{ "cells": [ { "cell_type": "markdown", "id": "aa8c8102-d4ea-4d9e-b0d7-ceeea82070d9", "metadata": { "tags": [] }, "source": [ "# Introduction to Thermodynamics and Statistical Physics" ] }, { "cell_type": "markdown", "id": "816bb359-4cd2-4f53-81cd-b87c47011da3", "metadata": {}, "source": [ "In this lecture, we are going to discuss:\n", "\n", "* The Debye theory for a solid." ] }, { "cell_type": "markdown", "id": "9ddf9065-095d-42cb-a1ef-c90c6b25271e", "metadata": { "tags": [] }, "source": [ "## The Debye model" ] }, { "cell_type": "markdown", "id": "4c2f0c52-2a58-416a-a647-c1781ef62d72", "metadata": {}, "source": [ "The key difference between Einstein's theory and Debye's is that in the Einstein model, it is assumed that all of the atoms are vibrating about their equilibrium positions independantly with the exact same frequency. The Debye model builds on this by allowing the oscillators within the system to have a distribution of frequencies.\n", "\n", "Fortunately, we have already developed part of the framework we need for this task. Recalling the definition of the density of states from Lecture 12, we will modify it to represent the density of vibrational states, $g(\\omega)$. We will impose the requirement that if we intergate the density of vibrational states over the entire frequency range, we should get back the total number of phonons in our system, $3N$. That is\n", "$$\n", " \\int g(\\omega) {\\rm d} \\omega = 3N\n", "$$\n", "\n", "Debye used the following knowledge to determine an appropriate distribution of frequencies - we know that vibrational waves will travel through the solid with a speed equal to the speed of sound of the solid. That is\n", "$$\n", " \\omega = v_{s}q\n", "$$\n", "where q is the wave vector of the lattice vibrations. The density of these vibrations is given as\n", "$$\n", " g(q) {\\rm d} q = \\frac{4\\pi q^2 {\\rm d} q}{(2\\pi/L)^3} \\times 3\n", "$$\n", "where the factor of 3 comes from the allowed polarisations of the wave, and we have assumed the crystal is a cube of side $L$. Tidying up a bit gives\n", "$$\n", " g(q) {\\rm d} q = \\frac{3 V q^2 {\\rm d} q}{2\\pi^2}\n", "$$\n", "which, in terms of $\\omega$, is\n", "$$\n", " g(\\omega) {\\rm d} \\omega = \\frac{3 V \\omega^2 {\\rm d} \\omega}{2\\pi^2 v_{s}^3}\n", "$$\n", "The next assumption Debye allowed for is that, since there is a maximum of $3N$ modes in the crystal, there exists a maximum frequency (the Debye frequency) such that\n", "$$\n", " \\int_0^{\\omega_{\\rm D}} g(\\omega) {\\rm d} \\omega = 3N\n", "$$\n", "which, after substituting in for $g(\\omega)$, gives\n", "$$\n", " \\omega_{\\rm D} = \\left( \\frac{6 N \\pi^2 v_{\\rm s}^3 }{V} \\right) ^{1/3}\n", "$$\n", "which also let's us write\n", "$$\n", " g(\\omega) {\\rm d} \\omega = \\frac{9 N \\omega^2 {\\rm d} \\omega}{\\omega_{\\rm D}^3}\n", "$$\n", "Now, we'll define the Debye temperature as\n", "$$\n", " \\Theta_{\\rm D} = \\frac{\\hbar \\omega_{\\rm D}}{k_{\\rm B}}\n", "$$\n", "\n", "So the question we now need to ask is \"is the predicted heat capacity versus temperature from this model a better match to our data?\". Let's work out an expression for it and see.\n", "\n", "Starting with the partition function, we'll have\n", "$$\n", " \\ln(Z) = \\int_0^{\\omega_{\\rm D}} {\\rm d} \\omega \\; g(\\omega) \\; ln \\left[ \\frac{e^{-\\hbar \\omega \\beta/2}}{1-e^{-\\hbar \\omega \\beta}} \\right]\n", "$$\n", "Breaking this integral up gives\n", "$$\n", " \\ln(Z) = -\\int_0^{\\omega_{\\rm D}} \\; \\frac{1}{2} \\hbar \\omega \\beta g(\\omega) {\\rm d} \\omega + \\int_0^{\\omega_{\\rm D}} \\; g(\\omega) \\ln[1-e^{-\\hbar \\omega \\beta}] {\\rm d} \\omega\n", "$$\n", "which in turn gives\n", "$$\n", " \\ln(Z) = -\\frac{9}{8} N \\hbar \\omega_{\\rm D} \\beta -\\frac{9 N}{\\omega_{\\rm D}^3} \\int_0^{\\omega_{\\rm D}} \\omega^2 \\ln[1-e^{-\\hbar \\omega \\beta}] {\\rm d} \\omega\n", "$$\n", "The internal energy is then\n", "$$\n", " U = - \\frac{\\partial \\ln(Z)}{\\partial \\beta} = -\\frac{9}{8} N \\hbar \\omega_{\\rm D} + \\frac{9 N \\hbar}{\\omega_{\\rm D}^3} \\int_0^{\\omega_{\\rm D}} \\frac{\\omega^2} {e^{\\hbar \\omega \\beta}-1} {\\rm d} \\omega\n", "$$\n", "Finally, the heat capacity is then\n", "$$\n", " C_{\\rm V} = \\left( \\frac{\\partial \\langle U \\rangle}{\\partial T} \\right)_V\n", "$$\n", "$$\n", " C_{\\rm V} = \\frac{9N \\hbar}{\\omega_{\\rm D}^3} \\int_0^{\\omega_{\\rm D}} \\frac{-\\omega^3 {\\rm d} \\omega}{e^{\\hbar \\omega \\beta}-1} e^{\\hbar \\omega \\beta} \\left( - \\frac{\\hbar \\omega} {k_{\\rm B} T^2} \\right)\n", "$$\n", "which simplifies to\n", "$$\n", " C_{\\rm V} = \\frac{9 R}{x_{\\rm D}^3} \\int_0^{x_{\\rm D}} \\frac{x^4e^{x}}{(e^{x}-1)^2}\n", "$$\n", "where $x=\\hbar \\beta \\omega$ and $x_{\\rm D}=\\hbar \\beta \\omega_{\\rm D}$." ] }, { "cell_type": "code", "execution_count": null, "id": "b897cf17-999e-48eb-a156-c4fbcac49a93", "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", 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" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "import numpy as np\n", "from scipy.integrate import quad\n", "import matplotlib.pyplot as plt\n", "import pandas as pd\n", "import astropy.units as u\n", "import astropy.constants as c\n", "\n", "def f(x):\n", " #This is simply the function in the integral above\n", " return x**4*np.exp(x)/(np.exp(x)-1)**2\n", "\n", "#First, we need to calculate x_D for all temperatures, assuming T_D = 1800*u.K\n", "T_D = 1800*u.K\n", "x_Ds = T_D/T\n", "\n", "#We now need to loop over the integration, for each x_D\n", "Cv_Debye = np.array([])*u.J/u.K/u.mol\n", "\n", "for x_D in x_Ds:\n", " res, err = quad(f, 0.0, x_D) # This numerical integration function returns both the integrated value and an estimate of the error\n", " Cv_Debye = np.append(Cv_Debye,9*c.R*res/x_D**3)\n", "\n", "plt.figure(figsize=[4,3], dpi=150)\n", "plt.plot(temp,Cv,'.',label='Experimental Data')\n", "plt.plot(T,Cv_Einstein,'-',label='Einstein Model')\n", "plt.plot(T,Cv_Debye,'-.',label='Debye Model')\n", "plt.axhline(3*c.R.value,linestyle='--')\n", "plt.text(200,25.5, '3R')\n", "plt.xlabel(r\"T (K)\")\n", "plt.ylabel(r\"C$_{\\rm V}$ (J/K/mol)\")\n", "plt.ylim(0,27.5)\n", "plt.xlim(0,1325)\n", "plt.legend()\n", "plt.tight_layout()\n", "plt.savefig(\"Figures/Debye_Einstein_Model_vs_Data.jpg\")\n", "plt.show()" ] } ], "metadata": { "kernelspec": { "display_name": "Python 3 (ipykernel)", "language": "python", "name": "python3" }, "language_info": { "codemirror_mode": { "name": "ipython", "version": 3 }, "file_extension": ".py", "mimetype": "text/x-python", "name": "python", "nbconvert_exporter": "python", "pygments_lexer": "ipython3", "version": "3.8.10" } }, "nbformat": 4, "nbformat_minor": 5 }