A crystallized layer can be formed on a substrate from a precursor layer deposited on a surface of the substrate. The precursor layer can be an oxide, a nitride, a carbide, or an oxynitride. The process for forming the crystallized layer includes melting the precursor layer formed on the surface of the substrate by localized topical heating of the precursor layer and then cooling the melted precursor layer so that it crystallized to form a scratch resistant crystallized layer. The scratch resistant crystallized layer can have a hardness of 15 GPa or greater.