Gibbs Free Energy in Superconductors

In summary, when discussing Ginzburg-Landau theory of superconductors, it is important to note that the appropriate thermodynamic potential is the Gibbs free energy ##G## with natural variable ##H##, rather than the Helmholtz free energy ##F## with natural variable ##B##. This means that in superconductors, the Gibbs free energy is minimal at constant temperature and magnetic field strength, rather than constant temperature and magnetic flux density. This topic is extensively discussed in Landau and Lifshitz's textbook on magnetism. However, the choice between using B or H as the preferred variables depends on the specific measurement and separation of system and surroundings.
  • #1
taishizhiqiu
63
4
When reading some material concerning Ginzburg-Landau theory of superconductors, I got the following sentence:

The appropriate thermodynamic potential for describing a superconductor in an applied magnetic field is the Gibbs free energy ##G## (natural variable ##H##) and not the Helmholtz free energy ##F## (natural variable ##B##).

I don't understand the sentence. In gas, Gibbs free energy is minimal in constant temperature and pressure. Does this sentence mean that in superconductors Gibbs free energy is minimal in constant ##T## and ##H##? I can't make sense out of it.
 
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  • #2
L&L discuss quite extensively their peferred thermodynamic variables in the case of magnetic fields in previous chapters.
 
  • #3
DrDu said:
L&L discuss quite extensively their peferred thermodynamic variables in the case of magnetic fields in previous chapters.
You mean Landau and Lifshitz‘s textbook?
 
  • #4
Sorry, yes, I had erroneously in mind that you had mentioned Landau & Lifshitz. The relevant pair of variables in case of magnetism is not p and V but B and H and you can analogously define energies and enthalpies with different natural variables.
I think that thermodynamics in the presence of fields is quite a non-trivial matter. Much of the distiction whether B or H are to be preferred depend on the measurement you have in mind and on the chosen separation into system and surrounding, especially, which part of the field belongs where.
 

1. What is Gibbs Free Energy in superconductors?

Gibbs Free Energy is a thermodynamic quantity that measures the amount of energy available to do work in a system. In superconductors, it represents the energy required to produce a pair of electrons and break Cooper pairs, which are responsible for the phenomenon of superconductivity.

2. How does Gibbs Free Energy relate to the superconducting transition?

In superconductors, Gibbs Free Energy is used to determine the critical temperature at which a material undergoes a phase transition from a normal to a superconducting state. At this critical temperature, the Gibbs Free Energy of the superconducting state is lower than that of the normal state, making the superconducting state more energetically favorable.

3. Can Gibbs Free Energy be used to predict the behavior of superconductors at different temperatures?

Yes, Gibbs Free Energy can be used to predict the stability of the superconducting state at different temperatures. If the Gibbs Free Energy of the superconducting state is lower than that of the normal state, the material will remain in the superconducting state at that temperature. However, if the Gibbs Free Energy of the normal state is lower, the material will undergo a phase transition to the normal state.

4. How does magnetic field affect Gibbs Free Energy in superconductors?

Magnetic fields can disrupt the superconducting state by causing vortices to form, which can increase the Gibbs Free Energy of the system. This can lead to a decrease in the critical temperature and can ultimately cause the material to lose its superconducting properties.

5. Can Gibbs Free Energy be used to determine the type of superconductivity in a material?

Yes, Gibbs Free Energy can be used to distinguish between different types of superconductivity, such as conventional and unconventional. The Gibbs Free Energy for conventional superconductors is typically lower than that of unconventional superconductors, which have more complex energy landscapes. This can provide insights into the mechanism of superconductivity in a material.

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