Neutron diffraction offers one of the most interesting and meaningful methods for non destructive quantitative determination of the phase composition of materials. However, it is well known that there is a detectability limit, which is commonly assumed to be between 0.1 and 1% for each phase present in the studied sample. A quantitative measurement of this limit, for selected samples of peculiar interest, depends on the particular instrument and the data acquisition technique. In this proposal, we address this problem, with the INES diffractometer, having in mind a class of standard experiments carried out on archaeometric interest materials.