The sensitivity of the method of neutron scattering to novel neutron–nucleon interactions is analyzed. Upper limits on the coupling constant of such interactions are imposed using the available data on neutron powder diffraction on polycrystalline silicon. For the forces acting at ranges of λ < 10^–11 m, these upper limits are already competitive with the best existing constraints on their coupling constant. A dedicated experiment can help improve the sensitivity to this coupling constant by nearly two orders of magnitude.