To create the windings of the magnetic system of the Future Circular Collider, it is necessary to modernize the Nb 3 Sn-based composite superconductors obtained by the method of internal tin sources, which also involves an increase in the thermal conductivity and electrical conductivity of the matrix copper as determined using the residual resistance ratio (RRR) parameter (the ratio of the values of the electrical resistivity of copper at 273 and 20 K). The achievement of high RRR values is controlled by the balance between the geometric dimensions, the volume fractions of the superconductor components, and the mode of reaction heat treatment (RHT) used for the formation of the Nb 3 Sn phase. The results of an experimental and theoretical study of the effect of the strand diameter and the RHT mode on the RRR parameter are given. The diffusion of tin from the zone of subelements into the stabilizing copper in the course of RHT in strands of various diameters has been investigated by scanning electron microscopy and electron probe microanalysis. The study was carried out on experimental samples of multifilamentary superconductors based on Nb 3 Sn with a distributed Nb barrier.