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Most applications of graphene need a suitable support substrate to present its excellent properties. But transferring graphene onto insulators or growing graphene on foreign substrates could cause properties diminishing. This paper reports the graphene growth directly out of diamond (111) by B doping, guided by first-principles calculations. The spontaneous graphene formation occurred due to the reconstruction of the diamond surface when the B doping density and profile are adequate. The resulting materials are defect free with high phase purity/carrier mobility, controllable layer number, and good uniformity, which can be potentially used directly for device fabrication, e.g., high-performance devices requiring good thermal conductivity. [ABSTRACT FROM AUTHOR]