The interface-modulated structure of TaSi0.360Te2

New insight on bismuth cuprates with incommensurate modulated structures

The incommensurate modulated crystal structure of Bi2.27Sr1.73CuO6 + δ (2201) phase [a = 5.3874 (5), b = 5.3869 (4), c = 24.579 (3) Å; β = 90.01 (1)°, q = 0.2105 (3)a(*) + 0.538 (4)c(*), Z = 4, the (3 + 1)-dimensional monoclinic A2/a(α0γ) group] has been refined with R = 0.041, wR = 0.052 from X-ray single-crystal data including up to third-order satellite reflections. The same structure has also been considered as incommensurate composite with a2 = 2.437, b2 = 5.387, c2 = 24.614, β2 = 93.06, q2 = 0.4524a2(*)-0.243c2(*) and the (3 + 1)-dimensional A2/m(α0γ)0s group for the second component. Both approaches give quite similar results. The structure possesses oxygen disorder in the oxygen-rich region of the BiO layer. An extra O atom is determined in the bridging position shifted ∼ 0.6 Å from BiO towards the SrO layer. Its presence is the cause of the tremendous increase of the bismuth U(11) atomic displacement parameter in ∼ 20% of the unit cells (t = -0.05-0.15). Vacancies are determined in the oxygen site of the SrO layer, which may result in the oxygen content variation with annealing at different oxygen pressures. The total refined oxygen content 6.18 (1) corresponds to the results of chemical analysis.

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).

(3 + 1)-Dimensional commensurately modulated structure and photoluminescence properties of diborate KSbOB2O5

This work reports the commensurately modulated structure of KSbOB₂O₅ using superspace formalism for aperiodic structures considering a modulation vector q = 5/12b*.

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.