Phonon and dispersion relation

In summary, 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.
  • #1
asifadio
10
1
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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  • #2
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.
 
  • #3
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 :)
 

What is a phonon?

A phonon is a quantum of lattice vibration, or a collective excitation of atoms in a solid material. It can be thought of as a particle-like entity that carries energy and momentum through a solid material.

How is the dispersion relation related to phonons?

The dispersion relation is a mathematical relationship that describes how the energy of a phonon varies with its momentum or wave vector. It is a crucial tool for understanding the behavior of phonons in a material and is often used to calculate phonon properties such as their velocity and frequency.

What factors influence the dispersion relation of phonons?

The dispersion relation of phonons is influenced by various factors such as the crystal structure, atomic mass, and interatomic forces of a material. It can also be affected by external factors such as temperature and pressure.

What is the significance of the dispersion relation in materials science?

The dispersion relation is of great significance in materials science as it provides important information about the thermal and mechanical properties of materials. It helps in understanding the behavior of phonons and their role in heat conduction, thermal expansion, and other phenomena in solids.

Can the dispersion relation be experimentally measured?

Yes, the dispersion relation can be experimentally measured using techniques such as inelastic neutron scattering, Raman spectroscopy, and Brillouin scattering. These methods allow for the direct observation of phonon energies and momenta in a material, providing valuable information for understanding its properties.

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