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If a negative ion meets a positive one, their opposite charges attract strongly and glue the atoms together.
This type of gluing is called an ionic bond.
Ionic bonds were first formed as atoms emerged from a supernova, and caused cosmic dust grains to form. They are important in holding the atoms together in many rocks on the Earth today.

An ionic bond is sometimes called an electrovalent bond. It can form when two atoms meet and an electron is permanently transferred from one to the other, because of the way their electron shells are formed. Thus when a sodium atom meets a chlorine atom, the solitary electron in the outer shell of the sodium atom moves over into the outer shell of the chlorine, which only needs that one extra electron to give itself a hard outer shell. These two ionized atoms then stick very tightly together to make sodium chloride -- also known as table salt.

Compare this with the other major type of bond which holds atoms together -- the covalent bond.

 

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