Phonon and dispersion relation

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SUMMARY

The discussion centers on the relationship between phonons, dispersion relations, and their propagation through solids. It establishes that long wavelengths, defined as being ten times the lattice spacing or more, allow phonons to travel long distances without distortion. The conversation also clarifies that while ultrasonic testing uses short wavelengths, propagation is still possible unless high absorption or scattering occurs. Additionally, it distinguishes between phonons related to sound and thermal energy, indicating that both can exist in different modes within the Debye model.

PREREQUISITES
  • Understanding of phonons and their role in solid-state physics
  • Familiarity with dispersion relations in wave mechanics
  • Knowledge of the Debye model for thermal energy in solids
  • Basic concepts of ultrasonic testing and its applications
NEXT STEPS
  • Research the mathematical formulation of dispersion relations in solid materials
  • Explore the Debye model and its implications for thermal conductivity
  • Study the effects of absorption and scattering on wave propagation in solids
  • Investigate the differences between phonons and photons in solid-state interactions
USEFUL FOR

Students and researchers in solid-state physics, materials scientists, and professionals involved in ultrasonic testing or thermal analysis of materials.

asifadio
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hello I am new in this forum.. and i would like to ask
first this is statement that i confused about
'At low values of k (i.e. long wavelengths), the dispersion relation is almost linear, and the speed of sound is approximately ω a, independent of the phonon frequency. As a result, packets of phonons with different (but long) wavelengths can propagate for large distances across the lattice without breaking apart. This is the reason that sound propagates through solids without significant distortion. This behavior fails at large values of k, i.e. short wavelengths, due to the microscopic details of the lattice.'

what is consider as 'long wavelength'? I am a bit confused with ultrasonic testing which is used short wavelength but still can propagates through material for large distance..

and how bout thermal energy? are this also consider as phonon at short wavelength? because i could see that there are exist mode in debye model.. so i assume that it is phonon but different energy from sound..

but i read that phonon is speed of sound in lattice.. thermal and sound doesn't seem similar to me..

im sorry, I am noob.. :'(
 
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Generally speaking if the wavelength is 10x the lattice spacing or more you can call it long.

Just because dispersion is high and wavelength is short that doesn't mean it won't propagate a long distance. You need high absorption and or scattering to attenuate the propagation.
 
can i say that photon wavelength are comparable to atomic spacing so it will only interact deeper in atom
and phonon wavelength is comparable to lattice spacing so it will interact with lattice not deeper than that?

and last question, is like statement below,
'As a result, packets of phonons with different (but long) wavelengths can propagate for large distances across the lattice without breaking apart. This is the reason that sound propagates through solids without significant distortion.'

can a phonon breaking lattice apart? can you give me any example?

thanks a lot for helping me :)
 

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