One dimensional diatomic lattice oscillations

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Discussion Overview

The discussion revolves around the behavior of oscillation frequencies in a one-dimensional diatomic lattice when the two masses become equal. Participants explore the implications for frequency gaps in both diatomic and monatomic lattices, touching on concepts related to oscillation modes.

Discussion Character

  • Exploratory
  • Technical explanation
  • Conceptual clarification
  • Homework-related

Main Points Raised

  • One participant questions the effect on the frequency gap when the masses M1 and M2 in a diatomic lattice become equal, and contrasts this with a monatomic lattice.
  • Another participant seeks clarification on whether the original question is homework-related and asks for definitions of A1 and A2.
  • A participant clarifies that A1 and A2 refer to amplitudes and indicates that the question is from a knowledge-testing section rather than formal homework.
  • One participant expresses uncertainty about the expectations from the original question and suggests considering the qualitative behavior of oscillations in a chain of equal mass molecules, such as H2.
  • A later reply references a specific textbook to provide a formula for the frequency gap between optical and acoustic modes, noting that if M1 equals M2, the frequency gap becomes zero, leading to only acoustic modes in a monatomic lattice.

Areas of Agreement / Disagreement

Participants do not reach a consensus on the implications of equal masses on frequency gaps, and multiple viewpoints regarding the nature of oscillations and the context of the question remain present.

Contextual Notes

There are limitations regarding the assumptions made about the nature of the oscillations and the specific definitions of terms like A1 and A2, which may depend on the context provided in the referenced textbook.

Who May Find This Useful

This discussion may be of interest to students and educators in solid state physics, particularly those exploring lattice dynamics and oscillation modes in diatomic and monatomic systems.

PsychonautQQ
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Suppose we allow two masses M1 and M2 in a one dimensional diatomic lattice to become equal. what happens to the frequency gap? what about in a monatomic lattice?
Knowing that (M1)(A2) + (M2)(A1) = 0
 
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a) is this homework?
b) what are A1 and A2?
 
it's one of those "test your knowledge" questions at the end of the chapter, not homework X_x but I've been trying to figure it out on my own and can't. A1 and A2 are amplitudes
 
I don't know what you were shown in that book, so I am not sure about what they expect you to do.
Qualitatively, what kind of oscillations do you expect in a chain made up of, say, H2 molecules (atoms of equal mass but different inter- versus intramolecular distances)?
 
Hey Psychonaut, I know this is probably coming too late, but I had to answer the same question recently on homework lol. Assuming you are also using Omar's book on solid state physics, refer to page 98. Here we see that the frequency gap between the optical and acoustic modes can be defined as (2α^2/M1)^(1/2) - (2α^2/M2)^(1/2) assuming M1<M2. If M1 = M2, then that expression goes to 0 and there is no frequency gap, just acoustic modes like we would expect to see in a typical monoatomic lattice.
 

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