Phonons and The Debye Model - Statistical Physics - University Physics

We finally tackle the problem that Einstein couldn't solve by himself. By considering phonons within a crystal lattice, we derive the empirically determined T^3 law for the heat capacity of insulators.
Link to my Patreon page: / pazzyboardmanphysicstu...

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[@pazzy768]

Thankyou for your kind words! l will do soon! :)

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The legend is back with yet another excellent and informative video!

[@MM-ig2it]

I'm watching u from Egypt. I'm going to explain this model next lecture to my students. Ur explanation is very creative and simple.

[@Mohamm4dT]

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[@itspunit01]

cool man. Loved the way you have explained this..

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[@學習中的哈密瓜]

Thanks for your video!!

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[@dbf72829]

hi isnt the density of state proportional to square root of E 38:09 thats what we derived in your dos video, please clarify this if its a different relation

[@pazzy768]

Hi, that would be true if it was a system of electrons - but we are considering a system full of phonons. The dispersion of phonons is given by E = hbar*k*v which leads to a different result for the density of states than in the case for electrons, namely proportional to E^2.

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[@yairl1]

Thank you!

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Thank you❤ for such a good explanation

[@sumaiyaseif3500]

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[@exciton007]

Nice video! Why is this model with the springs more accurate then Einsteins or Debye's model seen in the dispertion relation?

[@pazzy768]

Essentially, Einstein didn't take into account the interaction between the particles that make up the insulator. He assumed that each atom oscillated independently of one another, whereas Debye, through introducing phonons, included phonon modes which described collective oscillations of the atoms through the solid. This allows for more states to be available for low energies, therefore increasing the heat capacity dependence to a T^3 law.

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Series finale of heat capacity of solid

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[@Jack-sh4uv]

Are you able to define the debye frequency/temperature with respect to a phonon density of states? If so what physically does it mean?

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[@pazzy768]

I actually specialised in biophysics, but I’m now doing a PhD in atmospheric chemistry

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im a music producer far away from maths trying to understand the E=Hf, i want to know how much energy per frequency of a soundwave, and how to put it on a graph from 20hz to 20Khz, can someone help ? very informative video tho !