvgu73Q4AvbrWW1VVhfLycixfvty9LDExEZs3b0ZlZSXi4+PxzTffYO/evXjiiSe89tPe3o729nb3d4fD0YcKiIhouJL1W3iEEEhPT0diYiKMRuMV20dGRqKlpQWdnZ1YtmyZxxH0o48+ipaWFiQmJkIIgc7OTixevBgZGRle+8vNzUVOTo5faiEiouHH71N4Tp06hYMHD+K111676r7MZjNqamqwZcsWn9qXlpbi008/xVtvvYXXX3/dY7uioiK89NJLWLduHY4cOYIdO3bgv//7v/Gv//qvXvvLzMyE3W53fxobG6+6JiIiGj58vib717/+FS+++CKuvfZarFixAmFhYaivr0d1dTU+//xz9/+ePHkSQgio1Wq0trb2eWAWiwWFhYUoKSmBwWDo9fbLly/Hpk2b3Hcm33PPPbj77ruxatUqd5vNmzfj6aefxtmzZxEQcOV/b/CaLBERSXJN9vHHH8e8efNgMBhw6623orW1FefOnYNWq0VsbCyMRiM++OADbNiwATNnzkRUVFSfBi+EgMViwc6dO1FUVNSngL3Uz+XXU8+fP98lSJVKJYQQ6OW9X0RERD7xOWT/9re/wWg04oYbbkBzczOef/55/Pa3v8W4cePcbd555x3Ex8f3OWABwGQyoaCgALt27YJGo4HNZgMAaLVahISEALh4GrepqQkbN24EAKxduxbjx49HTEwMgIvzZlevXg2LxeLud9asWXjttddwxx134K677nIfmT/88MNQKpV9Hi8REZE3PofsG2+8gWeeeQajR4/GW2+9hTfeeAPHjx/HK6+8gokTJ/ptQHl5eQCA5ORkj+X5+fnuea1WqxUnTpxwr3O5XMjMzERDQwMCAwMRHR2NlStXYtGiRe42WVlZUCgUyMrKQlNTE0aPHo1Zs2bhpZde8tvYiYiILtfrebKXOJ1O5OXlYfny5fjHf/xHZGdnY9y4cfj8888RGxvr73HKAq/JEhFRb7Kgz3cXK5VK9wMelEolYmJi4HK54HQ6+9olERHRkHLVU3jCwsLwb//2bygrK8N9992HmTNnYvXq1fjpp5/8MT4iIqJBy2/zZGNjY/Hhhx/inXfewZ///GfccMMN/uqaiIhoUOp1yF5+w1F3HnroIRw9ehT/8i//AgBoamrq28iIiIgGuV6HbFxcHJ566ilUVlZ6bXP+/Hmo1WoYjUbs2LHjqgZIREQ0WPX62cVffPEFVqxYgdTUVAQFBWHq1KkYO3YsgoOD8eOPP6K2thbHjx/H1KlTsWrVKjz44INSjJuIiEj2+jyFp62tDXv37kVpaSm+/fZb/PTTT7juuutwxx134IEHHvDpgf6DDafwEBFRb7KgzyE7HDFkiYioX+bJEhERUc/89j7ZM2fO4MMPP0RTUxMUCgX0ej0eeOABhIWF+esniIiIBhW/HMlu2LAB8fHxqKiocD/1qaKiAnfffTc2bNjgj58gIiIadPxyTfbmm2/GZ599hpEjR3osb21txZ133omvvvrqan9CFnhNloiI+v2arEKhwNmzZ7ssP3v2LBQKhT9+goiIaNDp8zVZp9OJwsJCpKSkYPXq1ZgxYwaMRqP7/bLff/89jh8/jldffdVvgyUiIhpMrup0cUhICI4fP44bbrgBTqcTlZWVOHnyJIQQGDduHOLj44fUC9F5upiIiHqTBVd1d3F8fDwaGhpwww03QKlUIiEh4Wq6IyIiGlKu6prs7373O7zwwgtobGz013iIiIiGjKs6kv3lL38JALj11lvx8MMPIzk5GXfccQcmTZqEESNG+GWAREREg9VVhWxDQwOqq6vx+eefo7q6Grm5ufj222+hVCoRExODmpoaf42TiIho0LmqkJ0wYQImTJiARx55xL2stbUV1dXVDFgiIhr2+IKAXuDdxURExBcEEBERyQBDloiISCIMWSIiIonILmRzc3MRFxcHjUYDnU6HtLQ01NXV9bhNWVkZpk+fjlGjRiEkJAQxMTFYs2ZNl3ZnzpyByWSCXq9HcHAwbrnlFuzdu1eqUoiIaJjz2/tk/aW4uBgmkwlxcXHo7OzE0qVLkZKSgtraWqjV6m63UavVMJvNmDx5MtRqNcrKyrBo0SKo1Wo8/fTTAICOjg7cf//90Ol02L59OyIjI9HY2AiNRtOf5RER0TAi+7uLW1paoNPpUFxcjKSkJJ+3mz17NtRqNTZt2gQAeOutt7Bq1Sp8+eWXCAoK6tNYeHcxERENqbuL7XY7ACA8PNznbaqqqlBeXo4ZM2a4l+3evRsJCQkwmUwYM2YMjEYjVqxYAafT6bWf9vZ2OBwOjw8REZGvZB2yQgikp6cjMTERRqPxiu0jIyOhUqkwdepUmEwmPPnkk+5133zzDbZv3w6n04m9e/ciKysLr776Kl566SWv/eXm5kKr1bo/UVFRfqmLiIiGB1mfLjaZTHj//fdRVlaGyMjIK7ZvaGjA2bNnUVFRgYyMDLz55puYO3cuAGDixIloa2tDQ0OD+/V7r732GlatWgWr1dptf+3t7Whvb3d/dzgciIqK4uliIqJhrN9edScli8WC3bt3o6SkxKeABQCDwQAAmDRpEn744QcsW7bMHbJ6vR5BQUEe77e95ZZbYLPZ0NHR0e0LDVQqFVQqlR+qISKi4Uh2p4uFEDCbzdixYwcOHjzoDs6+9HP5Uej06dPx17/+FS6Xy73sq6++gl6v5xuDiIhIErILWZPJhM2bN6OgoAAajQY2mw02mw0//fSTu01mZiYWLFjg/r527Vrs2bMH9fX1qK+vR35+PlavXo158+a52yxevBinTp3CkiVL8NVXX+H999/HihUrYDKZ+rU+IiIaPmR3ujgvLw8AkJyc7LE8Pz8fCxcuBABYrVacOHHCvc7lciEzMxMNDQ0IDAxEdHQ0Vq5ciUWLFrnbREVFYf/+/Xj22WcxefJkjBs3DkuWLMHzzz8veU1ERDQ8yfrGJ7nhPFkazpwugcqG02hubYNOE4x4QziUAYqBHhZRvxsSNz4RkXzsO2ZFzp5aWO1t7mV6bTCyZ8Ui1agfwJERyZvsrskSkbzsO2bF4s1HPAIWAGz2NizefAT7jnU/BY6IGLJE1AOnSyBnTy26u6Z0aVnOnlo4XbzqRNQdhiwReVXZcLrLEezlBACrvQ2VDaf7b1BEgwhDloi8am71HrB9aUc03DBkicgrnSbYr+2IhhuGLBF5FW8Ih14bDG8TdRS4eJdxvMH3t2QRDScMWSLyShmgQPasWADoErSXvmfPiuV8WSIvGLJE1KNUox5586YgQut5SjhCG4y8eVM4T5aoB3wYBRFdUapRj/tjI/jEJ6JeYsgSkU+UAQokRI8a6GEQDSo8XUxERCQRhiwREZFEGLJEREQSYcgSERFJhCFLREQkEYYsERGRRBiyREREEmHIEhERSYQhS0REJBGGLBERkUQYskRERBJhyBIREUlEdiGbm5uLuLg4aDQa6HQ6pKWloa6ursdtysrKMH36dIwaNQohISGIiYnBmjVrvLbfunUrFAoF0tLS/Dx6IiKi/ye7t/AUFxfDZDIhLi4OnZ2dWLp0KVJSUlBbWwu1Wt3tNmq1GmazGZMnT4ZarUZZWRkWLVoEtVqNp59+2qPtd999h9///ve45557+qMcIiIaxhRCCDHQg+hJS0sLdDodiouLkZSU5PN2s2fPhlqtxqZNm9zLnE4nZsyYgV//+tcoLS3FmTNnUFhY6HOfDocDWq0WdrsdoaGhvSmDiIiGiN5kgexOF/+c3W4HAISHh/u8TVVVFcrLyzFjxgyP5X/84x8xevRo/OY3v/HrGImIiLoju9PFlxNCID09HYmJiTAajVdsHxkZiZaWFnR2dmLZsmV48skn3esOHTqEDRs2oLq62uffb29vR3t7u/u7w+Ho1fiJiGh4k3XIms1m1NTUoKyszKf2paWlOHv2LCoqKpCRkYEbb7wRc+fORWtrK+bNm4f169fjuuuu8/n3c3NzkZOT09fhExHRMCfba7IWiwWFhYUoKSmBwWDo9fbLly/Hpk2bUFdXh+rqatxxxx1QKpXu9S6XCwAQEBCAuro6REdHd+mjuyPZqKgoXpMlIhrGenNNVnZHskIIWCwW7Ny5E0VFRX0K2Ev9XArImJgYHD161GN9VlYWWltb8cYbbyAqKqrbPlQqFVQqVZ9+n4iISHYhazKZUFBQgF27dkGj0cBmswEAtFotQkJCAACZmZloamrCxo0bAQBr167F+PHjERMTA+DivNnVq1fDYrEAAIKDg7tc07322msBwKdrvURERH0hu5DNy8sDACQnJ3ssz8/Px8KFCwEAVqsVJ06ccK9zuVzIzMxEQ0MDAgMDER0djZUrV2LRokX9NWwiIqIuZHtNVo44T5aIiIbUPFkiIqLBiiFLREQkEYYsERGRRBiyREREEmHIEhERSUR2U3iIBhunS6Cy4TSaW9ug0wQj3hAOZYBioIdFRDLAkCW6CvuOWZGzpxZWe5t7mV4bjOxZsUg16gdwZEQkBzxdTNRH+45ZsXjzEY+ABQCbvQ2LNx/BvmPWARoZEckFQ5aoD5wugZw9tejuSS6XluXsqYXTxWe9EA1nDFmiPqhsON3lCPZyAoDV3obKhtP9Nygikh2GLFEfNLd6D9i+tCOioYkhS9QHOk2wX9sR0dDEkCXqg3hDOPTaYHibqKPAxbuM4w3h/TksIpIZhixRHygDFMieFQsAXYL20vfsWbGcL0s0zDFkifoo1ahH3rwpiNB6nhKO0AYjb94UzpMlIj6MguhqpBr1uD82gk98IqJuMWSJrpIyQIGE6FEDPQwikiGeLiYiIpIIQ5aIiEgiDFkiIiKJMGSJiIgkwpAlIiKSCEOWiIhIIgxZIiIiicguZHNzcxEXFweNRgOdToe0tDTU1dX1uE1ZWRmmT5+OUaNGISQkBDExMVizZo1Hm/Xr1+Oee+5BWFgYwsLCcN9996GyslLKUoiIaJiTXcgWFxfDZDKhoqICBw4cQGdnJ1JSUnDu3Dmv26jVapjNZpSUlOCLL75AVlYWsrKy8Pbbb7vbFBUVYe7cufj4449x+PBhjB8/HikpKWhqauqPsoiIaBhSCCHEQA+iJy0tLdDpdCguLkZSUpLP282ePRtqtRqbNm3qdr3T6URYWBjefPNNLFiwwKc+HQ4HtFot7HY7QkNDfR4LERENHb3JAtkdyf6c3W4HAISH+/7KsKqqKpSXl2PGjBle25w/fx4XLlzosd/29nY4HA6PDxERka9kHbJCCKSnpyMxMRFGo/GK7SMjI6FSqTB16lSYTCY8+eSTXttmZGRg3LhxuO+++7y2yc3NhVardX+ioqL6VAcREQ1Psn5BgNlsRk1NDcrKynxqX1pairNnz6KiogIZGRm48cYbMXfu3C7tXnnlFWzZsgVFRUUIDg7upqeLMjMzkZ6e7v7ucDgYtERE5DPZhqzFYsHu3btRUlKCyMhIn7YxGAwAgEmTJuGHH37AsmXLuoTs6tWrsWLFCnz00UeYPHlyj/2pVCqoVKq+FUBERMOe7EJWCAGLxYKdO3eiqKjIHZx96ae9vd1j2apVq7B8+XJ8+OGHmDp1qj+GS0RE5JXsQtZkMqGgoAC7du2CRqOBzWYDAGi1WoSEhAC4eBq3qakJGzduBACsXbsW48ePR0xMDICL82ZXr14Ni8Xi7veVV17Biy++iIKCAlx//fXufkeOHImRI0f2Z4lERDRMyC5k8/LyAADJyckey/Pz87Fw4UIAgNVqxYkTJ9zrXC4XMjMz0dDQgMDAQERHR2PlypVYtGiRu826devQ0dGBX/ziFx79ZmdnY9myZZLUQkREw5vs58nKCefJEhHRkJonS0RENFgxZImIiCTCkCUiIpIIQ5aIiEgiDFkiIiKJMGSJiIgkwpAlIiKSCEOWiIhIIgxZIiIiiTBkiYiIJCK7ZxfT0OB0CVQ2nEZzaxt0mmDEG8KhDFAM9LCIiPoVQ5b8bt8xK3L21MJqb3Mv02uDkT0rFqlG/QCOjIiof/F0MfnVvmNWLN58xCNgAcBmb8PizUew75h1gEZGRNT/GLLkN06XQM6eWnT3WqdLy3L21MLp4oufiGh4YMiS31Q2nO5yBHs5AcBqb0Nlw+n+GxQR0QBiyJLfNLd6D9i+tCMiGuwYsuQ3Ok2wX9sREQ12DFnym3hDOPTaYHibqKPAxbuM4w3h/TksIqIBw5Alv1EGKJA9KxYAugTtpe/Zs2I5X5aIhg2GLPlVqlGPvHlTEKH1PCUcoQ1G3rwpnCdLRMMKH0ZBfpdq1OP+2Ag+8YmIhj2GLElCGaBAQvSogR4GEdGA4uliIiIiiTBkiYiIJCK7kM3NzUVcXBw0Gg10Oh3S0tJQV1fX4zZlZWWYPn06Ro0ahZCQEMTExGDNmjVd2r333nuIjY2FSqVCbGwsdu7cKVUZRERE8gvZ4uJimEwmVFRU4MCBA+js7ERKSgrOnTvndRu1Wg2z2YySkhJ88cUXyMrKQlZWFt5++213m8OHD2POnDmYP38+Pv/8c8yfPx+/+tWv8Mknn/RHWURENAwphBCyflp7S0sLdDodiouLkZSU5PN2s2fPhlqtxqZNmwAAc+bMgcPhwAcffOBuk5qairCwMGzZssWnPh0OB7RaLex2O0JDQ3tXCBERDQm9yQLZHcn+nN1uBwCEh/v+lKCqqiqUl5djxowZ7mWHDx9GSkqKR7sHHngA5eXlXvtpb2+Hw+Hw+BAREflK1iErhEB6ejoSExNhNBqv2D4yMhIqlQpTp06FyWTCk08+6V5ns9kwZswYj/ZjxoyBzWbz2l9ubi60Wq37ExUV1fdiiIho2JF1yJrNZtTU1Ph8Ore0tBSffvop3nrrLbz++utdtlMoPB+GIITosuxymZmZsNvt7k9jY2PviyAiomFLtg+jsFgs2L17N0pKShAZGenTNgaDAQAwadIk/PDDD1i2bBnmzp0LAIiIiOhy1Nrc3Nzl6PZyKpUKKpWqjxUQEdFwJ7sjWSEEzGYzduzYgYMHD7qDsy/9tLe3u78nJCTgwIEDHm3279+PadOmXdV4iYiIvJHdkazJZEJBQQF27doFjUbjPvrUarUICQkBcPE0blNTEzZu3AgAWLt2LcaPH4+YmBgAF+fNrl69GhaLxd3vkiVLkJSUhJdffhmPPPIIdu3ahY8++ghlZWX9XCEREQ0XsgvZvLw8AEBycrLH8vz8fCxcuBAAYLVaceLECfc6l8uFzMxMNDQ0IDAwENHR0Vi5ciUWLVrkbjNt2jRs3boVWVlZePHFFxEdHY1t27bhrrvukrwmIiIanmQ/T1ZOrnaerNMl+GYaIqJBrjdZILsj2aFq3zErcvbUwmpvcy/Ta4ORPSuW71glIhqiZHfj01C075gVizcf8QhYALDZ27B48xHsO2YdoJEREZGUGLISc7oEcvbUortz8peW5eyphdPFs/ZEREMNQ1ZilQ2nuxzBXk4AsNrbUNlwuv8GRURE/YIhK7HmVu8B25d2REQ0eDBkJabTBPu1HRERDR4MWYnFG8Kh1wbD20QdBS7eZRxv8P0tQ0RENDgwZCWmDFAge1YsAHQJ2kvfs2fFcr4sEdEQxJDtB6lGPfLmTUGE1vOUcIQ2GHnzpnCeLBHREMWHUfSTVKMe98dG8IlPRETDCEO2HykDFEiIHjXQwyAion7C08VEREQSYcgSERFJhCFLREQkEYYsERGRRBiyREREEmHIEhERSYRTeHpBiIuvo3M4HAM8EiIiGiiXMuBSJvSEIdsLra2tAICoqKgBHgkREQ201tZWaLXaHtsohC9RTAAAl8uFkydPQqPRQKHo25OaHA4HoqKi0NjYiNDQUD+PUF5Y69AzXOoEWOtQ5Y9ahRBobW3F2LFjERDQ81VXHsn2QkBAACIjI/3SV2ho6JD/j/kS1jr0DJc6AdY6VF1trVc6gr2ENz4RERFJhCFLREQkEYZsP1OpVMjOzoZKpRrooUiOtQ49w6VOgLUOVf1dK298IiIikgiPZImIiCTCkCUiIpIIQ5aIiEgiDFkiIiKJMGT72bp162AwGBAcHIw777wTpaWlAz2kXlm2bBkUCoXHJyIiwr1eCIFly5Zh7NixCAkJQXJyMo4fP+7RR3t7OywWC6677jqo1Wo8/PDD+P777/u7lC5KSkowa9YsjB07FgqFAoWFhR7r/VXbjz/+iPnz50Or1UKr1WL+/Pk4c+aMxNX9vyvVuXDhwi77+O677/ZoMxjqzM3NRVxcHDQaDXQ6HdLS0lBXV+fRZqjsU19qHSr7NS8vD5MnT3Y/TCIhIQEffPCBe73s9qmgfrN161YRFBQk1q9fL2pra8WSJUuEWq0W33333UAPzWfZ2dni1ltvFVar1f1pbm52r1+5cqXQaDTivffeE0ePHhVz5swRer1eOBwOd5tnnnlGjBs3Thw4cEAcOXJE/N3f/Z247bbbRGdn50CU5LZ3716xdOlS8d577wkAYufOnR7r/VVbamqqMBqNory8XJSXlwuj0Sgeeuih/irzinU+8cQTIjU11WMfnzp1yqPNYKjzgQceEPn5+eLYsWOiurpa/MM//IMYP368OHv2rLvNUNmnvtQ6VPbr7t27xfvvvy/q6upEXV2deOGFF0RQUJA4duyYEEJ++5Qh24/i4+PFM88847EsJiZGZGRkDNCIei87O1vcdttt3a5zuVwiIiJCrFy50r2sra1NaLVa8dZbbwkhhDhz5owICgoSW7dudbdpamoSAQEBYt++fZKOvTd+Hj7+qq22tlYAEBUVFe42hw8fFgDEl19+KXFVXXkL2UceecTrNoOxTiGEaG5uFgBEcXGxEGLo7lMhutYqxNDdr0IIERYWJv785z/Lcp/ydHE/6ejowGeffYaUlBSP5SkpKSgvLx+gUfVNfX09xo4dC4PBgEcffRTffPMNAKChoQE2m82jRpVKhRkzZrhr/Oyzz3DhwgWPNmPHjoXRaJT134O/ajt8+DC0Wi3uuusud5u7774bWq1WVvUXFRVBp9Nh4sSJeOqpp9Dc3OxeN1jrtNvtAIDw8HAAQ3uf/rzWS4bafnU6ndi6dSvOnTuHhIQEWe5Thmw/+dvf/gan04kxY8Z4LB8zZgxsNtsAjar37rrrLmzcuBEffvgh1q9fD5vNhmnTpuHUqVPuOnqq0WazYcSIEQgLC/PaRo78VZvNZoNOp+vSv06nk039Dz74IN59910cPHgQr776Kv7yl7/g3nvvRXt7O4DBWacQAunp6UhMTITRaAQwdPdpd7UCQ2u/Hj16FCNHjoRKpcIzzzyDnTt3IjY2Vpb7lG/h6Wc/f0WeEKLPr80bCA8++KD7z5MmTUJCQgKio6Pxn//5n+6bKPpS42D5e/BHbd21l1P9c+bMcf/ZaDRi6tSpmDBhAt5//33Mnj3b63ZyrtNsNqOmpgZlZWVd1g21feqt1qG0X2+++WZUV1fjzJkzeO+99/DEE0+guLjY6xgHcp/ySLafXHfddVAqlV3+FdTc3NzlX12DiVqtxqRJk1BfX+++y7inGiMiItDR0YEff/zRaxs58ldtERER+OGHH7r039LSItv69Xo9JkyYgPr6egCDr06LxYLdu3fj448/9nhV5VDcp95q7c5g3q8jRozAjTfeiKlTpyI3Nxe33XYb3njjDVnuU4ZsPxkxYgTuvPNOHDhwwGP5gQMHMG3atAEa1dVrb2/HF198Ab1eD4PBgIiICI8aOzo6UFxc7K7xzjvvRFBQkEcbq9WKY8eOyfrvwV+1JSQkwG63o7Ky0t3mk08+gd1ul239p06dQmNjI/R6PYDBU6cQAmazGTt27MDBgwdhMBg81g+lfXqlWrszWPdrd4QQaG9vl+c+7dVtUnRVLk3h2bBhg6itrRX//M//LNRqtfj2228Hemg+e+6550RRUZH45ptvREVFhXjooYeERqNx17By5Uqh1WrFjh07xNGjR8XcuXO7vX0+MjJSfPTRR+LIkSPi3nvvlcUUntbWVlFVVSWqqqoEAPHaa6+Jqqoq9xQrf9WWmpoqJk+eLA4fPiwOHz4sJk2a1K9TIHqqs7W1VTz33HOivLxcNDQ0iI8//lgkJCSIcePGDbo6Fy9eLLRarSgqKvKYtnL+/Hl3m6GyT69U61Dar5mZmaKkpEQ0NDSImpoa8cILL4iAgACxf/9+IYT89ilDtp+tXbtWTJgwQYwYMUJMmTLF4xb7weDSnLOgoCAxduxYMXv2bHH8+HH3epfLJbKzs0VERIRQqVQiKSlJHD161KOPn376SZjNZhEeHi5CQkLEQw89JE6cONHfpXTx8ccfCwBdPk888YQQwn+1nTp1Sjz++ONCo9EIjUYjHn/8cfHjjz/2U5U913n+/HmRkpIiRo8eLYKCgsT48ePFE0880aWGwVBndzUCEPn5+e42Q2WfXqnWobRf/+mf/sn9/6GjR48WM2fOdAesEPLbp3zVHRERkUR4TZaIiEgiDFkiIiKJMGSJiIgkwpAlIiKSCEOWiIhIIgxZIiIiiTBkiYiIJMKQJSIikghDloh6pFAoevwsXLhwoIdIJFt81R0R9chqtbr/vG3bNvzhD39AXV2de1lISMhADItoUGDIElGPLr0+DAC0Wi0UCoXHMiLyjqeLiYiIJMKQJSIikghDloiISCIMWSIiIokwZImIiCTCkCUiIpIIQ5aIiEgiCiGEGOhBEBERDUU8kiUiIpIIQ5aIiEgiDFkiIiKJMGSJiIgkwpAlIiKSCEOWiIhIIgxZIiIiiTBkiYiIJMKQJSIikghDloiISCIMWSIiIokwZImIiCTyv9ILWYh/ry0YAAAAAElFTkSuQmCC", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "import pandas as pd\n", "\n", "df = pd.read_csv('out.csv', delimiter='\\\\t', dtype='float', names=('T', 'r', 'F'))\n", "\n", "print(\"Temperature list\")\n", "Tlist=df['T'].unique()\n", "print(Tlist)\n", "\n", "r0_T=[]\n", "\n", "for i in Tlist:\n", " PlotT = i\n", " #print(\\\"T=\\\",PlotT,\\\"K\\\")\n", "\n", " df2 = df[df['T'] == PlotT ]\n", "\n", " x=df2['T']\n", " r=df2['r']\n", " F=df2['F']\n", " #print(df2['r'][df2['F'].idxmin()])\n", " r0_T.append(df2['r'][df2['F'].idxmin()])\n", " \n", "plt.scatter(Tlist,r0_T)\n", "\n", "#plt.title(PlotT) # x軸ラベルの設定\n", "plt.xlabel('T') # x軸ラベルの設定\n", "plt.ylabel('$r_0 (\\AA)$'); # y軸ラベルの設定\n", "plt.legend()\n", "\n", "plt.show()" ] }, { "cell_type": "markdown", "id": "236a07c4", "metadata": { "tags": [] }, "source": [ "## 線熱膨張係数\n", "\n", " 線熱膨張系数$\\alpha$は以下の式で定義される。\n", "\n", "$$\n", "\\alpha = \\frac{1}{r_0} \\frac{dr_0}{dT}\n", "$$\n", "\n", "```\n", "*****here*****\n", "```\n", "\n", "に正しい式を記入して実行してください。" ] }, { "cell_type": "code", "execution_count": 15, "id": "aa7640cc", "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "α= 1.2060301913129738e-05 (1/K)\n" ] } ], "source": [ "#*****here*****\n", "\n", "print(\"α=\" ,alpha, \"(1/K)\")" ] }, { "cell_type": "markdown", "id": "3bd7a788", "metadata": {}, "source": [ "### (参考)極小値の求め方" ] }, { "cell_type": "code", "execution_count": 16, "id": "9e18057b", "metadata": { "tags": [] }, "outputs": [ { "name": "stderr", "output_type": "stream", "text": [ "/var/folders/qx/bp1cy1rx2g3b3fqmxf9knzph0000gn/T/ipykernel_14877/1048669438.py:5: ParserWarning: Falling back to the 'python' engine because the 'c' engine does not support regex separators (separators > 1 char and different from '\\s+' are interpreted as regex); you can avoid this warning by specifying engine='python'.\n", " df = pd.read_csv('out.csv', delimiter='\\\\t', dtype='float', names=('T', 'r', 'F'))\n", "No artists with labels found to put in legend. Note that artists whose label start with an underscore are ignored when legend() is called with no argument.\n" ] }, { "name": "stdout", "output_type": "stream", "text": [ "2.307654929948991\n" ] }, { "data": { "image/png": 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", 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" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "import pandas as pd\n", "from pylab import * #this includes numpy as np!\n", "from scipy.signal import argrelmin, argrelmax\n", "\n", "df = pd.read_csv('out.csv', delimiter='\\\\t', dtype='float', names=('T', 'r', 'F'))\n", "\n", "#print(\"Temperature list\")\n", "Tlist=df['T'].unique()\n", "#print(Tlist)\n", " \n", "PlotT = 500\n", "#print(\\\"T=\\\",PlotT,\\\"K\\\")\n", "\n", "df2 = df[df['T'] == PlotT ]\n", "\n", "x=df2['T']\n", "r=df2['r']\n", "F=df2['F']\n", "\n", "print(df2['r'][df2['F'].idxmin()])\n", "\n", "plt.scatter(r,F)\n", "\n", "#plt.title(PlotT) # x軸ラベルの設定\n", "plt.xlabel('r') # x軸ラベルの設定\n", "plt.ylabel('Free energy (J/mol)'); # y軸ラベルの設定\n", "plt.legend()\n", "\n", "plt.show()\n", "\n" ] }, { "cell_type": "code", "execution_count": null, "id": "8f257110", "metadata": {}, "outputs": [], "source": [] } ], "metadata": { "kernelspec": { "display_name": "Python 3 (ipykernel)", "language": "python", "name": "python3" }, "language_info": { "codemirror_mode": { "name": "ipython", "version": 3 }, "file_extension": ".py", "mimetype": "text/x-python", "name": "python", "nbconvert_exporter": "python", "pygments_lexer": "ipython3", "version": "3.11.6" } }, "nbformat": 4, "nbformat_minor": 5 }