Depending on how you slice the pie, there are either many kinds of superconductors or only two. From the perspective of how they behave in magnetic fields, however, scientists commonly classify them into two groups.
A Type I superconductor is usually made of a pure metal. When cooled below its critical temperature, such a material exhibits zero electrical resistivity and displays perfect diamagnetism, meaning magnetic fields cannot penetrate it while it is in the superconducting state.
Type II superconductors are usually alloys, and their diamagnetism is more complex. To understand why, we need to look at how superconductors respond to magnetism.
Just as every superconductor has a critical temperature that makes or breaks its superconducting state, each is also subject to a critical magnetic field. A Type I superconductor enters and leaves the superconducting state at one such threshold, but a Type II material changes states twice, at two different magnetic field thresholds.
The distinction between Type I and Type II materials resembles the difference between dry ice (solid carbon dioxide) and water ice. Both solids cool well, but they handle heat differently: Water ice melts into a mixed state, ice water, whereas dry ice sublimates: At normal pressure, it transitions directly from solid to gas.
With respect to magnetism, a Type I superconductor is like dry ice: When exposed to its critical field, its superconductivity burns off instantly. A Type II is more versatile.
While within a weak field, a Type II material exhibits behavior similar to a Type I, just as H2O and CO2 both cool effectively while in their solid states. Raise the magnetic field above a certain threshold, however, and the material reorganizes into a mixed state -- a vortex state in which small whirlpools of superconducting current flow around islands of normal material. Like ice water, it still does its job pretty well. If the magnetic field strength rises, however, the islands of normalcy grow together, thus destroying the surrounding whirlpools of superconductivity.
What does this mixed state mean for magnetism? We've discussed what happens when a superconductor gets warm. Now, let's look at it from the other direction.
In their normal, warm states, both Type I and Type II materials allow magnetic fields to flow through them, but as they cool toward their critical temperatures, they increasingly expel these fields; electrons in the material set up eddy currents that produce a counter-field, a phenomenon known as the Meissner effect.
When they reach their critical temperature, Type I superconductors evict any remaining magnetic field like so many deadbeat roommates. Depending on the strength of the magnetic field in which they exist, Type II fields might do the same -- or they might get a little clingy. If they're in a vortex state, the magnetic field that still flows through the islands of normal material in their superconducting streams can become stuck, a phenomenon known as flux pinning (see sidebar) Magnetic flux is a measure of the amount of magnetic field passing through a given surface.
Because they can remain superconductors in this stronger magnetic field, Type II materials like niobium-titanium (NbTi) make good candidates for the type of superconducting magnets found in, say, Fermilab's proton accelerator or in MRI machines.