The Meissner Effect is a label for the active expulsion of an applied magnetic field from the core of a superconducting material. Originally, this was considered to be a repercussion of the infinite conductivity of the material, but it is currently believed that shielding currents created in the incredibly thin (~ one tenth of a micrometer) outer surface of the material expel the magnetic field in the wake of the superconducting transition in a manner that is separate from the change in the conductive properties of the metal.
The effect may be complete, or only partial, depending on the nature of the material in question; materials that demonstrate full expulsions are referred to as Type I superconductors, while materials where the effect is only partial are labeled as Type II superconductors.
One consequence of the Meissner effect is the loss of superconductivity in the presence of a sufficiently large magnetic field (Bc). While the free energy of a non-superconducting material (FN) will remain constant in the presence of a magnetic field, a Type I superconductor must perform work on the field in order to maintain a zero field inside the material. The work (Wmag) performed by the material must equal the energy contained in the field, and result in a change in the total free energy of the superconductor (FS); over a given volume V, and at an absolute temperature T, this difference in the free energy for a superconducting versus non-superconducting material can be expressed
Wmag/V = (FN (T) - FS (T)) / V= B2/2μ 0
where μ 0 is the permeability of free space (1/4π). Thus, for any given temperature below the critical temperature (Tc) one can calculate a critical field Bc that will exactly bridge the difference in energies between the two states, resulting in a phase transition back to the normal state. Typically, experimentation and a minor amount of simplification of this basic model have confirmed a parabolic relationship between Hc and Tc for a variety of Type I superconductors.
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