{ "cells": [ { "cell_type": "markdown", "metadata": {}, "source": [ "# Densitat dels metalls" ] }, { "cell_type": "code", "execution_count": 1, "metadata": {}, "outputs": [], "source": [ "%matplotlib inline\n", "import matplotlib.pyplot as plt\n", "import numpy as np\n", "import pandas as pd" ] }, { "cell_type": "code", "execution_count": 3, "metadata": {}, "outputs": [ { "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", " \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", " \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", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", "
SímbolradiArhoestructura
0Mg0.16024.311.74hcp
1Al0.14326.982.70fcc
2Si0.11728.092.33dia.cub.
3Ti0.14747.904.51hcp
4Cr0.12552.007.19bcc
5Fe0.12455.857.87bcc
6Ni0.12558.718.91fcc
7Cu0.12863.558.93fcc
8Zn0.13365.387.13hcp
9Ag0.144107.8710.50fcc
10Sn0.158118.697.29bct
11W0.137183.8519.25bcc
12Pt0.138195.0921.44fcc
13Au0.144196.9719.28fcc
14Pb0.175207.2011.34fcc
15U0.138238.0319.05ortho.
\n", "
" ], "text/plain": [ " Símbol radi A rho estructura\n", "0 Mg 0.160 24.31 1.74 hcp\n", "1 Al 0.143 26.98 2.70 fcc\n", "2 Si 0.117 28.09 2.33 dia.cub.\n", "3 Ti 0.147 47.90 4.51 hcp\n", "4 Cr 0.125 52.00 7.19 bcc\n", "5 Fe 0.124 55.85 7.87 bcc\n", "6 Ni 0.125 58.71 8.91 fcc\n", "7 Cu 0.128 63.55 8.93 fcc\n", "8 Zn 0.133 65.38 7.13 hcp\n", "9 Ag 0.144 107.87 10.50 fcc\n", "10 Sn 0.158 118.69 7.29 bct\n", "11 W 0.137 183.85 19.25 bcc\n", "12 Pt 0.138 195.09 21.44 fcc\n", "13 Au 0.144 196.97 19.28 fcc\n", "14 Pb 0.175 207.20 11.34 fcc\n", "15 U 0.138 238.03 19.05 ortho." ] }, "execution_count": 3, "metadata": {}, "output_type": "execute_result" } ], "source": [ "metalls = pd.read_csv('data/Materials/metalls.csv')\n", "metalls" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Primer carregarem aquestes dades, tenint en compte que el radi atòmic el tenim en nm i volem la densitat en g/cm³ \n", "També definiren el nomnbre d'Avogadre Na" ] }, { "cell_type": "code", "execution_count": 4, "metadata": {}, "outputs": [], "source": [ "r=metalls['radi']*10**(-7)\n", "A=metalls['A']\n", "rho=metalls['rho']\n", "Na=6.023*10**23" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Càlcul de la densitat de l'or (FCC)\n", "\n", "En aquest cas el costat de la cel·la unitat és $a=\\frac{4}{\\sqrt{2}}\\cdot r$ \n", "En cada cel·la tenim 4 atoms complets \n", "La densitat es pot calcular com \n", "$\\rho = \\frac{4}{a^{3}}\\cdot \\frac{A}{N_{a}}$" ] }, { "cell_type": "code", "execution_count": 5, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "19.360864981492718" ] }, "execution_count": 5, "metadata": {}, "output_type": "execute_result" } ], "source": [ "n=13\n", "a=4/np.sqrt(2)*r[n]\n", "densitat=4/a**3*A[n]/Na\n", "densitat" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Com veiem es tracta d'una bona estimació del valor real" ] }, { "cell_type": "code", "execution_count": 6, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "19.28" ] }, "execution_count": 6, "metadata": {}, "output_type": "execute_result" } ], "source": [ "rho[n]" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Càlcul de la densitat del ferro (BCC)\n", "\n", "En aquest cas el costat de la cel·la unitat és $a=\\frac{4}{\\sqrt{3}}\\cdot r$ \n", "En cada cel·la tenim 2 atoms complets \n", "La densitat es pot calcular com \n", "$\\rho = \\frac{2}{a^{3}}\\cdot \\frac{A}{N_{a}}$" ] }, { "cell_type": "code", "execution_count": 7, "metadata": { "scrolled": true }, "outputs": [ { "data": { "text/plain": [ "7.89727320368215" ] }, "execution_count": 7, "metadata": {}, "output_type": "execute_result" } ], "source": [ "n=5\n", "a=4/np.sqrt(3)*r[n]\n", "densitat=2/a**3*A[n]/Na\n", "densitat" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Que s'acosta també molt al valor real" ] }, { "cell_type": "code", "execution_count": 8, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "7.87" ] }, "execution_count": 8, "metadata": {}, "output_type": "execute_result" } ], "source": [ "rho[n]" ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [] } ], "metadata": { "kernelspec": { "display_name": "venvPy3", "language": "python", "name": "venvpy3" }, "language_info": { "codemirror_mode": { "name": "ipython", "version": 3 }, "file_extension": ".py", "mimetype": "text/x-python", "name": "python", "nbconvert_exporter": "python", "pygments_lexer": "ipython3", "version": "3.10.12" } }, "nbformat": 4, "nbformat_minor": 4 }