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The first diodes used their filament as the cathode (Flaming Valve), they were quickly replaced by indirect heated diodes. The heater and rectifier circuits are in this manner separated.
The diodes allow to rectify (= convert to a direct current) a current because they let it flow in only one way. They are used in power supplies to convert the alternative current to a direct one that could be used by the apparatus.
The manufacturers often insert two identical diodes in one tube that lets you have a full-wave (both the sides of the sine wave are used) rectification much more effective than a half-wave one.
Some diodes use rare gases or mercury vapors instead of
They have usually a lower internal resistance and thus a more constant output voltage against the current variations in the tube.
The power supply chapter gives you more details.