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An ab initio density functional theory case study of a Cr/CrC_x/diamond adhesive layer system as it occurs in diamond-coated steel has been performed. We present bulk properties of chromium, chromium carbides of different stochiometries, and diamond. Certain phases were selected to model Cr/CrC_x and CrC_x/diamond interfaces. These are characterized by their work of separation, taking into account the influence of superimposed stresses and strains. The results show a systematic dependency of the characteristic quantities on the C concentration in the carbide.