Low Temperature Limit
The temperature of a Debye solid is said to be low if, leading to
This definite integral can be evaluated exactly:
In the low temperature limit, the limitations of the Debye model mentioned above do not apply, and it gives a correct relationship between (phononic) heat capacity, temperature, the elastic coefficients, and the volume per atom (the latter quantities being contained in the Debye temperature).
Read more about this topic: Debye Model
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