Incommensurately modulated structures of the <i>M</i> _1/8 Pr _5/8 MoO ₄ ( <i>M</i> = Li, Na, K) scheelites

The effect of cation substitutions in the scheelite-type framework is investigated to understand the ordering of M⁺/Pr³⁺ cations and vacancies in the structure. The cation deficient M_1/8Pr_5/8□_1/4MoO₄ (M = Li, Na, K) phases were synthesized using solid state reactions. The K:Pr ratio in the K_1/8Pr_5/8MoO₄ sample was determined by inductively coupled plasma mass spectroscopy, inductively coupled plasma optical emission spectrometry and total reflection X-ray fluorescence spectroscopy. The local element distributions in K_1/8Pr_5/8□_1/4MoO₄ were determined by energy-dispersive X-ray spectrometry. The incommensurately modulated crystal structures of the scheelite-based M_1/8Pr_5/8MoO₄ (M = Li, Na, K) phases were refined from synchrotron powder X-ray diffraction data. The analysis revealed that cation ordering in the M_1/8Pr_5/8MoO₄ (M = Li, Na) structures is incomplete and is more accurately described by continuous, rather than discontinuous (step-like), occupational modulation functions. The occupancy modulation waves for Li/Na and Pr atoms demonstrate an antiphase relation. Compared with M = Li, Na, the order of K and Pr cations in the A position in the K_1/8Pr_5/8MoO₄ structure is best approximated by crenel functions. Refining the coordinates and lengths of three atomic domains yields the composition of K_0.145Pr_0.618MoO₄. In all cases, the modulation arises from ordering of M/Pr cations and cation vacancies at the A-sublattice of the parent scheelite ABO₄ structure. The distortion of PrO₈ and MO₈ polyhedra is practically independent of the radius of the M⁺ cations. The refinements of the M_1/8Pr_5/8MoO₄ (M = Li, Na, K) structures reveal that MoO₄^2- tetrahedra in these scheelite-type compounds demonstrate a flexible geometry. Both Mo-O bond distances and O-Mo-O bond angles vary significantly with changing the population of the A site by cations with different sizes.