The lattice structure of several RxR'1-xNi2B2C (R = Y, La or rare earth) samples has been studied by X-ray diffraction measurements. All samples exhibit at least one LuNi2B2C-type structure, where the lattice parameters of samples with only one tetragonal structure show a linear dependence on x. For certain sample compositions miscibility gaps were obtained, yielding two tetragonal structures of the LuNi2B2C-type. The relative difference in the size of the ionic radii delta (r) of the R elements accounts for the miscibility gap. The width of that gap is a linear function of delta (r). This results in a critical value delta (r) (crit) congruent to 9% where miscibility gaps occur.