Atomic Vibration in Einstein & Debye Models

In summary, according to Einstein, all atoms in a solid vibrate with the same frequency. However, in the Debye model, there is a band of frequencies, meaning not all atoms vibrate with the same frequency. The idea behind the Debye model is that vibrations can have any wavelength within the periodicity of the crystal. This is why the frequency of vibrating atoms differs from one another in the same type of crystal. The Debye model is more accurate than Einstein's model at low temperatures.
  • #1
sirwan
12
0
according to Einstein all atoms in solid vibrating with the same frequency , while in the Debye's mode there are a band of frequency i.e not all the atoms would have the same frequency, my question is that , that is the idea behind the Debye's model? or why the frequency of vibrating of atoms differ from one other in the same type of crystal.
 
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  • #2
sirwan said:
according to Einstein all atoms in solid vibrating with the same frequency , while in the Debye's mode there are a band of frequency i.e not all the atoms would have the same frequency, my question is that , that is the idea behind the Debye's model? or why the frequency of vibrating of atoms differ from one other in the same type of crystal.

Sorry, I do not completely understand what your question is. Could you say that again?
 
  • #3
In solid crystal, according to Debye Model .why the frequency of vibration of one atom Different from one another? or why all atoms not vibrating with the same frequency. thanks
 
  • #4
Well, the Debye model differs a little from the model of Einstein.
At low temperatures, the Debye model is more accurate than that of Einstein.

But to fully answer your question, just take a look at this:
Debye model - Wikipedia, the free encyclopedia

Hope this helps you, otherwise just tell me.
 
  • #5
In the Debye model, vibrations can have any wavelength that is consistent with the periodicity of the crystal.

The smallest wavelength (highest frequency) corresponds to the interatomic spacing. The longest wavelength (lowest frequency) corresponds to the size of the crystal itself. The allowed wavelengths in between these limits are multiples of the interatomic spacing.

The above conditions need to be applied in 3-dimensional space, but that does not change much. The actual relationship between frequency and wavelength is material dependent, and is only linear at low frequencies.
 

What is atomic vibration?

Atomic vibration refers to the movement of atoms in a solid material. This movement is caused by thermal energy, and it can affect the physical properties of the material.

How do Einstein and Debye models explain atomic vibration?

The Einstein and Debye models are two theoretical models that describe atomic vibration in solids. The Einstein model assumes that all atoms vibrate at the same frequency, while the Debye model considers the vibrations of all atoms in a solid as a whole.

What is the difference between the Einstein and Debye models?

The main difference between the Einstein and Debye models is that the Einstein model assumes that all atoms have the same vibrational frequency, while the Debye model takes into account the different vibrational frequencies of all atoms in a solid material.

How do these models relate to temperature?

Both the Einstein and Debye models show that the amplitude of atomic vibrations increases with temperature. The higher the temperature, the more energy is available for atomic vibrations, leading to greater movement of atoms in a solid material.

What are the practical applications of understanding atomic vibration in Einstein and Debye models?

Understanding atomic vibration in Einstein and Debye models has practical applications in material science and engineering. It can help predict the behavior of materials at different temperatures and provide insights for designing and improving materials for various applications.

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