Calculating Sound Velocity in Diamond Using Debye Approximation

In summary, the Debye temperature of diamond is 2000 K with a density of 3500 kg/m3 and a distance between nearest neighbors of 0.15 nm. Using the Debye approximation and a formula connecting the given parameters, one can determine the velocity of sound. Further understanding may require referencing a book such as Kittel.
  • #1
CF.Gauss
8
1
Diamond has a Debye temperature of Dt = 2000 K and a density of 3500 kg/m3.
The distance between nearest neighbors is 0.15 nm. Determine the velocity of
sound using the Debye approximation.

I have no idea where to even start with this question. Most books don't even mention the Debye approx. and all the others have very little or are so confusing!
 
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  • #2
Refer http://en.wikipedia.org/wiki/Debye_model

There is a formula in there, that connects all the given parameters with the sound velocity. You can also follow the derivation.

Of course to understand more, you might have to refer to some book such as Kittel.
 

What is the Debye approximation?

The Debye approximation is a mathematical model used to describe the behavior of matter, specifically in the context of thermal and electrical properties. It was developed by Peter Debye in 1912 and is based on the assumption that all atoms in a material vibrate at the same frequency, known as the Debye frequency.

How is the Debye approximation used in scientific research?

The Debye approximation is commonly used in the fields of solid state physics and materials science to study the thermal and electrical properties of materials. It is often used to analyze how heat and electricity flow through a material and can provide valuable insights into the behavior of different substances.

What are the limitations of the Debye approximation?

While the Debye approximation is a useful tool for understanding the behavior of materials, it does have its limitations. One major limitation is that it assumes all atoms in a material are vibrating at the same frequency, which is not always the case. It also does not take into account the effects of impurities or defects in the material.

How does the Debye approximation relate to the Debye model of specific heat?

The Debye approximation is based on the Debye model of specific heat, which was also developed by Peter Debye. The Debye model predicts the heat capacity of a material at various temperatures, and the Debye approximation uses this information to calculate other thermal and electrical properties of the material.

Can the Debye approximation be applied to all materials?

The Debye approximation is most accurate for materials with simple crystal structures, such as metals and insulators. It can also be used for more complex materials, but the results may not be as accurate. In general, the Debye approximation is not suitable for highly disordered materials or materials with a high concentration of defects.

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