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Metallic structures have a lattice of positive metal ions surrounded by delocalised electrons.
All metals are good conductors, because the delocalised electrons can move through the structure. The freedom of the electron movement is limited by their collisions with the positive ions in the metallic lattice – this effect gives rise to the resistance of the metal.
As the temperature is lowered, the ions in the structure vibrate less and, in effect, take up less room. This allows the electrons to pass with fewer collisions with the positive ions and the electrical resistance of a metal decreases, (and the conductivity increases) until eventually it disappears completely below a certain temperature. The temperature at which electrical resistance disappears completely is called the critical temperature. When it reaches the critical temperature the metal is called a superconductor.
In superconductors an electrical current can continue even without a power source.
Some alloys and ceramics show the same effect and often at much higher temperatures which makes them useful in the operation of powerful electromagnets.