A cylinder of natural lithium carbonate, supported on a slab of graphite, was irradiated from above by a low-intensity source of 14-MeV neutrons and the tritium produced within it subsequently determined from measurements of beta activity. Results obtained for small lithium carbonate detectors highly enriched in 6Li (96%) or 7Li (99.9%) at six positions along the cylinder axis were compared with predictions based on three-dimensional Monte Carlo calculations and multi-group cross-section data. The experimental accuracy was sufficient to detect deviations from theory > 7% with a 95% level of confidence. On this basis, good agreement with theoretical predictions was obtained for the 7Li results. For the 6Li data, however, significant differences were observed in the lower half of the assembly. A detailed analysis indicated that these deviations could not be explained in terms of conceivable environmental perturbations of the neutron flux and may arise as a consequence of inadequate representation of anisotropic neutron scattering.