Does amorphous solids support phonons or nomal modes of vibration.?

[ns_phonon]

Does amorphous solids support phonons or nomal modes of vibration.??

Can we apply the concept of phonons and Debye Model in case of amorphous and poly-crystalline solids??

http://en.wikipedia.org/wiki/Phonon

http://en.wikipedia.org/wiki/Debye_model

The links I have attached above discusses only about quantization of normal vibrational modes in case of monocrystals. But, in real world most objects which we see around seems to be appearing polycrystalline(i.e. with grains and grain boundaries) or amorphous.

So,how can we apply highly simplified concepts of phonons and debye model in case of such non-crystalline objects...?

"Does an amorphous solid also has normal modes of vibrations of atoms/molecules just like crystals do have...?"

Please answer me as simple as possible as I am not an expert in this field.This question is not for homework,the question was born just out of curiosity...

I have already searched about this matter on google but I did not find appropriate material,rather the material which I explored contained too high level mathematics which is out of my mind's regime.

Please help by answering the basic concept and being as simple as possible..

"THANKS FOR READING THIS THREAD"​

 

[f95toli]

The answer to your questuion is yes, there are definately phonons and the basiuc physics is the same.
However, the details become very messy very quickly; and I am not even going to pretend that I understand the full theory,

That said, note that impurities/defects that are much smaller than the wavelengh of the phonon can to first approximation be ignored; this does not always work (it fails completely for e.g. the heat capacity in the low temperature limit) but it helps explain why the difference between perfect crystals and real materials isn't bigger than it it.

 

[ns_phonon]

Thanks Mr. f95toli. I also believed the same. I believe that quantization(of vibrational modes) is there due to the "boundary conditions" which I assume to be free boundaries at the end of the solids.Now to support the phonons,an antinode(point where displacement is maximum) must be formed at all the boundaries of the solid and "any arbitary vibration in a solid can be considered as a superposition of these phonons." So finally, I believe as long as the boundaries exist, quantisation exist,no matter what type of material is,crystalline,polycrystalline or even amorphous.

So, what I believe is "as long as the boundaries of the solid exist" , quantized normal modes are ought to happen,irrespective of material/arrangement of atoms in materials. Only the methods to obtain energies of this normal modes become complex but quantization still pervades through the material.

I just wanted to confirm that.

Is my thinking right...? Or am I thinking on the wrong track...? If I am wrong please explain me why,being as simple as possible.

Once again "Thanks" for replying...I am almost clear now... though I am still unaware of how quantization occurs and methods to obtain quantized energy levels in such ploy-crystalline or amorphous solids. But I am satisfied almost now.

 

[Claude Bile]

Yes.

The main consideration with amorphous solids, are that they contain a spectrum of bond lengths/directions, whereas a crystalline solid contains only specific spatial frequencies.

As a result the normal modes a far more dispersed for amorphous solids than for crystalline solids; because the normal modes actually represent a sum of a whole bunch of normal modes at a slightly different spatial frequency (1 normal mode for each spatial frequency).

Claude.