| MadSci Network: Physics |
Hello Jonny,
Interesting assignment you have there. As you know, superconductors are perfect conductors of electricity. Kamerlingh Onnes discovered this phenomenon in 1911, in common metals such as tin and lead. When these metals are cooled to a very low temperature, typically a few Kelvin above absolute zero, their resistance suddenly drops to zero. Not to a very low value, but to absolute 100% zero. These are so-called Type I superconductors. Zero resistance is a very neat property of a material, as it allows the transfer of current without any voltage loss, over any distance.
Superconductors have another very peculiar property, which is known as the Meissner Effect, after Walter Meissner, who discovered it. Basically, any magnetic field is forced out of a superconductor: no magnetic field can exist in one (Actually, there is slight penetration, which is typically a few tens of nanometers. This is called the London penetration depth.) However, subjecting a superconductor to a magnetic field does reduce its transition temperature. In fact, if the magnetic field is high enough, no more superconductivity is possible at any positive temperature. Because putting currents through the superconductor generates a magnetic field, this limits the total current that can be carried.
In 1930, De Haas and Voogd discovered that an alloy of bismuth and lead also superconducts. It was later discovered by L.V. Shubnikov that this compound had markedly different superconducting properties. It is therefore known as a Type II superconductor.
In a type II superconductor, there are two superconductucting states. The lower state basically acts like a type I superconductor. The higher state appears for higher magnetic fields. In this case, the superconductive phase of the material gets confined to small flux tubes, in a non-superconductive matrix. This allows for much higher currents to be carried, and is known as the mixed mode.
Now, having skimmed the theory, let's take a look at the question again. The intercept of the graph with the y-axis basically gives the highest magnetic field that can exist in the material, while it is in the superconducting state-in other words, the second critical field. When you subject the superconductor to an external magnetic field that is 0, as you do at to the x-axis, then you are in the lower state, i.e. type I superconductive behavior. The position of intercept now gives the critical electric current, which is the current at which the current-generated magnetic field destroys the superconductivity. By extrapolating this to the y-axis along the slope of the line, which is determined by the linear relation between the current-generated magnetic field and the current you can find the critical magnetic field for the first phase transition.
I hope this helps, if not, I advise you to check the references, I found them quite helpful.
Regards, and good luck with the assignment,
Bart Broks
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