- Interstitial solid solutions could be formed at the matrix–fibre interface in the processing of metal matrix composites. Typically these solutions are of small concentrations and the solubility is usually diffusion-controled. To calculate the diffusivity, a model of the interstitial solid solution is used which gives the possibility of choosing whether octahedral or tetrahedral interstitial positions are occupied by the fibre atoms dissolved in the matrix. Analysis of Ag–C and Cu–C solid solutions allow a comparison of the occupation of the interstitial positions and its temperature dependences. The results obtained on the basis of non-empirical calculations predict the preferable occupation of octahedral positions up to T ~ 1200 K. This confirms the structure of the interstitial solid solution. In the framework of this model we calculate the heights of diffusion barriers and the temperature dependences of carbon diffusion in silver and copper hosts.