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Wed Jul 6 14:13:09 CEST 2005

TS=U-P*V-mu*N
where, as you see no differential is used (as opposed to the first and second laws). The fundamental equation of thermodynamics with respect to Gibbs free energy, G=U-TS-PV, can be rewritten as follows:
G=mu*N. 

Thus for monatomic system (here we also have one type of particle that is electron) always we can say that mu=G/N (for sure see B.5 formula, Appendix B, page 759, Solid state physics, by N. W. Ashcroft, N. D. Mermin), and it can be reduced to U/N for the case of T=0 and P=0.

> can this defination be treated as mu=U/N?so do in the WIEN2K?
I hope so.

> Does this mean that the chemical potential alway be negative? so does the Fermi energy?
The sign of the chemical potential (Fermi energy at T=0 K) depends on the Energy reference: as in wien2k sometimes the Fermi energy is set to zero eV.

Your,
S. Jalali.

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<DIV>thanks for your patient explanation!</DIV>
<DIV>best regards</DIV>
<DIV>L.Z.Sun</DIV>
<DIV>
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<DIV>
<DIV>&gt; and i remember the defination of the chemical potential is :</DIV>
<DIV>&gt; mu=d(G)/d(N)</DIV></DIV>
<DIV>&nbsp;</DIV>
<DIV>From the first and second laws of thermodynamics, and the fact that entropy 
is an state variable, i.e. exact differential, one can drive the fundamental 
equation of thermodynamics, i.e. Euler's equation, which for&nbsp;monatomic 
systems reads:</DIV>
<DIV>TS=U-P*V-mu*N</DIV>
<DIV>where, as you see no differential is used (as&nbsp;opposed to the first and 
second laws). The fundamental equation of thermodynamics with respect to Gibbs 
free energy, G=U-TS-PV, can be rewritten as follows:</DIV>
<DIV>G=mu*N. </DIV>
<DIV>&nbsp;</DIV>
<DIV>Thus for monatomic system (here we also have one type of particle that is 
electron) always we can say that mu=G/N (for sure see B.5 formula, Appendix B, 
page 759, Solid state physics, by N. W. Ashcroft, N. D. Mermin), and it can be 
reduced to U/N for the case of T=0 and P=0.</DIV>
<DIV>&nbsp;</DIV>
<DIV>
<DIV>&gt; can this defination be treated as mu=U/N?so do in the WIEN2K?</DIV>
<DIV>I hope so.</DIV>
<DIV>&nbsp;</DIV></DIV>
<DIV>
<DIV>&gt; Does this mean that the chemical potential alway be negative? so does 
the Fermi energy?</DIV></DIV>
<DIV>The sign of the chemical potential&nbsp;(Fermi energy at T=0 K) depends on 
the Energy reference: as&nbsp;in wien2k sometimes the Fermi energy is set to 
zero eV.</DIV>
<DIV>&nbsp;</DIV>
<DIV>Your,</DIV>
<DIV>S. Jalali.</DIV></FONT></DIV>
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