We report a systematic study of the $c$-lattice parameter in the Na${}_x$CoO${}_2$ phases versus Na content $x>0.5$, in which sodium always displays ordered arrangements. This allows us to single out the first phase which exhibits an antiferromagnetic order at a Néel temperature $T_N=$22 K, which is found to occur for $x\approx 0.77\left(1\right)$. Pure samples of this phase have been studied both as aligned powders and single crystals. They exhibit identical ${}^{23}$Na NMR spectra in which three sets of Na sites could be fully resolved, and are found to display $T$ dependencies of their NMR shifts, which scale with each other. This allows us to establish that the $T$ variation of the shifts is due to the paramagnetism of the Co sites with formal charge state larger than 3${}^{+}$. The existence of a sodium site with axial charge symmetry and the intensity ratio between the sets of ${}^{23}$Na lines permits us to reveal that the two-dimensional structure of the Na order corresponds to ten Na sites on top of a thirteen-Co-sites unit cell, that is with $x=10/13\approx 0.77$. This structure fits with that determined from local density calculations and involves triangles of three Na sites located on top of Co sites [so-called Na1 sites]. The associated ordering of the Na vacancies is quite distinct from that found for $x<0.75$. DOI: http://dx.doi.org/10.1103/PhysRevB.85.134433 ©2012 American Physical Society

In recent years, rare earth silicate compounds have attracted the extensive attention of researchers owing to their potential for applications in scintillation crystals in gamma ray or X-ray detectors, as well as in thermal or environmental barrier coatings. Large high quality crystals of three members of the rare earth monosilicates family of compounds, $R_2{\mathrm{SiO}}_5$ (with R = Dy, Ho, and Er), have been grown by the floating zone method, using a laser-diode-heated floating zone furnace. Crystal growths attempts were carried out using different parameters in order to determine the optimum conditions for the growth of these materials. The phase purity and the crystalline quality of the crystal boules were analysed using powder and Laue X-ray diffraction. Single crystal X-ray diffraction experiments were carried out to determine the crystal structures of the boules. The optimum conditions used for the crystal growth of $R_2{\mathrm{SiO}}_5$ materials are reported. The phase purity and high crystalline quality of the crystals produced makes them ideal for detailed investigations of the intrinsic physical and chemical properties of these materials.

Rare earth silicate materials received growing attention in recent years, driven by their potential for use in thermal/environmental barrier coatings and for scintillation applications for gamma-ray and X-ray detectors. $R_2$SiO₅, R₂Si₂O₇ and $R_{4.67}$(SiO₄)₃O (where R = Dy, Ho and Er) have been prepared by the conventional solid-state synthesis method. Through a systematic study, we have optimized the synthesis conditions, from the choice of the precursor to the optimal temperature profile for the chemical reaction. We demonstrate that, despite an overlap of the thermal stability ranges of different rare earth silicate compounds and their polymorphs in the phase diagrams of the R-Si-O systems, it is feasible to prepare polycrystalline materials with a high yield of the target phase. Moreover, we offer our perspectives into the kinetics of the different chemical phases within the rare earth silicate systems. We show that the chemical reactions are faster when employing the $\alpha$-cristobalite polymorph of SiO₂ as a precursor, and we establish a reliable and reproducible solid-state synthesis protocol for Dy₂SiO₅, Ho₂SiO₅, Er₂SiO₅, Ho₂Si₂O₇, Er₂Si₂O₇, Dy_4.67(SiO₄)₃O and Ho_4.67(SiO₄)₃O. We reveal the results of our efforts to optimize the synthesis conditions for the preparation of all Dy-, Ho-, and Er-based silicate phases, which can be extended to other members of the rare earth silicate families, enabling the synthesis of bulk materials with improved phase purity.