KNd(MoO₄)₂:  A New Incommensurate Modulated Structure in the Scheelite Family

Abstract

Potassium neodymium molybdenum oxide, KNd(MoO 4 ) 2 , has been synthesized by the solid-state method. The structure and microstructure have been studied by X-ray powder diffraction and transmission electron microscopy (TEM). TEM revealed that the KNd(MoO 4 ) 2 structure is incommensurately modulated. The scheelite-like structure of KNd(MoO 4 ) 2 has been refined from X-ray powder diffraction intensities in the (3 + 1)D superspace group I2/b(R 0)00 with a ) 5.5202(2) Å, b ) 5.33376(5) Å, c ) 11.8977(3) Å, γ ) 90.9591(7)°, and modulation vector q ) 0.57789(4)a* -0.14748(6)b* (R P ) 3.09%, R wP ) 4.04%). The ordering of the K and Nd cations appears to be the primary parameter of the structure modulations. The compositional wave of the {KMoO 4 } and {NdMoO 4 } distribution is observed in the ab structure projection. The incommensurability of the compositional wave direction with respect to the a and b lattice constants is regarded as the origin of the incommensurate structure modulations.

Effect of cation vacancies on the crystal structure and luminescent properties of Ca 0.85−1.5x Gd x Eu 0.1 □ 0.05+0.5x WO 4 (0 ≤ x ≤ 0.567) scheelite-based red phosphors

“…1). These reflections are attributed to cation-vacancy ordering and the formation of modulated structures [20,22,26,[28][29][30]. …”

“…Typically, occupational modulations in scheelite-based structures are confined to the ab planes, so that the ED taken along the [001] zone axis are the most informative [20,22,26,[28][29][30]. …”

“…However, in stoichiometric scheelites (a = b in the formula), ordering between the A'/A'' cations is rare. Typically, it is realized when the ionic radius of A' is about 0.35 Å larger than that of A'', provided that the A' cation has a formal charge larger than that of A'' [18][19][20][21][22][23][24]. On the other hand, scheelite-based materials can accommodate a large amount of vacancies in the A sublattice (compounds with a < b) [25][26][27][28][29] In these structures, A'/A'' cation ordering is more common, because it is also coupled to the ordering between cations and vacancies; and can occur for the A'/A'' ionic radii differences as low as ∼ 0.1 Å.…”

Validating the model of a (3 + 1)-dimensional incommensurately modulated structure as generator of a family of compounds for the Eu2(MoO4)3scheelite structure

“…Similar to Eu 2 (WO 4 ) 3 , this structure is characterised by the modulation vector q ¼ (2/3)a* þ (2/3)b*, t 0 ¼ 0 and the crenel occupation function for A ¼ Eu atomic domain with the length Á Eu ¼ 2/3 along the internal space coordinate x 4 and the domain centre x 4 ¼ 0.5 [7]. The incommensurately modulated structure KNd(MoO 4 ) 2 [9] has been used as a starting model.…”

“…Eight known types of ordered distributions have already been described as three-dimensional (3D) periodic compounds [7]. Two incommensurately modulated structures, KNd(MoO 4 ) 2 and KSm(MoO 4 ) 2 , also belong to this family [7][8][9].…”