Graphene layers made of primarily sp2 bonded atoms and associated methods are disclosed. In one aspect, for example, a method of forming a graphite film can include heating a solid substrate under vacuum to a solubilizing temperature that is less than a melting point of the solid substrate, solubilizing carbon atoms from a graphite source into the heated solid substrate, and cooling the heated solid substrate at a rate sufficient to form a graphite film from the solubilized carbon atoms on at least one surface of the solid substrate. The graphite film is formed to be substantially free of lattice defects.