- Existence of dilute copper–carbon solid solutions is one of the characteristic features of the interfaces of the metal matrix composites widely used in the electrical applications. Experimental high-resolution SEM study allows to visualize the formation of the interaction zone on carbon fibre. We model interstitial solid solutions formed in this interaction zone non-empirically within the embedded-cluster and supercell approaches. Atomistic approach allows selection of the geometry of the solid solution. Electronic structure studies show that the most favourable position of the carbon atom is shifted along the  direction from the centre of the octahedral position. Investigation of this physical phenomenon allows us to understand the nature of the chemical bonding in copper-based solid solutions with carbon.