Compositely modulated structures of phosphor materials Sr x Li2+x Al2–x O4:Eu2+

Composite crystals Sr x Li2+ x Al2−x O4:Eu2+ were synthesized and their structures were determined using single-crystal X-ray diffraction. The commensurate structure with a modulation wavevector q = 5c*/6 was analyzed in a conventional manner in 3D space, while a structure model in (3+1)-dimensional superspace was used for the other two crystals with modulation wavevectors slightly differing from 5c*/6. The superstructure of the commensurate phase was described using the space group P4/n and a common superspace group I4/m(00γ)00 was used for the (3+1)D structures of all three crystals. The whole structure of each crystal consists of two substructures. Basis vectors a and b are common, but c is different for the two substructures. The first substructure is a host framework constructed by (Li/Al)O4 tetrahedra sharing edges. A linear connection of cavities is seen to be channel-like, in which Sr ions locate as guest cations forming the second substructure. The crystal of q = 5c*/6 contains five Sr ions per six cavities in a channel. Sr ions are distributed at seven sites, some of which are partially occupied. Statistical disorder of local structure models for the location of Sr ions in the channel was assumed to explain the results. Such a partially disordered character was also seen in the incommensurate phases and properly embodied by a (3+1)D model containing an atomic domain of the Sr ion with occupational modulation. Plots of the occupation factor, interatomic distances and the bond valence sum at each metal site as functions of t (= x 4 − q·r) are roughly identical in the three crystals, which are considered as members of the same series of composite crystals.

Impact of the Flexoelectric Coupling and Electrostriction on the Dispersion of Soft Phonon Modes and Neutron Scattering in Ferroelectrics

Within the Landau–Ginzburg–Devonshire (LGD) theory framework, the impact of the flexocoupling and electrostriction on the soft phonon dispersion and neutron scattering spectra is analyzed, and analytical expressions are derived. The impact of the higher gradient term in the LGD functional is studied analytically. The existence of incommensurate modulations in a temperature interval higher than the Curie temperature TC, but lower than the temperature of incommensurate phase transition TIC, TC < T < TIC, and under the condition of the flexocoefficient magnitude ranging over the critical value, |f| > fcr(T), is established. The influence of the dynamic flexocoefficient M, suggested in [1], on phonon spectra is studied. We consider various parameters of the free energy functional; especially, we have discovered a significant contribution of the electrostriction to the appearance of a commensurate phase. In the recent years, the various methods based on the neutron scattering acquire more applications to study phonons in solid crystals. We have analyzed neutron scattering spectra and shown that theoretical predictions are in a very good agreement with observed data.

Low-temperature behaviour of K2Sc[Si2O6]F: determination of the lock-in phase and its relationships with fresnoite- and melilite-type compounds

K2Sc[Si2O6]F exhibits, at room temperature, a (3 + 2)-dimensional incommensurately modulated structure [a= 8.9878 (1),c= 8.2694 (2) Å,V= 668.01 (2) Å3; superspace groupP42/mnm(α,α,0)000s(−α,α,0)0000] with modulation wavevectorsq1= 0.2982 (4)(a* +b*) andq2= 0.2982 (4)(−a* +b*). Its low-temperature behaviour has been studied by single-crystal X-ray diffraction. Down to 45 K, the irrational component α of the modulation wavevectors is quite constant varying from 0.2982 (4) (RT), through 0.2955 (8) (120 K), 0.297 (1) (90 K), 0.298 (1) (75 K), to 0.299 (1) (45 K). At 25 K it approaches the commensurate value of one-third [i.e.0.332 (3)]: thus indicating that the incommensurate–commensurate phase transition takes place between 45 K and 25 K. The commensurate lock-in phase of K2Sc[Si2O6]F has been solved and refined with a 3 × 3 × 1 supercell compared with the tetragonal incommensurately modulated structure stable at room temperature. This corresponds to a 3 × 1 × 3 supercell in the pseudo-orthorhombic monoclinic setting of the low-temperature structure, space groupP2/m, with lattice parametersa= 26.786 (3),b= 8.245 (2)c= 26.824 (3) Å, β = 90.00 (1)°. The structure is a mixed tetrahedral–octahedral framework composed of chains of [ScO4F2] octahedra that are interconnected by [Si4O12] rings with K atoms in fourfold to ninefold coordination. Distorted [ScO4F2] octahedra are connected to distorted Si tetrahedra to form octagonal arrangements closely resembling those observed in the incommensurate structure of fresnoite- and melilite-type compounds.

The low-temperature crystal structure of the multiferroic melilite Ca2CoSi2O7

In the antiferromagnetic ground state, belowTN≃ 5.7 K, Ca2CoSi2O7exhibits strong magnetoelectric coupling. For a symmetry-consistent theoretical description of this multiferroic phase, precise knowledge of its crystal structure is a prerequisite. Here we report the results of single-crystal neutron diffraction on Ca2CoSi2O7at temperatures between 10 and 250 K. The low-temperature structure at 10 K was refined assuming twinning in the orthorhombic space groupP21212 with a 3 × 3 × 1 supercell [a= 23.52 (1),b= 23.52 (1),c= 5.030 (3) Å] compared with the high-temperature normal state [tetragonal space group P\overline {4}2_{1}m,a=b≃ 7.86,c≃ 5.03 Å]. The precise structural parameters of Ca2CoSi2O7at 10 K are presented and compared with the literature X-ray diffraction results at 130 and 170 K (low-temperature commensurate phase), as well as at ∼ 500 K (high-temperature normal phase).