Structure refinement of the incommensurate composite crystal Sr1.145TiS3 through the Rietveld analysis process

Colossal Optical Anisotropy from Atomic-Scale Modulations

Materials with large birefringence (Δn, where n is the refractive index) are sought after for polarization control (e.g., in wave plates, polarizing beam splitters, etc.), nonlinear optics, micromanipulation, and as a platform for unconventional light-matter coupling, such as hyperbolic phonon polaritons. Layered 2D materials can feature some of the largest optical anisotropy; however, their use in most optical systems is limited because their optical axis is out of the plane of the layers and the layers are weakly attached. This work demonstrates that a bulk crystal with subtle periodic modulations in its structure-Sr9/8 TiS3 -is transparent and positive-uniaxial, with extraordinary index ne = 4.5 and ordinary index no = 2.4 in the mid- to far-infrared. The excess Sr, compared to stoichiometric SrTiS3 , results in the formation of TiS6 trigonal-prismatic units that break the chains of face-sharing TiS6 octahedra in SrTiS3 into periodic blocks of five TiS6 octahedral units. The additional electrons introduced by the excess Sr form highly oriented electron clouds, which selectively boost the extraordinary index ne and result in record birefringence (Δn > 2.1 with low loss). The connection between subtle structural modulations and large changes in refractive index suggests new categories of anisotropic materials and also tunable optical materials with large refractive-index modulation.

Material research from the viewpoint of functional motifs

As early as 2001, the need for the ‘functional motif theory’ was pointed out to assist the rational design of functional materials. The properties of materials are determined by their functional motifs and by how they are arranged in the materials. Uncovering the functional motifs and their arrangements is crucial in understanding the properties of materials and rationally designing new materials of desired properties. The functional motifs of materials are the critical microstructural units (e.g. constituent components and building blocks) that play a decisive role in generating certain material functions, and could not be replaced with other structural units without losing or significantly suppressing the relevant functions. The role of functional motifs and their arrangements in materials with representative examples was presented. These examples could be classified into six types of material microscopic structures on a length scale smaller than ∼10 nm with maximum subatomic resolution, i.e. the crystal, magnetic, aperiodic, defect, local, and electronic structures. The method of functional motif analysis could be employed in the function-oriented design of materials, as elucidated by taking infrared nonlinear optical materials as an example. Machine learning is more efficient in predicting material properties and screening materials with high efficiency than high-throughput experimentation and high-throughput calculations. In extracting the functional motifs and finding their quantitative relationships, developing sufficiently reliable databases for material structures and properties is imperative.

Electrochemical calcium extraction from 1D-Ca3Co2O6

The electrochemical oxidation of a transition metal oxide through calcium extraction is achieved for the first time. The 1D framework of Ca3Co2O6 is maintained upon oxidation and the new phase formed exhibits a modulated structure. The process occurs at high potential and is partially reversible, which opens prospects for a calcium battery proof-of-concept.

Synergy between transmission electron microscopy and powder diffraction: application to modulated structures

The crystal structure solution of modulated compounds is often very challenging, even using the well established methodology of single-crystal X-ray crystallography. This task becomes even more difficult for materials that cannot be prepared in a single-crystal form, so that only polycrystalline powders are available. This paper illustrates that the combined application of transmission electron microscopy (TEM) and powder diffraction is a possible solution to the problem. Using examples of anion-deficient perovskites modulated by periodic crystallographic shear planes, it is demonstrated what kind of local structural information can be obtained using various TEM techniques and how this information can be implemented in the crystal structure refinement against the powder diffraction data. The following TEM methods are discussed: electron diffraction (selected area electron diffraction, precession electron diffraction), imaging (conventional high-resolution TEM imaging, high-angle annular dark-field and annular bright-field scanning transmission electron microscopy) and state-of-the-art spectroscopic techniques (atomic resolution mapping using energy-dispersive X-ray analysis and electron energy loss spectroscopy).

Equivalence of superspace groups

An algorithm is presented which determines the equivalence of two settings of a (3 + d)-dimensional superspace group (d = 1, 2, 3). The algorithm has been implemented as a web tool findssg on SSG(3+d)D, providing the transformation of any user-given superspace group to the standard setting of this superspace group in SSG(3+d)D. It is shown how the standard setting of a superspace group can be directly obtained by an appropriate transformation of the external-space lattice vectors (the basic structure unit cell) and a transformation of the internal-space lattice vectors (new modulation wavevectors are linear combinations of old modulation wavevectors plus a three-dimensional reciprocal-lattice vector). The need for non-standard settings in some cases and the desirability of employing standard settings of superspace groups in other cases are illustrated by an analysis of the symmetries of a series of compounds, comparing published and standard settings and the transformations between them. A compilation is provided of standard settings of compounds with two- and three-dimensional modulations. The problem of settings of superspace groups is discussed for incommensurate composite crystals and for chiral superspace groups.

Structural studies of a mixed-valence state in the incommensurate composite crystal Sr1.261CoO3

The incommensurate modulated crystal structure of the hexagonal cobalt oxide Sr_1.261CoO₃ has been studied using a four-dimensional (4D) superspace profile analysis of neutron powder diffraction data. Sr_1.261CoO₃ is a composite crystal that consists of the [CoO₃] and [2Sr] subsystems. The [CoO₃] subsystem forms 1D chains that run parallel to the c-axis and consist of face-sharing CoO₆ polyhedra with octahedral (Oh) and trigonal prismatic (TP) coordinations. The structure analysis reveals that the [CoO₃] chains contain 73.9% Oh and 26.1% TP sites, and that the TP sites have longer Co-O bonds than the Oh sites: d_av. =2.039(4) Å (TP) and 1.895(3) Å (Oh). The averaged Co bond valences are Co^3.56(3)+ in the Oh sites and Co^2.45(3)+ in the TP sites, suggesting that a considerable amount of Co³⁺ ions are mixed with Co⁴⁺ions in the Oh sites and with Co²⁺ ions in the TP sites. The observed magnetic susceptibility can be well explained assuming that the compound has the Co mixed-valence state with the spin configurations of S=0 low-spin state for Co³⁺(dε⁶), S=1/2 low-spin state for Co⁴⁺(dε⁵) and S=3/2 high-spin state for Co²⁺(dε⁵dγ²). The Weiss temperature, approximately 0.8 K, implies that Sr_1.261CoO₃ naturally assumes a Curie paramagnetic state, probably owing to the obstruction of the intrachain magnetic interaction by the nonmagnetic Co³⁺ ions. These results suggest that the nonmagnetic Co³⁺ ions play an essential role in the magnetism of Sr_2γCoO₃ systems.

Synthesis, structure determination, and twinning of two new composite compounds in the hexagonal perovskite-like sulfide family: Eu8/7TiS3 and Sr8/7TiS3

Eu8/7TiS3 and Sr8/7TiS3, two members in the hexagonal perovskite-like A x TiS3 family, have been obtained as single crystals and their structure solved from twinned crystal X-ray data within the (3+1)-dimensional [(3+1)D] formalism. Eu8/7TiS3 and Sr8/7TiS3 crystallizes in the trigonal symmetry, R3̅m(00γ)0s superspace group with the following lattice parameters: Eu8/7TiS3, as = 11.3892(13) Å, cs = 2.989(2) Å, q = 0.5741(4) c* and Vs = 335.8(3) Å3; Sr8/7TiS3, as = 11.480(5) Å, cs = 2.9940(13) Å, q = 0.5716(2) c* and Vs = 341.7(5) Å3. The structures were considered as commensurate (P three-dimensional (3D) spacegroup) but refined within the (3+1)D formalism (t = 0 section) to a residual factor: Eu8/7TiS3, R = 3.84% for 128 parameters and 4500 independent reflections; Sr8/7TiS3, R = 4.92% for 125 parameters and 2719 independent reflections. The two structures are isotypic and resemble that of Sr9/8TiS3. They differ from the structures of the oxide counterparts by the presence of original PO [TiS6] units, intermediate between octahedra (Oh) and trigonal prisms (TP), and replacing the TP units found in the oxides. In addition, they are different from the Sr9/8TiS3 structure by the occurrence of a particular twinning and the presence of two different [TiS3] chain types, with two consecutive PO units in one of them.