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I know when two metals are in contact, the Fermi level must line up, somewhere between the two original metals for thermodynamic equilibrium.

When this happens, I wonder how much does the Fermi level change.

For example, what would the Fermi level be if 1 mole of copper and 1 mole of lithium are in contact at $T = 0\ {\rm K}$ (or finite $T$) ?

I'm guessing if the same quantity of two different metals are in contact, the Fermi level would exactly be in the center of the two metals, which is $$\frac{ 7(\rm copper) + 4.74(\rm lithium) } { 2} = 5.87\ {\rm eV},$$ but I'm not sure. Is this right?

The reason why I'm asking this question is related to voltage measurement with a voltmeter.

For example, for voltage measurement of a battery, if material of one probe wire is different from the other, would the measured voltage be different compared to the voltage measured when both probe wires are the same material? (in perspective of fundamental)

I would like to know universal method for calculation of Fermi level change when metal-metal junction happens.

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    $\begingroup$ Does this answer your question? Fermi level alignment and electrochemical potential between two metals $\endgroup$
    – Rococo
    Commented Jul 31, 2020 at 17:50
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    $\begingroup$ @Rococo, I read the post before I posted this question. And that is somewhat related to my question, but doesn’t give clear answer for this. I understand when two different metals are in contact, they change their Fermi level into single value for thermodynamic equilibrium. What I wonder is, like I posted, how much does their Fermi level change when different metals are in contact. If some tiny piece of metal is in contact to other bulky metal, this combined metal may show no difference with pristine bulky one. But what about other situation like I posted? I don’t know... $\endgroup$ Commented Aug 2, 2020 at 12:05

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