電気抵抗計算_グリューナイゼン.ipynb

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   "source": [
    "# 電気抵抗計算：グリューナイゼンの式  \n",
    "\n",
    "（初版：2020年3月、更新：2023年2月21日）  \n",
    "\n",
    "フォノンによる電気抵抗（グリューナイゼンの式）は、下記のように表されます。  \n",
    "\n",
    "　　$\\rho (T) = C \\bigl( \\frac{T}{\\Theta_D} \\bigr)^5 \\int_{0}^{\\Theta_D /T} \\frac{x^5}{(e^x - 1)(1 - e^x)} dx$  \n",
    "  \n",
    "この計算をJuliaですると、以下のようになります。"
   ]
  },
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   "execution_count": 1,
   "metadata": {},
   "outputs": [
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     "output_type": "stream",
     "text": [
      "  0.000158 seconds (114 allocations: 36.484 KiB)\n"
     ]
    },
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3061.56,153.406 3062.48,153.134 3063.39,152.864 3064.31,152.595 3065.22,152.327 3066.12,152.061 3067.03,151.797 3067.92,151.533 3068.82,151.272 3069.71,151.011 3070.6,150.752 3071.48,150.495 3072.36,150.238 3073.24,149.983 3074.11,149.73 3074.98,149.477 3075.85,149.226 3076.71,148.976 3077.57,148.728 3078.42,148.481 3079.27,148.234 3080.12,147.99 3080.97,147.746 3081.81,147.504 3082.65,147.262 3083.49,147.022 3084.32,146.783 3085.15,146.545 3085.97,146.309 3086.8,146.073 3087.62,145.839 3088.43,145.605 3089.25,145.373 3090.06,145.142 3090.86,144.912 3091.67,144.683 3092.47,144.455 3093.27,144.228 3094.06,144.002 3094.86,143.777 3095.65,143.553 3096.43,143.331 3097.22,143.109 3098,142.888 3098.77,142.668 3099.55,142.449 3100.32,142.231 3101.09,142.014 3101.86,141.798 3102.62,141.583 3103.39,141.369 3104.14,141.155 3104.9,140.943 3105.65,140.731 3106.41,140.521 3107.15,140.311 3107.9,140.102 3108.64,139.894 3109.38,139.687 3110.12,139.481 3110.86,139.276 3111.59,139.071 3112.32,138.867 3113.05,138.664 3113.78,138.462 3114.5,138.261 3115.22,138.061 3115.94,137.861 \"/>\n",
       "</svg>\n"
      ]
     },
     "execution_count": 1,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "using Plots\n",
    "using Plots.PlotMeasures\n",
    "using QuadGK\n",
    "using LaTeXStrings\n",
    "\n",
    "#//---------- 図の描画のための関数 ----------//\n",
    "function DataPlot(xwave, ywave, titlename)\n",
    "    Plots.reset_defaults()\n",
    "    Plots.gr(\n",
    "        titlefont=Plots.font(\"sans-serif\", 12),\n",
    "        legendfont=Plots.font(\"sans-serif\", 8),\n",
    "        guidefont=Plots.font(\"sans-serif\", 10),\n",
    "        tickfont=Plots.font(\"sans-serif\", 8),\n",
    "    )\n",
    "    Plots.plot(size=(400, 400))\n",
    "    p1 = Plots.plot(xwave, ywave,\n",
    "        xscale = :identity, yscale = :identity,\n",
    "        seriestype=:line, title=titlename, legend=false\n",
    "    )\n",
    "    p2 = Plots.plot(xwave, ywave,\n",
    "        xscale = :log10, yscale = :log10,\n",
    "        seriestype=:line, title=titlename, legend=false\n",
    "    )\n",
    "    Plots.plot(p1,p2,layout=(1,2),size=(800,400), bottom_margin = 20px, left_margin = [15px 15px 15px])\n",
    "    Plots.plot!(ylabel=L\"R_\\textrm{phonon}\")\n",
    "    Plots.plot!(xlabel=L\"T\\quad \\textrm{(K)}\")\n",
    "end\n",
    "\n",
    "#//---------- グリューナイゼンの式の計算をする関数 ----------//\n",
    "function ResistivityCalc()\n",
    "    \n",
    "    DT = 300 # デバイ温度 (K)。\n",
    "    C = 10000 # 適当な定数。\n",
    "    \n",
    "    #温度の設定\n",
    "    temp = collect(1:1:300)\n",
    "    #グリューナイゼンの式の計算\n",
    "    f(x) = x^5/((exp(x)-1)*(1-exp(-x))) #積分する式の定義\n",
    "    intpart1 = quadgk.(f, 0, DT./temp) #積分部分の実行\n",
    "    intpart2 = [intpart1[i][1] for i in 1:length(intpart1)] #TupleをArrayに変換とか\n",
    "    calcR = (C/DT)*((temp./DT).^5).*intpart2\n",
    "\n",
    "    return temp, calcR\n",
    "end\n",
    "\n",
    "#//---------- 計算の実行 ----------//\n",
    "@time temp, calcR = ResistivityCalc()\n",
    "\n",
    "#//---------- 図の描画とデータ保存 ----------//\n",
    "DataPlot(temp, calcR, \"Grüneisen Low\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "\"GruneisenR.csv\""
      ]
     },
     "execution_count": 2,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "using CSV, DataFrames\n",
    "function saveData2(xwave, y1wave, filename::String)\n",
    "    df = DataFrame(temp = xwave, resistivity = y1wave);\n",
    "    df |> CSV.write(filename)\n",
    "end\n",
    "\n",
    "saveData2(temp, calcR, \"GruneisenR.csv\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  }
 ],
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