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(Solid state physics) Consider the normal modes of a linear chain in which the force constants between nearest- neighbor atoms are alternately C and 10C. Let the masses be equal, and let the nearest-neighbor separation be a/2. (a) Find the expression for a²(k) for ka<<1. (b) Find the values of @ (k) at k = 0 and k = a. (c) Sketch in the dispersion relation by eye. (d) Discuss the motions for two neighboring atoms for at k = 0 for the corresponding two modes (in the real space). This problem simulates a crystal of diatomic molecules such as H₂. с Vs Us+1 Vs+ 10C C 10C C a

(Solid state physics) Consider the normal modes of a linear chain in which the force constants between nearest- neighbor atoms are alternately C and 10C. Let the masses be equal, and let the nearest-neighbor separation be a/2. (a) Find the expression for a²(k) for ka<<1. (b) Find the values of @ (k) at k = 0 and k = a. (c) Sketch in the dispersion relation by eye. (d) Discuss the motions for two neighboring atoms for at k = 0 for the corresponding two modes (in the real space). This problem simulates a crystal of diatomic molecules such as H₂. с Vs Us+1 Vs+ 10C C 10C C a

College Physics
College Physics
11th Edition
ISBN:9781305952300
Author:Raymond A. Serway, Chris Vuille
Publisher:Raymond A. Serway, Chris Vuille
Chapter1: Units, Trigonometry. And Vectors
Section: Chapter Questions
Problem 1CQ: Estimate the order of magnitude of the length, in meters, of each of the following; (a) a mouse, (b)...
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(Solid state physics) Consider the normal modes of a linear chain in which the force constants between nearest- neighbor atoms are alternately C and 10C. Let the masses be equal, and let the nearest-neighbor separation be a/2. (a) Find the expression for a²(k) for ka<<1. (b) Find the values of @ (k) at k = 0 and k = a. (c) Sketch in the dispersion relation by eye. (d) Discuss the motions for two neighboring atoms for at k = 0 for the corresponding two modes (in the real space). This problem simulates a crystal of diatomic molecules such as H₂. с Vs Us+1 Vs+ 10C C 10C C a
Transcribed Image Text:(Solid state physics) Consider the normal modes of a linear chain in which the force constants between nearest- neighbor atoms are alternately C and 10C. Let the masses be equal, and let the nearest-neighbor separation be a/2. (a) Find the expression for a²(k) for ka<<1. (b) Find the values of @ (k) at k = 0 and k = a. (c) Sketch in the dispersion relation by eye. (d) Discuss the motions for two neighboring atoms for at k = 0 for the corresponding two modes (in the real space). This problem simulates a crystal of diatomic molecules such as H₂. с Vs Us+1 Vs+ 10C C 10C C a
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