Advanced solid state physics. The attached photo may help you.
Posted: Thu Jul 07, 2022 12:03 pm
Advanced solid state physics.
The attached photo may help you.
Use the Debye model to calculate the heat capacity of a monatomic lattice in one dimnsion at temperatures small compared with the Debye temperature 0₂ = hлv/(ka) where v is the sound velocity, a is the lattice constnat spacing.
than the total energy itself. We do not have to distinguish between c, and c, in the harmonic approxima- tion since this approximation does not include thermal expansion of the lattice. We obtain the specific heat from the Debye approximation by differentiating (3.147), (3.150) with respect to the temperature. (9) T CD(T) = 3NKBfD 3 with fo(x) = f(edy 1)². (3.153) For large D/T (low temperatures), f(x) is approximately given by 4/5x²³. In this approximation the specific heat is then proportional to T³ (Debye's T³-law).
The attached photo may help you.
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than the total energy itself. We do not have to distinguish between c, and c, in the harmonic approxima- tion since this approximation does not include thermal expansion of the lattice. We obtain the specific heat from the Debye approximation by differentiating (3.147), (3.150) with respect to the temperature. (9) T CD(T) = 3NKBfD 3 with fo(x) = f(edy 1)². (3.153) For large D/T (low temperatures), f(x) is approximately given by 4/5x²³. In this approximation the specific heat is then proportional to T³ (Debye's T³-law).