High resolution neutron powder diffraction experiments on NaDS and KDS were carried out as a function of temperature between T=4 K and T=470 K at ROTAX (ISIS, UK). The probability density function (pdf) of the atoms was studied in detail, in particular that of deuterium. Several forms of temperature dependent reorientational disorder of the anions are the reason for structural polymorphism of these compounds. A monoclinic low (LTM), a rhombohedral middle (MTM), and a cubic high temperature (HTM) modification are the polymorphs. For the structures of the different modifications the parameters were refined by the use of split-atom models, Fourier synthesis, and/or cubic harmonics. As a main result of this study the anisotropy of the pdf of deuterium in NaDS and KDS was evaluated. It is due to large amplitudes of librations of the anions.