NOVELTY - The method comprises applying a metal layer to a crystallographic face of a diamond substrate (12), heating the diamond substrate to a temperature of 600-1400 degrees C under vacuum of 10-4 to 10-6 torr to convert a portion of the diamond substrate at a (100) crystallographic face into graphene by martensitic transformation, removing the graphene from the diamond substrate, heating the diamond substrate to a temperature of greater than or equal to 700 degrees C in a hydrogen atmosphere to gasify non-epitaxial carbon atoms, and epitaxially depositing a semiconductor material (16) on the graphene.    USE - The method is useful for making graphene on a nanodiamond substrate, which is useful in a diamond-graphene device such as molecule sensors, LEDs, LCDs, solar panels, pressure sensors, surface acoustic wave filters and/or resonators (all claimed), where the graphene is a one-atom-thick planar sheet of sp2 bonded carbon atoms.    ADVANTAGE - The method is capable of efficiently making graphene on the diamond substrate with high quality, excellent electron mobility and improved thermal and electrical conductivity.    DETAILED DESCRIPTION - The method comprises applying a metal layer to a crystallographic face of a diamond substrate (12), heating the diamond substrate to a temperature of 600-1400 degrees C under vacuum of 10-4 to 10-6 torr to convert a portion of the diamond substrate at a (100) crystallographic face into graphene by martensitic transformation, removing the graphene from the diamond substrate, heating the diamond substrate to a temperature of greater than or equal to 700 degrees C in a hydrogen atmosphere to gasify non-epitaxial carbon atoms, and epitaxially depositing a semiconductor material (16) on the graphene. The metal layer is applied only on single (111) crystallographic face of the diamond substrate having a same crystallographic orientation. An epitaxial relationship is maintained between the diamond substrate and the graphene. An INDEPENDENT CLAIM is included for a diamond-graphene device.    DESCRIPTION OF DRAWING(S) - The diagram shows a schematic cross-sectional view of a graphene on diamond device.    Diamond substrate (12)    Graphene material (14)    Semi-conductor material. (16)