Disclosed are non-noble element compositions of matter, structures, and methods for producing the catalysts that can catalyze oxygen reduction reactions (ORR). The disclosed composition of matter can be comprised of graphitic carbon doped with nitrogen and associated with one or two kinds of transition metals. The disclosed structure is a three dimensional, porous structure comprised of a plurality of the disclosed compositions of matter. The disclosed structure can be fashioned into an electrode of an electrochemical cell to serve as a diffusion layer and also to catalyze an ORR. Two methods are disclosed for producing the disclosed composition of matter and structure. The first method is comprised of two steps, and the second method is comprised of a single step.