From ab007e3cada3b86847d0a4bd2ad37f58bdc70291 Mon Sep 17 00:00:00 2001 From: "T. van der Sar" <t.vandersar@tudelft.nl> Date: Wed, 12 Feb 2020 11:50:27 +0000 Subject: [PATCH] Update 2_debye_model.md --- src/2_debye_model.md | 4 ++-- 1 file changed, 2 insertions(+), 2 deletions(-) diff --git a/src/2_debye_model.md b/src/2_debye_model.md index c6c7e4aa..41e2f155 100644 --- a/src/2_debye_model.md +++ b/src/2_debye_model.md @@ -276,10 +276,10 @@ ax.legend(loc='lower right'); ## Conclusions 1. The Debye model assumes that atoms in materials move in a collective fashion, described by normal modes / sound waves with a dispersion relation $ω = v_{\rm s}|\mathbf{k}|$. -2. The normal modes have a constant density of $(L/2π)^3$ in the reciprocal space. +2. The normal modes have a constant density of $(L/2π)^3$ in $k$-space. 3. The total energy and heat capacity are given by integrating the contribution of the individual modes over $k$-space. 4. The density of states $g(ω)$ counts the number of modes per unit frequency. $g(ω)$ is proportional to $ω^2$ for 3D bosons with a dispersion relation $ω = v_{\rm s}|\mathbf{k}|$. -5. At low temperatures the phonon heat capacity is $∼T^3$. +5. At low temperatures the phonon heat capacity is $\propto T^3$. ## Exercises -- GitLab