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Corrosion is a natural process that seeks to reduce the binding energy in metals. The end result of corrosion involves a metal atom M being oxidized, whereby it loses one or more electrons and leaves the bulk metal,
M  M m+ + m e -
The lost electrons are conducted through the bulk metal to another site where they reduce (i.e. combine with) a non-metallic element N or another metallic ion G+ that is in contact with the bulk metal,
N + n e -  N n-
G m+ + m e -  G
In corrosion parlance, the site where metal atoms lose electrons is called the anode, and the site where electrons are transfered to the reducing species is called the cathode. These sites can be located close to each other on the metal's surface, or far apart depending on the circumstances.
Anode/cathode pairs, known as corrosion cells, come in a variety of forms including composition cells (also known as Galvanic Cells), stress cells, and concentration cells.
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