{ "cells": [ { "cell_type": "markdown", "metadata": {}, "source": [ "# Attività nelle soluzioni non ideali\n", "\n", "In questa esercitazione, collegata alla lezione 20 del modulo di termodinamica, utilizziamo le capacità offerte dalla libreria [Sympy](https://www.sympy.org/en/index.html) di Python per l'elaborazione *simbolica* di espressioni matematiche, per ottenere il potenziale chimico dei componenti *a* e *b* di una soluzione binaria non ideale e, da quello, derivare l'attività di *a* e di *b*, da confrontarsi con le rispettive frazioni molari. \n", "\n", "Oltre alla libreria numpy, importiamo anche la libreria sympy (con l'alias sym), e invochiamo il comando sym.init_printing per avere un chiaro *rendering* delle espressioni matematiche." ] }, { "cell_type": "code", "execution_count": 1, "metadata": {}, "outputs": [], "source": [ "import numpy as np\n", "import sympy as sym\n", "import matplotlib.pyplot as plt\n", "%matplotlib inline\n", "sym.init_printing()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "In sympy si possono definire dei simboli che possono essere assegnati a variabili python (variabili con lo stesso nome, o anche con nomi diversi da quelle dei simboli). Questi simboli possono poi essere *manipolati* in vario modo seguendo le regole del calcolo algebrico. Per esempio, definiamo due simboli *y* e *z* e poi scriviamone la differenza tra i rispettivi quadrati che assegniamo alla variabile *expr*" ] }, { "cell_type": "code", "execution_count": 2, "metadata": {}, "outputs": [], "source": [ "y,z=sym.symbols('y z')" ] }, { "cell_type": "code", "execution_count": 3, "metadata": {}, "outputs": [ { "data": { "image/png": "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\n", "text/latex": [ "$\\displaystyle y^{2} - z^{2}$" ], "text/plain": [ " 2 2\n", "y - z " ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "expr=(y**2-z**2)\n", "display(expr)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Adesso chiediamo di fattorizzare *expr* e, per far questo, usiamo il metodo *factor*:" ] }, { "cell_type": "code", "execution_count": 4, "metadata": {}, "outputs": [ { "data": { "image/png": "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\n", "text/latex": [ "$\\displaystyle \\left(y - z\\right) \\left(y + z\\right)$" ], "text/plain": [ "(y - z)⋅(y + z)" ] }, "execution_count": 4, "metadata": {}, "output_type": "execute_result" } ], "source": [ "expr.factor()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Possiamo poi decidere di derivare *expr* rispetto a *y* e *z*, e di sommare le due derivate:" ] }, { "cell_type": "code", "execution_count": 5, "metadata": {}, "outputs": [ { "data": { "image/png": "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\n", "text/latex": [ "$\\displaystyle 2 y - 2 z$" ], "text/plain": [ "2⋅y - 2⋅z" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "der=expr.diff(y,1)+expr.diff(z,1)\n", "display(der)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "e di raccogliere \"2\"..." ] }, { "cell_type": "code", "execution_count": 6, "metadata": {}, "outputs": [ { "data": { "image/png": "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\n", "text/latex": [ "$\\displaystyle 2 \\left(y - z\\right)$" ], "text/plain": [ "2⋅(y - z)" ] }, "execution_count": 6, "metadata": {}, "output_type": "execute_result" } ], "source": [ "der.factor()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Queste e mille altre operazioni possono essere fatte con sympy... \n", "\n", "Ma veniamo alle soluzioni solide *non* ideali. Cominciamo con il definirci i simboli necessari come le frazioni molari, per le quali specifichiamo anche che sono dei numeri reali positivi (avere informazioni sulle variabili che definiamo, *aiuta* sympy nel fare i conti...)" ] }, { "cell_type": "code", "execution_count": 7, "metadata": {}, "outputs": [], "source": [ "xa, xb=sym.symbols('x_a x_b', positive=True, real=True)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Poi definiamo i simboli per l'energia libera di soluzione e i potenziali chimici (numeri *reali*):" ] }, { "cell_type": "code", "execution_count": 8, "metadata": {}, "outputs": [], "source": [ "mu, mua, mub, mu0a, mu0b=sym.symbols('mu mu_a mu_b mu_a^0 mu_b^0', real=True)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Quindi definiamo i simboli per la costante dei gas (R) e per la temperatura (T), che sono numeri reali e positivi, nonché i simboli dei parametri (W e V) che vogliamo usare per costruire un modello di soluzione solida *non* simmetrico:" ] }, { "cell_type": "code", "execution_count": 9, "metadata": {}, "outputs": [], "source": [ "R,T=sym.symbols('R T', positive=True, real=True)\n", "W, V=sym.symbols('W V', real=True)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Più avanti nel notebook, vorremo avere la possibilità di fare dei calcoli con le espressioni simboliche che abbiamo ottenuto; perciò dovremmo poter attribuire dei valori numerici ai potenziali chimici dei componenti puri, ai parametri W e V, a R e alla temperatura. Questi valori numerici li conserviamo in una variabile che chiamiamo *p* che sia l'istanza di una classe *param*. Dotiamo la classe anche di un metodo *set_T* che consenta di cambiare il valore della temperatura conservata nella variabile p.T:" ] }, { "cell_type": "code", "execution_count": 10, "metadata": {}, "outputs": [], "source": [ "class param():\n", " def __init__(self):\n", " self.R=8.3145\n", " self.T=1000\n", " self.W=12000\n", " self.V=-5000\n", " self.mu0a=-12000\n", " self.mu0b=-10000\n", " def set_T(self,temp):\n", " self.T=temp\n", " \n", "p=param()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Adesso siamo pronti per scrivere la funzione $\\mu$: l'energia libera molare della nostra soluzione non ideale. Qui andiamo *oltre* il modello quadratico simmetrico discusso nelle lezioni: ne usiamo uno volutamente più complicato (un modello *quartico*, *non simmetrico*) e affideremo alle funzioni per il calcolo simbolico di *Sympy* il compito di derivare le corrette espressioni dei potenziali chimici dei due componenti. \n", "\n", "Sia perciò $Wx_ax_b + Vx_bx_a^3$ il termine non ideale (a due parametri $W$ e $V$) che vogliamo aggiungere all'energia libera della soluzione ideale:\n", "\n", "$$\\mu = x_a\\mu_a^0 + x_b\\mu_b^0 + RT\\left(x_a \\log x_a + x_b\\log x_b\\right)+Wx_ax_b + Vx_bx_a^3$$\n", "\n", "Scriviamo questa espressione come una normale espressione Python, usando le variabili che abbiamo associato ai vari simboli:" ] }, { "cell_type": "code", "execution_count": 11, "metadata": {}, "outputs": [], "source": [ "mu=xa*mu0a+xb*mu0b+R*T*(xa*sym.log(xa)+xb*sym.log(xb))+W*xa*xb + V*xb*xa**3" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Controlliamo che quanto abbiamo scritto corrisponda a ciò che volevamo, usando la funzione *display*:" ] }, { "cell_type": "code", "execution_count": 12, "metadata": {}, "outputs": [ { "data": { "image/png": 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i8SrPlu6kOmJteOlgyV0otjzZuasl2y3JlO5H+y0sRuUZS6eRGKmOJWUdY2c0XbxeuQytIlSY8cIb5ZWXPlrPQGJUHgPletF3CdMe858iwKOG3l0VZzdGmFfsRCSRN65qjbvZcC4deyW4OPCYk288ILkj/MoLl3iDY2STR1f0zoHHPZ9ai1cJiEllHO/PXObmDFf++3oQLMdWvhXrsh07S/df7TF5OS7Eqt+pg4CTx52RaUyesfRO908iqD5zpMI/8WR3lRcR7uegXyYb+KpjpxNHQGOGXQsM43s5XVX+kx53E3DhikbzT3VVB5sRrD9V1vvNGjoMJHUa6/lG7lI7BDS7GVqq/2qHQcbbuf/WsRkcTomRJWQak2cs/ZTw9vuifrNQ8caHgcPXR+gXXkCOPrxQeKcdgR4CGj+8qHI/J+u489TH3QRceNng3hIGD//dnROXKvR/MYWLGjAnBCQAAAAASUVORK5CYII=\n", "text/latex": [ "$\\displaystyle R T \\left(x_{a} \\log{\\left(x_{a} \\right)} + x_{b} \\log{\\left(x_{b} \\right)}\\right) + V x_{a}^{3} x_{b} + W x_{a} x_{b} + \\mu^{0}_{a} x_{a} + \\mu^{0}_{b} x_{b}$" ], "text/plain": [ " 3 \n", "R⋅T⋅(xₐ⋅log(xₐ) + x_b⋅log(x_b)) + V⋅xₐ ⋅x_b + W⋅xₐ⋅x_b + μ⁰ₐ⋅xₐ + μ_b__0⋅x_b" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "display(mu)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "In effetti l'espressione è corretta, anche se i vari termini sono scritti in un ordine differente. \n", "\n", "Adesso facciamo una cosa *difficile*... ci scriviamo una funzione *mu_f* che ci serva per fare dei grafici di $\\mu$ a temperature diverse. Per far questo,\n", "\n", "- ci costruiamo un *dizionario* che chiamiamo *parameters*: una lista, messa tra parentesi graffe, di simboli a cui assegniamo una variabile; quindi, con la scrittura \"R: p.R\" assegniamo al simbolo R la variabile p.R (della classe *param*) che contiene il valore di R (8.3145), perciò il simbolo R sarà sostituito con 8.3145. Lo stesso dicasi per tutti gli altri simboli.\n", "\n", "- Sostituiamo le *occorrenze* del simbolo *xb* con il simbolo (1-*xa*), perchè vogliamo ottenere una funzione $\\mu(x_a)$ e, in effetti, $x_b=1-x_a$; sostituiamo anche tutti i parametri (W, V, R...) che compaiono in $\\mu$ con i valori del dizionario *parameters*. Tutto questo è fatto operando su *mu* con il metodo *subs* (come vedete, possiamo usare due *subs* in cascata). La nuova funzione ottenuta dopo queste sostituzioni viene assegnata alla variabile mu_fp.\n", "\n", "- Adesso *lambdifichiamo* (non me ne volete... è un termine *tecnico* di sympy...) la funzione simbolica mu_fp con il metodo *lambdify*: la sintassi di *lambdify* prevede come argomenti: la variabile indipendente (per noi è *xa*), l'espressione da *lambdificare* (ehm... la funzione simbolica da rendere come funzione *lambda*, *anonima*) e un argomento opzionale (in questo caso 'numpy') che dica al metodo di produrre una funzione di tipo *numpy*. La funzione *lambda* ottenuta è assegnata alla variabile *mu_ff* \n", "\n", "Notate che *mu_ff* è una funzione definita all'interno della funzione *mu_f*, quindi è *locale* e non può perciò essere invocata al di fuori di *mu_f*. \n", "\n", "La funzione *mu_f* riceve come argomento la temperatura (*temp*), e lo usa per assegnare il valore della variabile *p.T*, che è poi richiamata nel *dizionario*. *mu_f* costruisce anche una lista *x* di valori della variabile indipendente (*xa*) che restituisce (*return*) insieme ai corrispondenti valori *mu_ff* (valori calcolati per ogni *xa* nella lista *x*) " ] }, { "cell_type": "code", "execution_count": 13, "metadata": {}, "outputs": [], "source": [ "def mu_f(temp):\n", " p.set_T(temp)\n", " parameters={R: p.R, T: p.T, W: p.W, V: p.V, mu0a: p.mu0a, mu0b: p.mu0b}\n", " mu_fp=mu.subs(xb,1-xa).subs(parameters) \n", " mu_ff=sym.lambdify(xa, mu_fp, 'numpy')\n", " \n", " x=np.linspace(0.001, 0.999,50)\n", " return x, mu_ff(x)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Siamo ora pronti per fare dei plot dell'energia libera della soluzione a varie temperature: \n", "\n", "- Scegliamo 4 temperature diverse che inseriamo nella lista *t_list*;\n", "- apriamo un ciclo sui valori di temperatura contenuti in *t_list* e invochiamo *mu_f* ponendo il suo output nelle variabili *x* e *mx*; \n", "- il resto è solo grafica..." ] }, { "cell_type": "code", "execution_count": 14, "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", 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" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "t_list=(500, 700, 900, 1100)\n", "\n", "plt.figure()\n", "\n", "for it in t_list: # ciclo su tutti i valori contenuti in t_list\n", " x, mx=mu_f(it)\n", " lg=\"T: \"+str(it)\n", " plt.plot(x,mx,label=lg)\n", "\n", "plt.xlim(0,1)\n", "plt.xlabel(\"Xa\")\n", "plt.ylabel(\"mu\")\n", "plt.legend(frameon=False)\n", "plt.title(\"Energia libera molare di soluzione\")\n", "plt.show()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Notate l'andamento della curva per T=500K... descrive un sistema che si *smescola* in due fasi a composizione diversa, come discusso nella lezione termodinamica_19 e nelle dispense.\n", "\n", "## Dall'energia libera molare della soluzione ai potenziali chimici\n", "\n", "Adesso cominciamo a predisporre le condizioni per calcolare il potenziale chimico di ogni componente. Per far questo, avremo bisogno delle derivate di $\\mu$ rispetto ad $x_a$ e rispetto a $x_b$; questo perchè:\n", "\n", "
\n", "\n", "\\begin{equation}\n", "\\left\\{%\n", "\\begin{array}{l}\n", "\\mu_a = \\mu -\\left(\\frac{\\partial\\mu}{\\partial x_b}\\right)x_b\\\\[6pt]\n", "\\mu_b = \\mu -\\left(\\frac{\\partial\\mu}{\\partial x_a}\\right)x_a\n", "\\end{array}\n", "\\right .\n", "\\end{equation}\n", "\n", "
\n", "\n", "Perciò, per prima cosa, definiamo due espressioni diverse di $\\mu$, di cui una dipenda solo da $x_a$ e l'altra dipenda solo da $x_b$, in modo da poter fare agevolmente appunto le derivate rispetto a $x_a$ e $x_b$. Poniamo queste espressioni, ottenute con il metodo *subs*, nelle variabili *musa* e *musb*:" ] }, { "cell_type": "code", "execution_count": 15, "metadata": {}, "outputs": [], "source": [ "musa=mu.subs(xb,1-xa)\n", "musb=mu.subs(xa,1-xb)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Quindi, calcoliamo le due derivate di cui sopra con il metodo *diff*. Come argomenti, il metodo accetta la variabile rispetto a cui fare l'integrazione e l'ordine della derivata: per esempio, *musa.diff(xa,1)* farà la derivata prima rispetto a *xa* della funzione *musa* che è la *mu* definita in modo tale da farla dipendere solo da *xa* e non da *xb*. Poniamo le due derivate nelle variabili *dera* e *derb*:" ] }, { "cell_type": "code", "execution_count": 16, "metadata": {}, "outputs": [], "source": [ "dera=musa.diff(xa,1)\n", "derb=musb.diff(xb,1)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Usando le due variabili *dera* e *derb*, possiamo adesso facilmente calcolare i potenziali chimici dei due componenti (salvati nelle variabili *mub* e *mua*):" ] }, { "cell_type": "code", "execution_count": 17, "metadata": {}, "outputs": [], "source": [ "mub=mu-dera*xa\n", "mua=mu-derb*xb" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Guardiamo cosa abbiamo ottenuto per $\\mu_a$:" ] }, { "cell_type": "code", "execution_count": 18, "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", "text/latex": [ "$\\displaystyle R T \\left(x_{a} \\log{\\left(x_{a} \\right)} + x_{b} \\log{\\left(x_{b} \\right)}\\right) + V x_{a}^{3} x_{b} + W x_{a} x_{b} + \\mu^{0}_{a} x_{a} + \\mu^{0}_{b} x_{b} - x_{b} \\left(R T \\left(\\log{\\left(x_{b} \\right)} - \\log{\\left(1 - x_{b} \\right)}\\right) - 3 V x_{b} \\left(1 - x_{b}\\right)^{2} + V \\left(1 - x_{b}\\right)^{3} - W x_{b} + W \\left(1 - x_{b}\\right) - \\mu^{0}_{a} + \\mu^{0}_{b}\\right)$" ], "text/plain": [ " 3 \n", "R⋅T⋅(xₐ⋅log(xₐ) + x_b⋅log(x_b)) + V⋅xₐ ⋅x_b + W⋅xₐ⋅x_b + μ⁰ₐ⋅xₐ + μ_b__0⋅x_b -\n", "\n", " ⎛ 2 3 \n", " x_b⋅⎝R⋅T⋅(log(x_b) - log(1 - x_b)) - 3⋅V⋅x_b⋅(1 - x_b) + V⋅(1 - x_b) - W⋅x_\n", "\n", " ⎞\n", "b + W⋅(1 - x_b) - μ⁰ₐ + μ_b__0⎠" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "display(mua)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Ummm... Facciamo qualche *semplificazione* e *sostituzione* al fine di ottenere espressioni più facilmente leggibili: " ] }, { "cell_type": "code", "execution_count": 19, "metadata": {}, "outputs": [], "source": [ "mua=mua.simplify().subs(xa,1-xb).simplify().subs(1-xb,xa)\n", "mub=mub.simplify().subs(xb,1-xa).simplify().subs(1-xa,xb)" ] }, { "cell_type": "code", "execution_count": 20, "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", "text/latex": [ "$\\displaystyle R T \\log{\\left(x_{a} \\right)} + V \\left(3 x_{b}^{4} - 6 x_{b}^{3} + 3 x_{b}^{2}\\right) + W x_{b}^{2} + \\mu^{0}_{a}$" ], "text/plain": [ " ⎛ 4 3 2⎞ 2 \n", "R⋅T⋅log(xₐ) + V⋅⎝3⋅x_b - 6⋅x_b + 3⋅x_b ⎠ + W⋅x_b + μ⁰ₐ" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "display(mua.collect(V))" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "OK! Così va decisamente meglio... Vediamo anche $\\mu_b$:" ] }, { "cell_type": "code", "execution_count": 21, "metadata": {}, "outputs": [ { "data": { "image/png": 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7YM9foibm9xX1vXHoUg53SUQq7v8vlLu7KOUPlVAA9+12b6lqJ+CMuf9sOOHOUdFDT6vPUePwoLWXgA6UuBvkTy2X7kKKdCL8zH9wWCqzI2X3w06Gv2Y5+qqhiJGZO4+Uk4A62pZnFmkx9CN1Nyd/7LQr8VUaKEMw19jk9L83Dt0rhgU9eTfoJ547qUulWRyBnwhoBCeEDHsI7BzYpc/q0L3eCI4Ebu6L+VrCHBmnpH2CwXJ6O+PuPDiBfVLECFkG624E7tIh7LLHBFpkyJ7+9+qlaKk2D/2X0YCcCe83+IKl78SyDEP3hIr0zXEeZz7GadwTLe2XmEf7Jc5Bmm3UgBwKu3PeS3AFcoDlNEAAZTd3gHuigf8BfTkgAQZbiaUAAAAASUVORK5CYII=\n", "text/latex": [ "$\\displaystyle R T \\log{\\left(x_{b} \\right)} + V \\left(3 x_{a}^{4} - 2 x_{a}^{3}\\right) + W x_{a}^{2} + \\mu^{0}_{b}$" ], "text/plain": [ " ⎛ 4 3⎞ 2 \n", "R⋅T⋅log(x_b) + V⋅⎝3⋅xₐ - 2⋅xₐ ⎠ + W⋅xₐ + μ_b__0" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "display(mub.collect(V))" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Vediamo allora di rappresentare queste funzioni; consideriamo $\\mu_a$: confrontiamo l'andamento di $\\mu_a$ con $x_a$, confrontato con l'andamento del potenziale chimico della stessa componente nel caso ideale. Lo facciamo per una temperatura di 1000K. La procedura non è molto diversa da quella che abbiamo già usato sopra nel caso dell'energia $\\mu$: fissiamo la temperatura; sostituiamo in *mua* ogni occorrenza di $x_b$ con $1-x_a$, e tutti i parametri simbolici con i valori contenuti nel dizionario, producendo così *mua_f*; *lambdifichiamo* la funzione *mua_f* (ottenendo *mua_ff*)" ] }, { "cell_type": "code", "execution_count": 22, "metadata": {}, "outputs": [], "source": [ "p.set_T(1000)\n", "parameters={R:p.R, T:p.T , W: p.W, V: p.V, mu0a: p.mu0a, mu0b: p.mu0b}\n", "mua_f=mua.subs(xb,1-xa).subs(parameters)\n", "mua_ff=sym.lambdify(xa, mua_f, 'numpy')" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Definiamo *velocemente* anche le funzioni che calcolano il potenziale chimico dei componenti nel caso ideale:" ] }, { "cell_type": "code", "execution_count": 23, "metadata": {}, "outputs": [ { "data": { "image/png": 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"text/latex": [ "$\\displaystyle R T \\log{\\left(x_{a} \\right)} + \\mu^{0}_{a}$" ], "text/plain": [ "R⋅T⋅log(xₐ) + μ⁰ₐ" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "ideal_a=mu0a+R*T*sym.log(xa)\n", "ideal_b=mu0b+R*T*sym.log(xb)\n", "\n", "display(ideal_a)\n", "\n", "ideal_af=ideal_a.subs(parameters)\n", "ideal_aff=sym.lambdify(xa,ideal_af,'numpy')" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "E adesso calcoliamo $\\mu_a$ nei casi *ideale* e *non ideale* e facciamone il plot:" ] }, { "cell_type": "code", "execution_count": 24, "metadata": {}, "outputs": [ { "data": { "image/png": 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hmZqEfHYlFVKXNYHK9KEEsoaTmDOCtLyRZBQWkzt0FHlDihialESPp6zuhywIGWNMBC3tHVQ3tlLV0EpVYytVDS3sqq2mtXYzWruVxMZtpDZtJ7NlJ7ntlQyjihFSwzh2kSD7XvrSRhK1iUNoSC2kOXUiGzNHQPYIknKLSB9STHZhCbnDSkjNLGCESMT5zgYqC0LGmEGhua2DqsZWahpdUKlubKGqodUFmvoWmuprSGzYQkrjNjKaK8jvqGQE1RRJFUVSzbFSTbbs3u+4jYm5NGQNpSW9mMas42jKGUly3igyC0vIGjqKxJyRJGcMYWhCwoCoufQ2C0LGmENOc1sHNU2t1DS2UdvUSnVTKzVNbdQ0uqDi0vY+b2qsJ799B0VSxUipYiRVFEkVk6SKkQku0GTSvPcFBDRJ2J06lNaMEWjOUWhuMc0FxaQWlCA5xZBTBNlFZCankxm/U3HIsyBkjIkLVWV3Wwd1u9uobWoLuW+ltqmN2rDnNU0u4NQ0tdLcFgg9EoXsYqRUUiyVjEuu4cjkakYlVDGCSgo7dpCVWOfWZA7Rnj4UcotJzDsGyR0FOcWQW+zuc4qR7BFkJCaT0adnZfCxIGSMOWBtHQHqm9vZtbvN3Te3sWt3m79vp84/rtu9722Xv2/r6HzasKQEIS8jhYL0BMam1jMtrYrRGVWMZCdDOyooaKsgu2UbGbu3kdDRsu/Okgm5JZA7BnJP9cFlFOSV+CAzkqSk1BifHRMNC0LGDEKBgNLY2k5DSzsNzf7eP65vaae+2T9udsGlocUFmPqQtPrmdna3dXT5OgkCOenJ5KQlk5ueTE56EkW5aeSmJ5ObnuLu0xIZnlDHsI7t5LVuI7d5K+lNW0jatQmp/QTqNkN9274Hzhzqgszw6ZB7EeSN9kFnlLul50M/HpZs9rIgZMwhIBBQmto6aGppp7G1g8aWdndrbaexxT1vaGmnqXXfxw0+X2iQafTHiEZGSiJZqUlkpyWRnZZMdloSI/PSyPGPs9OSyUlLIic9eZ/H7nkSWSlJJCQINO+C2o1Qs8HfNkLVBpdW+wm0N+/7wlnDXWApPhamXuoe542G3NEuyKRYI9lAYUHImF7W1hGgqaWDxtZ2mlqDgaGDplb35R8MJHvufSDZb3tIelOUQQMgNSmBrNQkMlOTyEhJJDstiYLMFEoKMshKSSIrzW3LSk0kKzWZrDT3ODsteU/AyUp1t6TEKFd7UYX67VCzFravh5r1UL3eB5z10FQVVshcyB8DQw+HiedB/ljIG+PSckssyAwiFoTMoNcR0H1qCuG1hj21iVZ339TSsU9NIxgsGlvdttaOQPcv6qUkJZCRkkhmigsYGSmJZKYmkZeRQlZqIukpLkBk+O2ZqUlk+udZPshkpSaRkepqHRmpiSRHGzh6KhCAXZuhel3Ibf3e+/aQ4cuS6GosBeNg8sUuwBSM2xtsMsKnwzSDlQUhc8gLBHRP53dwVFVo53ewLyO08zzYt9HQHH3TVEpiwj4BIDPV1TJG5KSRkeqCQXpKog8GSWSGBI305KQ92zNTE8lIjnHAOFCq0FABVeX+9rG7VX/sAk3oAIDEVBdUhoyHwz7lgkzBOMgf55rOEpPj9jbMocOCkOl3Wto7qGxopbK+harGFir9BYXBW02juy7EDdttpW53G12tzZiSmEBOetI+/RgjctJ8s1MwzTdBhTRFZaUlkbkn4CSRktTPAsbBaGmAqo+gstzdhwad1oa9+RJTXFAZMgEmnOMCTsFhUDDejTJLGEDnxMSFBSHTZzoCys76FrbW7WZ7XTPb65qp2OVuO+pb2FHfws76Fup2t0XcPzUpgYLMFPIzUijITKE4L538jBTyM5LJzUghLz2ZvAx32zsaK5m05IOfbv6QpAq7tkLlh1D5kb/3j+u3hmQUV3MZMgFGn+zuCw5z97mjIGGQnj/TJywImV6jquyob+GT6iY+qWrik+omNtU0saVmN1tqXeBpD+xbZUlJTGB4birDstOYOCyLU8YPYWhWKoXZqRRmpTIkK4XCTHefkZKI2LDb/QU63ACAnWth5wfuvnKtCzahtZrUHCicCIed4QJM4UQYMtEFnOS0uBXfDG4WhEyPNba0s25nI+U76ynf0cC6nY2sr2xkY1XTPteNiMCInDRG5adTOiaf4vx0inLTKcpNoyg3nRG5aeRnJFtgidaeYPMB7Fjjgs2OD1ztJrSvJnskDJ0ER/+bCzSFk9wotKzhdu2M6XcsCJlOBQLKJ9VNlG3dxZptdazd3sDail1sqt47CioxQRhdkMG4wkxOGV/IuMIMRg/JZHRBBiPz0khNsqacHgsOd64oc8Fmx/t7g07oCLTcEhh6hKvZDD0Chk12QSctN35lN6aHLAgZwDWlba1r5p1Panl3cy3vbqqlbOsuGlraARdsDivMZNqoPK44roRJw7MYPzSLMUMyB1aHfV9r2+0CTEWZu21fDTvKYHfN3jxZI1yAKb0Whk1xj4ceDqnhS50Zc+ixIDRIBQLK2op6/rmuiuUba1i5oYbtu9xV6ymJCUwemcNlxxQzdWQOU0fmMnF41uDt4O8t9RWw/T3YvsrdV6x2I9LUX1eUnOkCzORLYPhUH3CmQOaQ+JbbmBiyIDSIbK5p4uUPd/LqR5UsW1dFTZMbhTYyN43jxxVQOiafY0bnccSIHKvdHAxV13ez7V13274Ktq2Cxh178+SOhhFHwdTLYPiRMOJIyBtrQ57NoGNBaADrCCgrNlSzeE0FS9fu4OOdjYALOmcdMZyTxw/h5PFDKM5Lj3NJD2GqbsaAbe/A1rdh6zsu4LTUue0JSa6/ZsI5UDTNBZ7hR0J6XnzLbUw/EZcgJCI/BC4GWoGPgWtVtdZv+wZwHdABfEVVF/n0C4Cf41YF+Z2q3ufTxwHzgQLgLeALqtoqIqnAI8BxQBVwpapu6LM3GSdtHQFeK6/kr6u28eIHO6hubCUlMYETDyvgcyeO4YxJQxk/NNNGpB2I4HU3W1bC1rd80Hkbmn3ASUxxzWhHfgZGHg0jprnmNBv+bEyn4lUTWgx8Q1XbReQHwDeA20RkCjATmAqMBJaIyCS/z6+Ac4HNwHIRWaiqa4AfAD9V1fki8htcAHvA39eo6gQRmenzXdmH77HPqCpvb6rlqbe28Nf3tlHd2Ep2ahJnTR7GeVNGcMbhQ8lKtUpvj7XUw5a3YPNyd79lJTRsd9sSklzAmXoZjDzWBZ2hkyEpJb5lNuYQE5dvJlV9IeTpMuBy/3gGMF9VW4D1IlIOnOC3lavqOgARmQ/MEJH3gbOAz/k8DwN34YLQDP8YYAHwSxER1a4meDm01DS28ue3t/DH5Z/wYUUDackJnD15OJdMH8mZhw+14dE9EQi46Ws2vQmb34TNK9zQaPzHpWC8GwpdXOqWFxh+pNVwjOkF/eHn8b8Df/SPi3FBKWizTwPYFJZ+IjAEqFXV9gj5i4P7+BpXnc9f2dtvoK99sH0XD726gafe2UJre4DpJXl8/zNHcdG0IrLTbNLIqLQ2uZrNpmUu8Gx6E5pr3ba0XBh1PEyZAaNKXU3HZn02JiZiFoREZAkwIsKmO1T1aZ/nDqAdeCy4W4T8CkQaMqRd5O/qWJHKej1wPcDo0aMjZYk7VeWNj6v41UvlvFZeRVpyAlccN4rPnzSGyUU58S5e/9dUDZ8sg09ed/db34GAn6Ou8HC33EDJiVBygpvKxkapGdMnYhaEVPWcrraLyCzgIuDskCayzUBJSLZRQHCmxUjplUCeiCT52lBo/uCxNotIEpALVHdS1tnAbIDS0tJ+1VynqrxWXsXPX/yQ5RtqGJadytcvOJyrjh9Nfqb1P3SqYSdsfBU2vAYbX3MXhIIbPFB8HJx8s5uss+QEq+UYE0fxGh13AXAbcIaqNoVsWgg8LiI/wQ1MmAi8iavVTPQj4bbgBi98TlVVRJbi+pTmA7OAp0OONQt4w2//+6HWH7R6Sx33PLuGf66vZkROGnfPmMpnS0vsotFImqphw6uw/hXY8A83vxq4C0BLTnAj1kaf4gKQ9eUY02/Eq0/ol0AqsNgPFV6mqjeoapmIPAGswTXT3ayqHQAicguwCDdEe66qlvlj3QbMF5F7gbeBOT59DvCoH9xQjQtch4SKXc3c/7e1/PntzRRkpHD3jKlceXyJDTQI1doEG1+H9S/BupfdDASoCzpjTobpM2HMqW7Umi2uZky/JYdY5SDmSktLdcWKFXF57UBAeXTZRn7wtw9o71CuPXUsN39qAjk22MCNXtu+Cj7+O6xb6vp1Olpd81rJiTDuDBh3uhu5ZkHHmD4nIitVtbSn+/WH0XEGKN/RwO1/WsWKjTWcPmko9844ktFDMuJdrPhqrHJBp3wJfPwiNO506cOPhBOuh/Gfck1sKYP8PBlzCLMgFGeqyrzXN/D95z4gIzWRH18xnc8cWzw4ZzRQdbWdDxfBRy+4a3VQyBgC48+C8We7++zh8S6pMaaXWBCKo7rdbXx9wbssKqvg7COGcd//m8bQ7NR4F6tvtTXD+pdh7fMu+NRvBcQ1q515O0w4F0YeY0OmjRmgLAjFyXub67jp8ZVsq23mW/86metOHTd4aj+7a11N54Nn4aMl0NYIKVmuljPpAph4HmQNjXcpjTF9wIJQHCxZU8Etf3iLgowU/vjlkzluTH68ixR7jZUu6Lz/jBvNFmhzi7VNvxIO/1cYdxokDbJaoDHGglBf+/2yjXz76dUcWZzLnFnHD+zmt8YqeH8hlD3lruHRDsgfCyfd6BZuKz7OmtmMGeQsCPURVeVHL6zlV0s/5qwjhvHLzx1DRsoAPP3Nu+CDv8LqBfDxUhd4Cg6DU/8Tplzq1tMZLM2OxphuDcBvwf7ph4vW8uuXPmbm8SXce+mRJCUOoBpAR5sbSv3ufFj7HLQ3u5VDT7nVzVQwYpoFHmNMRBaE+sCvlpbz65c+5qoTRvO9y44cOAMQtq+Gdx6DVU9AUyWkF8Axn4ejPutmobamNmNMNywIxdi819bzw0VrmXH0SO69dAAEoN218N6T8PajsO1dSEiGwy+E6Ve5JaxtUTdjTA9YEIqhZ97dyl3PrOG8KcP50RXTSUw4RAOQqltvZ+U8N8igfbfr27nwfjjqCpuF2hhzwCwIxciHFfV8fcEqSsfk83+fO4bkQ7EPqKUB3nsCls+BitXuWp7pM+G4We4CUmOMOUgWhGKgvrmNGx5dSWZqEr/+t2MPvdmvq9fBP2e7/p6WXTD8KLjoZ67Wk5oV79IZYwYQC0K9TFX5nydXsbG6ice/eCLDcg6RtWtU3eJvb/zajXBLSISpl7mJQkcdb6PbjDExYUGol815dT1/K9vOHZ+ezImHDYl3cboX6HCzGLz2c9j6lpss9PSvQel1kFMU79IZYwY4C0K9aGNVIz9ctJZzpwzni6eNi3dxutbeCu/+AV77mWt+KzgMLvqpG+WWnB7v0hljBgkLQr1EVfn202UkJyb076HYbc1uePVrP4e6TVB0NHz2ETjiItcEZ4wxfciCUC957r3tvPzhTu68eArD+2M/UHsrvPN7ePmHbrmEkhPdYIMJZ1t/jzEmbiwI9YL65ja+80wZRxbn8IWTxsS7OPsKdLgZDV76PtRudMHnst+4pbAt+Bhj4syCUC/48QsfsrOhhQevLu1fc8KVL4HFd7prfIqmw7/+2M1qYMHHGNNPWBA6SOt2NvDIGxv4/IljmF6SF+/iOBVrYNE3Yd1SyBsDl8+FKZfZXG7GmH7HgtBBmv3KOpISE/jK2RPjXRTYXQMv3QdvPgip2XD+9+D4L9piccaYfsuC0EHYsauZP7+1hc8ePyq+i9OputkNFn8bmqqh9Fo4639tTjdjTL9nQeggzHltPe2BANefNj5+haj8CJ79L9jwDyg5Cb5wv+v/McaYQ4AFoQO0q7mNx5d9wqePKmL0kIy+L0BHG7z6M3jlfndx6cU/h2Outn4fY8whxYLQAXps2SfUt7RzwxlxqAXteB+e+rJbz2fqZ+CC+yB7eN+XwxhjDlJcfjaLyD0iskpE3hGRF0RkpE8XEfmFiJT77ceG7DNLRD7yt1kh6ceJyHt+n1+In6pARApEZLHPv1hE8nur/M1tHcx5dT2nTdmvejIAAB35SURBVCzkyOLc3jps9wId8Nov4LdnQN0W+OyjcMVDFoCMMYeseLXd/FBVp6nq0cCzwLd9+oXARH+7HngAXEAB7gROBE4A7gwJKg/4vMH9LvDptwMvqupE4EX/vFcsfHcrlQ0t3NiXtaD67fDopbD4f2HiuXDTMphySd+9vjHGxEBcgpCq7gp5mgmofzwDeESdZUCeiBQB5wOLVbVaVWuAxcAFfluOqr6hqgo8AlwacqyH/eOHQ9IP2rOrtjG6IIOTx/fRLNnlS+CBf4FNy+GSX8KVv4esoX3z2sYYE0Nx6xMSke8CVwN1wKd8cjGwKSTbZp/WVfrmCOkAw1V1G4CqbhORYV2U5XpcbYrRo0d3We66pjZeL6/kulPHxX6S0kAHLP0e/ONHMGwKXP4QDDsitq9pjDF9KGY1IRFZIiKrI9xmAKjqHapaAjwG3BLcLcKh9ADSe0RVZ6tqqaqWDh3adQ1jyfsVtAeUC44c0dOX6ZnmOvjDTBeAjvkCfOnvFoCMMQNOzGpCqnpOlFkfB/6K6/PZDJSEbBsFbPXpZ4alv+TTR0XID1AhIkW+FlQE7OjhW4job2XbKcpNY/qoGE7Rs/NDmH8V1Gxw872VXmfzvRljBqR4jY4LnePmEuAD/3ghcLUfJXcSUOeb1BYB54lIvh+QcB6wyG+rF5GT/Ki4q4GnQ44VHEU3KyT9gDW2tPPKhzs5f+oIEhJiFBTWvwK/Owd218LVC920OxaAjDEDVLz6hO4TkcOBALARuMGnPwd8GigHmoBrAVS1WkTuAZb7fHerarV/fCMwD0gHnvc3gPuAJ0TkOuAT4IqDLfTStTtoaQ9wYaya4lb/CZ66wa1y+m9PQl7X/VPGGHOoi0sQUtX/10m6Ajd3sm0uMDdC+grgyAjpVcDZB1fSfT2/ejuFWSmUjo3BnGxv/BoWfQNGnwwzH7d534wxg4LN8RKl5rYOln6wg3OnjCCxN5viVN0IuEXfgMkXwxf+YgHIGDNo2LQ9UXrlw500tXb0blNcMAC9cj8c83m4+BeQkNh7xzfGmH7OakJR+lvZdnLTk3vvAtV9AtAX4OL/swBkjBl0LAhF6c311Zw6oZDk3lq+++UfuAB07NW+BmR/CmPM4GPffFGoa2pjc81uphbn9M4BV8yFl74PR38eLvq5BSBjzKBl335RWLPNTXU3dWQvzJi99nn463/DxPPcGkAWgIwxg5h9A0YhGISmFB1kTWjzSnjyWrfy6eUPQaKNCzHGDG4WhKJQtrWOYdmpDM1OPfCD1G6Cxz8LWcPgc09AalbvFdAYYw5R9lM8Cmu27mLKyIOoBbW3wpPXQHszXPu8C0TGGGOsJtSdlvYOync0HFxT3Avfgi0rYMavYOik3iucMcYc4iwIdeOjigbaA3rggxLeWwBv/hZOugmm9tq6esYYMyBYEOrGmq1+UMKBNMdVfgQLvwIlJ8K5d/dyyYwx5tBnQagbZVvryExJZExBRs92DHTAX26EpBS4Yh4kJsekfMYYcyizgQndWLNtF5OLcnq+ftCbs2HzcrhsNuSMjE3hjDHmEGc1oS4EAnpgI+Oq18OLd7sLUqd9NjaFM8aYAcCCUBc+qW6isbWDqT0JQqrwzH+AJMJFP7VVUY0xpgvWHNeFsuCghKIejIx7+1FY/7ILQLmjYlQyY4wZGKwm1IU12+pIShAmDo9ydoPmXbDkLhjzL3DsNbEsmjHGDAgWhLqwZusuJgzLIi05ynV+3vglNFXBeffaxKTGGBMF+6bsQtnWXdHPlNCwA17/JUy5FIqPjW3BjDFmgIi6T0hE8oGJQFowTVVfiUWh+oOqhhZ21LdEPzLulR+6ueHO+t/YFswYYwaQqIKQiHwR+A9gFPAOcBLwBnBW7IoWXzVNrQAMy0nrJiduSPaKh9wqqYUTYlwyY4wZOKJtjvsP4Hhgo6p+CjgG2BmzUvUDDS0dAGSlRtEftPS7kJAEZ9wW41IZY8zAEm0QalbVZgARSVXVD4DDY1es+GtsaQcgI6WbymLVx/Dek3DSDZBT1AclM8aYgSPaPqHNIpIH/AVYLCI1wNbYFSv+gkEoK7WbU7T8d5CQ7GbJNsYY0yNR1YRU9TJVrVXVu4D/BeYAe9Yl8IMWekxEviYiKiKF/rmIyC9EpFxEVonIsSF5Z4nIR/42KyT9OBF5z+/zCxE3RYGIFIjIYp9/cU/L2NjqglBmV0GotRHefgymzLCF6owx5gD0eIi2qr6sqgtVtTUk+cWeHkdESoBzgU9Cki/EjcCbCFwPPODzFgB3AicCJwB3hgSVB3ze4H4X+PTbgRdVdaIv3+09KV+j7xPKTOmiT+i9J6GlDk74Uk8ObYwxxuut64QOZIK0nwJfBzQkbQbwiDrLgDwRKQLOBxararWq1gCLgQv8thxVfUNVFXiEvTW0GcDD/vHDIelRCTbHdVoTUoU3fwfDj3LrBRljjOmx3gpC2n2WvUTkEmCLqr4btqkY2BTyfLNP6yp9c4R0gOGqug3A33faXiYi14vIChFZsXOnG/TX2NKOCKR3NlvCpn9CxXtw/HU2SakxxhygmE1gKiJLgBERNt0BfBM4L9JuEdL0ANJ7RFVnA7MBSktLFaCxtYOM5MTO1xF680FIzbWlGowx5iD0VhDa75taVc+JmFHkKGAc8K4fQzAKeEtETsDVZEpCso/CjcLbDJwZlv6STx8VIT9AhYgUqeo232y3oydvqLGlvfOmuIYdsOZpOP6LkJLZk8MaY4wJEVVznIiMjnQLyXJ2tC+oqu+p6jBVHauqY3GB5FhV3Q4sBK72o+ROAup8U9oi4DwRyfcDEs4DFvlt9SJykh8VdzXwtH+phUBwFN2skPSoNHQVhN6dD4E21xRnjDHmgEVbE/ore5u/0nA1mbXAVABVre6l8jwHfBooB5qAa4PHF5F7gOU+390hr3kjMA9IB573N4D7gCdE5DrcCLwrelKQptYOMjubLeHDv7kBCYUTe3JIY4wxYaIKQqp6VOhzf/3Ol3ujAL42FHyswM2d5JsLzI2QvgI4MkJ6FT2ooYVraGknM9JsCU3V8MkyOO2rB3poY4wx3gGNjlPVt3BzyQ1YTa2dNMeVLwHtgEkX9n2hjDFmgIl2Fu3Qn/0JwHEM8AlMG1s6yCyMcHrWPg+Zw2DkMX1fKGOMGWCi7RPKZu/Q53bgGeBPMSlRP+Ga48L6hDraoPxFmHKxrZxqjDG9INog9Bzu2p6xIfvcDkyLQZn6haZIo+M+ecNN02NNccYY0yuiDUK/B74GrAYCsStO/xAIKI2tHfsHobV/g8RUOOzMeBTLGGMGnGiD0E5VfSamJelHdrdFmLxUFT58HsadBqlZcSqZMcYMLNEGoTtF5He42ahbgomq+ueYlCrOIk5eWvkRVK+zdYOMMaYXRRuErgWOAJLZ2xynwIAMQg2RFrT70F8DO+mCCHsYY4w5ENEGoenhF6wOZE2trjkuI7Q57qPFMPxIyCvpZC9jjDE9Fe0442UiMiWmJelH9qsJqcK2VVByQhxLZYwxA0+0NaFTgVkish7XJyS4WXYG5BDtJr+0d0YwCNVtdkOzh+83O5AxxpiDEG0QGlQdIQ1+ae+s4ASmFWXu3oKQMcb0qmgnMN0Y64L0J/uNjqt4z90PmxynEhljzMBkc89EEAxCGcFZtCvKIG8MpOXEsVTGGDPwWBCKoLEl7GLVijIYMWgGBxpjTJ+xIBRBY2s7qUkJJCUmQNtuqCqH4VPjXSxjjBlwLAhF0NjSvnd49s4PQAMWhIwxJgYsCEXQGDqD9vbV7t5GxhljTK+zIBRBY2vH3tkSKsogOQPyx8a1TMYYMxBZEIpgn+a4itUwbAokJHa9kzHGmB6zIBTBnuY4VVcTsv4gY4yJCQtCEbgF7RKhfjvsrrb+IGOMiRELQhE0trSTmZLkmuLAakLGGBMjFoQi2NMctycIDZoJxI0xpk9ZEIpgT3NcRRnklkB6fryLZIwxA5IFoTCq0BFQXxOyQQnGGBNLcQlCInKXiGwRkXf87dMh274hIuUislZEzg9Jv8CnlYvI7SHp40TknyLykYj8UURSfHqqf17ut4+NpmwdqgBkJwWg8kMLQsYYE0PxrAn9VFWP9rfnAPzqrTOBqbg1jH4tIokikgj8CrgQmAJcFbLS6w/8sSYCNcB1Pv06oEZVJwA/9fm6FQi4IFQYqIRAOxSM74W3aowxJpL+1hw3A5ivqi2quh4oB07wt3JVXaeqrcB8YIaICHAWsMDv/zBwacixHvaPFwBn+/xdCgRrQtLsEmz5BmOMiZl4BqFbRGSViMwVkWDPfzGwKSTPZp/WWfoQoFZV28PS9zmW317n8+9HRK4XkRUisqK6phaArGAQSsk6iLdojDGmKzELQiKyRERWR7jNAB4AxgNHA9uAHwd3i3AoPYD0ro61f6LqbFUtVdXS7JxcADItCBljTMxFtbz3gVDVc6LJJyIPAs/6p5uBkpDNo4Ct/nGk9EogT0SSfG0nNH/wWJtFJAnIBaq7K0+wOS4DH4RSLQgZY0ysxGt0XFHI08sAf1UoC4GZfmTbOGAi8CawHJjoR8Kl4AYvLFRVBZYCl/v9ZwFPhxxrln98OfB3n79LwSCUHtjtElIyD+AdGmOMiUbMakLduF9EjsY1j20AvgygqmUi8gSwBmgHblbVDgARuQVYBCQCc1W1zB/rNmC+iNwLvA3M8elzgEdFpBxXA5oZTcE6/Oi4NA0GIasJGWNMrMQlCKnqF7rY9l3guxHSnwOei5C+Djd6Ljy9Gbiip2ULqKsepgSaXIIFIWOMiZn+NkQ77gKqJCcKSe1NkJAMSSnxLpIxxgxYFoTCBAJKRkoStDTYoARjjIkxC0JhAopbVbW10ZrijDEmxiwIhXGTlyZCa70FIWOMiTELQmEC6pvjWhtteLYxxsSYBaEwAVXXHGd9QsYYE3MWhMIEAvjmOOsTMsaYWLMgFKZDlcyUJOsTMsaYPmBBKExA/aqq1idkjDExZ0EoTCCgZASb46xPyBhjYsqCUBgFspOB9mZrjjPGmBizIBRBXmKre2DNccYYE1MWhCLISWxxD6wmZIwxMWVBKIKchGAQspqQMcbEkgWhCLKCS3unZse3IMYYM8BZEIogU6wmZIwxfcGCUASZ2KqqxhjTFywIRZCuvjnOgpAxxsSUBaEI0tQv7W0XqxpjTExZEIogLRBsjrM+IWOMiSULQmGK89JJ6vA1oWQLQsYYE0sWhMIUZKYgrY0uACXY6THGmFiyb9lIWm1BO2OM6QsWhCJpabD+IGOM6QMWhCKxVVWNMaZPxC0IicitIrJWRMpE5P6Q9G+ISLnfdn5I+gU+rVxEbg9JHyci/xSRj0TkjyKS4tNT/fNyv31s1IVrbbAgZIwxfSAuQUhEPgXMAKap6lTgRz59CjATmApcAPxaRBJFJBH4FXAhMAW4yucF+AHwU1WdCNQA1/n064AaVZ0A/NTni06rNccZY0xfiFdN6EbgPlVtAVDVHT59BjBfVVtUdT1QDpzgb+Wquk5VW4H5wAwREeAsYIHf/2Hg0pBjPewfLwDO9vm712IDE4wxpi/EKwhNAk7zzWQvi8jxPr0Y2BSSb7NP6yx9CFCrqu1h6fscy2+v8/n3IyLXi8gKEVmxc+dO3ydkNSFjjIm1pFgdWESWACMibLrDv24+cBJwPPCEiBwGRKqpKJGDpXaRn2627ZuoOhuYDVBaWqq0VkCKLeNgjDGxFrMgpKrndLZNRG4E/qyqCrwpIgGgEFeTKQnJOgrY6h9HSq8E8kQkydd2QvMHj7VZRJKAXKA6qsJbn5AxxvSJeDXH/QXXl4OITAJScAFlITDTj2wbB0wE3gSWAxP9SLgU3OCFhT6ILQUu98edBTztHy/0z/Hb/+7zd00D7mZ9QsYYE3Mxqwl1Yy4wV0RWA63ALB8gykTkCWAN0A7crKodACJyC7AISATmqmqZP9ZtwHwRuRd4G5jj0+cAj4pIOa4GNDOqkmnA3dsQbWOMibm4BCE/wu3znWz7LvDdCOnPAc9FSF+HGz0Xnt4MXNHjwgU63L0FIWOMiTmbMSHcnpqQ9QkZY0ysWRAKFwxC1idkjDExZ0EonFpznDHG9BULQuECNjDBGGP6igWhcNYnZIw5xGzdupXLL7884rYzzzyTFStWHNBxr7nmGhYsWNB9xoNgQShcsDku1WZMMMYcGkaOHBnzYBEr8bpOqP+ympAxg8J3niljzdZdvXrMKSNzuPPiqZ1u37BhAxdeeCGnnnoqr7/+OsXFxTz99NOkp6fzzjvvcMMNN9DU1MT48eOZO3cu+fn5nHnmmZx44oksXbqU2tpa5syZw2mnnbbfcS+66CJWr17N7t27ufbaa1mzZg2TJ09m9+7de/K98MIL3HnnnbS0tDB+/HgeeughsrKyuPvuu3nmmWfYvXs3p5xyCr/97W+Jdr7ng2U1oXCBDkhIgsSUeJfEGDMAffTRR9x8882UlZWRl5fHn/70JwCuvvpqfvCDH7Bq1SqOOuoovvOd7+zZp729nTfffJOf/exn+6RH8sADD5CRkcGqVau44447WLlyJQCVlZXce++9LFmyhLfeeovS0lJ+8pOfAHDLLbewfPnyPUHs2WefjdG735/VhMJpwA1K6KNfAcaY+OiqxhJL48aN4+ijjwbguOOOY8OGDdTV1VFbW8sZZ5wBwKxZs7jiir3X2n/mM5/ZJ39XXnnlFb7yla8AMG3aNKZNmwbAsmXLWLNmDf/yL/8CQGtrKyeffDIAS5cu5f7776epqYnq6mqmTp3KxRdf3HtvugsWhMIFg5AxxsRAamrqnseJiYn7NJd1t09iYiLt7e3d5CZiU5qqcu655/KHP/xhn/Tm5mZuuukmVqxYQUlJCXfddRfNzc3dvkZvsea4cNphF6oaY/pUbm4u+fn5/OMf/wDg0Ucf3VMr6qnTTz+dxx57DIDVq1ezatUqAE466SRee+01ysvLAWhqauLDDz/cE3AKCwtpaGjo8wEOVhMKFwjYoARjTJ97+OGH9wxMOOyww3jooYcO6Dg33ngj1157LdOmTePoo4/mhBPc1JpDhw5l3rx5XHXVVbS0tABw7733MmnSJL70pS9x1FFHMXbsWI4//viuDt/rJJrVDQaT0rG5uuI7Z8CshfEuijHGHDJEZKWqlvZ0P2uOC6cd1idkjDF9xIJQOFvQzhhj+owFoXCBDusTMsaYPmJBKJwN0TbGmD5jQSicBSFjjOkzFoQisT4hY4zpExaEIrE+IWNMDJxyyikR0w9myYS77rqLH/3oRwdTrLiyIBSJNccZY2Lg9ddfj3cR+h2bMSESC0LGDHzP3w7b3+vdY444Ci68r9PNWVlZNDQ0oKrceuut/P3vf2fcuHGEThqwcuVKvvrVr9LQ0EBhYSHz5s2jqKiIBx98kNmzZ9Pa2sqECRN49NFHycjI6N3yx4HVhCKx5jhjTAw99dRTrF27lvfee48HH3xwTw2pra2NW2+9lQULFrBy5Ur+/d//nTvuuANwM2kvX76cd999l8mTJzNnzpx4voVeYzWhSGxggjEDXxc1llh75ZVXuOqqq0hMTGTkyJGcddZZAKxdu5bVq1dz7rnnAtDR0UFRURHgJiP91re+RW1tLQ0NDZx//vlxK39vsiAUiTXHGWNirLPlFqZOncobb7yx37ZrrrmGv/zlL0yfPp158+bx0ksv9UEpY8+a4yKxIGSMiaHTTz+d+fPn09HRwbZt21i6dCkAhx9+ODt37twThNra2igrKwOgvr6eoqIi2tra9izVMBDEJQiJyB9F5B1/2yAi74Rs+4aIlIvIWhE5PyT9Ap9WLiK3h6SPE5F/ishH/rgpPj3VPy/328dGXUDrEzLGxNBll13GxIkTOeqoo7jxxhv3rB2UkpLCggULuO2225g+fTpHH330nv6ie+65hxNPPJFzzz2XI444Ip7F71VxX8pBRH4M1Knq3SIyBfgDcAIwElgCTPJZPwTOBTYDy4GrVHWNiDwB/FlV54vIb4B3VfUBEbkJmKaqN4jITOAyVb2yu/KUHjZEV5TvgITEXn+vxhgzUB2SSzmIaxT9LC7wAMwA5qtqi6quB8pxAekEoFxV16lqKzAfmOH3PwsIXuX1MHBpyLEe9o8XAGdLpEbYcAXjLAAZY0wfiXef0GlAhap+5J8XA5tCtm/2aZ2lDwFqVbU9LH2fY/ntdT7/fkTkehFZISIrdu7cedBvyhhjTHRiNjpORJYAIyJsukNVn/aPr2JvLQggUk1FiRwstYv8XR1r/0TV2cBsgNLSUltq1hhj+kjMgpCqntPVdhFJAj4DHBeSvBkoCXk+CtjqH0dKrwTyRCTJ13ZC8wePtdm/Vi5QfWDvxhhjTCzEsznuHOADVd0ckrYQmOlHto0DJgJv4gYiTPQj4VKAmcBCdaMqlgKX+/1nAU+HHGuWf3w58HeN9ygMY4wx+4jnxaoz2bcpDlUt86Pd1gDtwM2q2gEgIrcAi4BEYK6qlvndbgPmi8i9wNtAcC6LOcCjIlKOqwHNjPH7McYY00NxH6Ld35SWluqKFSviXQxjjDmkHJJDtI0xxgxuFoSMMcbEjTXHhRGRemBtvMvRTxTiRiAaOxeh7FzsZedir8NVNbunO9ks2vtbeyDtmgORiKywc+HYudjLzsVedi72EpED6ky35jhjjDFxY0HIGGNM3FgQ2t/seBegH7FzsZedi73sXOxl52KvAzoXNjDBGGNM3FhNyBhjTNxYEDLGGBM3gzYIdbZceMj2A18e/BATxbn4qoisEZFVIvKiiIyJRzn7QnfnIiTf5SKiIjJgh+dGcy5E5LP+s1EmIo/3dRn7ShT/I6NFZKmIvO3/Tz4dj3LGmojMFZEdIrK6k+0iIr/w52mViBzb7UFVddDdcJOgfgwcBqQA7wJTwvLcBPzGP54J/DHe5Y7jufgUkOEf3ziYz4XPlw28AiwDSuNd7jh+LibiJg3O98+HxbvccTwXs4Eb/eMpwIZ4lztG5+J04FhgdSfbPw08j1vP7STgn90dc7DWhCIuFx6W58CWBz/0dHsuVHWpqjb5p8tw6zYNRNF8LgDuAe4HmvuycH0smnPxJeBXqloDoKo7+riMfSWac6FAjn+cy951zQYUVX2FrtdlmwE8os4y3HpvRV0dc7AGoc6WC4+YR7tZHvwQF825CHUd7pfOQNTtuRCRY4ASVX22LwsWB9F8LiYBk0TkNRFZJiIX9Fnp+lY05+Iu4PMishl4Dri1b4rW7/T0+2TQTtsTzdLfUS8PfoiL+n2KyOeBUuCMmJYofro8FyKSAPwUuKavChRH0XwuknBNcmfiasf/EJEjVbU2xmXra9Gci6uAear6YxE5GbeW2ZGqGoh98fqVHn9vDtaaUFfLiO+XZ4AvDx7NuUBEzgHuAC5R1ZY+Kltf6+5cZANHAi+JyAZcm/fCATo4Idr/kadVtU1V1+Mm/p3YR+XrS9Gci+uAJwBU9Q0gDTe56WAT1fdJqMEahCIuFx6WZ7AsD97tufBNUL/FBaCB2u4P3ZwLVa1T1UJVHauqY3H9Y5eo6kBcBTGa/5G/4AatICKFuOa5dX1ayr4Rzbn4BDgbQEQm44LQzj4tZf+wELjaj5I7CahT1W1d7TAom+NUtT3ScuEicjewQlUXMkiWB4/yXPwQyAKe9GMzPlHVS+JW6BiJ8lwMClGei0XAeSKyBugA/kdVq+JX6tiI8lz8N/CgiPwXrvnpmoH4o1VE/oBrfi30/V93AskAqvobXH/Yp4FyoAm4tttjDsDzZIwx5hAxWJvjjDHG9AMWhIwxxsSNBSFjjDFxY0HIGGNM3FgQMsYYEzcWhIzpZ0SkRETWi0iBf57vnw/Y2cvN4GVByJh+RlU3AQ8A9/mk+4DZqroxfqUyJjbsOiFj+iERSQZWAnNxs1Ufg1tG4GkgH3eB4LdU9em4FdKYXmBByJh+SkTOB/4GnKeqi/0chhmqustPk7MMmDgQr8w3g4c1xxnTf10IbMNNmgpuhuLvicgqYAluivzhcSqbMb1iUM4dZ0x/JyJHA+fiZup+VUTmA+cDQ4HjVLXNz+SdFr9SGnPwrCZkTD/jV/B9APhPVf0EN4Hsj3DLiezwAehTgI2WM4c8C0LG9D9fws1Uvtg//zVwBPAOUCoiK4B/Az6IU/mM6TU2MMEYY0zcWE3IGGNM3FgQMsYYEzcWhIwxxsSNBSFjjDFxY0HIGGNM3FgQMsYYEzcWhIwxxsTN/wejE/6HMOxTeQAAAABJRU5ErkJggg==\n", "text/plain": [ "
" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "x=np.linspace(0.001,0.990,100)\n", "m=mua_ff(x)\n", "im=ideal_aff(x)\n", "\n", "plt.figure()\n", "plt.plot(x,m,label=\"non ideal\")\n", "plt.plot(x,im,label=\"ideal\")\n", "plt.xlim(0,1)\n", "plt.xlabel(\"Xa\")\n", "plt.ylabel(\"mu_a\")\n", "ttl=\"Potenziale chimico del componente a, T= \"+str(p.T)+\" K\"\n", "plt.title(ttl)\n", "plt.legend(frameon=False, loc='lower right')\n", "plt.show()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Notate come, sia nel caso ideale sia in quello *non* ideale, il potenziale chimico del componente *a* scenda a valori molto bassi al tendere di $x_a$ a 0. Ciò è dovuto al termine logaritmico in *xa*, per cui \n", "\n", "$$\n", "\\lim_{x_a \\rightarrow 0} \\log x_a = -\\infty\n", "$$\n", "\n", "Questo ci dice che, in generale, il potenziale chimico del componente diventa relativamente molto basso quando sia presente in basse concentrazioni. Se mettiamo a contatto due fasi minerali anche molto diverse (dal punto di vista chimico, strutturale e energetico) è certo che una minima frazione di ogni componente di una delle due fasi, migri nell'altra fase per arrivare a stabilire l'uguaglianza dei potenziali chimici (il componente migra dalla fase dove ha potenziale chimico maggiore verso quella dove ha potenziale chimico minore). Sappiamo per esempio che il calcio non entra negli ortopirosseni; però se mettiamo a contatto del diopside con l'ortoenstatite, possiamo essere certi che una minima traccia di calcio entri nella fase ortorombica, infatti all'equilibrio deve essere:\n", "\n", "$$\\mu_{Ca}^{diop}=\\mu_{Ca}^{ens}$$\n", "\n", "
\n", "\n", "e se fosse $x_{Ca}^{ens}=0$, avremmo $\\mu_{Ca}^{ens}=-\\infty$ che è sicuramente minore di $\\mu_{Ca}^{diop}$. Queste idee si applicano nello stesso modo anche nella geochimica degli *elementi in traccia* che avete già visto: ogni fase minerale deve contenere, seppur in traccia, ogni elemento presente in qualsivoglia concentrazione nell'ambiente in cui il minerale si equilibra dal punto di vista termodinamico. \n", "\n", "## Attività\n", "\n", "Come visto nella lezione *termodinamica_20*, ai fini della determinazione dell'attività ($a$) di un componente, ciò che conta è la differenza ($f$) tra il potenziale chimico della soluzione non ideale e il potenziale chimico della corrispondente soluzione ideale. Per esempio, per il componente $a$:\n", "\n", "$$\n", "\\mu_a^0 + RT\\log a_a = \\mu_a^0 + RT\\log x_a + f \\ \\rightarrow \\ \\log a_a = \\log x_ae^{f/RT} \\ \\rightarrow \\ a_a=x_ae^{f/RT}\n", "$$\n", "\n", "calcoliamo perciò queste differenze nel caso dei due componenti *a* e *b*, e poi definiamone le rispettive attività (*act_a* e *act_b*): " ] }, { "cell_type": "code", "execution_count": 25, "metadata": {}, "outputs": [], "source": [ "real_a_ideal=mua-ideal_a\n", "real_b_ideal=mub-ideal_b\n", "\n", "act_a=xa*sym.exp(real_a_ideal/(R*T))\n", "act_b=xb*sym.exp(real_b_ideal/(R*T))" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Vediamo cosa abbiamo:" ] }, { "cell_type": "code", "execution_count": 26, "metadata": {}, "outputs": [ { "data": { "image/png": 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"text/latex": [ "$\\displaystyle x_{a} e^{\\frac{3 V x_{b}^{4} - 6 V x_{b}^{3} + 3 V x_{b}^{2} + W x_{b}^{2}}{R T}}$" ], "text/plain": [ " 4 3 2 2\n", " 3⋅V⋅x_b - 6⋅V⋅x_b + 3⋅V⋅x_b + W⋅x_b \n", " ───────────────────────────────────────\n", " R⋅T \n", "xₐ⋅ℯ " ] }, "metadata": {}, "output_type": "display_data" }, { "data": { "image/png": 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"text/latex": [ "$\\displaystyle x_{b} e^{\\frac{3 V x_{a}^{4} - 2 V x_{a}^{3} + W x_{a}^{2}}{R T}}$" ], "text/plain": [ " 4 3 2\n", " 3⋅V⋅xₐ - 2⋅V⋅xₐ + W⋅xₐ \n", " ─────────────────────────\n", " R⋅T \n", "x_b⋅ℯ " ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "display(act_a)\n", "display(act_b)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Adesso non ci resta che farne i plot: scegliamo due diverse temperature alle quali visualizziamo le curve; naturalmente, come già fatto precedentemente, dovremo sostituire i parametri necessari con i valori del dizionario, *lambdificare*... e:" ] }, { "cell_type": "code", "execution_count": 27, "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", "text/plain": [ "
" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "act_p={R:p.R, W: p.W, V: p.V} # dizionario\n", "\n", "act_af=act_a.subs(act_p).subs(xb,1-xa)\n", "act_bf=act_b.subs(act_p).subs(xb,1-xa)\n", "\n", "t_list=(1000, 1500) # temperature da considerare\n", "x=np.linspace(0.001,0.999,50) # frazioni molari\n", "\n", "plt.figure(figsize=(6,6))\n", "plt.plot(x,x,\"k--\",label=\"Ideal reference\")\n", "plt.plot(1-x,x,\"k--\")\n", "\n", "for it in t_list:\n", " p.set_T(it)\n", " act_af=act_a.subs(act_p).subs(T,p.T).subs(xb,1-xa)\n", " act_bf=act_b.subs(act_p).subs(T,p.T).subs(xb,1-xa)\n", " \n", " act_aff=sym.lambdify(xa, act_af, 'numpy')\n", " act_bff=sym.lambdify(xa, act_bf, 'numpy')\n", " \n", " a_a=act_aff(x)\n", " a_b=act_bff(x)\n", " \n", " lbl_a=\"a; T: \"+str(it)+\" K\"\n", " lbl_b=\"b; T: \"+str(it)+\" K\"\n", " \n", " plot_ca=plt.plot(x,a_a, \"-\", label=lbl_a)\n", " color=plot_ca[-1].get_color()\n", " plt.plot(x,a_b, \"--\", color=color, label=lbl_b)\n", " \n", "plt.xlim(0,1)\n", "plt.ylim(0,1)\n", "plt.xlabel(\"Xa, Xb\")\n", "plt.ylabel(\"Activity\")\n", "plt.legend(frameon=False, loc='lower right')\n", "plt.show()\n" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Le due linee tratteggiate in nero corrispondono al riferimento ideale (sono le diagonali della figura *quadrata*): $x_a=x_a$ e $x_b=x_a-1$.\n", "\n", "Le curve continue in colore rappresentano l'attività del componente $a$, mentre le curve tratteggiate rappresentano l'attività del componente $b$ (notate che l'asse a sinistra corrisponde al componente $b$ puro, mentre quello a destra corrisponde al componente $a$ puro). Come si vede, l'attività è sempre maggiore della frazione molare a causa del termine non ideale *W* che è relativamente grande e positivo; per valori di $x_a$ maggiori di circa 0.7, l'attività $a_a$ è minore di $x_a$ a causa del termine $Vx_bx_a^3$, con $V$ negativo (questo termine diventa preponderante su quello in $W$ per alti valori di $x_a$). \n", "\n", "La curva dell'attività si avvicina al riferimento ideale al salire della temperatura a causa dell'aumento relativo del termine entropico configurazionale (*ideale*).\n", "\n", "Provate a sperimentare con valori diversi dei parametri e/o con modifiche della forma dei termini non ideali.\n", "\n", "## Un esempio *reale*: l'olivina\n", "\n", "Come esempio consideriamo il caso *reale* dell'olivina che forma una soluzione solida che non si allontana molto dal comportamento *ideale*. Il modello implementato nei database termodinamici è *regolare* e *simmetrico* (quindi $W\\neq 0$ e $V=0$), con $W=8400$. \n", "\n", "Notate che per fare il calcolo abbiamo bisogno dell'energia libera dei componenti puri alle temperature volute; possiamo allora usare il programma *gibbs_tp.py* che abbiamo usato nelle esercitazioni precedenti per calcolarci la $G$ della forsterite e della fayalite, a mezzo delle funzioni *g_tp*. Perciò carichiamo *gibbs_tp.py* (che deve essere presente nello stesso folder di questo notebook, insieme al database termodinamico di cui fa uso (*perplex_db.dat*). Per evitare *conflitti* con variabili o funzioni che abbiamo già definito in precedenza in questo notebook, anzichè caricare e lanciare *gibbs_tp* con il *magic command*\n", "\n", "%run gibbs_tp.py\n", "\n", "usiamo una istruzione *import*, e assegniamo l'alias *gibbs*: " ] }, { "cell_type": "code", "execution_count": 28, "metadata": {}, "outputs": [], "source": [ "import gibbs_tp as gibbs" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Per usare le funzioni di *gibbs_tp* dovremo farle precedere dal suffisso che specifica l'alias; per esempio:" ] }, { "cell_type": "code", "execution_count": 29, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Mineral: forsterite\n", "\n", "K0: 125.00 GPa, Kp: 4.00, dK0/dT: -0.0187 GPa/K, V0: 4.3660 J/bar\n", "G0: -2053138.00 J/mol, S0: 95.10 J/mol K\n", "\n", "Cp coefficients and powers:\n", "+2.3330e+02 +0.0\n", "+1.4940e-03 +1.0\n", "-6.0380e+05 -2.0\n", "-1.8697e+03 -0.5\n", "\n", "Alpha coefficients and powers:\n", "+6.1300e-05 +0.0\n", "-6.1300e-04 -0.5\n" ] } ], "source": [ "gibbs.fo.info()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Ora, assegniamo il corretto parametro di Margules per l'olivina (*W*=8400 J/mole) e passiamo a un modello quadratico simmetrico. Possiamo cambiare modello rispetto a quello *quartico asimmetrico* che abbiamo costruito, semplicemente ponendo a zero il parametro *V* (quello del termine $Vx_bx_a^3$):" ] }, { "cell_type": "code", "execution_count": 30, "metadata": {}, "outputs": [], "source": [ "# Nota informatica:\n", "# assegniamo i valori dei parametri accedendo direttamente \n", "# alle variabili p.W e p.V, senza passare da metodi appositamente\n", "# predisposti (come, per esempio, per la temperatura). Questa è\n", "# una pratica possibile ma in generale sconsigliata. \n", "# In molti casi si rendono \"private\" le variabili\n", "# di una classe, in modo che non siano accessibili\n", "# e/o modificabili se non usando gli opportuni metodi\n", "\n", "p.W=8400. \n", "p.V=0. # \"spegniamo il termine quartico...\"" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Calcoliamo le attività e i coefficienti di attività di Mg e Fe nell'olivina, alle temperature di 1600 e 2100 K (e pressione 0)." ] }, { "cell_type": "code", "execution_count": 31, "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", 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joyO5cuVi//79jBo1Cj8/P06ePMncuXP57ruUKuhrmn1RSh0RkXR1b9NXFJqWiitXrtC7d2/i4uJwcnLi559/BqBmzZo6SWg5hk4UmpaKSpUqcezYMVuHoWk2pW9ma5qmaanSiULTNE1LlU4UmqZpWqp0otA0TdNSleUSRdbqzKvZO0dHx4RS4D4+PgQGBj7zPrp3746Pjw9eXl64urom7Gvfvn0pvubUqVM0adKEPHnyMHny5CfWhYSE8NJLL1G1alWqVavGwYMHAbh79y6tWrWiUqVKtGvXjrCwMMAYPf7666/j5eVF7dq1k61YGxMTQ6FChRKe//bbb1SpUuWJUdyaliIRyVIPF/fKciooTDQtM7i4uGTavnbs2CGdOnUya9ubN2/KoUOH5KOPPpLvv//+iXX9+/eXefPmiYhIZGSkhIaGiojIO++8I5MmTRIRkQkTJsjYsWNFRGTdunXSuXNnERHZvXu3NG3a9KnjRUdHi6urq4iIbN26VSpWrCgXL1589jepZTn3wiPl6OUQAQ5LOr93s94VhQjvrzxOdKwuZKZZRmxsLB988AENGjTA29ubmTNnJqzz8fHJlGOUKFGC+vXrkyvXkz3UQ0JC+Pvvvxk0aBBgVIZ1dXUFniwt/uqrryZMYrRu3ToGDhwIGCVHbt68SXBwcLLH3bFjB6NGjWLz5s14enpmynvR7NvnvwXQZ9aBDO0jy42jcC/kTMCN+0zfcYG3W1eydThaJuozc/9Tyzp7l+KVJuV5FBXLoHkHn1rfs54HveqXISQ8ilGLn5x34ZcRaZfPfvToUcKXv6enJ2vWrGHOnDm4urpy6NAhIiMj8fX1pW3btnh6epo1EVFin3zyCb6+vk9VpU3JxYsXcXNzY+DAgZw4cYIGDRowefJk8uXLx927d3FzcwPA3d2dGzduADxRchz+V1o8ftt4ERER9OjRI6FkuZb9bQu4xZpjQbzVqhLvTUz/frLcFUVB59x09SnNj3+ey/T5C7Scx9nZGT8/P/z8/FizZg1gFP9buHAhPj4+NGrUiLt373Lu3Ll07X/ixIlmJwkw7iUcPnyYt956i6NHj+Lk5MSkSZOS3Ta+fLiYWVo8b968NGrUKKFelJa9hUZEMXbNCaqWLMAbLbwytK8sd0UB8NmLNdh7/i4frDrO2tG+5HbMcvlOS0ZqVwDOTo6pri/i4mTWFYQ5RIQff/yRdu3aZcr+noWHhwflypVLmHGuR48eCTe7ixYtSnBwcMLERSVLlkx4zdWrV2ncuDGQcmlxBwcHVq1aRcuWLfnmm28S5rbQsqdZuy4SEh7FvEENcMqVse/ILPkNW9jFiYnda3Lq+n1m7Lxg63C0bKZdu3bMmDGD6OhoAP755x/Cw8MBqFq1qkWP7eHhQfHixRPmzk6ptPiCBQvo2rVrwvKFCxcCxkRLJUqUeKrZKZ6LiwsbN25k3rx5CfvSsqe3W1diweCG1HR3zfjO0nsX3FaPevXqJdzNf3PpUfEau1ECruteUFr6JNfrKTY2VsaMGSM1a9aUGjVqSPPmzSU0NFSCg4OlcuXKKe4ruV5PY8eOlY0bNz617dWrV8Xd3V0KFCggrq6u4u7uLuHh4SIicvjwYalbt67UqlVLunXrltDr6fbt29K8eXPx8vKSNm3aSEhISEK8I0aMkAoVKkitWrXk6NGjTx0vca8nEZHAwEApV66cbNiwwYxPSctKwh5Fyf1HUU8tJwO9nrJ0mfGQ8Cjafv8XJV3zsuZ13QSlWdaGDRu4ePEib731lq1D0bQUvbfiOIcCQ/j9nefJm9sxYXlGyoxn6W/WIi5OfNGtFieD7vOTboLSLKxz5846SWh27c8zt/j16DW61C79RJLIqCydKADa1yzJi7VL88Of5zhzU/eC0jQtZwp7FM2Y1SeoUqIAb7bKWC+npLJ8ogD4vEsNCubNrQfiaZqWY03YEMCdh1FM6uVNnlyZdzUB2SRRFDH1gjoZdJ+pf563dTiapmlWFRkTy42wR4x8oQLeHoXSfsEzypLjKJLTvmYpXqrrztQd52lexY06ZQvbOiRN0zSryJPLkUVDGhFnoc5J2eKKIt5nXWpQsmBe3vnFj4ioGFuHo2maZlEiwpTt57gZ9hgHB0UuC/X8zFaJomDe3HzbuzaXQyKYuPG0rcPRsgClFK+88krC85iYGNzc3OjcuXO69jd69Gh8fHyoXr06zs7OCSXHV61aleJrtmzZQt26dalVqxb16tVj586dCes+/vhjPDw8nigRDvD48WN69uyJl5cXTZo04cqVKwnrvvjiC7y8vKhatSrbt29P9pgeHh6EhoYCcPDgQTw9PfH390/Xe9ZsZ/mhq3y//R+2nrpp2QOldwBGWg9gLnAbOJnCelfgN+A4cAoYbM5+Ew+4S8mXGwOk3Ecb5I/TN9PcVsvZXFxcxMfHRyIiIkREZNOmTVK7dm2zy4Wn5NKlS1KjRg2ztj1y5Ihcv35dRET8/PzEw8MjYd2+ffvk6tWrTwyWExGZMmWKjB49WkREFi1aJP379xcRkePHj0udOnUkMjJSzp8/L15eXhIbG/vUMd3d3eXevXty7NgxKV++vBw6dChd71OznUvBD6Xa/22W/j/vl9jYuDS3x07LjM8H2qeyfjQQICK1gebAt0opp8w48LttK1O1ZAE+XHWCuw8jM2OXWjbWoUMHNm7cCMCyZcvo169fwrrg4GDatGlD3bp1GTFiBOXKlePOnTsAdOzYkevXr2f4+HXr1qVUqVIA1KpVi4cPHyaUD2nSpElCTafEEpcc7927N1u3bk1Y3q9fP5ycnKhYsSJly5blyJEjT70ejMmTunfvztKlSxNqS2lZQ0xsHO+s8COXg+K/vWrj4PB0EcjMZLGb2SKySylVPrVNgALKKHOZHwgBMuXGQp5cjkzu60OXH/cyZvUJZr5SL9lqmpod2fwx3DyRufssWQs6/CfNzfr27cv48ePp3Lkz/v7+DBkyhN27dwPw+eef07JlS8aMGcOWLVuYNWtWwus2bdr0TOFMmzaNPHnyMHTo0BS3WbFiBY0aNSJ37typ7itxaXEnJydcXFwIDQ0lKCiI5s2bJ2wXX3K8QYMGT+3jxRdfZPny5TRpkjnFFDXrmb8vkGNXQvmhXx1KuTpb/Hi27PU0FVgPXAcKAH1EJNlBEEqp4cBwgLJly5q186olC/JBuypM3HSalUeu0bt+mbRfpOVI3t7eBAYGsmzZsqdKgu/Zsyeh/Hj79u0pXDj9velGjx6d6voTJ07w73//m23btqW5L0mhtHhKy5PTunVrZs+eTevWrXFwyFa3K7O9XvXLkCe3I11qP10l2BJsmSjaAX5AS6AisE0ptVtEnhpeLSKzgFlg1Hoy9wCvNfPkjzO3+Hz9KZpUKEqZIvkyKXQt05lx5m9JXbp04f3332fnzp3cvXs3YXlyX7yWcOXKFV566SUWL15s1sxz8aXFS5YsSVRUFOHh4bi6uiYsj5dSyXGAGTNmMGTIEN58802mTZuWae9Fs5zH0bE4KIWrc25eaVzOase15WnEYGC16T7LeeASkKk1nB3i2++U4p1f/IjRo7a1FAwZMoRPP/2UWrVqPbG8WbNmrFixAjAmNLp3717CulatWhEUFJThY9+7d49OnTrx3//+N2FOibQkLjm+YsUK2rZtm7B82bJlREVFceHCBS5fvky9evWS3YejoyPLly/H39+f8ePHZ/h9aJb31abTvDRjL4+jY616XFsmiitAKwClVAmgCnAxsw/iUTgfE7rV5PDle/yoR21rKfDw8ODtt99+avm4ceP4/fffqVu3Lps3b6ZUqVIUKFCAuLg4zp8/T5EiRcw+xrRp05g9e/ZTy6dMmcKlS5cYN25cQnfa+Kuad999l/Lly3P//n08PDz44osvABg+fDg3btzAy8uLqVOn8uWXXwJQu3ZtunXrRrVq1ejYsSPTp09PtVnJ2dmZ9evXs3LlyifmBtfsz7aAWyzYf5lGnkUzteCfOSxWZlwptQyjN1Mx4BYwDsgNICI/KaVKY/SMKgUo4D8isjit/SYuM/4s3l3hx9pjQSwb1phGFYo+8+u1nCkyMhJHR0dy5crF/v37GTVqFH5+fpw8eZK5c+fy3Xff2TpELQe4EfaIDlN241HYmV9HNU1XLaeMlBnP0vNRPIuHkTG8+OMeHkfHsumt5yjskik9cbVs7ty5c/Tu3Zu4uDicnJyYPn16sj2INM1SYuOE/j8f4ERQGBvebEYFt/zp2k9GEkW2qfWUlvx5cvFD3zq8NGMvH/7qzyzdZVYzQ6VKlTh27Jitw9BysLvhkYRGRDOha810J4mMylF94mp5uPJR+6psC7jF4gOXbR2OpmlamooXyMtvbzajRz0Pm8WQoxIFwBBfT5pXcWPCxtOcvqEnOtI0zT6FRkQx/rcAHkbG4JTLtl/VOS5RxHeZdXXOzZvLjukqs5qm2R0R4aNf/Vl0IJDAO+G2DifnJQqAYvnzMLmPDxeCHzJhQ4Ctw9E0TXvCkr+vsPXULT5sV5Wa7q62Dsf8RKGUKq6UKhv/sGRQ1uDrVYyRL1Rk2cGrbPDPeGE3LWtydHRMGLvg4+NDYGDgM++je/fu+Pj44OXlhaura8K+9u3bl+JrFi5cSK1atfD29sbX15cTJ/5X5+rVV1/Fzc0NHx+fJ15z9+5dWrVqRaVKlWjXrh1hYWGAcfb5+uuv4+XlRe3atfHz83vqeDExMU+UKv/tt9+oUqXKE6O4Nftw9uYDJmwI4PnKbrzWLO1R+laRVnlZoAtwDgjHGD0dB5xKb7najD7MKTNurqiYWOk2bY/U/HSLXAp+mGn71bIOFxeXTNvXjh07zC5PvmfPHrl3756IiKxfv16aNm2asG7nzp3y999/S+3atZ94zTvvvCOTJk0SEZEJEybI2LFjRURk3bp10rlzZxER2b179xP7ihcdHZ1Qqnzr1q1SsWJFuXjx4jO+Q83S4uLipMf0vVJvwja5ff9xpu4bS5UZV0pVBCYAjYF/RMQTYzT1XgvmLqvJ7ejA1P51cXRUjFpy1OrD4jX7FBsbywcffECDBg3w9vZ+YsRy0rP89PL19U04w2/cuDHXrl1LWPfCCy8kO+I7cWnxV199lbVr1yYsHzhwIGCUHLl58ybBwcHJHnfHjh2MGjWKzZs3m1VTSrMupRST+/owa2A93ArksXU4CZIdR6GU8gK+Bb4GokXkrlLKQSnlICI7lFJfWzVKC3Iv5Mz3fXwYPO8Q49ad4uue3rYOKeea1+npZTW6QcNhEBUBS3o9vd6nP9R5GcLvwoqBT64bvDHNQz569Cjhy9/T05M1a9YwZ84cXF1dOXToEJGRkfj6+tK2bVs8PT2TbdZJzSeffIKvr+9TVWkTmzNnDh06dEhzX3fv3sXNzQ0Ad3d3bty4ATxZchz+V1o8ftt4ERER9OjRg127dlGpUqVneh+a5Z0MCqN6qYJ4FM6HR2H7KmCa0oC7msCbInJFKRWqlMoP7AKWKKVuk0nzRtiLFlWK80YLL6buOE8DzyL0tGF/Zc26nJ2dn/ry//333/H390+YvjQsLIxz586l6wx84sSJqa7fvn07ixYtYs+ePc+87/gBo2JmafG8efPSqFEj5s2bx7fffvvMx9Ms5/jVUHr9tJ+3WnnxRkv7S+LJJgoRWZvoaVfgEfAO8DLGFKafWz4063qnTWWOXL7Hv9eeoKZ7QaqWLGjrkHKe1K4AnPKlvt6lqFlXEOYQEX788UfatWuXKftLiZ+fHyNGjGDr1q1mzXNRtGhRgoODcXNzIygoKGHmu/jS4vGVZ1MqLe7g4MCqVato2bIl33zzDR9++GHmviEtXUIjonh9yVHcCuTh5UbWKx3+LMzp9fSpiMSJSIyILBCRH4CPLB2YtTk6KKb086FA3ty8vvgoDx5H2zokzUbatWvHjBkzEqYj/eeffwgPN/qyV62aOZXwAwMD6dmzJ0uXLsXLy8us1yQuLb5gwQK6du2asHzhwoWAMdFSiRIlnmp2iufi4sLGjRuZN29ewr4024mLE95bcZzbDx4ztX8du61BZ06iaJPMsrQbVLOg4gXyMrVfHS6HRPDx6hNWm7RGsy9Dhw6levXq1K1bl5o1a/AnKVUAACAASURBVDJixAhiYmK4c+fOM/9NfPLJJ8lOmfrZZ58REhLCiBEj8PHxoVGjRgnrevXqxXPPPUdAQAAeHh7Mnz8fgLFjx7Jx40YqVarErl27+OCDDwBjSlN3d3cqVqzI66+/nuYkRMWKFWPLli2MGzcuYa5wzTZ+2nWBP87c5pOO1ahTNv2zJ1paitVjlVKjgNeBCsCFRKsKAHtFZIDlw3taeqvHPosZOy/w9ZYzfPZidQb56p4hmmHDhg1cvHiRt956y9ahaNnEgYt32XziBp91qWHxIqUWKTOulHIFCgNfAR8nWvVARELSc7DMYI1EERcnDFt4mF3nglkxooldZ3pN07Ke6Ng4cjtatzBGRhJFapGKiAQCo4EHiR4opcyf1isLcnBQfNfbhxIF8zJq8VGCH0TaOiRN07KJqJg4Xp79N1P/PGfrUMyWWqJYavp5BDhs+nkk0fNszTVfbma+Uo/QR1GMXnKUaD3ftqZpmeCLjQEcvBRCmSL2NVYiNSkmChHpbPrpKSIVTD/jHxWsF6Lt1Cjtytc9vDkYGMIXunigpmkZtOLwVRbuv8yw5zzp6uNu63DMlmYjmVJqnVKqn1Iq66S/TNTVx51hz3myYP9lVh7WBdQ0TUsfv6uh/HvNSXy9ivJR+8zpZm0t5txN+Q54DjitlFqplOqplMpr4bjsykftq+LrVZRP1p7k+NVQW4ejaVoWFHgnHI/CzvzYry65rHwjO6NS7PX01IZKOQItgWFAexGxydBla/R6Sk5IeBQv/riHOBHWv9HMrgp2aZqWNUTFxNlstjpL9XpKfABnoAcwEmgA5LghnUVcnJj5Sj3uRUQxeqm+ua1pmnm+2nyajf5GAUdbT2maXubco/gFOI1xNTENqCgib1o6MHtU0910c/tSCBM3nrZ1OJqm2bmVh68y86+LHLtyz9ahZEhK1WMTmwf0FxE9WQPGze0T18KYvecS1UsVpHeDMmm/SNO0HOfYlXt8svYkTSsW5eMOWevmdVIpJgqlVEsR+RPIB3RNOrxcRFZbODa79XGHqpy99YBP1p6gfDEXGnpm6/GHmqY9o+uhjxi28AglCuZhav+sd/M6qdSif8H088VkHp0tHJddy+XowNR+dSlTJB8jFh3myt0IW4ekaZod2XTiBpHRscx9tQFF7LQi7LNIs9eTUspTRC6ltcxabNXrKTmX7oTTbdpeihfIw6+vN6Vg3ty2DknTNDtxPfQRpQs52zqMBJbu9fRrMstWpedg2Y1nMRdmDKjLpTvhvLn0GDG6J5Sm5Wizdl3gZFAYgF0liYxKMVEopaoqpXoArkqplxI9BgE5asBdappWLMbnXWvw1z/BfLnpjK3D0TTNRn49co0vN51h1ZFrtg4l06XW66kKxr2IQhj3JeI9wBh0p5m83Kgc528/ZO7eS3gVz0//RmVtHZKmaVZ0ODCEMatP0LhCET7pVM3W4WS6FBOFiKwD1imlnheRXYnXKaV8LR5ZFvNJx2pcDA7n03UnKV8sH00rFrN1SJqmWcHVkAhGLDpC6UJ5+WlAPavPM2EN5ryjycks+zGzA8nqcjk68GP/OpQv5sKoxUe5GPzQ1iFpmmYFs3dfJCo2jjmDGlAoX9bv4ZSc1Ga4awI0Bf4FfJ9oVUGgu4jUtnx4T6tf10cOH/WzxaHNcuVuBN2n78UlTy5Wv96UYvl1TShNy86iY+O4EPyQqiVtUv7ObJbq9eQE5MdoniqQ6HEf6Jmeg2WKWwEQsM5mh09L2aL5mP1qfW4/eMxrCw7zKEoPaNe07EZEmLbjPHceRpLb0cG+k8QNfzi+PEO7SG3ior9E5HOgsYh8nujxnYikOYefUmquUuq2UupkKts0V0r5KaVOKaX+Mivi3Hlh5WA4tcaszW2hTtnCTOlbB/9roby1/BixceZV6NU0LWuY8sc5Jm09yzq/67YOJXXX/WDBi/DnxAztxpx7FBFKqUlKqU1KqT/jH2a8bj7QPqWVSqlCwHSgi4jUAHqZFXFRL/BoAKteg5PJDfGwD+1qlGRc5+psC7jF+N9OYW45d03T7NvKw1eZvP0cPet5MMS3vK3DSdn1Y7CwC+QpAK+uz9CuzEkUS4AzgCfwORAIHErrRaaeUiGpbNIfWC0iV0zb3zYjFlAOMGAVlGkEvw6FE/Y79m+Qr2fC7Hhz9thkILumaZlo97lgxqw+wXOVivHVS7VIWgPPrpzfDnldYdBGKOKZoV2ZkyiKisgcINrUHDUEaJyhoxoqA4WVUjuVUkeUUgNT2lApNVwpdVgpdTg4ONjIkC+vhLJNYfUwOP5LJoRjGWM6VKNjrZJ8sfF/Nek1Tct64uKEb7acxat4fqa/XNd+u8HGxhg/n3sfRuyCwuUyvEtz3mm06ecNpVQnpVQdwCPDRzZuktcDOgHtgP9TSlVObkMRmSUi9UWkvpubm7EwT354eQWU84U1I8BvWSaElPkcHBTf9fahfrnCvLPCj8OBqV1kaZpmrxwcFAuGNGT+4IYUsNe6blcPwtT6RqcfpcC5cKbs1pxE8YVSyhV4D3gfmA28kwnHvgZsEZFwEbkD7AKercutkwv0XwEVXoC1o+DYkkwIK/Plze3IzwPr417ImaELD3Pu1gNbh6RpmpnCIqKZtPUMUTFxFHFxoqSrnVYwuvI3LHrJSBB5XTN112kmChHZICJhInJSRFqISD0RydidEcM64DmlVC6lVD6gEcZMes/GKR/0Ww4VW8C60XBoTiaElvkKuzixYHBDcjs6MHDuQYJCH9k6JE3T0vAoKpbXFhzi512XOHPzvq3DSdmlXbCoOxQoYdyTcHXP1N1brJFNKbUM2A9UUUpdU0q9ppQaqZQaCSAip4EtgD9wEJgtIil2pU1Vbmfouwwqt4eN78LeHzLpXWSuskXzsXBIQx5GxvDKnL8JCY+ydUiapqUgOjaO15cc4ciVe0zu64O3RyFbh5S8q4dgSS8oVNZIEgVLZ/oh0pyPwt6kOh9FbDSsHg6nVsMLH0HzMcZlmJ05eCmEV+b8TdWSBVgyrDH585gzI62madYSFye8t/I4a44FMbF7TV5ulPEbwhYT/Qi2f2Z85+VLebZNS89HkXU45oYes6HOAPjra9j6CdhhImzoWYRp/ety8vp9Ri46QmSMHr2tafbkckgE2wNu8V6byvabJE7/Bo/uGS0qHb5ONUlkVGq1ngaIyGKl1LvJrReR7ywWVSrMmuEuLg62joG/f4K6r0Ln78HB0ToBPoOVh6/ywSp/OnmX4oe+dXB0sL+rH03Lqa6HPqKUa177HCtx8GfY9D40eQPamTfqOiNXFKm1ebiYfhZIz45tysEB2v/H6BW1+1uIjoBuM4wrDjvSq34Z7kVE8eWmMxTJ58T4rjXs849S03KI5QevcP9xNMOfr2i/M9Tt+d5oaqrSCVr+n1UOmdp8FDNNPz+3SiSZTSlo9Sk45Yc/PoeoCOg516gVZUeGP1+Ruw+jmLnrIoVdnHi3TbJDSTRNs7AtJ28wds0JnqvkxmvNKtjfFb4I/DnBOPmt1cuqJ78pJgqlVKpdh0TkrcwPxwKee9cYyb3pfVjcA/otzfQ+xhn1cYeq3IuI4oc/zuHi5MiIFyraOiRNy1F2nL3Nm8uO4VOmEDMG1LW/JAHG/Qj/lTZpTk+t6emI6acvUB2Ir5PRK9G6rKHhMGOE4pqRMK8TDPjV6G9sJ5RSfPWSNxFRsXy1+QzOTo4MbFLe1mFpWo6w78IdRi46QuUSBZg3uCH5nOysF2L0Y3DIZdysHvYnuBSzem/O1JqeFgAopQYBLUQk2vT8J+B3q0SXmWr1NJLFL6/A3LbwyhooUsHWUSVwdFB838eHyJg4Pl13iry5Heldv4ytw9K0bO/y3Qg8i7mw6LVGuDrb131MHofBsv5QrBK8OBnyu9kkDHO6x5bmyRva+U3Lsh6vVvDqb/D4PsxpBzeO2zqiJ+R2dGBq/zo8V6kYH/3qzzq/IFuHpGnZVny39H4Ny7L+jWYUcbGzaUwf3DJaQK4eMGra2ZA5ieI/wDGl1Hyl1HzgKPClRaOyJI96MGQrODoZv4RLu20d0RPy5HJk1iv1aVC+CO+uOM7WUzdtHZKmZTtnbt6nxaSd7LtwBwCnXHY2pCzkotHyEXIB+v0C3uZN12Mp5tR6modRh2mN6dEkvlkqy3KrDK/9btRDWfwSBGRG6arM4+zkyNxBDajl7sqbS4+x86x5U3Vompa2C8EPGTD7b2JFcLfHLrCx0UbdpsdhRgtIpda2jiiblfB4VhEhsLQPXDtkjLtoPDJz9ptJwh5F0//nA5y//ZB5gxvQtGIxW4ekaVna1ZAIev20n+jYOH4Z0QSv4vltHVLyLvwJBd3BrUqm7VKX8EivfEVg4Dqo2gm2fARbxhqjuu2Eq3NuFr3WiHJF8/Ha/MPsv3DX1iFpWpZ1+/5j+s46wOOYWBYPbWR/SeLoov9Vv67YMlOTREbl7EQBRpny3guh4Qg4MA1WDTK6o9mJIi5OLBnaGI/CzgyefzChTVXTtGdTNH8e2lQvweLXGlGtVEFbh/M/IrDjS1j/BpzdbFcnq/HMShRKqWZKqcGmf7sppTI2Aau9cXA0imq1nQgB62BhV6NZyk64FcjDsuGNKVskH0PmH2LfeZ0sNM1cl++Gcz30EY4Ois+61KCmux0NuI2JgrWvG0VMfQZAv2VGCSI7k2ZESqlxwEfAGNOi3MBiSwZlE0pB0zeg13y4fgzmtIGQS7aOKkGx/HlYOqwx5Yq4MGTBIfbqZKFpaQq8E07fWQcYteQodnc/Ni4WlvWB40uNKRG6TrW7enTxzEld3YEuQDiAiFwnKxYKNFeN7sZ9i4i7MLs1XLOfQehGsmhkJIv5h9hzTicLTUtJfJJ4HB3LV91r2V/BTQdHqNAcuk6D5h/b5dw58cxJFFFipGIBUEq5pLF91leuCby2zag+O78jnFxt64gSFDUlC89iLry24BC7zwXbOiRNszuX7oTTZ9Z+omLjWDqsMdVL29E9iaCjELjH+Lfv28b8OXbOnESxQik1EyiklBoGbAdmWzYsO1CsklFXpZQPrBoMf31jN5MgFTU1Q3kWc2HogsP89Y9OFpqW2BcbAoiOFZYOs7Mb16fWwryOsHWs3XyfmMOscRRKqTZAW0ABW0Vkm6UDS0mmjqMwR0wkrH8L/JdDrd7Q5Ue7KVUeEh7FgNl/c/72Q37oV4f2NUvaOiRNswuhEVEEP4ikUgk7aSUXgd3/hT+/gDKNoM8Sq9dtsug4CqXU1yKyTUQ+EJH3RWSbUurr9BwsS8qVB7r/ZEwQcmIFLHgRHtrHGXwRFyeWDWtMDfeCjF56lDXHrtk6JE2zmWNX7vHWsmNExsRSKJ+T/SSJ2GhYM8JIErV6w8D1Nivul17mND21SWZZh8wOxK4pBc+/D70WwM0T8HNLuBVg66gAcM1nDMpraKoNtfTvK7YOSdOsbv+FuwyY/Td+V0O5Fx5t63Ce5JALJA5a/BtemmU3LRLPIsVEoZQapZQ6AVRRSvknelwC/K0Xoh2p0Q0Gb4LYKJjTFs5usXVEAOTPk4t5gxvQokpxxq45wc+7Lto6JE2zmh1nbzNo3kFKF3Jm5cgmlHS1ky/iW6fg7gXjRPOln+GFD+y6Z1NqUruiWAq8CKw3/Yx/1BMR+79NbynudY2b3EUrwLK+sOu/dnFTKm9uR34aUI9OtUoxcdNpJm//x/76jWtaJtt66ibDFx6mUon8/DKiCSUK2kmSCFgHs9vAxveM51k0QcRLMVGISJiIBIpIP+AaEI3RRTa/UqqstQK0S67uRqnyWr2MOWxXDoKocFtHhVMuB37oV4ee9TyYvP0cX246rZOFlq15FHbmuUpuLB3W2D7mk4iLgz8nwoqBUKK6Ma91NpDmnH9KqTeAz4BbQHwREgG8LRdWFpDb2WhvLFkLto+Du+eh7xIoXN6mYTk6KL7p4Y2LkyM/775E2KNovuxei1yO9lcWQNPS6+ClEBp6FqFGaVfmDmpg63AMkQ9g9XA4u8kYG9HpO6MzTDZgzrfHv4AqIlJDRGqZHjk7ScRTCnzfgpdXQthVmNUCLv5l66hwMNW0eatVJVYcvsbIxUd4FBVr67A0LcNEhK+3nKH3zP32N6mXQy54eBs6TIIuU7NNkgDzEsVVIMzSgWRpXq1h2A7IX9yYcOTADJvft1BK8W6byozvWoM/ztzmlTl/ExZhZ71BNO0ZxMTG8eEqf2bsvED/RmVpXa2ErUMyXPzLmF45t7MxIVqj4Vn+nkRS5iSKi8BOpdQYpdS78Q9LB5blFK0IQ7dD5faw5WOj37Qd3LcY2KQ8U/vVxf9aGL1m7uNmmP2UUNc0cz2KimXEoiOsPHKNt1tVYmK3mjg62PjLOC7OqNiwsKtR/RWM+k3ZkDmJ4gqwDXDCKAYY/9CSylMA+iw2+kv7rzCKCt69YOuo6ORdivmDG3A99DE9Zuzj/O2Htg5J057J4csh/PVPMBO61eSdNpVtX+Dv0T2j1+OOiUanlhZjbRuPhZk9FapSykVEbH6KbPUSHul1/g/4dSjExRg9H6p1tnVEnAwKY9C8g8TGCfMGN8SnTCFbh6RpqYqKicMpl3E+ezUkgjJF8tk4IuD2aWMK5fvXof1X0GBolmhqsnQJjyZKqQDgtOl5baXU9PQcLEfxagUj/jKapH55GbZ9CrExNg2pprsrq0Y2pUDe3PSbdYDtAbdsGo+mpebMzfu0/u6vhKKXdpEkAPIUBOdCMHgzNByWJZJERpnT9DQZaAfcBRCR48Dzlgwq2yhU1hhvUW8w7J0Ci7oZvSJsqHwxF1aNakKlEvkZvugwC/YF2jQeTUvO7nPB9Jyxn8iYWIrlt4PxEdGP4cBPxn0JV3cY/heUsZNuuVZgVud6EbmaZJHua2muXHngxclG89O1QzDzebi8z6YhFS+Ql+XDG9OyagnGrT/FhA0BxMbpgXmaffjl0BUGzzuER2Fn1o72pUZpG09dGnIR5raFLR9B4C5jWQ64ikjMrO6xSqmmgCilnJRS72NqhtKegU9/YzKk3PlgfifYNcmmk6jnc8rFzFfqMahpeebsucTrS/RYC8329p2/w0e/nqCpVzFWjmxCKVdn2wZ0ag3MfAHuBULfZcaMdDlQmjezlVLFgClAa4z5KH4H3haRu5YP72lZ5mZ2SiIfwG//gpOroEILo1iYjUsOz91ziQkbA/D2KMTsgfVxK5B9BgppWYuI8OvRILr6lCa3rasJ7PwP7PwK3OtDr3lGU3IWZtGb2SJyR0ReFpESIlJcRAaYkySUUnOVUreVUifT2K6BUipWKdXzWQLPsvIUgB6z4cUpcGU//NQMLu22aUhDmnkyc0A9zt68T/fpezl/+4FN49FylnvhUQxfeJhLd8JRStGznoftkwRAxZbQ9E3jpnUWTxIZlVqZ8Q9NP39USv2Q9GHGvucD7VPbQCnlCHwNbH2GmLM+paDeIBj6h5E4FnaBnV9DnO2aftrWKMkvw5vwODqW7tP3sUtPr6pZwfnbD3lpxj52/hNsH+N7TqwyivoBlGkIbb+AXHZwM93GUkvb8fchDgNHknmkSkR2ASFpbPYm8Ctg265AtlKyJgzfaQzY2fmlMcLz/nWbhVO7TCHWvO6LeyFnBs07yNw9l3T1Wc1idp69Tffpe3nwOJqlQxvRproNS3JEhcP6N+HX1yBwN8RE2S4WO2T2gLt07Vyp8sAGEamZzDp3jDkvWgJzTNutSmE/w4HhAGXLlq13+fJlS4VsGyLgtwQ2fWD0kuryI1R70WbhPIyM4Z1f/NgWcIu+DcowvmvNhEFPmpYZdpy9zWvzD1GlZEF+HlgPj8I2HCNx3c9IEHcvQLN3jFHWjrltF4+FWHrA3TalVKFEzwsrpTKjqWgy8JGIpNneIiKzRKS+iNR3c8tac82aRSmjLPGI3VCoHPwyAH5722a1ovLnycXMAfUY3aIiyw9dZcCcvwkJ12dYWuZpUqEoI1+oyKqRTWybJB7fhwVdICoCXl0PrcdlyySRUeacJrqJSGj8ExG5BxTPhGPXB5YrpQKBnsB0pVS3TNhv1lXMy+hC6/s2HFkAs5rDjeM2CcXBQfFBu6pM6euD39VQukzdw5mb920Si5Y93HkYyQcrj3P/cTR5czvyYfuquORJc0ocy3h0z/iZtyD0mguj9oKnHkecEnMSRWziGe2UUuUwJi7KEBHxFJHyIlIeWAW8LiJrM7rfLC+XE7QZDwPXGl1pf24F+6babMxFVx93VoxoQlRMHD2m7+N3e5sDQMsSAq7fp+vUvaw/fp1TQTY+4TizCX6oaxTuBGOagHxFbBuTnTMnUXwC7FFKLVJKLQJ2AWPSepFSahmwH6iilLqmlHpNKTVSKTUyYyHnEBWaw6h9ULkd/P4JLO4OYddsEopPmUKsf6MZFYvnZ/iiI3y37R/i9EhuzUzr/IJ4acZeYuLiWDmyCU0qFrVNIJEPjSbd5f3A1QNK+dgmjizIrJvZpkF3jTEG3O0XkTuWDiwlWX7A3bMSgSPzYesnxgxanf5r9JKyQQmBx9Gx/N/ak6w8co0WVdyY3KcOrvl0e66WsgX7Ahm3/hQNyxdh6st1KF4gr20CuXLAmCPm3mVjbETLf2erGejMYZGb2UqpqqafdYGywHUgCChrWqZZg1JQfzCM2gPFq8HqYcbE7eHWHxifN7cj3/T05otuNdlz/g4vTt3D6Rv6voWWsrY1SjC6RUWWDGtkuyQB8PCWcdI1eBO0nZDjkkRGpXhFoZSaJSLDlVI7klktItLSsqElL8ddUSQWFwv7fjAGBDkXNrrRVkl1TKPFHL1yj1GLjxD2KJqve3jT1cfdJnFo9ufI5Xv8cugK/3nJGwdbzkJ38wTcOgW1+xrPox9DbhsmKxuzVPfYbaafr4lIiyQPmySJHM/B0ejnPXynMT/3sj6w7g2ji5+V1S1bmN/ebIa3eyHeXu7H+N8CiI61XZFDzfZEhMUHLtN31n4OXAzh9oNI2wQSGwO7v4VZLYyTqmjT9L85OElkVGqJIv6GdbKD4DQbKlkThv1pJA2/JTCjqTGjnpUVL5CXJcMaMdi3PHP3XqLfrAPcCHtk9Tg024uIiuG9Fcf599qT+HoV47c3mlHS1QZfzLcCYE4b+GM8VO1kTB6mE0SGpdb0tB1wBOpg9HR6goh0sWxoycvRTU/JuXoQ1o2GO/9AnVeg3UTIa/36/ev8ghi7+gR5cjvyXe/aNK+SGUNttKzilTl/s+f8Hd5uVYk3W1bC0RZNTg9vw2RvyO0MHSdBzR45bt6I1GSk6Sm1ROEE1AUWAUOTrheRv9JzwIzSiSIZ0Y+Ncsj7foD8JY3KtJXbWj2MC8EPGb3kKGduPmB0i4q807oyueyhCqhmMXFxgoOD4sjlECKj42jqVcz6QTy4CQVKGv/2X2l0Lbdx6X57ZKlEsUhEXlFKfSgi32QowkykE0Uqgo7A2tEQfBpq9zMmfncubNUQHkfH8vlvp1h28CoNPYvwY786lCioL/2zm4ioGP5v7SmKFXBiTIdqtgkiJsq4F7HnOxiwGjyfs00cWYSlbmbXM43CftlU36lI4kf6QtUsyr2e0Sb7/AfGqNNpjSBgvdEt0Ery5nbkq5e8mdzHh5NBYXScsluXLM9mzt16QNepe1l97Bp5cznapsJw0BH4uQX89R+o3g1K1LB+DDlIalcUbwGjgAoY4ycSN/aJiFSwfHhP01cUZrpx3Lh3cfMEVOlktNm6WrcL6/nbRlPUP7cfMPKFirzbprJ9TEijpYuIsOLwVT5bH4BLHkcm96lDs0o2aGr6Yzzs/s5obur8PVTpYP0YsiCLND0l2vkMERmVrsgsQCeKZxAbAwemw44vjVHdrT6FBq8Z3Wyt5FFULOM3GE1RtT1cmdK3DuWLuVjt+FrmuRoSQavv/qJ+ucJ838fH+k2KIsbN6b9nwp1zxt9z3oLWjSELs2iiMB2gGVBJROaZynkUEJFL6TlgRulEkQ73AmHDu3DhD2P+3y4/WP1SffOJG3y8+gQxsXF83rUmPeq6o3SPlCzhQvBDKrrlB+BkUBjVSxW07kC6Bzdh80dQpSPU7mO942Yzlp6PYhzwEf8bV+EELE7PwTQbKVweBvwKL802ksbM52H7Z0YNfivpUKsUm99+jprurry/8jhvLjtG2KNoqx1fe3bRsXH8d+tZWn/3F1tOGlWDa7q7Wi9JxMXB4bkwtSGc3QyPQ9N+jWYR5jQYdwe6AOEAInIdKGDJoDQLUAq8e8Ebh8C7D+z53rjZfWaT1UIoXciZpcMa80G7Kmw+eZOOU3ZzKDCt2XI1W7h8N5xeP+1n6o7z9KzrwXPWvhdxwx/mtIYN70Apb3h9PzQaYd0YtATmJIooMdqnBEAppRuYs7J8RaDbdBi0CZxcjJLLS/sYVxpW4OigGN3Ci1Ujm+DooOgzcz/fbDlDZEyaEx1qVrL2WBAdp+zmQvBDpvavw6Reta0/wVDYVQi9Ci/9DK/+BkUrWvf42hPMSRQrlFIzgUJKqWHAduBny4alWVx5Xxi5G9pMgEu7jauLXZMgxjr1eeqULczGt5rRs54H03deoOvUvboSrZ1wdFB4exRi89vP0dm7tHUOKgLHf4EDPxnPq3SEt46Bd289utoOmHszuw3QFqOL7FYR2ZbGSyxG38y2gLAg2DoGAtZBUS+jK21F69V93B5wi49XnyDsURT/al2ZEc9X0CO6rWyD/3UePI6hX0NjMksRsV5ng9unYeP7cHkPlGtmXEE46N9/ZrPozWwTf+AvYCdgm0mcNctxdYfeC40b3hIHi7rD8pchxDod21pXL8Hv7zxPm+olmLT1LL1n7ufSnXCrHDunC42I4s1lx3hj6THWHgtKmLnQKkni0T2jN9MMX7h9yig9o5OEXTJnHEVvYBJGklDAc8AHImKTqrL6isLCoh/DgWmw61uIY5lruAAAIABJREFUi4Gmb0CzdyFPfosfWkRYf/w6n647RVRMHGM6VmVAo3K2ndMgG9tx5jYf/epPSHgU/2pdiZEvVLTuldwNf/i5JdQdCC0+ARcbTZGaQ1h6wN1xoI2I3DY9dwO2i0jt9Bwwo3SisJL7140utP6/QIFS0Ga81aZgvXX/MR+u8uevf4Jp6FmEr3t446kH6WWqS3fCafntTioXL8C3vWtT091KFYcD98LlvfDCh8bz+zegYCnrHDuHs3SiOCEitRI9dwCOJ15mTTpRWNmVv2Hzh3DDD8o0gg5fQ+k6Fj+siLDyyDW+2BBAZEwc77apzGvNPPW9iwwQEQJu3KdGaSMp/HnmFr5exciTywoj9UOvwrZP4dRqcC0Lo/bqUdVWZulEMQnwBpaZFvUBTojIh+k5YEbpRGEDcXHgt9iosRMebIzDaPUpuHpY/NC37z/m32tP8nvALbw9XPm6hzfVSukvmGd1+/5j/m+d8TmuG+2Lt0ch6xw48oFRl+nAdOO577/A921wymed42sJrFHC4yWgGcY9il0isiY9B8sMOlHY0OMwY6De/ulGE1ST0cYse3ksO/5SRNh44gbj1p0i7FE0r7fwYnSLitY5E87iRIRVR64xYUMAj01XZkOteWX24Bb8WA+qdoSW/weFyljnuNpTLDUfhRdQQkT2Jln+PBAkIhfSc8CM0onCDoReMa4uTqwEFzdoPgbqvgqOlh2UFRIexYQNAaw5FkSl4vmZ2L0WDT11xfuUiAjDFx1hW8AtGpQvzNc9vKngZuFOCSJw7nejq3XXacYJRfgdcLFBlVntCZbqHjsZeJDM8gjTOi2nKlQWesyGoX8a4y42vgs/+cLZLRad+6KIixPf9/Fh7qD6RETF0nvmfj5cdZx74VEWO2ZWFBUTlzAO4rlKxZjQtQa/DG9i+SRx3Q8WdoWlveHKAXh4y1iuk0SWl9oVxUkRqZnCuhP6ZrYGGInhzAbjRmXIRSjbBFp/DmUbWfSwEVExTPnjHLN3X8LVOTdjO1bTFWmB/2/vzOOjrO79/z6TZCb7vm8khISwg+wpIIuiKEWtS116ra11rdalWmvtvba/9t7aqvW2tmqxtbZWUfRXXFBQERCVXSAhEbISsu97Mpn13D/OYFiSMEAmG+f9ej2vyTzzzHnOc5I8n+ec77ajuJHH3j7IgxdnDF5UdWcDfPCwMlT7hcPin8Ks74OXz+CcX+MWnppR9Jds3u9sTqYZhQgBE74JP9wNl/9eicVLy2HNDSri1kP4G715dMUE3v/RAlIi/HnozWxueHEnRXUdHjvncKaxw8KDaw9ww4s7sTmchPkbPX9Spys/lzEQanNh4UNw3wGVvE+LxKiivxnFGmCzlPLFk/bfCiyXUg5JYng9oxjmWDth5/PwxR/A2qFqdy9+1KNGTKdT8vqecp7YcAizzcEdi9K4e0ka/sZBTmQ3RLyXXcV/vpNLR7ed2xeN5d6l6fgZPWjo726FL/4Ih99XpXe9TapIlodtVJpzw1PG7BhgHWAFvnTtnoWqR3GVlLLmbE54rmihGCF0NanC97tdzxmzvq88pIJiPHbK+nYL//PBIdbtryQ+xJfHLp/IZVNiR+1y1DE7xHvZVbyy4yi/vmoyGTEe9ECzdqrf5xd/AHMTTL4aVjypI6pHCJ6Oo1gCHLNV5EkpN5/NiQYKLRQjjJZy+PQJOLAGvIww5zblS+/Bm8ue0iYefyePr6rbmD82gl9eMcmzN9BBpq69m99uyGdcdCB3LU7j2P+wRwWxuRT+epGKoxl3kXJ1jZ/uufNpBhyPx1EMJ7RQjFAai+HT30LOWlUHY+6dKo+UX5hHTudwSl7bXcZTH+bTYbFz8/wx3H9RBiF+I3ft3OZw8o/tpfzvpkIsdgf3Lk3nR8vSPXdCuwVqciFxpnJa+OBhlcbFw44KGs+ghUIzcqjPh62/gbx1YApRQXvz7gRfz+Qaauq08tRH+azZXUZEgJGHlo/n2llJeI2wRINfHm3ikf9/kKK6DpaMj+K/vjnJc/mv7FbIfg22PQXmFnggF/wGKZJb4zG0UGhGHjW5SjAOr1eCMfcOmHeXqsDnAXIrW/nFu3nsPdpMZmwQj10+gYXpUR4510ByzA6xv6yZB9dm8/PLJ7BsgofsPLZu2P+KskG0lkPCTJXVNW2pLh40CtBCoRm5VGerynqH3lNulnNug/n3eCRIS0rJhtwafrPhEOVNZpaMj+Jnl00gfRjaL+rbLfz+4wIMAv77KhWy5HBKz86EqrPhL4sgcQ5c+AiMW6YFYhShhUIz8qnNU0sdeevAx095SWX9yCNeUha7g39sL+XZzUV0WR3cOCeZ+y9KJyLQNODnOlO6bQ7+9vkRnttShMXu5JasFB67fIJnDNXWTtj7koqgXv5rta86G2KnaoEYhQxLoRBCvASsBOp6i/AWQtwEPOJ62wHcJaU8bfU8LRSjnPp85VZ78E0w+MCM70DWvRCeOuCnauq08odNBfxrVxn+Pl7cceFYvr8gdcjiL/aUNnH/6weobDFz8cQYHl2R6Zm0G11Nys111wvKzTVtGdz0Jhh0ksXRzHAVikUoAfhnH0KRBRySUjYLIVYAv5BSntadQgvFeUJjsVorz16jKu1N+hYsuB9iBz5zTFFdO09syGfToVqigkz8aFk6189OwmcQMqxKKWm32An29aGyxcx9a/bz4PIMstI8lB/p0Hr4921g64KMFbDwQUia45lzaYYVw1IoAIQQKcD6vnJGHXdcGJArpUw4XZtaKM4z2qpVLYO9L6lI73EXq8C9MVkDvjyyt7SJ3248zJ7SZsZE+PPj5eNZOSXOY6VYdx9R5/M3evHKrR50Oa3PV2IbMwlaK2Dzr9WyXsxEz51TM+wYDULxEJAppfxBH5/fDtwOkJycPPPo0aMD3FPNsMfcDHv+ptKDdDVA4mxl9M5cOaCpI6SUbM2v57cbD3O4pp1J8cE8fMl4LsyIGjA7waHqNp78MJ/Nh+uICTZx/0UZXD87aWDtEFLC0e2w48+Q/wGkL4eb1g5c+5oRx4gWClfk93PAAill4+na1DOK8xybGfb/S90Am4+olOfz7la2jAEsoOR0St7JruTpjwqoaDYza0wYD1ycQVZaxDnd0DccrOauV/cR7OvNXYvHcUtWysDnZcrfqKLhq/arbK6zf6Dcj3W67/OaESsUQoipqHxSK6SUBe60qYVCA6jMpfkfKMEo26FiMWZ+V90QB7BEq9Xu5I09Zfx5SzE1bd3MSQ3nwYszmDfW/RQkRXXttJptzBwTTofFzt8+O8ItWSmE+A9glHh3K/j4q6ytnz+jxHT+D2Hq9brsqAYYoUIhhEgGNgM3Sym3u9umFgrNKVR8CTueVVXVhAEmXqkEI3H2gNkxum0OXt9dxnNbi6lrtzB/bAQPLs9gdkrfAYIl9R388ZNC3smuYmpCCO/cs2BA+nICjcWwezXsfxVW/h6mXqdSbxh8wDBI5U41I4JhKRSuNOWLgUigFngc8AGQUr4ghPgrcDVwzOBgd+citFBo+qT5KOz6i4outrRB/AyYcwdM/pZKhT0AdNscvLqrjOe3FtPQYWHBuEjuWTqOuanhXy9JFdd38OfNRbx9oBKTtxc3Z43h9oVjBy5OQ0oo2qSutehjJQqTrlJeYTGTBuYcmlHHsBQKT6GFQnNaLB2Q8zrsWg0N+eAfCbO+p4L4ggem6pvZ6uCVnaWs3lZCQ4eVWWPCuHtxGksyo1m3v5LH1uVy09xk7rgwjaigARKIYzUfpITn5qsYiFnfh5nf82j6ds3oQAuFRtMbUkLJVrU0k79BBZRlXg6zboXURQOyLNVtc/C7jYd5dVcZFruTSfHB3HlhGvPHRhA5UAJRk6vcg/M3wD27ldG+qQSCE8F7ECrZaUYF5yIUuiSVZvQiBKQtUVvTEdjzVzjwqrJlRIxTT+PTbjirRIRSSj4tqOf5rcXsOtJEmL8Pl02O40BFC/eu2U9aVAB3LR7HqmnxGL3PwlZg64av3lYCUb4LvH3V8pKlQwlF+Ngzb1OjOUv0jEJzftHXDXjWrZA4y+1Zxs/WHeS1XWXEBJu4fVEaN8xJwt/ojcMpef9gNc9tKeJwTTsxwSa+941UbpybTLCvG15Ox5aXqnPgLwvPWdA0mmPopSeN5myoOQh7/w45b6io7+iJcMHNMPXbp9yU27ptvLarjFXT4okP9WNvaROljV19zhiOzThWbythe3EjgSZvrp+dxPcXpBIf6nfiwTazyp67758QkgRXPa/2V+xVqb51gj7NAKCFQqM5FyztKgnhvlegap8q2Zq5Ei64mfLQ2fxjRxmv7ymnw2LnV1dO5j/mjTmj5nMrW1m9rYT3D1YjgJVT4/jBwrFM9iqHL1+Gg2tVHERYigqOy7rXE1epOc/RQqHRDBQ1ubD/FWT264juFsplFG85LqQl4xquXZbF5ISzr8RX0dzFa1uz+ef+Zjqskj+Gv8Xl3esRE1dhmPldGLNAxz5oPIYWCo1mAOi2OfiiqEFVkLN1s/bVF5jT/D4prbvVASkLla1g4qozSxfisEHhx6q8aP5GOq9Zw5rGNN7Zns3RZisBIZF8Z94YbpiTTHiA9mLSeAYtFBrNOVDe1MVru8tYs7uMli4bmx68kHHRx9WBaD4KOWvVjb6pRKXKmLAKpt8AKYv6ngV0t8GW/1HLWl0NKp5j6nVqeSkiDYdTsuVwHS9vL+XzogaM3gaunB7PzfNTzmnmotH0hhYKjeYsKGvs4vF3c9laUI8Alk+M5ZZvpJwQZX0CUkL5biUYuevA0grBCTD5aphyraqV0VKmkhWOXaw8mJ6doSLEp90A4y5SuZh6oaC2nX9sL+Xf+yox2xxMSwzhprlj+Oa0+IFPGqg5L9FCodG4SW1bN/XtFiYnhNDWbWPVs5+zanoC189OOtUbqT9sZpWUMOdNKPwIpEO52tq7ISAafpyvZhoOW5/i0ButZhvr9lXw6q4yCus6CPL15uoLErlxbjIZw7C2t2bkoIVCo+kHu8PJtsJ63thTzqZDdUyMC+a9e1WCPinludWB+OKPsOkXSih8/FXlOICEWTDlGph4xVmlDZFSsqe0mVd3HWXDwRqsDidzUsL59uwkVkyJHbJyrZqRixYKjaYPXt9dxjObCqhtsxARYOTqmYncOCeZlMiAM2+su1Wl0ch7G5b+HGInQ+kXakYx9TqVkK+lHPL+rWYatQfV95Lnq4y2E6+A4LgzPm1jh4U3v6xgze4yjjZ2EWjy5pvT4rh2VhIzkkIHtuCRZtSihUKjcdFltfPBwRqWZkYTHmDkrS8r+OBgNdfNSmRpZsyZp9OwdauUH1+9rTK2Oqwqx9LKZyBjef/fbShUopK3DuryAKFEY9KVyhh+hqIhpWT3kSbW7lXXZLY5SI8O5LpZSVw5I2Hgkg9qRiVaKDTnNQ6n5IuiBt7eX8nGvBq6rA6e+NYUrp+TfHYNdtRBezXETQNrJ/xuLPhHqFnBpCvVstKZxjvUFyixyVsHdV+pfQmzYMI31RaRdkbNtXfbeD+nmrV7y9lX1oKXQbAoPZKrLkjk4gkx2gCuOQUtFJrzlg6LnWVPb6W2zUKQrzcrp8Zx1YxEZqeEndmSTHMpHFoPh9dD2U4lEnd8qj5rKITwtIELhqvPVyk7Dr0H1QfUvuiJKhp8wkqInXpGaTuK6tp568tK3jlQSXVrN4Emby6dHMtVMxKYNzYCL4NemtJoodCcRxxt7GR9TjVNnVb+c+VEAJ788DCT40NYkhmNr4+bT9JOZ8+N//2HYM+L6ueYKepmnblS2SA8TUsZHH5fiVTZdpBOle8p4xLIWAEpC8DH162mnE7JziONrNtXyYbcGjosdmKDfVk1PZ6VU+OYkhCi7RnnMVooNKOayhYz67OrWJ9TzcHKVgDmpobz2m3zzuxp2dIBxZuhYKOKlL5jm7IT5G+ExiJVqyI81UNX4QadDcrlNn8jlGxRHlQ+ASpN+vgVkH4JBEa51VS3zcGmQ7Ws21fJpwX12J2S5HB/Vk6NY+XUeCbEBWnROM/QQqEZdVS2mIkIMOLr48WfNhfy1EcFTEsM4fKpcVw2JY7EMH/3G6vNg42PwtHt4LSBbwiMuxiW/OyMbQODhs0MRz6Dgg1KONqrAAHx01Xf0y9WmWUNp59BtXRZ+TCvhvU51WwvbsThlIyNCmDllDgumxrH+BgtGucDWig0o4KiunY+zKvlw7wacipaef6mC1gxJY6GDgtdFgfJEW6Ig6UdSj5VtaRTF6mo6dZK+NfVMG4ZZFwKyfPOKAhuyJESanKg4EM1E6rcq5ao/MIgbamK+B53EQRGn7apxg4LG/NqWJ9dzc4jjUgJKRH+XDIplksmxzI9MRSDtmmMSrRQaEY0DR0Wvv2XHRTXdwIwPSmUSybFsmp6PAnuREtLCdueguJPoGIPOO1gDIRFD8GCBzzc+yGgq0ktTRVuUi67nXVqf8xklTokbQkkZ4Gxf2Gta+/m469q+TCvlu1FDdidkuggE8snxXDppDjmjg3Hx0tnsx0taKHQjBi6rHY+L2xg8+E6Qvx8ePSyCUgpeeCNA1wwJozlE2OJDenHeCslNBSoWYO5GRY/ovavXqxexy5RT9lJc8+PetJOpwrsK9qk6oOX7VSxHl5GNQZpSyB1sfLi8uo7mrvVbGPL4To+zKtha349ZpuDIJM3izKiWJoZzeLxUUQE6jiNkYwWCs2w550Dlfx7XyU7Shqx2p0Emby5ckYCv7rSTc+i/I2qwE/p59BRq/ZFT4S7titXUrv1/BCG02HtUt5TxVuUcNTmqv2mYBXsl7pQpUuPndKnfaPb5mBbQT2bD9fxyeE66tstCAEzkkJZNiGGpZnRZMZqu8ZIQwuFZljRZbWzs6SRnSVNPHJpJl4GwePv5LKtsIFlmdEsnRDN7JQ+ljWOzRiOboeyHXD578EUCFt+o6rBpS5ULqOpiyB87KBf24ijow6ObFMCW/qZ8u4CZdAf8w3XNh9ie59xOJ2SvKo2Pjlcy+bDdeRUKK+zmGATC9OjWJQRxYJxkbqOxghAC4VmyKlqMfNudhXbCurZW9qM1eHE5G3gg/sWkhYViMXuwOTdj4dOdTZ8+jslDl2Nal9AFPzHOvX0a7eo5RT9FHtutFX1iMaRz1RKdFBuuEmzlW1jzHwVNd6LjaOurZut+fV8WljP54UNtJptCAFTEkJY5BKO6UmhZ54qReNxtFBoBhUpJcX1newobmB2ajiZscFsK6jn5pd2Mz4miEUZkSzKiGJ2SvipAXCdjVCxW9V1qNgDc+9QKSyqDsCb3+25USVnKddVLQyepa1aLVWV7YSjO1xLVRIM3ipCPGkOJM5WryFJJ/w+HE5JTkUL2woa+Kywnv3lLTicEj8fL2alhJGVFklWWgSTE0J0dPgwQAuFxuN02xy8vb+SnSWNbC9upK7dAsBPLh3P3YvHYbE7aO60nWiItluVu2pAhDI8v7hUVYgD141oivJKmnjFEFyRplfMLUrEy7ZD+R6o2teTOj0wVs06EueoGI64aWpZ0EWr2caO4kbX30gDBbUdAAT5ejM3NYJ5Y8OZkxrOxLhgvLU31aCjhUIzoNgdTvKq2thT2kSwrw/XzU7C7nAy9Zcf4W/0Yr7rSTErLYLkcP8eo2Z9PlR+CZX71GttrhKBq/+qbA9v3wVR45U3Ttz007pvaoYBDrv6PVbscc0Cd6u8WADCAJHjIeECVcUvYaZy0XU5FdS1d7OzpIkdxQ3sKG6ktFEJToDRiwvGhDE7JZzZKeHMSA51P/WK5qzRQqEZEP76WQmbD9eRXd5Cp9UBwLLMaP52y2wAqlvNxAb7Ihw2qD+sgsAsHTDvTtXAc1kqnbYxUN044mfA2AtVMJhm9NBRD1X71Wzj2INBV4P6zOAD0RPUbOPYFjMJjAFUt5rZU9rMniNN7CltIr+2HSnBx0swKT6EGcmhzEgOY0ZSKIlhftqraoDRQqFxG7PVwVfVbeRUtLC/rIWa1m7W3jkfgPte309JfSczkkO/ftqLNXaDX6j68s4XIHuNSpPtsKp9wYnwQK5auy7bpbxpItPdSi2hGSVICa3lSjCq9qsHiOrsHqcEYYCIdIibqkQjehLETKLVO4ovy5vZfaSZfWXN5FS00G1zAhAZaGR6UhgzkkOZlhjKlIQQQvxHUDT9MEQLhaZXlCi0Mi0xFG8vA89+Usgzmwpwun7lcSG+TE8K5ZlvT8fXxwvZXIo4ukMJQW2eem2vgZ9VgjEAPntauVrGTVOGzrjpykV1oNJva0YPUkJbJVTn9AhHdQ60VfQc4xuqhCNmEkRPwB4xnkJnInvrYX9ZMwfKWyhxResDJIX7MTUhlMkJIUxJCGFyQjCh/tot1120UGgAONLQyfs5VRyqaedQdRulDZ04JWy4byET4oL5vLCBnIJiZgY1Md67htCOErWEdNmTEJaiZgwbH1FuqFHjv37yY+Yt4Bs81JenGQ2YW6DukLJ71Ob1PJBYO3qOCYiG6EyIyqQrZBxFzjj2dUWxu96Hg1VtlDeZvz40IdSPCXFBZMYGMyEumMy4IFIiArSXVS9ooThPkFJS126hsLaDorp2Cus6KKzr4P6L0slKi2RLfh3f+/se0sMEC8LbmRHUQqZPLQlzv0VA4mRV73nN9T0NepnUMtEVf1L2hI565Z0UnjqykuZpRjZOp5pp1OcrEanPVw8w9flgbe85zhgIEWlYQ9Oo9k4g3x5LTmcE25uDyG404HBNlf18vMiICSQ9Joj06EDGRQeSHh1EYpjfeZ3w8FyEou/kL5ohw2x1UNrYSWlDJyUNnVyQHMb8tAjya9u59H8/w4CTaJoZ79vMN4LbMdVbIG0x3whtoiTifgyddVB5XIOpqZA4WS0XLf9viBinBCJ0zInRuIFRbtc70GgGDIMBQpPVln5xz/5jy1cNhSqivLEIGgoxVu9lTMs6xiA5VrVcBofQHZhMg088R2UMX1kiOHA4hH/tC6FGRmDDG18fA2MjlXCkRgZ8vaVEBhDipx+M+kMLxRAgpaS+w0J5k5mK5i6igkxkpUVitjpY+vRW2lubiBVNxAn1Gj19OqTdRGqQg4NhPyGguwaDtKvG2oBOJ7AYY0i8qowWngphqeo1PK1n2SgkAbLuGarL1mjODCEgJFFtaUtO/MzWrWJymo9A0xFEUwl+zUdIaiogqWUTC6Ty2sMEEoHZN5oG71gqLJEUFoVSkBvCQRlOjQynSkZg8A8nJTKAlIgAEsP9SQrzIyncn6Rwf2KDfc/7pSwtFAOMlJJ2i52a1m6qW7upbjET5OvD5VPjALjr2bdoqy0jzNlEtGghWrTQFT+OrLt/gZ/Ri48ctxHk23hio943Ajdh8g/FlLEQgmJ7nsBCXK+gBOGKPw3uBWs0Q4GPL8RMVNvJOOzKC6u1HFrKEC3l+LeUkdxSRnJrIVnmSvBxnPAVmzTS0BhJdX0YFfZg6mQohTKUOhlGowiDoFh8Q2MJDo0kNsyf2BA/4oJ9iQv1JS7EjzB/n1HtzusxoRBCvASsBOqklKekCBVqVP8AXAZ0AbdIKfd5qj/ngt3h/DqSNLeylfLGDtrbmuloacTcVk+gj+C7114NwJ+efhy/lgIiRBsRtDFFtNHqlwxT1wPwq85fEuld9nXbToMRZ1RP+uaghXeCtwmCE1xbPAQpkUEIuOqFQbpqjWaE4uXtmk33UdbW6VDJEtuqlG2krQqftkriWiuJa69mRnstsiMbw7GIdIBuoAbsNQaaZRCNMphGGUwJQeyWIbSJQBymUPANQ/iH4xMUgV9wJAGhUQQGhxEW5E+ovw/hAUbC/I0jLsDQkzOKl4E/Af/s4/MVQLprmws873o9JyxWC+auLmxWKzabBZvNit1mY2zaeITBQFF+LnWVxdi6zTisZuxWM9itLL/xfgA+Xvsc1tJdGOxd+Di6MNo7cRp8WPz4xwCYX/0Ol3R+hkH0OAHUeMcDSiiuNe0kwpSD1RSB9I/AKzAdY+L0r4+NvOYZEF5qVhAYg8EvDMPxTyIX/uRch0Cj0fSHwUvVSg+OA2ae8rFwbVjaob0WOmqUm3hnA96d9UR01hPUWkdiex2iqxrv7lxM9g6wAx2ure7ENjuliXb8aZf+VONHpwjA4hWA3SsAp7cfTh9/MAYiTP4YTEF4mfzxMvrhbfTD2+SPj8kPo68/Rl8/jEZfvI0mfHxM+BiN+PgY8TGaMBpNeHt5IQQDPrvxmFBIKbcJIVL6OeQK4J9SuV3tFEKECiHipJTV/bXb2VRF1+PRGHBiQCKQGHDS+sM8wqMT2Pfyw8yv+scp3+t+pApfvwAaNz1DVv1bJ3xmlwak80cIg4HYxt2kmT/CYvDD5uWH3RSI1a8nn03yvG/R2DIDU2AY/iGReAeEExvQU4Iy9ocbwOBFn6YxHaWs0YwMTEFqixx3wm4DcEppLYcdulvB3KQ8B83NOLua6Gqtx9LejLWrFXtXK6buVkyWNmKs7fjYKvB2mDF2m/E1m/HGcXKrZ4VDCtfdEdfdUSA5N+HwqHusSyjW97H0tB54Qkr5uev9J8AjUspTfF+FELcDt7veTgZyPdXnEUYk0DDUnRgm6LHoQY9FD3osehgvpQw6my8OpTG7N4nrVbWklKuB1QBCiL1n6ws82tBj0YMeix70WPSgx6IHIcRZB6ANZe6FCiDpuPeJQNUQ9UWj0Wg0fTCUQvEucLNQzANaT2ef0Gg0Gs3g40n32DXAYiBSCFEBPA7KxiulfAH4AOUaW4Ryj/2em02vHvDOjlz0WPSgx6IHPRY96LHo4azHYsTletJoNBrN4KLzQ2s0Go2mX7RQaDQajaZfhq1QCCEuFULkCyGKhBA/7eVzkxDiDdfnu04T3DeicWMsHhRCfCWEyBFCfCKEGDMU/RwMTjcWxx13jRBCCiFGrWukO2MhhLjO9beRJ4S4FEFmAAAFSUlEQVR4bbD7OFi48T+SLITYIoTY7/o/uWwo+ulphBAvCSHqhBC9xpq5nIf+6BqnHCHEBW41LKUcdhvgBRQDYwEjkA1MPOmYu4EXXD9fD7wx1P0ewrFYAvi7fr7rfB4L13FBwDZgJzBrqPs9hH8X6cB+IMz1Pnqo+z2EY7EauMv180SgdKj77aGxWARcAOT28fllwAZUHNs8YJc77Q7XGcUcoEhKWSKltAKvo1J+HM8VwLFcHW8By8ToTN942rGQUm6RUh7LYLYTFZMyGnHn7wLgV8DvUKncRivujMVtwJ+llM0AUsqTMhCNGtwZCwkcK9MYwiiN2ZJSbgOa+jnk69RJUsqdQKgQIu507Q5XoUgAyo97X+Ha1+sxUko70ApEDErvBhd3xuJ4bkU9MYxGTjsWQogZQJKUcv1gdmwIcOfvIgPIEEJ8IYTYKYS4dNB6N7i4Mxa/AL7jctX/ALh3cLo27DjT+wkwfOtRuJPew+0UICMct69TCPEdYBZwoUd7NHT0OxZCCAPwDHDLYHVoCHHn78Ibtfy0GDXL/EwIMVlK2eLhvg027ozFDcDLUsqnhRDzgVdcY+H0fPeGFWd13xyuMwp30nt8fYwQwhs1nexvyjVScSvViRDiIuAxYJWU0jJIfRtsTjcWQaikkVuFEKWoNdh3R6lB293/kXeklDYp5REgHyUcow13xuJWYC2AlHIHKgFs5KD0bnhxVqmThqtQ7AHShRCpQggjylj97knHvAt81/XzNcBm6bLWjDJOOxau5Za/oERitK5Dw2nGQkrZKqWMlFKmSClTUPaaVbKXjMSjAHf+R95GOToghIhELUWVDGovBwd3xqIMWAYghJiAEor6Qe3l8OCsUicNy6UnKaVdCHEP8CHKo+ElKWWeEOL/AXullO8Cf0NNH4tQM4nrh67HnsPNsXgSCATedNnzy6SUq4as0x7CzbE4L3BzLD4ElgshvgIcwMNSysa+Wx2ZuDkWPwZeFEI8gFpquWU0Plh6KnWSTuGh0Wg0mn4ZrktPGo1GoxkmaKHQaDQaTb9oodBoNBpNv2ih0Gg0Gk2/aKHQaDQaTb9oodBoTkIIkSSEOCKECHe9D3O9HyOEiBNCrHftX+zKUHvrcd+d4dr30GnOMUUI8bJHL0SjGSC0UGg0JyGlLAeeB55w7XoCWC2lPAo8CLx43OEHgW8f9/56VPbS053jIJAohEgekE5rNB5EC4VG0zvPAPOEEPcDC4CnXfuvBjYed1wZ4CuEiHFlL76U45IyCiFmu/L+7xBCPHlSnYD3GKWBoprRhRYKjaYXpJQ24GGUYNwvpbQKIVKB5l5yab0FXAtkAfuA4z//O3CnlHI+Kjr6ePYCCz3Rf41mINFCodH0zQqgGpVoECCO3vMDrUUJxQ3AmmM7hRChQJCUcrtr18kV5uqA+IHssEbjCbRQaDS9IISYDlyMykD7gKu4ixmVTO4EpJQ1gM11/CfHN3Oa0/i62tRohjVaKDSak3DZGp5HLTmVoZIuPgUUACl9fO2/gEeklF8vL7kqy7W7snTCqfaIDKDX2sYazXBCC4VGcyq3oTLwfux6/xyQiSoKVSyEGHfyF6SU26WUb/fS1q3AaiHEDtQMo/W4z5YA7w9ozzUaD6Czx2o0Z4AQ4ipgppTy524eHyil7HD9/FMgTkp5nxDCBHwKLHCV8tVohi3Dsh6FRjNckVKuE0KcSW32y4UQj6L+147SU6Y1GfipFgnNSEDPKDQajUbTL9pGodFoNJp+0UKh0Wg0mn7RQqHRaDSaftFCodFoNJp+0UKh0Wg0mn75P7Pg5JGzyfxGAAAAAElFTkSuQmCC\n", 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" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "act_p={R:p.R, W: p.W, V: p.V} # dizionario\n", "\n", "act_af=act_a.subs(act_p).subs(xb,1-xa)\n", "act_bf=act_b.subs(act_p).subs(xb,1-xa)\n", "\n", "t_list=(1600, 2100) # temperature da considerare\n", "x=np.linspace(0.001,0.999,50) # frazioni molari\n", "\n", "plt.figure(figsize=(6,6))\n", "plt.plot(x,x,\"k--\",label=\"Ideal reference\")\n", "plt.plot(1-x,x,\"k--\")\n", "\n", "ca_a=np.array([])\n", "ca_b=np.array([])\n", "for it in t_list:\n", " p.mu0a=gibbs.fo.g_tp(it,0) # energia libera molare della forsterite\n", " # pura, alla temperatura it (e P=0)\n", " p.mu0b=gibbs.fa.g_tp(it,0) # energia libera molare della fayalite\n", " p.set_T(it)\n", " \n", " par={T: p.T, mu0a: p.mu0a, mu0b: p.mu0b}\n", " act_af=act_a.subs(act_p).subs(xb,1-xa).subs(par)\n", " act_bf=act_b.subs(act_p).subs(xb,1-xa).subs(par)\n", " \n", " act_aff=sym.lambdify(xa, act_af, 'numpy')\n", " act_bff=sym.lambdify(xa, act_bf, 'numpy')\n", " \n", " a_a=act_aff(x)\n", " a_b=act_bff(x)\n", " \n", " ica_a=a_a/x\n", " ica_b=a_b/(1.-x)\n", " \n", " ca_a=np.append(ca_a,ica_a)\n", " ca_b=np.append(ca_b,ica_b)\n", " \n", " lbl_a=\"Mg; T: \"+str(it)+\" K\"\n", " lbl_b=\"Fe; T: \"+str(it)+\" K\"\n", " \n", " plot_a=plt.plot(x,a_a, \"-\", label=lbl_a)\n", " color=plot_a[-1].get_color()\n", " plt.plot(x,a_b, \"--\", color=color, label=lbl_b)\n", " \n", "ca_a=np.reshape(ca_a,(len(t_list),len(x))) \n", "ca_b=np.reshape(ca_b,(len(t_list),len(x)))\n", " \n", "plt.xlim(0,1)\n", "plt.ylim(0,1)\n", "plt.xlabel(\"X(Mg)\")\n", "plt.ylabel(\"Activity\")\n", "plt.legend(frameon=False, loc='lower right')\n", "plt.title(\"Attività\")\n", "plt.show()\n", "\n", "plt.figure()\n", "for idx in range(len(t_list)):\n", " lbla=\"Mg; T: \"+str(t_list[idx])+\" K\"\n", " lblb=\"Fe; T: \"+str(t_list[idx])+\" K\"\n", " plot_a=plt.plot(x,ca_a[idx],label=lbla)\n", " color=plot_a[-1].get_color()\n", " plt.plot(x,ca_b[idx],\"--\",color=color,label=lblb)\n", "\n", "plt.legend(frameon=False)\n", "plt.xlim(0,1)\n", "plt.ylim(1,2)\n", "plt.xlabel(\"X(Mg)\")\n", "plt.ylabel(\"Coefficiente di attività\")\n", "tlt=\"Coefficiente di attività; T= \"+str(t_list[0])+\" K\"\n", "plt.title(tlt)\n", "\n", "plt.show()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Volendo, possiamo modificare leggermente il codice per rappresentare graficamente l'andamento dell'attività del magnesio nell'olivina alle basse concentrazioni (legge di Henry) e alle alte concentrazioni (legge di Rault). Si vedano in proposito le slide della lezione *termodinamica_20*: in particolare, dobbiamo calcolare il limite per $x_a$ che tende a zero della derivata della funzione $a_a$, rispetto a $x_a$, per avere il coefficiente angolare ($m$) della retta tangente alla curva $a_a$ nel punto $x_a=0$; questa retta, che deve passare per l'origine $a_0(0)=0$, definisce la legge di Henry.\n", "\n", "$$m=\\lim_{x_a\\rightarrow 0} \\ \\frac{da_a}{dx_a}$$\n", "\n", "Questo si può fare con Sympy, partendo dalla definizione di $a_a$ che abbiamo costruito sopra e salvato nella variabile *act_a*: \n", "\n", "- sostituiamo tutte le occorrenze di *xb* con 1-*xa* (metodo *subs*) \n", "- deriviamo rispetto a *xa* (metodo *diff*)\n", "- prendiamo il limite per *xa* tendente a 0 (funzione *limit*)\n" ] }, { "cell_type": "code", "execution_count": 32, "metadata": {}, "outputs": [ { "data": { "image/png": "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\n", "text/latex": [ "$\\displaystyle e^{\\frac{W}{R T}}$" ], "text/plain": [ " W \n", " ───\n", " R⋅T\n", "ℯ " ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "m=sym.limit(act_a.subs(xb,1-xa).diff(xa),xa,0)\n", "display(m)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Questo è il risultato scritto anche nelle slide delle lezioni (comunque è un calcolo che si può fare agevolemente anche a mano, senza usare *sympy*...)" ] }, { "cell_type": "code", "execution_count": 33, "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", 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" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "tm=1600 # temperatura\n", "p.mu0a=gibbs.fo.g_tp(tm,0) \n", "p.mu0b=gibbs.fa.g_tp(tm,0) \n", "p.set_T(tm)\n", "\n", "par={T: p.T, mu0a: p.mu0a, mu0b: p.mu0b}\n", "act_af=act_a.subs(act_p).subs(xb,1-xa).subs(par)\n", "m_f=m.subs(act_p).subs(par)\n", " \n", "act_aff=sym.lambdify(xa, act_af, 'numpy')\n", "gamma_0=float(m_f.evalf()) # Coeff. angolare retta di Henry\n", "\n", "H0=(0,1) # punti per il tracciamento della retta\n", "H1=(0,gamma_0) # di Henry\n", "\n", "R0=(0,1) # punti per il tracciamento della retta\n", "R1=(0,1) # di Rault\n", "\n", "a_a=act_aff(x) # valori dell'attività \n", "plt.figure(figsize=(6,6))\n", "plt.plot(x,a_a,label=\"Attività di Mg\")\n", "plt.plot(R0,R1,\"k--\",label=\"Legge di Rault\")\n", "plt.plot(H0,H1,\"k-.\", label=\"Legge di Henry\")\n", "plt.xlim(0,1)\n", "ymx=gamma_0*(1.+0.05)\n", "plt.ylim(0,ymx)\n", "plt.xlabel(\"X(Mg)\")\n", "plt.ylabel(\"Attività\")\n", "plt.legend(frameon=False)\n", "plt.show()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Come si evince dal grafico, la legge di Henry è approssimativamente rispettata per $x_{\\rm Mg}$ variabile da 0 fino a circa 0.1, mentre la legge di Rault può essere considerata valida per $x_{\\rm Mg}$ maggiore di circa 0.9. \n", "\n", "### Diagramma *TX* per l'olivina \n", "\n", "Possiamo calcolare il diagramma di stato *TX* dell'olivina utilizzando una versione più sofisticata del programma *melt* che avevamo già usato in una versione passata. Il nuovo programma che usiamo qui si chiama *melt_2* che, oltre a implementare il modello simmetrico (quadratico) per la soluzione solida forsterite-fayalite, presenta delle modifiche alle routine di ottimizzazione che ne aumentano la *stabilità*.\n", "\n", "Anche qui è meglio usare una istruzione *import* per caricare il programma (con l'alias *mp*):" ] }, { "cell_type": "code", "execution_count": 34, "metadata": {}, "outputs": [], "source": [ "import melt_2 as mp" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Calcoliamo il diagramma *TX* con il comando *melt* (che facciamo precedere dall'alias *mp*). La lista degli argomenti alla funzione *melt* la possiamo visualizzare con il comando *help*: " ] }, { "cell_type": "code", "execution_count": 35, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Help on function melt in module melt_2:\n", "\n", "melt(ip=0, nt=10, tfmax=0.0, W=8400.0, ideal=False, nt_prt=0)\n", " Calcola il diagramma di stato TX del sistema fayalite-forsterite\n", " \n", " Input:\n", " ip - pressione (GPa)\n", " nt - numero di punti in temperatura\n", " tfmax - se non 0, fissa il massimo di temperatura per il grafico\n", " W - Parametro di Margules per la soluzione solida\n", " (default: 8400 J/mole)\n", " ideal - calcola un diagramma di riferimento ideale (default: False)\n", " nt_ptr - se > 0 fissa il numero di valori di temperatura per\n", " la stampa della tabella T(X) (default: 0; stampa tutti\n", " gli nt valori calcolati)\n", "\n" ] } ], "source": [ "help(mp.melt)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Facciamo il calcolo a 0 GPa, volendo anche le curve calcolate con il modello ideale per il confronto:" ] }, { "cell_type": "code", "execution_count": 36, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "\n", "Modello simmetrico di soluzione per il solido:\n", "W*Xa*Xb; W= 8400.0 J/mole\n", "\n", "Temperatura di fusione della forsterite: 2161.01 K\n", "Temperatura di fusione della fayalite: 1480.31 K\n" ] }, { "data": { "image/png": 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\n", 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" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" }, { "name": "stdout", "output_type": "stream", "text": [ "\n", " T (K) X(Mg)sol X(Fe)sol X(Mg)liq X(Fe)liq\n", " 1480.31 0.01 0.99 0.00 1.00 \n", " 1551.97 0.40 0.60 0.07 0.93 \n", " 1623.62 0.65 0.35 0.12 0.88 \n", " 1695.27 0.78 0.22 0.17 0.83 \n", " 1766.92 0.86 0.14 0.24 0.76 \n", " 1838.58 0.91 0.09 0.32 0.68 \n", " 1910.23 0.94 0.06 0.42 0.58 \n", " 1981.88 0.96 0.04 0.55 0.45 \n", " 2053.53 0.98 0.02 0.70 0.30 \n", " 2125.19 0.99 0.01 0.89 0.11 \n" ] } ], "source": [ "mp.melt(0,nt=20,ideal=True,nt_prt=10)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Usiamo la funzione *composition* per calcolare le composizioni a *T* e *P* fissate, per una composizione globale del sistema specifica (per esempio X(Mg)=0.8), sia nel caso ideale, sia in quello non ideale." ] }, { "cell_type": "code", "execution_count": 37, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Help on function composition in module melt_2:\n", "\n", "composition(it, ip, W_val, prt=True, xval=-1.0)\n", " Determina la composizione delle fasi liquida e solida all'equilibrio\n", " e le quantità di liquido e solido data una composizione globale\n", " \n", " Input:\n", " it - temperatura (K)\n", " ip - pressione (GPa)\n", " W_val - parametro di Margules \n", " prt - stampa i risultati (default: True)\n", " xval - se diverso da -1 calcola le quantita' di solido e liquido\n", " per la composizione globale xval; se xval=-1 il calcolo\n", " viene fatto alla composizione per la quale le due curve\n", " di energia libera si intersecano (default xval = -1)\n", "\n" ] } ], "source": [ "help(mp.composition)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Caso ideale (W=0.):" ] }, { "cell_type": "code", "execution_count": 38, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Pressione 0.0 GPa, Temperatura 1900.0 K\n", "\n", "Per una composizione X(Mg) globale pari a 0.80: \n", "X(Mg) fase solida 0.89, quantità fase solida 0.82\n", "X(Mg) fase liquida 0.39, quantità fase liquida 0.18\n" ] } ], "source": [ "mp.composition(1900,0,0.,xval=0.8,prt=True)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Caso non ideale (W=8400 J/mole):" ] }, { "cell_type": "code", "execution_count": 39, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Pressione 0.0 GPa, Temperatura 1900.0 K\n", "\n", "Per una composizione X(Mg) globale pari a 0.80: \n", "X(Mg) fase solida 0.93, quantità fase solida 0.75\n", "X(Mg) fase liquida 0.41, quantità fase liquida 0.25\n" ] } ], "source": [ "mp.composition(1900,0,8400,xval=0.8,prt=True)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Da notare le differenze ottenute tra caso ideale e non, sia per quanto riguarda le composizioni delle due fasi, sia per quanto riguarda le quantità relative di fase liquida e solida.\n", "\n", "Le funzioni *melt* e *composition* possono essere anche usate specificando pressioni diverse da quella ambiente. Per esempio, a 5 GPa abbiamo: " ] }, { "cell_type": "code", "execution_count": 40, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "\n", "Modello simmetrico di soluzione per il solido:\n", "W*Xa*Xb; W= 8400.0 J/mole\n", "\n", "Temperatura di fusione della forsterite: 2497.40 K\n", "Temperatura di fusione della fayalite: 1836.95 K\n" ] }, { "data": { "image/png": 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\n", 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" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" }, { "name": "stdout", "output_type": "stream", "text": [ "\n", " T (K) X(Mg)sol X(Fe)sol X(Mg)liq X(Fe)liq\n", " 1836.95 0.01 0.99 0.00 1.00 \n", " 1906.47 0.26 0.74 0.08 0.92 \n", " 1975.99 0.49 0.51 0.15 0.85 \n", " 2045.51 0.64 0.36 0.22 0.78 \n", " 2115.04 0.74 0.26 0.30 0.70 \n", " 2184.56 0.82 0.18 0.39 0.61 \n", " 2254.08 0.87 0.13 0.49 0.51 \n", " 2323.60 0.92 0.08 0.61 0.39 \n", " 2393.12 0.95 0.05 0.75 0.25 \n", " 2462.64 0.99 0.01 0.91 0.09 \n" ] } ], "source": [ "mp.melt(5,nt=20,ideal=True,nt_prt=10)" ] } ], "metadata": { "kernelspec": { "display_name": "Python 3", "language": "python", "name": "python3" }, "language_info": { "codemirror_mode": { "name": "ipython", "version": 3 }, "file_extension": ".py", "mimetype": "text/x-python", "name": "python", "nbconvert_exporter": "python", "pygments_lexer": "ipython3", "version": "3.7.6" } }, "nbformat": 4, "nbformat_minor": 4 }