There are two types of solids, crystalline and amorphous. In crystalline solids (salts, ice, napthalene etc) the structure is very regular. In amorphous solids (glass, many rocks etc) the structure is higglety-pigglety. A crystalline solid will have a sharp melting point as the key bonds that break are all the same. The amorphous material has many different strengths of bonds which break at different temperatures so they dont have a sharp transition.
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