Gotzon Madariaga

Magnetic symmetry plays a critical part in the description of magnetic structures and their relations to their paramagnetic parent phases as well as to other magnetic structures through phase transitions. Here, we present the symmetry-based computational tools developed by the Bilbao Crystallographic Server for the analysis of magnetic structures, and their relations are illustrated through worked-out cases from the literature.

This article presents a web-based framework to build a database without in-depth programming knowledge given a set of CIF dictionaries and a collection of CIFs. The framework consists of two main elements: the public site that displays the information contained in the CIFs in an ordered manner, and the restricted administrative site which defines how that information is stored, processed and, eventually, displayed. Thus, the web application allows users to easily explore, filter and access the data, download the original CIFs, and visualize the structures via JSmol. The modulated structures open database B-IncStrDB, the official International Union of Crystallography repository for this type of material and available through the Bilbao Crystallographic Server, has been re-implemented following the proposed framework.

Perchlorate ions induce structural diversity in a thiosemicarbazone copper(ii) system, whose aqueous chemistry includes desulfurization reactions even at physiological pH values.

Experimental magnetic studies performed on the [{CuLX}₂] system (HL = pyridine-2-carbaldehyde thiosemicarbazone, X = Cl⁻, Br⁻, I⁻) point to the larger electronegativity in X, the lower magnitude of the antiferromagnetic interactions. In order to confirm this and other trends observed and to dip into them, computational studies on the [{CuLX}₂] (X = Cl⁻ (1), I⁻ (2)) compounds are here reported. The chemical and structural comparisons have been extended to the compounds obtained in acid medium. In this regard, chlorido ligands yield the [Cu(HL)Cl₂]∙H₂O (3) complex, whose crystal structure shows that thiosemicarbazone links as a tridentate chelate ligand to square pyramidal Cu(II) ions. On the other hand, iodido ligands provoke the formation of the [{Cu(H₂L)I₂}₂] (4) derivative, which contains pyridine-protonated cationic H₂L⁺ as a S-donor monodentate ligand bonded to Cu(I) ions. Crystallographic, infrared and electron paramagnetic resonance spectroscopic results are discussed. Computational calculations predict a greater stability for the chlorido species, containing both the neutral (HL) and anionic (L⁻) ligand. The theoretical magnetic studies considering isolated dimeric entities reproduce the sign and magnitude of the antiferromagnetism in 1, but no good agreement is found for compound 2. The sensitivity to the basis set and the presence of interdimer magnetic interactions are debated.

The section of the Bilbao Crystallographic Server (https://www.cryst.ehu.es/) dedicated to subperiodic groups contains crystallographic and Brillouin-zone databases for the layer groups. The crystallographic databases include the generators/general positions (GENPOS), Wyckoff positions (WYCKPOS) and maximal subgroups (MAXSUB). The Brillouin-zone database (LKVEC) offers k-vector tables and Brillouin-zone figures of all 80 layer groups which form the background of the classification of their irreducible representations. The symmetry properties of the wavevectors are described applying the so-called reciprocal-space-group approach and this classification scheme is compared with that of Litvin & Wike [(1991), Character Tables and Compatibility Relations of the Eighty Layer Groups and Seventeen Plane Groups. New York: Plenum Press]. The specification of independent parameter ranges of k vectors in the representation domains of the Brillouin zones provides a solution to the problems of uniqueness and completeness of layer-group representations. The Brillouin-zone figures and k-vector tables are described in detail and illustrated by several examples.

During the last decades, metal-organic compounds constitute an active field of research, and among them, complexes that combine thiosemicarbazone ligands with copper(II) are appealing from the point of view of material science due to their interesting structural and magnetic properties [1].

The benefit of computational methods applying density functional theory for the description and understanding of modulated crystal structures is investigated. A method is presented which allows one to establish, improve and test superspace models including displacive and occupational modulation functions from first-principles calculations on commensurate structures. The total energies of different configurations allow one to distinguish stable and less stable structure models. The study is based on a series of geometrically optimized superstructures of mullite (Al_4+2xSi_2−2xO_10−x) derived from the superspace groupPbam(α0½)0ss. Despite the disordered and structurally complex nature of mullite, the calculations on ordered superstructures are very useful for determining the ideal Al/Si ordering in mullite, extracting atomic modulation functions as well as understanding the SiO₂–Al₂O₃phase diagram. The results are compared with experimentally established models which confirm the validity and utility of the presented method.

Synchrotron single-crystal X-ray diffraction has revealed diffuse scattering alongside sharp satellite reflections for different samples of mullite (Al_4+2xSi_2−2xO_10−x). Structural models have been developed in (3+1)-dimensional superspace that account for vacancy ordering and Al/Si ordering based on harmonic modulation functions. A constraint scheme is presented which explains the crystal-chemical relationships between the split sites of the average structure. The modulation amplitudes of the refinements differ significantly by a factor of ∼3, which is explained in terms of different degrees of ordering,i.e.vacancies follow the same ordering principle in all samples but to different extents. A new approach is applied for the first time to determine Al/Si ordering by combining density functional theory with the modulated volumes of the tetrahedra. The presence of Si–Si diclusters indicates that the mineral classification of mullite needs to be reviewed. A description of the crystal structure of mullite must consider both the chemical composition and the degree of ordering. This is of particular importance for applications such as advanced ceramics, because the physical properties depend on the intrinsic structure of mullite.

Modulated structures with a harmonic occupational modulation are not suitable for force field methods (including molecular dynamics) or density functional theory (DFT) calculations because fully occupied sites are required. Instead of assuming a random distribution with some constraints, which is a common approach, the harmonic occupational modulation function from a refinement in superspace can be replaced by a block wave function resulting in a model, that represents the hypothetical completely ordered structure with fully occupied sites. If the modulation wave vector corresponds to a commensurate modulation, the corresponding model in physical space can be used for DFT calculations, otherwise a commensurate approximation is needed. As an example, the present approach is applied to the modulated structure of mullite to determine the ideal Al/Si ordering for different compositions and supercell sizes. For the analyzed composition, the calculations yield consistently the same Al/Si ordering pattern. The results are also in qualitative agreement with the refinement of the not fully ordered structure, i.e. the volumes of tetrahedra with Al/Si disorder follow the trend of the Al/Si ordering pattern from the DFT calculations. The example shows that the approach allows to determine structural parameters, that are very difficult or even impossible to access experimentally.