It is well-known that Kirkendall shift occurs in binary systems. We investigated diffusion on the nanometer scale in the framework of our conceptual model [Erdelyi and Schmitz, Acta. Mater. 60 (2012) 1807]. Since on this lengthscale the characteristic distances between the vacancy sources/sinks can be comparable to the dimensions of the sample, the usual vacancy annihilation processes, leading to the Kirkendall shift, cannot operate. In this situation, we studied the Kirkendall shift in planar geometry in case of miscible and restrictedly miscible systems by computer simulation. (C) 2015 Elsevier B.V. All rights reserved.