1. Not finding help here? Sign up for a free 30min tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Derivation of electrical conductivity, Seebeck coefficient and thermal conductivity

  1. Mar 23, 2011 #1
    1. The problem statement, all variables and given/known data

    Hi...

    Don't know if it's actually homework, since it's not, but I hope it's okay to post in here.
    I am looking for a paper/website/article of some sort, that might have the derivations of the above mentioned coefficients ?
    It's for calculating the figure of merit:

    [tex]Z=\frac{\sigma {{S}^{2}}}{\kappa }[/tex]


    2. Relevant equations

    The equations if was hoping to maybe find some derivatins of is these three:

    [tex]\sigma ={{e}^{2}}\int{d\varepsilon \left( -\frac{\partial {{f}_{0}}}{\partial \varepsilon } \right)\Xi \left( \varepsilon \right)}[/tex]

    [tex]S=\frac{e{{k}_{B}}}{\sigma }\int{d\varepsilon \left( -\frac{\partial {{f}_{0}}}{\partial \varepsilon } \right)\Xi \left( \varepsilon \right)}\frac{\varepsilon -\mu }{{{k}_{B}}T}[/tex]

    [tex]{{\kappa }_{0}}={{k}_{B}}T\int{d\varepsilon \left( -\frac{\partial {{f}_{0}}}{\partial \varepsilon } \right)\Xi \left( \varepsilon \right)}{{\left[ \frac{\varepsilon -\mu }{{{k}_{B}}T} \right]}^{2}}[/tex]

    where:

    [tex]\[\Xi =\sum\limits_{\overrightarrow{k}}{{{\overrightarrow{v}}_{\overrightarrow{k}}}{{\overrightarrow{v}}_{\overrightarrow{k}}}{{\tau }_{\overrightarrow{k}}}}\][/tex]


    3. The attempt at a solution

    Don't know if it is possible to find derivations of these, or somewhat similar, or I have to calculate it myself. But I just wanted to try.

    Thanks in advance.


    Regards.
     
  2. jcsd
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook

Have something to add?
Draft saved Draft deleted
Similar Discussions: Derivation of electrical conductivity, Seebeck coefficient and thermal conductivity
  1. Thermal Conduction (Replies: 1)

  2. Thermal Conductivity (Replies: 2)

  3. Thermal conductivity (Replies: 0)

Loading...