Cite the differences between type I and type II superconductors.

Superconductors are materials that can conduct electric current with zero electrical resistance below a certain critical temperature (Tc). There are two different types of superconductors: type I and type II.

Type I superconductors are also known as "low temperature" or "soft" superconductors. They follow Meissner effect, and thus, below their critical temperature (Tc), the magnetic field gets expelled out of the material. There is an exact critical magnetic field (Hc) that this type of superconductors obey. When the applied magnetic field is less than Hc, the superconductor behaves perfectly, but when the applied magnetic field exceeds Hc, the material loses its superconducting properties and becomes a normal conductor. Examples: elemental superconductors such as Aluminium (Al), Mercury (Hg), and Lead (Pb).

Type II superconductors are also referred to as "high temperature" or "hard" superconductors. These materials exhibit a mixed state called vortex state, in which the magnetic field partially penetrates the superconductor. Type II superconductors have two critical magnetic fields, Hc1 and Hc2. When the applied magnetic field is less than Hc1, the superconductor is in its Meissner state like Type I, with no magnetic field penetration. When the applied magnetic field is between Hc1 and Hc2, the superconductor enters the vortex state, and the magnetic field partially penetrates as quantized magnetic flux lines called vortices. When the applied magnetic field exceeds Hc2, the material loses its superconducting state and becomes a normal conductor. Examples: Some compound materials like Yttrium Barium Copper Oxide (YBCO) and Niobium-Tin (Nb3Sn).

The penetration depth for type I superconductors is smaller than for type II superconductors. Because of the Meissner effect, type I superconductors expel the magnetic field completely, while type II superconductors allow the magnetic field to partially penetrate the material.

Type I superconductors are used in applications such as sensitive magnetic field sensors, shielding, and low current devices due to their low critical magnetic field. Type II superconductors, on the other hand, have higher critical magnetic fields, making them suitable for applications involving larger currents and higher magnetic fields, such as magnets in particle accelerators and nuclear magnetic resonance (NMR) spectrometers, as well as in MRI machines and high-speed levitating trains (maglev). In conclusion, the main differences between type I and type II superconductors lie in their critical magnetic fields, magnetic field penetration depth, and applications. Type I superconductors have lower critical magnetic fields and follow the Meissner effect, while type II superconductors have higher critical magnetic fields and can be in a vortex state.