In the framework of a unified approach the diffusion coefficient (the prefactor and activation barrier) of an interstitial oxygen Oi, the hydrogen molecule H2, vacancy, oxygen dimer in silicon crystals and Oiin Si1-xGexsolid solutions, silicon nanotubes and nanowires has been calculated. For all the above cases, the calculated values of the diffusion coefficient are in good agreement with the experimental data. The calculated equilibrium structures, electrical activity, the vibrational spectrum, the mechanism of diffusion of oxygen dimer fully describe the experimental results. Our study has revealed that the diffusivity of impurities (defects) in alloys can decrease considerably and this variation results from the fact that the prefactor depends on the concentration of component elements of the alloy.