- #1
espen180
- 834
- 2
I am trying to work out the heat capacity of a body-centered cubic iron lattice using stat.mech., but am having some trouble.
Firstly, I assumed that the iron atoms behaved as harmonic occilators, not taking electronic or nuclear spin into account. Is this a good or bad approximation?
Then, when I compute the partition function and calculate the heat capacity [tex]C_V=\frac{dU}{dT}|_V[/tex], I get
[tex]C_V=\frac{N\hbar^2\omega^2}{kT^2}\left(\frac{e^{\frac{\hbar\omega}{kT}}}{\left(1-e^{\frac{\hbar\omega}{kT}}\right)}+\frac{e^{\frac{2\hbar\omega}{kT}}}{\left(1-e^{\frac{\hbar\omega}{kT}}\right)^2}\right)[/tex].
I can provide intermediate steps if neccesary.
For large T, the value of this expression is [tex]C_V=Nk[/tex]. I find this an indication that either my model isn't working or I have messed up, since I think the heat capacity should be dependent on the bond strength and packing density of the lattice.
If I want to make a better approximation, how do take the influence the different iron atoms have on each other into account?
Thanks in advance.
Firstly, I assumed that the iron atoms behaved as harmonic occilators, not taking electronic or nuclear spin into account. Is this a good or bad approximation?
Then, when I compute the partition function and calculate the heat capacity [tex]C_V=\frac{dU}{dT}|_V[/tex], I get
[tex]C_V=\frac{N\hbar^2\omega^2}{kT^2}\left(\frac{e^{\frac{\hbar\omega}{kT}}}{\left(1-e^{\frac{\hbar\omega}{kT}}\right)}+\frac{e^{\frac{2\hbar\omega}{kT}}}{\left(1-e^{\frac{\hbar\omega}{kT}}\right)^2}\right)[/tex].
I can provide intermediate steps if neccesary.
For large T, the value of this expression is [tex]C_V=Nk[/tex]. I find this an indication that either my model isn't working or I have messed up, since I think the heat capacity should be dependent on the bond strength and packing density of the lattice.
If I want to make a better approximation, how do take the influence the different iron atoms have on each other into account?
Thanks in advance.