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m mu not micro per MOS:NUM#Specific units and Unicode compatibility characters (via WP:JWB) |
In the calculation of <math>L=\left\{\begin{matrix}\displaystyle \frac{3}{2}\left(\frac{k_{\rm B}}{e}\right)^2\;, & \text{Drude}\\ \displaystyle\frac{\pi^2}{3}\left(\frac{k_{\rm B}}{e}\right)^2\;,&\text{free electron model.} \end{matrix}\right.</math> there |
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\end{matrix}\right.</math>
The free electron model is closer to the measured value of <math>L=2.44\times10^{-
However, Drude's mode predicts the wrong order of magnitude for the [[Seebeck coefficient]] (thermopower), which relates the generation of a potential difference by applying a temperature gradient across a sample <math>\nabla V =-S \nabla T</math>. This coefficient can be showed to be <math>S=-{c_{\rm V}}/{|ne|}</math>, which is just proportional to the heat capacity, so the Drude model predicts a constant that is hundred times larger than the value of the free electron model.<ref name=":7" group="Ashcroft & Mermin">{{Harvnb|Ashcroft|Mermin|1976|pp=|p=23|ps=}}</ref> While the latter get as coefficient that is linear in temperature and provides much more accurate absolute values in the order of a few tens of μV/K at room temperature.<ref name=":6" group="Ashcroft & Mermin" /><ref name=":7" group="Ashcroft & Mermin" /> However this models fails to predict the sign change<ref name=":4" group="Ashcroft & Mermin" /> of the thermopower in [[lithium]] and noble metals like gold and silver.<ref>{{Cite journal |last=Xu |first=Bin |last2=Verstraete |first2=Matthieu J. |date=2014-05-14 |title=First Principles Explanation of the Positive Seebeck Coefficient of Lithium |url=https://link.aps.org/doi/10.1103/PhysRevLett.112.196603 |journal=Physical Review Letters |volume=112 |issue=19 |pages=196603 |doi=10.1103/PhysRevLett.112.196603|arxiv=1311.6805 }}</ref>
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