{"cells": [{"cell_type": "markdown", "metadata": {"tags": ["module-ltg"]}, "source": ["# Stability Diagram\n", "[Low-Temperature Geochemistry](module-ltg) \n", "```{index} Stability Diagram\n", "```\n", "\n", "Stability diagrams (dominance diagrams) are graphical representations of equilibria between minerals and aqueous solutions. They are useful in predicting what will happen when aqueous solutions of given composition interact with specific minerals. \n", "\n", "Stability diagrams can be built from thermodynamic data on $\\Delta G$ of various reactions, $\\Delta G^\\circ = -RT \\ln(K)$, and expressions of thermodynamic equilibrium constants ($K$). Let's recall Problem 1 in Practical 3 of Low-Temperature Geochemistry."]}, {"cell_type": "code", "execution_count": 1, "metadata": {"tags": ["hide-input"]}, "outputs": [], "source": ["# import relevant modules\n", "\n", "%matplotlib inline\n", "import numpy as np\n", "import matplotlib.pyplot as plt\n", "import pandas as pd\n", "from IPython.display import display"]}, {"cell_type": "markdown", "metadata": {}, "source": ["Consider the weathering of the mineral albite (a Na-plagioclase feldspar)\n", "\n", "$$2NaAlSi_{3}O_{8}(s)+2H^{+}(aq)+9H_{2}O(l)=Al_{2}Si_{2}O_{5}(OH)_{4}(s)+2Na^{+}(aq)+4H_{4}SiO_{4}(aq)$$\n", "\n", "a) Write the reaction quotient for this reaction ($Q=\u2026$).\n", "\n", "$$Q=\\frac{a_{Al_{2}Si_{2}O_{5}(OH)_{4}} \\cdot a_{Na^+}^2 \\cdot a_{H_{4}SiO_{4}}^4}{a_{NaAlSi_{3}O_{8}}^2 \\cdot a_{H^{+}}^2 \\cdot a_{H_{2}O}^9}$$\n", "\n", "b) Now assume this reaction is at equilibrium, write the equilibrium constant for this reaction ($K_{eq}=\u2026$).\n", "\n", "At equilibrium, $Q=K_{eq}$, so it\u2019s the same:\n", "\n", "$$Q=K_{eq}=\\frac{a_{Al_{2}Si_{2}O_{5}(OH)_{4}} \\cdot a_{Na^+}^2 \\cdot a_{H_{4}SiO_{4}}^4}{a_{NaAlSi_{3}O_{8}}^2 \\cdot a_{H^{+}}^2 \\cdot a_{H_{2}O}^9}$$\n", "\n", "c) Assume that you know the activities of each species ($a_i$), how would you simplify your answer in part a or b? Remember that for pure solids and liquids $a_j=1$.\n", "\n", "The key is to note that the activity for pure liquids and pure solids are 1, so we can simplify the expression as follows:\n", "\n", "$$K_{eq}=\\frac{1 \\cdot a_{Na^+}^2 \\cdot a_{H_{4}SiO_{4}}^4}{1 \\cdot a_{H^{+}}^2 \\cdot 1}=\\frac{a_{Na^+}^2 \\cdot a_{H_{4}SiO_{4}}^4}{a_{H^{+}}^2}$$\n", "\n", "d) The answer to part c should be\n", "\n", "$$K_{eq}=a_{H_{4}SiO_{4}}^4 \\cdot \\frac{a_{Na^+}^2}{a_{H^{+}}^2}$$\n", "\n", "Now take the logarithm on both side:\n", "\n", "$$\\log (K_{eq})=\\log \\left(a_{H_{4}SiO_{4}}^4 \\cdot \\frac{a_{Na^+}^2}{a_{H^{+}}^2}\\right)$$\n", "\n", "Simplify this expression by evaluating the logs:\n", "\n", "$$\\log (K_{eq})=4\\log (a_{H_{4}SiO_{4}}) + 2\\log \\left(\\frac{a_{Na^+}}{a_{H^{+}}}\\right)$$\n", "\n", "Rearrange to get:\n", "\n", "$$\\log \\left(\\frac{a_{Na^+}}{a_{H^{+}}}\\right) = -2\\log (a_{H_{4}SiO_{4}}) + \\frac{1}{2}\\log (K_{eq})$$\n", "\n", "Note this could be the equation of a straight line: $y=mx+b$, with slope $m=-2$, $y=\\ln\\left(\\frac{a_{Na^+}}{a_{H^{+}}}\\right)$, $x=\\log (a_{H_{4}SiO_{4}})$ and the y-intercept $b=\\frac{1}{2}\\log (K_{eq})$ If you were to plot this on a log-log plot, the slope is known, ($m=-2$), so all there is to define, is the intercept, meaning that one needs to evaluate $K_{eq}$.\n", "\n", "(i) Evaluate $K_{eq}$ by applying Hess\u2019 law to calculate the Gibbs free energy using the data in Table 1 (taken from P. Ryan\u2019s book, p. 278) and then applying this to the expression $\\Delta G_r^\\circ = -RT \\ln(K_{eq})$ and solving for $K_{eq}$."]}, {"cell_type": "code", "execution_count": 4, "metadata": {}, "outputs": [{"name": "stdout", "output_type": "stream", "text": ["Table 1: Thermodynamic data from P. Ryan's book, p278.\n"]}, {"data": {"text/html": ["\n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", "
Chemical formula of compound or species Name $G_{f}^{o}$
$NaAlSi_{3}O_{8}$Albite (low albite)-3712
$Al_{2}Si_{2}O_{5}(OH)_{4}$Kaolinite-3778
$Na_{0.33}Al_{2}(Si_{3.67}Al_{0.33})O_{10}(OH)_{2}$Na-beidellite-5354
$Al(OH)_3$Gibbsite-1144
$H^+$Hydrogen ion0
$H_{2}O(l)$Water-237.2
$Na^{+}(aq)$Sodium ion-261.7
$H_{4}SiO_{4}$Dissolved silica-1316
"], "text/plain": [""]}, "metadata": {}, "output_type": "display_data"}], "source": ["# Table 1\n", "# data\n", "compounds = [\"$NaAlSi_{3}O_{8}$\",\n", " \"$Al_{2}Si_{2}O_{5}(OH)_{4}$\",\n", " \"$Na_{0.33}Al_{2}(Si_{3.67}Al_{0.33})O_{10}(OH)_{2}$\",\n", " \"$Al(OH)_3$\",\n", " \"$H^+$\",\n", " \"$H_{2}O(l)$\",\n", " \"$Na^{+}(aq)$\",\n", " \"$H_{4}SiO_{4}$\"]\n", "names = [\"Albite (low albite)\", \"Kaolinite\", \"Na-beidellite\", \"Gibbsite\", \"Hydrogen ion\", \"Water\", \"Sodium ion\", \"Dissolved silica\"]\n", "std_Gf = [-3712, -3778, -5354, -1144, 0, -237.2, -261.7, -1316] # kJ/mol\n", "\n", "dict1 = {'Chemical formula of compound or species' : compounds,\n", " 'Name' : names,\n", " '$G_{f}^{o}$' : std_Gf}\n", "df1 = pd.DataFrame(dict1)\n", "df1.loc[:, '$G_{f}^{o}$'] = df1['$G_{f}^{o}$'].map('{:g}'.format)\n", " \n", "print(\"Table 1: Thermodynamic data from P. Ryan's book, p278.\")\n", "# displaying the DataFrame\n", "display(df1.style.hide_index())"]}, {"cell_type": "markdown", "metadata": {}, "source": ["By Hess' law,\n", " \n", "$$\\Delta G_r = \\left(\\Delta G_f^\\circ\\left(Al_{2}Si_{2}O_{5}(OH)_{4}(s)\\right) + 2\\Delta G_f^\\circ\\left(Na^{+}(aq)\\right) + 4\\Delta G_f^\\circ\\left(H_{4}SiO_{4}(aq)\\right)\\right) \\\\ - \\left(2\\Delta G_f^\\circ\\left(NaAlSi_{3}O_{8}(s)\\right) + 2\\Delta G_f^\\circ\\left(H^{+}(aq)\\right) + 9\\Delta G_f^\\circ\\left(H_{2}O(l)\\right)\\right) $$\n", "\n", "Using the data in Table 1 above:"]}, {"cell_type": "code", "execution_count": 5, "metadata": {}, "outputs": [{"name": "stdout", "output_type": "stream", "text": ["The Gibbs free energy of the reaction is -6.6 kJ.\n"]}], "source": ["# Delta_Gr = (kaolinite + 2 Na ion + 4 dissolved silica) - (2 albite + 2 H ion + 9 water)\n", "\n", "# calculate Delta_Gr\n", "Delta_Gr = ((1*std_Gf[names.index(\"Kaolinite\")] + 2*std_Gf[names.index(\"Sodium ion\")] + 4*std_Gf[names.index(\"Dissolved silica\")]) - \n", " (2*std_Gf[names.index(\"Albite (low albite)\")] + 2*std_Gf[names.index(\"Hydrogen ion\")] + 9*std_Gf[names.index(\"Water\")]))\n", "print(f\"The Gibbs free energy of the reaction is {Delta_Gr:.1f} kJ.\")"]}, {"cell_type": "markdown", "metadata": {}, "source": ["So, $\\Delta G_r = 6.6\\,kJ$.\n", " \n", "We also know that\n", " \n", "$$\\Delta G_r = -RT \\ln(K_{eq})$$\n", "\n", "So we can calculate $K_{eq}$:\n", " \n", "$$\\ln(K_{eq}) = -\\frac{\\Delta G_r}{RT}$$\n", "\n", "It is also helpful to change natural log to base-10 log, as the numbers are much easier and intuitive to understand in base-10 log. To do this, let\u2019s review how to convert from $\\ln(x)$ to $\\log(x)$. \n", " \n", "By definition of what logarithms do: $y=\\log_{10}x$ and so $10^{y}=x$. Taking the natural log ($\\ln$) on both sides: $\\ln(10^y) = \\ln(x)$. This is the same as $y\\cdot\\ln(10)=\\ln(x)$ and so $y=\\frac{\\ln(x)}{\\ln(10)}=\\log_{10}x$, and we see that to convert $\\ln(K_{eq})$ to $\\log(K_{eq})$, we just have to divide both sides by $\\ln(10)$, so\n", "\n", "$$\\log(K_{eq}) = \\frac{\\ln(K_{eq})}{\\ln(10)} = -\\frac{\\Delta G_r}{RT\\ln(10)}$$\n", "\n", "Numerically, with $R=8.314\\,(J\\,mol^{-1}K^{-1})$ and $T=298\\,K$,\n", "\n", "$$\\log(K_{eq}) = -\\frac{-6.6}{8.314\\cdot298\\cdot\\ln(10)} = 1.2$$\n", "\n", "which means that\n", "\n", "$$K_{eq} = 10^{\\log(K_{eq})} = 10^{1.2}$$\n", "\n", "Thus, $\\Delta G_r = 6.6\\,kJ$ and $K_{eq} = 10^{1.2}$"]}, {"cell_type": "markdown", "metadata": {}, "source": ["(ii) The line equation becomes:\n", "\n", "$$\\log \\left(\\frac{a_{Na^+}}{a_{H^{+}}}\\right) = -2\\log (a_{H_{4}SiO_{4}}) + 0.6$$\n", "\n", "Sketch a plot of this line with $\\log (a_{H_{4}SiO_{4}})$ on the x-axis and $\\log \\left(\\frac{a_{Na^+}}{a_{H^{+}}}\\right)$ on the y-axis."]}, {"cell_type": "code", "execution_count": 6, "metadata": {}, "outputs": [{"data": {"text/plain": [""]}, "execution_count": 6, "metadata": {}, "output_type": "execute_result"}, {"data": {"image/png": 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\n", 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"]}, "metadata": {"needs_background": "light"}, "output_type": "display_data"}], "source": ["# create a function to return y (log(a_Na+/a_H+)) for the kaolinite-albite equilibrium line\n", "def y_KA(x):\n", " return -2*x + 0.6\n", "\n", "# plot\n", "plt.figure(figsize=(8,6))\n", "log_silica = np.array([-6, 0]) # Set the begin and end of line\n", "plt.plot(log_silica, y_KA(log_silica), 'b', label='Kaolinite-Albite')\n", "plt.xlabel('$\\log (a_{H_{4}SiO_{4}})$')\n", "plt.ylabel('$\\log (a_{Na^+}/a_{H^+})$')\n", "plt.xlim([-6, 0])\n", "plt.ylim([0, 11])\n", "plt.title('The boundary between the stability fields of kaolinite and albite', fontsize=14)\n", "plt.legend(loc='best', fontsize=10)"]}, {"cell_type": "markdown", "metadata": {}, "source": ["e) Repeat steps a-d above for the weathering reaction between gibbsite and kaolinite, given by the following reaction:\n", "\n", "$$Al_{2}Si_{2}O_{5}(OH)_{4}(s)+5H_{2}O(l)=2Al(OH)_{3}(s)+2H_{4}SiO_{4}(aq)$$\n", "\n", "(i) Write an expression for the equilibrium constant (like steps a-c above). Noting that all species but one are pure liquids or solids, you should get:\n", "\n", "$$K_{eq}=a_{H_{4}SiO_{4}}^2$$\n", "\n", "Again, taking logs on both sides and putting this expression in the same \u201cline\u201d form as earlier, we get:\n", "\n", "$$0 = -\\log(a_{H_{4}SiO_{4}})+\\frac{1}{2}\\log(K_{eq})$$\n", "\n", "Using the thermodynamic data from Table 1 and the same way to calculate $\\Delta G_r$ as above, we get $K_{eq}=10^{-7.7}$.\n", "\n", "So, $\\log(a_{H_{4}SiO_{4}})=\\frac{1}{2}(-7.7)=-3.85$, and we see that this line is vertical on the $\\log(a_{H_{4}SiO_{4}})$ VS $\\log \\left(\\frac{a_{Na^+}}{a_{H^{+}}}\\right)$ plot."]}, {"cell_type": "code", "execution_count": 7, "metadata": {}, "outputs": [{"data": {"text/plain": [""]}, "execution_count": 7, "metadata": {}, "output_type": "execute_result"}, {"data": {"image/png": 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EpfPO853YfvsNmjeH7duDjkgke7333nv069ePBQsWULly5RM61vDhw4mPj09zm3bt2nH//fcDJ5a8p0yZQv369Zk5c2am9qtYsSIzZswAlLyP4ZzbDIwBNgK/AjudcwuTb2dmvc1slZmt2rZtW7jCE8m0Bg38Y2T//S+0agVJPuiLRLUPP/yQG2+8kXnz5nHmmWcC8OKLL1K/fn1q165Np06d2LdvHwA///wzcXFxnHfeecTFxaVYS+/Vq1diYqxSpQpDhgzh/PPPp1atWvznP/8BYOLEidx66618/PHHzJkzh3vvvZc6deqwfv161q9fT6tWrahXrx5NmjRJ3Ce59evXs2fPHkaMGMGUKVNSPb+vvvqKSy65hGrVqvHiiy8CsGHDBmrWrMnBgwcZPHgw06ZNo06dOkybNo29e/dy3XXXUb9+ferWrcvs2bOzfnGzSdh6m5tZKaA9UBX4C3jDzHo4515Lup1zbhwwDiA2NlbzlUpEu/himDEDLr8c2raFd9/1z4aLnKg77oDVq7P3mHXqwBNPpL3NgQMHaN++PUuXLuWcc85JXN6xY0duvPFGAB588EHGjx9Pv379uPXWW7nmmmvo2bMnL7/8MrfddhuzZs1Ks4yyZcvyxRdf8NxzzzFmzBheeumlxHUXXngh7dq1o23btonN2HFxcbzwwgtUq1aNTz/9lL59+7IkhUEXpkyZQrdu3WjSpAnr1q3j999/p3z58sdt9/XXX/PJJ5+wd+9e6tatS5s2bRLXFSpUiOHDh7Nq1SqeeeYZAAYMGMAll1zCyy+/zF9//cUFF1xAfHw8xYsXT/ti5qBwNpvHAz8557Y55w4BbwEXhrF8kRzRpg1MngwffwwdOsCBA0FHJJJ1BQsW5MILL2T8+PHHLF+zZg1NmjShVq1aTJ48mbVr1wKwYsUKrrrqKgCuvvpqli9fnm4ZHTt2BKBevXpsSKfX5549e/j444+54oorqFOnDjfddBO//vprittOnTqVrl27ki9fPjp27Mgbb7yR4nbt27enaNGilC1blosvvpiVK1emGcPChQsZNWoUderUoVmzZiQkJGSpH0B2Cudz3huBhmZWDNgPxAGadURyhS5dfAe266+Hbt1g+nQooFEU5ASkV0POKfny5WP69OnEx8fz8MMPM2DAAMA3fc+aNYvatWszceJEli5dmuL+GelFXbhwYQDy58/P4cOH09z2yJEjnHzyyaxO1gzx999/U69ePcDfL+/cuTM//PADzZs3B+DgwYOcccYZ3HLLLenGmF7MzjnefPNNzj777DS3C6dw3vP+FJgBfAF8Eyp7XLjKF8lp113n/+HOnOm/P3Ik6IhEsqZYsWLMnTuXyZMnJ9bAd+/eTYUKFTh06BCTJ09O3PbCCy9k6tSpAEyePJnGjRufcPklSpRg9+7dAJQsWZKqVasm1qKdc3z11Vfkz5+f1atXs3r1aoYPH86UKVMYOnQoGzZsYMOGDWzZsoXNmzfz88/HT9I1e/ZsEhIS+OOPP1i6dCn169dPtXyAli1b8vTTT+Ocv5P75ZdfnvA5nqiw9jZ3zg1xzp3jnKvpnLvaOacGRslVbr8dHnoIXn0V+vUDp14bEqVKly7NggULGDFiBLNnz+ahhx6iQYMGNG/e/Jh74U899RQTJkzgvPPO49VXX+XJJ5884bK7du3Ko48+St26dVm/fn3ih4jatWtTo0aNFDuMTZ06lQ4dOhyzrEOHDokfLJK64IILaNOmDQ0bNmTQoEFUrFjxmPUXX3wx3377bWKHtUGDBnHo0CHOO+88atasyaBBg074HE+UuQj+7xIbG+s0n7cEolkz/zWVpsG0OAf9+8Ojj/qvjzziB3URSc93333HP//5z6DDkDBJ6edtZp8752LT21d35USymRmMHg27d/uvJUtC6LahiEi2UPIWyQFm8OyzvhPbwIFQooRvRhcRyQ5K3iI5JF8+mDDBJ/DbbvMTmlx7bdBRiUhuoFnFRHJQgQIwdaofQvWGGyCVx05FRDJFyVskhxUu7B8fa9QIuneHCB8yWUSigJK3SBgULw7z5kGtWtCpU5Y6sYuIJFLyFgmTk07yY5+fcQZcdhmkMyKjSCB+++03rrrqKs444wzq1atHo0aNmDlzJqtWreK2224DUp9WM+nUmxmRdKrQJ554InGyk4w6OpnIUS+++CLnn38+f/75Z6aOA8dOnnLDDTekO6vZCy+8wCuvvAL4SVW2hHluYHVYEwmjsmX9XOBNmviZyJYt87VxkUjgnOPyyy+nZ8+evP7664CfNWzOnDl06NCB2Nh0Hz/OlOHDhyd+/8QTT9CjRw+KZXFmn1dffZWnn36aJUuWUKpUqROKK+lEKanp06dP4vcTJ06kZs2axw32kpNU8xYJs4oVYfFiP/tY8+bw/fdBRyTiLVmyhEKFCh2TmE4//XT69et3XK06pWk1AXbt2kWHDh0499xz6dOnD0eOHOHvv/+mV69e1KxZk1q1ajF27Fjgf7Xdp556ii1btnDxxRdz8cUXA34ykEaNGnH++edzxRVXsGfPnlTjnj59OqNGjWLhwoWULVsW8B8M6tevT82aNendu3fi0KarV6+mYcOGnHfeeXTo0CHFWnqzZs04OkBYTEwMAwcOpHbt2jRs2JDffvsN+F/rw4wZM1i1ahXdu3enTp067N+/n88//5ymTZtSr149WrZsmepEKidCNW+RAFSt6hN4kyYQHw/Ll0PlykFHJRElgDlB165dy/nnn5+hQ6U2rebKlSv59ttvOf3002nVqhVvvfUWVatWZfPmzaxZswaAv/7665hj3XbbbTz++OO8//77lC1blu3btzNixAgWL15M8eLFGT16NI8//jiDBw8+Lo6ff/6ZW2+9lS+//JJTTz01cfmtt96auP3VV1/N3Llzueyyy7jmmmt4+umnadq0KYMHD2bYsGE8kcY12bt3Lw0bNmTkyJHcd999vPjiizz44IOJ6zt37swzzzzDmDFjiI2N5dChQ/Tr14/Zs2dTrlw5pk2bxsCBA3n55ZczdF0zSjVvkYCccw4sXAi7dkFcHGzdGnREIse65ZZbqF279nETd0Dq02pecMEFnHHGGeTPn59u3bqxfPlyzjjjDP773//Sr18/FixYQMmSJdMs95NPPuHbb7/lX//6F3Xq1GHSpEkpTjACUK5cOSpXrsz06dOPWf7+++/ToEEDatWqxZIlS1i7di07d+7kr7/+omnTpgD07NmTDz74IM1YChUqlNjikJEpTNetW8eaNWto3rw5derUYcSIEWzatCnNfbJCNW+RANWt6x8da9HCv5YuhdKlg45KIkIAc4LWqFGDN998M/H9s88+y/bt21O8153atJopLS9VqhRfffUV7777Ls8++yzTp09PsybqnKN58+ZMmTLlmOWffvopN910E+Cbxc877zyKFSvGO++8Q+PGjSlfvjzdu3cnISGBvn37smrVKv7xj38wdOhQEhISMncxQgoWLJh4ThmZwtQ5R40aNVixYkWWysso1bxFAnbhhTB7Nqxb5zuxJZmJUCSsLrnkEhISEnj++ecTl6XWAzy1aTVXrlzJTz/9xJEjR5g2bRqNGzdm+/btHDlyhE6dOvHQQw/xxRdfHHe8pNNwNmzYkI8++ogff/wxMYbvv/+eBg0aJE4D2q5du8R9y5Urx4IFCxgwYADvvvtuYqIuW7Yse/bsSexFftJJJ1GqVCk+/PBDwHdyO1oLPxFJYz/77LPZtm1bYvI+dOgQa9euPeEyklPNWyQCxMX50dc6dvSPkb3zDhQtGnRUkteYGbNmzeLOO+/k3//+N+XKlUu855zc0Wk1N27cmDit5vfff0+jRo24//77+eabb7jooovo0KED33zzDddeey1HQpPcP/LII8cdr3fv3lx66aVUqFCB999/n4kTJ9KtWzcOHPAzR48YMYLq1aunGnvVqlWZM2cOrVu35q233uLGG2+kVq1aVKlS5Zhm/0mTJtGnTx/27dvHGWecwYQJE070stGrVy/69OlD0aJFWbFiBTNmzOC2225j586dHD58mDvuuIMaNWqccDlJaUpQkZScwJSgJ2LKFD8KW6tWMGsWFCoU1uIlYJoSNG85kSlB1WwuEkG6dYP/+z9f8+7eHdK5vSYieZSazUUizI03+vved9/tZyIbP97PUCYicpSSt0gEuusun8CHDvVzgT/5pJ8jXEQElLxFItbgwf4Z8Mcfh5IlYcSIoCOScHDOHfe4leQ+J9rfTMlbJEKZwZgxvgY+cqSvgffvH3RUkpOKFCnCH3/8QZkyZZTAczHnHH/88QdFihTJ8jGUvEUimBk8/zzs2QP33+8TeN++QUclOaVSpUps2rSJbdu2BR2K5LAiRYpQqVKlLO+v5C0S4fLnh0mTfAK/5Rbfie2aa4KOSnJCwYIFqVq1atBhSBRQH1aRKFCwIEyf7gdzufZaeOutoCMSkSApeYtEiSJF/MAtDRpA167w7rtBRyQiQVHyFokiMTF+IpMaNaBDBwgN0SwieYySt0iUOflkX+s+/XRo0wY0grBI3qPkLRKFypeHRYugTBlo2RLWrAk6IhEJJyVvkShVqRIsXgyFC0Pz5hCaPVFE8gAlb5EoduaZPoEfOgTx8fDLL0FHJCLhELbkbWZnm9nqJK9dZnZHuMoXya3OPdffA//zT5/Af/896IhEJKeFLXk759Y55+o45+oA9YB9wMxwlS+Sm9WrB/Pm+Zp3ixY+kYtI7hVUs3kcsN4593NA5YvkOo0b++fAv/sOWrf2Y6KLSO4UVPLuCkwJqGyRXKtFC5g6FT77DNq3h4SEoCMSkZwQ9uRtZoWAdsAbqazvbWarzGyVBucXybwOHWDiRHj/fbjiCt+ZTURylyBq3pcCXzjnfktppXNunHMu1jkXW65cuTCHJpI79OgBzz0Hc+fC1VfD338HHZGIZKcgZhXrhprMRXLczTf7mcjuu88Pq/rii36KURGJfmFN3mZWDGgO3BTOckXyqnvvhV27YMQIPxf4448rgYvkBmFN3s65fUCZcJYpktcNH+4T+BNPQMmSMGxY0BGJyIkKotlcRMLIDMaO9U3ow4f7Gvg99wQdlYicCCVvkTwgXz4YN84/+33vvb4G3rt30FGJSFYpeYvkEfnzw2uvwb590KcPFC8O3bsHHZWIZIUmJhHJQwoVgjfegKZNoWdPmD076IhEJCuUvEXymKJFYc4cPx56ly5+VjIRiS5K3iJ5UIkS8M47cM45fhjVjz4KOiIRyQwlb5E8qnRpWLgQTjvNT2TyxRdBRyQiGaXkLZKHnXKKbzY/+WRo2dLPSCYikU/JWySPq1zZJ/D8+SE+Hv7736AjEpH0KHmLCNWq+QSekOAT+ObNQUckImlR8hYRAGrWhAULYPt2n8A1I69I5FLyFpFE9ev7aUQ3bPD3wP/6K+iIRCQlSt4icoyLLoKZM2HNGmjTBvbuDToiEUlOyVtEjtOqFUyZAp98Apdf7u+Fi0jkUPIWkRR16gQvv+w7snXtCocOBR2RiByl5C0iqerZE55+2o+B3qsXHDkSdEQiAppVTETSceutfirRAQP8sKrPP+/nCBeR4Ch5i0i6HnjAJ/BHHoGYGHj0USVwkSApeYtIhowcCbt2wWOPwUknwaBBQUckkncpeYtIhpjBU0/Bnj0weLBvQr/jjqCjEsmblLxFJMPy5YOXXvIJ/M47fRP6DTcEHZVI3qPkLSKZUqAATJ7sB2/p3dvXwK+8MuioRPIWPSomIplWuDC8+SY0aQI9esDbbwcdkUjeouQtIllSrJhP2nXqwBVXwJIlQUckqbnhhhswM+66667j1g0dOhRL9uiAmfHggw+me9xmzZrRrFmzxPerV69m6NCh7Nix44RjlrQpeYtIlpUs6WciO+ssaNfOD6cqkWX//v288cYbAEyePJnDhw9n27Gfe+45nnvuucT3q1evZtiwYUreYaDkLSInpEwZWLQIKlSASy+F1auDjkiSmjlzJrt27aJ169b8/vvvLFiwINuOfe6553Luuedm2/Ek45S8ReSEVajgx0CPiYEWLWDduqAjkqMmTZpEqVKlmDhxIkWLFuWVV17J0H7OOUaOHEmlSpUoWrQoF110EauTfTJL2mw+ceJErr32WgCqVauGmWFmbNiwAYDDhw/zyCOPcM4551C4cGEqVqzI3XffTYJmvckSJW8RyRannw7vveefB4+P93OCS7C2bNnC4sWLufLKKylXrhyXX345c+bM4c8//0x331deeYX58+fzzDPPMHHiRH777Tfi4uJSbRJv06ZN4n3yN954gxUrVrBixQoqVKgAQI8ePRgxYgRXXXUV8+bN44EHHmD8+PF07949+044D9GjYiKSbapXh4ULoVkzn8A//NDXyiUYr776KkeOHOGaa64BoGfPnkyZMoVp06bRp0+fNPfdv38/CxcupHjx4gA0aNCAatWqMXbsWB566KHjti9XrhxnnnkmAHXq1OGss85KXPfhhx8ybdo0Jk2alBhLfHw8pUuXpkePHqxevZo6depkxynnGap5i0i2ql3bd2LbutUn8O3bg44o73rllVeoVq0ajRo1AnzCrFixYoaazlu3bp2YuAGqVKlCw4YNWbFiRabjWLBgAYUKFaJTp04cPnw48dWiRQsAPvjgg0wfM69T8haRbNeggX+MbP16aNXKj4ku4fXZZ5/x7bff0rFjR/766y/++usvdu/eTceOHVmxYgXff/99mvufcsopKS7bvHlzpmP5/fffOXjwIDExMRQsWDDxVb58eQD++OOPTB8zrwtrs7mZnQy8BNQEHHCdcy7zH+NEJOJdfLEfyOXyy6FtW18bL1Ys6KjyjkmTJgEwevRoRo8efdz6V155hREjRqS6/2+//ZbistNOOy3TsZQpU4YiRYrw4Ycfpri+YsWKmT5mXhfumveTwALn3DlAbeC7MJcvImHUpo0fSvWjj6BDBzhwIOiI8oaDBw8ydepUGjRowPvvv3/cq06dOrz66qs451I9xvz589m7d2/i+w0bNvDJJ58kNsGnpHDhwoC/X55Uq1atSEhIYOfOncTGxh73UvLOvLDVvM2sJHAR0AvAOXcQOBiu8kUkGF26+IlMrr8erroKpk3z46NLzpk7dy5//PEHjz322DEjoB110003cfPNN7N06dJUj1G0aFFatGjBvffey4EDBxgyZAglS5bkzjvvTHWfo898P/vss/Ts2ZOCBQty3nnn0axZM7p160bnzp256667uOCCC8iXLx8bNmxg/vz5jB49murVq5/oaecp4ax5nwFsAyaY2Zdm9pKZFU++kZn1NrNVZrZq27ZtYQxPRHLKddfBE0/AW2/5748cCTqi3G3SpEmUKFGCK664IsX13bp1o2jRoolN6ym55ppraNOmDbfeeis9e/akXLlyvPfee5QuXTrVfWrXrs3QoUN5++23ady4MfXr12fLli0AvPbaawwdOpQZM2bQvn17OnfuzDPPPEO1atVSvL8uabO0mk2ytSCzWOAT4F/OuU/N7Elgl3NuUGr7xMbGulWrVoUlPpFjHK2tpFEzkcwbMQIGDYK+feGZZ/wz4SLyP2b2uXMuNr3twtl4tQnY5Jz7NPR+BnB/GMsXkYANHOh7nj/6qB8X/ZFHgo5IJDqFLXk757aa2S9mdrZzbh0QB3wbrvJFJHhmMHo07N4No0b5ucAHDAg6KpHoE+5uI/2AyWZWCPgvcG2YyxeRgJnBs8/6TmwDB/oE3q9f0FGJRJewJm/n3Gog3bZ8Ecnd8uWDCRN8Ar/tNp/Ae/UKOiqR6KER1kQkEAUKwNSp0Ly5f4wsNOW0iGSAkreIBKZwYZg5Exo1gu7dYf78oCMSiQ5K3iISqOLFYd48qFULOnWCZcuCjkgk8il5i0jgTjrJj31etaofB33lyqAjEolsSt4iEhHKlYPFi6F8eT8T2TffBB2RSORS8haRiFGxok/gxYr5jmzpzFopkmcpeYtIRKla1Sfwv/+G+HjYuDHoiEQij5K3iEScc86BhQv9UKpxcbB1a9ARiUQWJW8RiUh16/pHx379FVq0gB07go5IJHIoeYtIxLrwQpg9G9at853Ydu8OOiKRyKDkLSIRLS7Oj772xRdw2WWwf3/QEYkET8lbRCJeu3bw6qvwwQd+IJeDB4OOSCRYSt4iEhW6dYP/+z945x0/lOrhw0FHJBKccE8JKiKSZTfe6O973303xMTA+PF+hjKRvEbJW0Siyl13+UfIhg3zU4k++aSfI1wkL1HyFpGoM2SIr4E//jiULAkjRgQdkUh4KXmLSNQxgzFjfA185EhfA+/fP+ioRMJHyVtEopIZvPAC7N0L99/vE3jfvkFHJRIeSt4iErXy54dJk2DPHrjlFt+J7Zprgo5KJOepn6aIRLWCBWH6dLjkErj2WnjrraAjEsl5St4iEvWKFPHDqDZoAF27wrvvBh2RSM5S8haRXCEmxk9kUqMGdOgAH34YdEQiOUfJW0RyjZNP9rXuypWhTRtYtSroiERyhpK3iOQq5cvD4sVQpoyfiWzt2qAjEsl+St4ikutUquQTeKFCEB8PP/4YdEQi2UvJW0RypTPPhEWL4NAhn8A3bQo6IpHso+QtIrlWjRr+Hviff/oE/vvvQUckkj2UvEUkV6tXD+bNg40boUULn8hFop2St4jkeo0bw6xZ8N130Lq1H5FNJJopeYtIntCiBUydCp99Bu3bQ0JC0BGJZF1Yk7eZbTCzb8xstZnpCUwRCasOHWDiRFiyBK64wndmE4lGQUxMcrFzbnsA5YqI0KOHnwu8b18/iclrr/kJTkSiiWYVE5E85+abfQLv398PqzpunJ9iVCRahDt5O2ChmTng/5xz45JvYGa9gd4AlStXDnN4IpJX3HefT+AjRvgE/vjjSuASPcKdvP/lnNtiZuWBRWb2H+fcB0k3CCX0cQCxsbEuzPGJSB4yfDjs2gVPPAEnnQRDhwYdkUjGZDp5m1lxIME593dm93XObQl9/d3MZgIXAB+kvZeISM4wg7FjfQ182DAoUQLuvjvoqETSl27yNrN8QFegO1AfOAAUNrNtwHxgnHPuhwwcpziQzzm3O/R9C2D4iQQvInKi8uWDF1/0z37fc49P4L17Bx2VSNoyUvN+H1gMPACscc4dATCz0sDFwCgzm+mcey2d45wCzDR/U6kA8LpzbkGWIxcRySb58/te5/v2QZ8+ULw4dO8edFQiqctI8o53zh33NKRzbgfwJvCmmRVM7yDOuf8CtTMfoohIzitUCN54w4/A1rOn78TWvn3QUYmkLN1BWlJK3FnZRkQk0hUtCnPm+PHQu3Tx04qKRCINjyoikkSJEvDOO3DOOb7m/dFHQUckcrxMJ28zuzQnAhERiRSlS8PChXDaab4Z/Ysvgo5I5FgZTt5mVtnMrgS6mFmXHIxJRCRwp5zim81PPhlatvQzkolEiszUvLcDnwAbQ19FRHK1ypV9As+fH+Lj4b//DToiES/Dyds5t8859zMwyzm3MQdjEhGJGNWq+QSekOAT+ObNQUckkrUOa6uzOwgRkUhWsyYsWADbtkHz5v6rSJCykrynmdkbZvakmV1jZjWyPSoRkQhTvz7MnQs//eTvgf/1V9ARSV6W6eTtnOvinLsCOAl/H7xztkclIhKBmjaFmTNhzRpo0wb27g06IsmrTuQ5733OufnOuWHZFo2ISIRr1Qpefx0++QQuv9zfCxcJt6w85z3LzJ4DzjWzemYW7mlFRUQC1bkzvPyy78jWtSsc0hiTEmZZaTa/HHgYGAu0B6Zlc0wiIhGvZ094+mmYPRt69YIjR4KOSPKSDNeazawM0AVIANYCC51zs3MqMBGRSHfrrX4u8AED/LCqzz/v5wgXyWmZafKeiZ8a9Gbge6CRma13zv0zRyITEYkCDzwAu3bBqFE+gf/730rgkvMyk7xLOOeGm1lH51xTM+sEnJVTgYmIRIuHH/Y18DFjoGRJGDQo6Igkt8tM8j7ap/KAmRV1zr1pZsuA0TkQl4hI1DCDp57yCXzwYF8Dv+OOoKOS3CwzyXuMmZXGd1B72cw+Bk7LmbBERKJLvnwwfrx/9vvOO30Cv/76oKOS3CrDyds592bo28fN7GqgFr63uYiIAAUKwOTJPoHfeCPExMCVVwYdleRG6SZvM2sEfOKcc0eXOedezdGoRESiVOHC8OabfjCXHj2geHFo2zboqCS3ychz3j2Bz81sqpn1MrNTczooEZFoVqyYHwe9Th0/oMuSJUFHJLlNusnbOdfHOXc+MBQoBUw0sxVm9rCZXWRm+XM6SBGRaFOypJ+J7KyzoF07P5yqSHbJzHze/3HOjXXOtQIuAZYDVwCf5lRwIiLRrEwZWLQITj0VLr0Uvvoq6Igkt8jSxCTOuf2hSUn6OediszuoaLJixQq6du1KpUqVKFSoECVLlqR+/foMGjSIX3/9FYANGzZgZkycODFxv169elGpUqV0jz9x4kTMjB9//PGEY61SpQq9evVKfL906VKGDh3KEY3rKJJjKlSA997zndeaN4d164KOSHKDrExMcmlOBBKNHnvsMf71r3+xbds2RowYweLFi5k6dSotW7Zk3LhxXHfddQBUqFCBFStW0KZNm0DjnTlzJoOSjB6xdOlShg0bpuQtksNOP90ncDOIj4cNG4KOSKJdZsY2rww0AlqZWQnn3PScCyvyvf/++9x7773cfvvtjB079ph1rVu35oEHHuCNN94AoHDhwjRs2DCIMI9Rt27doEMQybOqV4eFC6FZM5/AP/zQ18pFsiIzNe/twCfAxtDXPG306NGULVuW0aNTHmCuePHiiU3UKTWbH/Xxxx9Tv359ihQpQpUqVXj66adTPN6WLVu4/PLLiYmJoUyZMtxyyy3s378/cf3hw4cZNGgQZ555JkWKFKFs2bI0btyY5cuXJ26TtNl86NChDBvmp2IvWLAgZoYlGZB537599O/fn6pVq1KoUCGqVq3KyJEjVUsXOQG1a8M778DWrb4Jffv2oCOSaJWZQVr2AT+b2Szn3MYcjCniHT58mGXLltGxY0cKFSqU5ePs2rWLK6+8kv79+3PWWWcxdepUbrvtNkqUKHHMvWmAHj160KVLF/r27cvKlSsZPnw4e/fuTfxAMHr0aMaOHcvIkSOpU6cOu3btYtWqVezYsSPFsm+44QY2bdrE+PHjWb58Ofnz/++hgcOHD9OyZUu+/fZbBg0aRK1atfjkk0946KGH2LFjB4899liWz1kkr2vYEN5+23dga9XKP0ZWsmTQUUm0yczwqAA4577MiUCiyR9//EFCQgKVK1c+bt3hw4ePeV+gQOqXePfu3YwbN46uXbsC0KpVKzZv3syQIUPo2bPnMTXh1q1bM2bMGABatGiBmTF48GAGDBhA9erVWbFiBS1atOD2229P3Oeyyy5LtexKlSoldphr0KDBMXFOmTKF5cuXs2zZMi666CIA4uLiABg2bBj9+/enfPnyqR5bRNJ28cUwYwZ06OAHcFmwwD8bLpJRWeptntclGWzuGFu3bqVgwYLHvJIn86Ty589Pp06djlnWtWtXNm7cyObNm49Z3qVLl+O2O3LkCCtXrgSgfv36zJ8/n4EDB7J8+XIOHjyYlVMDYMGCBZx++ulceOGFHD58OPHVokULDh06xCd6YFXkhLVtC6+9Bh99BB07woEDQUck0SRLydvMhprZO2b2kpndkt1BRbqyZctSpEgRNm7ceNzyzz77jM8++4wbb7wx3eOUKlWKggULHrPslFNOATgueR9dntp2AwYMYNiwYcyZM4cmTZpQpkwZrr32WrZn4aba77//zs8//3zcB5ELLrgA8C0PInLirrwSXnwR3n0XrroK0visL3KMTDebh5yM77T2CnBnZnYMjci2CtjsnIvKEX8LFCjARRddxKJFizh48GDife8CBQoQG+sfe587d266x/nzzz85dOjQMQn8t99+A+C0046dsO23336jRo0aqW5XsGBB+vfvT//+/dm6dStz587lrrvuYt++fUybNi1T51emTBmqVq3K9OkpP1BQpUqVTB1PRFJ33XWwa5efiez662HCBD9DmUhasvorsgPID/we+j4zbge+y2K5EeO+++5j+/bt9O/fP8vH+Pvvv3nzzTePWTZ16lQqV658XPJOnkinTp1Kvnz5EmvDSZ166qnccMMNxMfHs2bNmlTLL1y4MMAxvdbB33v/5ZdfiImJITY29rhX2bJlM3WeIpK2O+6A4cPhlVegXz9I5c6cSKIs1bydc8PNrCLwFJB6dkjGzCoBbYCRwF1ZKTtSxMXFMWrUKO6//36+/vprrrnmGqpWrUpCQgLff/89U6dOpXjx4sd0OkuuRIkSiR8CqlWrxpQpU1i8eHHiqGpJzZ8/n3vvvZcWLVqwcuVKhg0bxjXXXEP16tUBaN++PbVr1+b888+nVKlSfPnllyxYsICbbrop1fLPPfdcwA82c+mll5I/f35iY2Pp3r07EyZMIC4ujrvvvpvatWtz8OBB1q9fz5w5c5g1axbF1LtGJFs9+CDs3g2PPup7nz/ySNARSURzzmXqBUwPvR4FugFnZ2LfGUA9oBkwN73t69Wr5yLd8uXL3RVXXOEqVqzoChYs6EqUKOFiY2Pd4MGD3ZYtW5xzzv30008OcBMmTEjcr2fPnu60005zH330kYuNjXWFCxd2lStXdk8++eQxx58wYYID3LJly1y7du1c8eLFXalSpVzfvn3dvn37ErcbM2aMa9CggStdurQrUqSIq169uhsyZIg7ePBg4jann36669mzZ+L7w4cPu759+7py5co5M3P+18Hbv3+/GzJkiDv77LNdoUKFXKlSpVxsbKwbMmSIO3ToUDZfxQjUtKl/iYTRkSPO9enjHDg3cmTQ0UgQgFUuA/nUXBbbZ8zsTHzt+WrnXLpPKZpZW6C1c66vmTUD7nEp3PM2s95Ab4DKlSvX+/nnn7MUn8gJadbMf126NMgoJA86cgR69vQ90Z96yjejS95hZp+7DMwZkulmczOLA9oCxYAPgQEZ3PVfQDszaw0UAUqa2WvOuR5JN3LOjQPGAcTGxurOj4jkKfny+U5re/bAbbdBiRKQbMwmkSx1WJuAT9zLgJXOuZ0Z2ck594BzrpJzrgrQFViSPHGLiAgUKABTp/ohVK+/HkLTJIgkynTyds5VBh4C9gI9zGxKtkclIpLHFS4MM2dCo0bQvTvMnx90RBJJMjOrWBmgC5AArAUWOudmZ6VQ59xSYGlW9hURySuKF4d58+CSS6BTJz+MatOmQUclkSAzNe+ZQDngYXxP851mFvXPa4uIRLKTTvJJu2pVP6RqaERkyeMyk7xLOOeGA78555riHxObmCNRiYhIonLlYPFiKF/ez0T2zTdBRyRBy0zyTgh9PWBmRZ1zbwKtcyAmERFJpmJFn8CLFvUd2X74IeiIJEiZSd5jzKw0MA142cz6Aaels4+IiGSTqlV9Av/7b4iLg2RzI0kekuHk7Zx70zm3wzn3ODAf+AfQPsciExGR4/zzn7BwoZ/MJC4Otm4NOiIJQrrJ21IYnNs596pz7j7n3NrUthERkZxRt65/dGzLFmjRAnZkdnooiXoZqXm/b2b9zKxy0oVmVsjMLjGzSUDPnAlPRERScuGFMHs2rFsHl17qJzWRvCMjybsV8Dcwxcy2mNm3ZvYT8AO+x/lY59zEHIxRRERSEB/vR1/7/HO47DJINruv5GLpDtLinEsAngOeM7OCQFlgv3PurxyOTURE0tGunZ8HvEcP6NzZj8pWqFDQUUlOy9TwqM65Q865X5W4RUQix1VXwQsv+PvgPXrA4cNBRyQ5LTPDo96VwuKdwOfOudXZFpGIiGRa795+JrK77/bDqo4f72cok9wpM1OCxoZeb4fetwE+A/qY2RvOuX9nd3AiIpJxd93lHyEbNgxKloQnngA9C5Q7ZSZ5lwHOd87tATCzIcAM4CLgc0DJW0QkYEOG+AQ+dqyfC3zEiKAjkpyQmeRdGTiY5P0h4HTn3H4zO5C9YYmISFaYwWOP+UfHRo70Cbx//6CjkuyWmeT9OvCJmc0GDGiLf3ysOPBtTgQnIiKZZ+Y7sO3ZA/ff7xN4375BRyXZKcPJ2zn3kJnNBxrjk3cf59yq0OruORGciIhkTf78/hGyvXvhllt8Ar/66qCjkuyS2b6Ih4Ejoa+Hsj8cERHJLgULwvTpcMkl0KsXvPVW0BFJdslw8jaz24HJ+EFaygOvhWYWExGRCFWkiB9G9YILoGtXePfdoCOS7JCZmvf1QAPn3BDn3GCgIXBjzoQlIiLZJSbGD+BSowZ06AAffhh0RHKiMpO8DT/G+VF/h5aJiEiEK1XK17orV4Y2bWDVqvT3kciVmeQ9AfjUzIaa2TDgU+DlnAlLRESyW/nysHgxlC4NrVrB2rVBRyRZleHk7Zx7HLgW+CP06umcG5tTgYmISParVAnee89PXtK8OaxfH3REkhXpJm8z221mu8xsF7AUeBgYCXwYWiYiudDEiRMxM3788cdjln/22WeULl2aunXrsn379mwts1evXlSpUiXx/YYNGzAzJk6cmOljHY1/w4YNicuGDh3KkiVLTjzQKHfmmbBoERw8CHFxsGlT0BFJZqWbvJ1zJZxzJZO8SiR5lQxHkCISGT7++GPi4+OpVq0aS5YsoWzZsjlaXoUKFVixYgVt2rTJ9L5t2rRhxYoVVKhQIXHZsGHDlLxDatTw98B37PDzgv/+e9ARSWZozhkRyZBly5bRsmVLatWqxaJFiyhVqlSOl1m4cGEaNmxIuXLlMr1vuXLlaNiwIYULF86ByHKHevVg3jzYuBFatIA//ww6IskoJW8RSdeiRYu49NJLqV+/Pu+++y4lS/pGt4SEBO68805q1qxJTEwMp556Kpdddhn/+c9/jjvGypUriY+PJyYmhuLFixMXF8fKlSvTLDelZvNevXpRqVIlvvzyS5o0aUKxYsWoVq0aL7zwwjH7Jm82t9D0WiNHjsTMMDOGDh2auP2yZcuIi4ujRIkSFC9enJYtW7JmzZosXK3o0qQJzJoF330HrVv7IVUl8il5i0ia5s2bx2WXXcZFF13EvHnzKF68eOK6AwcOsHv3bh588EHmzZvH888/T0JCAg0bNmTr1q2J23399dc0bdqUP//8k4kTJ/LKK6+wa9cumjZtyldffZXpmHbt2sVVV11Fjx49mD17NvXr1+fmm2/m/fffT3WfFStWAD75r1ixghUrVnDDDTcknmNcXBwxMTG89tprvP766+zevZsmTZrwyy+/ZDq+aNOiBUydCp99Bu3bQ0JC0BFJupxzEfuqV6+eEwlE06b+lYdNmDDBAQ5wZ555pktISEh3n8OHD7u9e/e6mJgY9/jjjycu79SpkzvppJPcn3/+mbhs586drlSpUq5Dhw6Jy3r27OlOP/30xPc//fSTA9yECROO2QZwS5YsSVyWkJDgypQp42688cbj4v/pp58SlwFu4MCBx8V95plnuksuueSYZTt37nRlypRxt99+e7rnnVu8+qpz4Fzbts4dPBh0NHkTsMplID+q5i0iaWrTpg3r16/nkUceSXH99OnTadCgASeffDIFChSgePHi7Nmzh3Xr1iVu88EHH9C2bVtOPvnkxGUlS5akXbt2LFu2LNMxFStWjIsvvjjxfeHChalWrRobN27M9LF++OEH1q9fT/fu3Tl8+HDiq1ixYjRq1IgPPvgg08eMVj16wHPPwdy5cM018Pff6e8jwcjMlKAikgeNHTuWU089lWHDhlGkSBHuv//+xHVvv/02V155JT179mTIkCGULVuWfPny0bp1axKStL3u2LHjmF7fR5166qn8mYVeUil1litcuPAxZWbU76Fu1tdffz3XX3/9cesrV66c6WNGs5tv9nOB9+/vh1UdN85PMSqRJWzJ28yKAB8AhUPlznDODQlX+SKSNWbGuHHjOHDgAA888ABFihThjjvuAGDq1KmcddZZx3QoO3ToEDt27DjmGKVLlz7mHvhRW7dupXTp0jkZfrrKlCkDwCOPPEJ8fPxx6wsVKhTukAJ3330+gY8Y4RP4448rgUeacNa8DwCXOOf2mFlBYLmZveOc+ySMMYhIFuTLl4+JEydy8OBB7rzzTooUKUKfPn3Yt28fBQoc+2/k1Vdf5e9k7a1NmzZl3rx57N69mxIlSgCwe/du3n77bZo1axau06BQoULs37//mGVnn302VapUYe3atce0KuR1w4fDrl3wxBNw0kmQpGO+RICwJe/QjfijDyEUDL1cuMoXkROTP39+Jk+ezIEDB+jbty+FCxemVatWzJo1izvvvJO2bdvy+eef89RTTx1zbxtg0KBBzJ07l7i4OPr374+ZMXr0aPbt28fgwYPDdg7nnnsu8+bNo1WrVpQqVYqKFStSsWJFnn32Wdq3b8/Bgwfp0qULZcuW5bfffuPjjz+mcuXK3HXXXWGLMVKYwdixvgY+bBiUKAF33x10VHJUWDusmVl+M1sN/A4scs59Gs7yReTEFChQgOnTp9OqVStuuOEGSpQowcCBA5k2bRqXXXYZ8+bN4+233+akk046Zr/zzjuPpUuXUrJkSXr27MnVV19NTEwMy5Yto3bt2mGL/5lnnqF48eJcdtll1K9fn3HjxgHQunVrPvjgA/bu3csNN9xAy5Ytue+++9i6dSuNGjUKW3yRJl8+ePFFuOIKuOcef/9bIoP5CnGYCzU7GZgJ9HPOrUm2rjfQG6By5cr1fv7557DHJ8LRptylS4OMQiQiHDzo5wF/5x147TW46qqgI8q9zOxz51xsetsF8qiYc+4v/CQnrVJYN845F+uci83KkIgiIpK9ChWCGTOgaVP/CNns2UFHJGFL3mZWLlTjxsyKAvHA8WMoiohIxClaFObM8eOhd+ni5wWX4ISz5l0BeN/MvgY+w9/znhvG8kVE5ASUKOGbzs8+2w+j+vHHQUeUd4Wzt/nXQN1wlSciItmvdGk/F3iTJn4ikyVL4Pzzg44q79HwqCIikimnnOKbzU86CVq29DOSSXgpeYuISKZVruwTeP78EB8PP/0UdER5i5K3iIhkSbVqvgk9IQHi4mDz5qAjyjuUvEVEJMtq1YIFC2DbNmje3H+VnKfkLSIiJ6R+fT+N6E8/+XvgO3cGHVHup+QtIiInrGlTeOstWLMG2rSBvXuDjih3U/IWEZFsceml8PrrsGIFXH65vxcuOUPJW0REsk3nzjB+vO+J3rUrHDoUdES5k5K3iIhkq1694Omn/Rjo114LR44EHVHuE7YR1kREJO+49VY/F/iAARATA88/7+cIl+yh5C0iIjnigQdg1y4YNcqPi/7vfyuBZxclbxERyTEPP+xr4GPGQMmSMGhQ0BHlDkreIiKSY8zgqad8Ah882NfA77gj6Kiin5K3iIjkqHz5fA/0PXvgzjt9Ar/++qCjim7qbS4iIjmuQAH/DHirVnDjjTBtWtARRTclbxERCYvCheHNN6FxY+jRww+pKlmj5C0iImFTrJhP2nXq+AFd3n8/6Iiik5K3iIiEVcmSfiays86Cyy6DTz4JOqLoo+QtIiJhV6aMnwv81FP9mOhffRV0RNFFyVtERAJRoQK8954fga1FC1i3LuiIooeSt4iIBOb0030CB4iPhw0bAg0naih5i4hIoKpXh4UL/XPg8fHw669BRxT5lLxFRCRwtWvDO+/A1q3QvDls3x50RJFNyVtERCJCw4bw9tvw449+MJddu4KOKHIpeYuISMS4+GKYMcP3Pm/bFvbtCzqiyKTkLSIiEaVtW3jtNfjoI+jYEQ4cCDqiyKPkLSIiEefKK+HFF+Hdd+Gqq+Dw4aAjiixK3iIiEpGuuw7GjoW33vKzkB05EnREkUNTgoqISMS6447/zQUeEwPPPOPnCM/rlLxFRCSiPfigT+CPPurHRX/kkaAjCp6St4iIRDQzGD3aJ/BRo3wCf+CBoKMKVtiSt5n9A3gFOBU4Aoxzzj0ZrvJFRCR6mcGzz/oEPmCAb0Lv1y/oqIITzpr3YeBu59wXZlYC+NzMFjnnvg1jDCIiEqXy5YOJE2HvXrjtNihRAnr1CjqqYIStt7lz7lfn3Beh73cD3wGnhat8ERGJfgUKwNSpfgjV66/3A7rkRYE8KmZmVYC6wKcprOttZqvMbNW2bdvCHpuIiES2woVh5kxo1Mg/Az5/ftARhV/Yk7eZxQBvAnc4544budY5N845F+uciy1Xrly4wxMRkShQvDjMmwe1akGnTrBsWdARhVdYk7eZFcQn7snOubfCWbaIiOQuJ50ECxZA1ap+SNWVK4OOKHzClrzNzIDxwHfOucfDVa6IiORe5crBokX+a6tW8M03QUcUHuGsef8LuBq4xMxWh16tw1i+iIjkQqedBu+9B0WL+o5sP/wQdEQ5L5y9zZc758w5d55zrk7olQe7GYiISHarWhUWL4a//4b4eNi4MeiIcpYmJhERkVzhn/+EhQth506fwLduDTqinKPkLSIiuUbduv7Rsc2boUUL2LEj6IhyhpK3iIjkKhdeCLNnw7p1cOmlfkjV3EbJW0REcp34eJg+HT7/HNq1g/37g44oeyl5i4hIrtS+Pbzyih/ApXNnOHgw6Iiyj5K3iIjkWlddBS+84O+D9+jhe6PnBprPW0REcrXevf1973vu8VOJvvSSn6Esmil5i4hIrnf33T6BDxvmpxJ94gk/R3i0UvIWEZE8YcgQ2LULxo6FkiXhoYeCjijrlLxFRCRPMIPHHvM18BEjfA38vvuCjiprlLxFRCTPMPMd2Pbsgf79/T3wvn2DjirzlLxFRCRPyZ/fP0K2dy/ccouvgV99ddBRZU6U97cTERHJvIIF/SAul1wC114LM2cGHVHmKHmLiEieVKSIH0a1fn248kp4992gI8o4JW8REcmzYmL8AC41akCHDvDhh0FHlDFK3iIikqeVKuVr3ZUrQ5s2sGpV0BGlT8lbRETyvPLlYfFiKF0aWrWCtWuDjihtSt4iIiJApUrw3ntQqBA0bw7r1wcdUeqUvEVERELOPBMWLfIzkMXFwaZNQUeUMiVvERGRJGrU8PfAd+zw84L//nvQER1PyVtERCSZevVg3jzYuBFatIA//ww6omMpeYuIiKSgSROYNQu++w5at/ZDqkYKJW8REZFUtGgBU6fCZ59B+/aQkBB0RJ6St4iISBo6dIAJE2DJEujSBQ4dCjoiJW8REZF0XX01PPccvP02XHMN/P13sPFoVjEREZEMuPlmPxf40alEx43zU4wGQclbREQkg+67D3btgpEj/VSijz0WTAJX8hYREcmEhx7yNfCxY6FkSRg6NPwxKHmLiIhkgplP3Lt3w7BhvgZ+993hjUHJW0REJJPy5YMXX/TPft9zj0/gvXuHr/ywJW8zexloC/zunKsZrnJFRERyQv788NprsHcv9OnjO7FddVV4yg7no2ITgVZhLE9ERCRHFSoEM2bARRf5R8hmzw5PuWFL3s65D4Ad4SpPREQkHIoW9c9/16vnB3FZvDjny4y4QVrMrLeZrTKzVdu2bQs6HBERkXSVKAHvvANnn+2HUf3445wtL+KSt3NunHMu1jkXW65cuaDDERERyZDSpWHhQjjtND+RyZdf5lxZEZe8RUREotWpp/pm85NO8pOafPddzpSj5C0iIpKNKlf2CTx/foiPh59+yv4ywpa8zWwKsAI428w2mdn14SpbREQknKpVg0WLYP9+iIuDzZuz9/jh7G3ezTlXwTlX0DlXyTk3Plxli4iIhFutWrBgAWzbBs2b+6/ZRc3mIiIiOeSCC2DuXN903rIl7NyZPcdV8hYREclBTZvCW2/BmjXQpo0fke1EKXmLiIjksEsvhddfhxUroEMHSEg4seMpeYuIiIRB584wfrzvyNa1Kxw6lPVjKXmLiIiESa9e8NRTfgz0a6+FI0eydhxNCSoiIhJG/fr5ucAHDvTDqj73nJ8jPDOUvEVERMJswACfwEeN8lOJ/vvfmUvgSt4iIiIBePhhn8DHjPHDqT74YMb3VfIWEREJgJm//717Nwwa5GvgGaXkLSIiEpB8+XwP9D174M47M7FfzoUkIiIi6SlQwD8D3qpVxvdR8hYREQlY4cJ+FLaMUvIWERGJAEWLZnxbJW8REZEoo+QtIiISZZS8RUREooySt4iISJRR8hYREYkySt4iIiJRRslbREQkyih5i4iIRBklbxERkSij5C0iIhJllLxFRESijJK3iIhIlFHyFhERiTJK3iIiIlFGyVtERCTKKHmLiIhEGSVvERGRKBPW5G1mrcxsnZn9aGb3h7NsERGR3CJsydvM8gPPApcC5wLdzOzccJUvIiKSW4Sz5n0B8KNz7r/OuYPAVKB9GMsXERHJFcKZvE8DfknyflNomYiIiGRCgTCWZSksc8dtZNYb6B16e8DM1uRoVLlDWWB70EFEgcxfJ0vp1zZP0O9Uxug6ZZyuVcacnZGNwpm8NwH/SPK+ErAl+UbOuXHAOAAzW+Wciw1PeNFL1yljdJ0yTtcqY3SdMk7XKmPMbFVGtgtns/lnQDUzq2pmhYCuwJwwli8iIpIrhK3m7Zw7bGa3Au8C+YGXnXNrw1W+iIhIbhHOZnOcc/OB+ZnYZVxOxZLL6DpljK5TxulaZYyuU8bpWmVMhq6TOXdcnzERERGJYBoeVUREJMpEfPI2s36hIVXXmtm/g44nUpnZUDPbbGarQ6/WQccUyczsHjNzZlY26FgilZk9ZGZfh36fFppZxaBjikRm9qiZ/Sd0rWaa2clBxxSJzOyK0P/xI2amXufJZHb48IhO3mZ2MX4UtvOcczWAMQGHFOnGOufqhF6Z6VuQp5jZP4DmwMagY4lwjzrnznPO1QHmAoMDjidSLQJqOufOA74HHgg4nki1BugIfBB0IJEmK8OHR3TyBm4GRjnnDgA4534POB7JHcYC95HCIEHyP865XUneFkfXK0XOuYXOucOht5/gx7CQZJxz3znn1gUdR4TK9PDhkZ68qwNNzOxTM1tmZvWDDijC3RpqunvZzEoFHUwkMrN2wGbn3FdBxxINzGykmf0CdEc174y4Dngn6CAk6mR6+PCwPiqWEjNbDJyawqqB+PhKAQ2B+sB0MzvD5dEu8ulcq+eBh/C1o4eAx/D/SPKcdK7TAKBFeCOKXGldK+fcbOfcQGCgmT0A3AoMCWuAESK96xTaZiBwGJgcztgiSUauk6QoQ8OHJxV48nbOxae2zsxuBt4KJeuVZnYEPz7utnDFF0nSulZJmdmL+HuUeVJq18nMagFVga/Mj1leCfjCzC5wzm0NY4gRI6O/U8DrwDzyaPJO7zqZWU+gLRCXVysXkKnfJzlWhoYPTyrSm81nAZcAmFl1oBAa2D5FZlYhydsO+M4hkoRz7hvnXHnnXBXnXBX8H8z5eTVxp8fMqiV52w74T1CxRDIzawX0B9o55/YFHY9EpUwPHx54zTsdLwMvh2YWOwj0zMufatPxbzOrg29q2QDcFGg0khuMMrOzgSPAz0CfgOOJVM8AhYFFoRadT5xzulbJmFkH4GmgHDDPzFY751oGHFZEyMrw4RphTUREJMpEerO5iIiIJKPkLSIiEmWUvEVERKKMkreIiEiUUfIWERGJMkreIiIiUUbJWyTKmNmeE9i3aGiegPzZGVMmYyhkZh+YWaSPMyESsZS8RfKW6/BDDv8dVAChWZPeA64MKgaRaKfkLRKlzOwuM1sTet2RZPkgM/uPmS0ysylmdk+S3boDs5Ns29nMPjGzr8xsuZmVC1P4s0KxiEgWqNlKJAqZWT3gWqABfkaiT81sGX5oxU5AXfzf9xfA56F9CgFnOOc2JDnU+865GaH1Q4AuwLNhOIU1+JkCRSQLVPMWiU6NgZnOub3OuT3AW0CT0PLZzrn9zrndwNtJ9ikL/JXsOL3MbKWZfQX0BRIAzCxp7fyNpPfIQ/esnzazJ8xsopmdFlr+UOjrFWb2pJk9Y2YjUwo+1Gx/0MxKnNBVEMmjVPMWiU4pzf+b1nKA/UCRxA3NrgEuAC5xzu0xsw+AtWb2D+DXJPvlS3aPvDGwzTk3PMmxTgUKmNm/gFjn3O2h5S+Y2dnOuXUpxFOY0IcFEckc1bxFotMHwOVmVszMiuOngf0QWA5cZmZFzCwGaHN0B+fcn0B+MzuawGsBH4cSdyfgQuAboB5wbijxTuL4eYVXAIXN7FUz6xFaVhdYDVyPnzkqqYPJgzezMvgPAIeyeP4ieZpq3iJRyDn3hZlNBFaGFr3knPsSwMzmAF/hp/FcBexMsutCfM15MTAJmG1mnYH5wH+dc3tD99Pvds59ZmZt8FM4YmYPAD8556YCA80sH/AR8BpQB9903xY/LS1mVhUo75z7Kdm+ABeHyhSRLNCUoCK5jJnFhGrTxfA19N7OuS9C6+oCdznnrk5j/5nAlc65g2Y2DJgBlAJKAjHARcDh0PcznXNvm9l44EagBjAQ+B0oCAwCzj2679HkbWZvAQ+k0pwuIulQ8hbJZczsdXzCLAJMcs49kmz9daHlGX7W28zuAk4GSjrn7shkPMfsG+r13tU590pmjiMi/6PkLSIZYmZVgIZJmr7Dsq+IHE/JW0REJMqot7mIiEiUUfIWERGJMkreIiIiUUbJW0REJMooeYuIiEQZJW8REZEoo+QtIiISZZS8RUREooySt4iISJT5f6Wy17+FEYWzAAAAAElFTkSuQmCC\n", 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"]}, "metadata": {"needs_background": "light"}, "output_type": "display_data"}], "source": ["# plot\n", "plt.figure(figsize=(8,6))\n", "log_silica_KA = np.array([-3.85, 0]) # Set the new begin and end of the kaolinite-albite equilibrium line\n", "plt.plot(log_silica_KA, y_KA(log_silica_KA), 'b', label='Kaolinite-Albite') # plot the kaolinite-albite equilibrium line\n", "plt.plot([-3.85, -3.85], [0, y_KA(-3.85)], 'r', label='Gibbsite-Kaolinite') # plot the gibbsite-kaolinite equilibrium line\n", "plt.xlabel('$\\log (a_{H_{4}SiO_{4}})$')\n", "plt.ylabel('$\\log (a_{Na^+}/a_{H^+})$')\n", "plt.xlim([-6, 0])\n", "plt.ylim([0, y_KA(-3.85)])\n", "plt.title('Gibbsite-Kaolinite-Albite stability diagram', fontsize=14)\n", "plt.text(-5.5, 4, 'Gibbsite', fontsize=16)\n", "plt.text(-3, 3, 'Kaolinite', fontsize=16)\n", "plt.text(-1.5, 6, 'Albite', fontsize=16)\n", "plt.legend(loc='best', fontsize=10)"]}, {"cell_type": "markdown", "metadata": {}, "source": ["The stability diagram above is a simplified version, acquired from the given information. A more complex version of it is shown in Figure 1 below.\n", "\n", "

\n", "\n", "$\\quad$Figure 1: A mineral stability diagram showing stability fields for gibbsite, kaolinite, Na-beidellite (smectite), and albite at $25^\\circ C$ and $1\\,atm$ (Ryan, 2019)."]}, {"cell_type": "markdown", "metadata": {}, "source": ["## References\n", "\n", "- Lecture slide for Lecture 7 of the Low-Temperature Geochemistry module\n", "- Practical for Lecture 3 of the Low-Temperature Geochemistry module\n", "- Ryan, P. (2019) Environmental and Low-Temperature Geochemistry. Wiley-Blackwell."]}], "metadata": {"celltoolbar": "Tags", "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": "3.8.8"}}, "nbformat": 4, "nbformat_minor": 4}