G. Madariaga

Bilbao Crystallographic Server: I. Databases and crystallographic computing programs

Abstract The Bilbao Crystallographic Server is a web site with crystallographic databases and programs available on-line at www.cryst.ehu.es. It has been operating for about six years and new applications are being added regularly. The programs available on the server do not need a local installation and can be used free of charge. The only requirement is an Internet connection and a web browser. The server is built on a core of databases, and contains different shells. The innermost one is formed by simple retrieval tools which serve as an interface to the databases and permit to obtain the stored symmetry information for space groups and layer groups. The k-vector database includes the Brillouin zones and the wave-vector types for all space groups. As a part of the server one can find also the database of incommensurate structures. The second shell contains applications which are essential for prob lems involving group-subgroup relations between space groups (e.g. subgroups and supergroups of space groups, splittings of Wyckoff positions), while the third shell contains more sophisticated programs for the computation of space-group representations and their correlations for group-subgroup related space groups. There are also programs for calculations focused on specific problems of solid-state physics. The aim of the article is to report on the current state of the server and to provide a brief description of the accessible databases and crystallographic computing programs. The use of the programs is demonstrated by illustrative examples.

Defective Dicubane-like Tetranuclear Nickel(II) Cyanate and Azide Nanoscale Magnets

Four tetrameric nickel(II) pseudohalide complexes have been synthesized and structurally, spectroscopically, and magnetically characterized. Compounds 1-3 are isostructural and exhibit the general formula [Ni(2)(dpk·OH)(dpk·CH(3)O)(L)(H(2)O)](2)A(2)·2H(2)O, where dpk = di-2-pyridylketone; L = N(3)(-), and A = ClO(4)(-) for 1, L = NCO(-) and A = ClO(4)(-) for 2, and L = NCO(-) and A = NO(3)(-) for 3. The formula for 4 is [Ni(4)(dpk·OH)(3) (dpk·CH(3)O)(2)(NCO)](BF(4))(2)·3H(2)O. The ligands dpk·OH(-) and dpk·CH(3)O(-) result from solvolysis and ulterior deprotonation of dpk in water and methanol, respectively. The four tetramers exhibit a dicubane-like core with two missing vertexes where the Ni(II) ions are connected through end-on pseudohalide and oxo bridges. Magnetic measurements showed that compounds 1-4 are ferromagnetic. The values of the exchange constants were determined by means of a theoretical model based on three different types of coupling. Thus, the calculated J values (J(1) = J(2), J(3), and D) were 5.6, 11.8, and 5.6 cm(-1) for 1, 5.5, 12.0, and 5.6 cm(-1) for 2, 6.3, 4.9, and 6.2 cm(-1) for 3, and (J(1), J(2), J(3), and D) 6.9, 7.0, 15.2, and 4.8 cm(-1) for 4.

Structural analysis, spectroscopic, and magnetic properties of the 1D triple-bridged compounds [M(dca)2(bpa)] (M = Mn, Fe, Co, Zn; dca = dicyanamide; bpa = 1,2-bis(4-pyridyl)ethane) and the 3D [Ni(dca)(bpa)2]dca·6H2O.

The family of compounds [Mn(dca)(2)(bpa)] (1), [Fe(dca)(2)(bpa)] (2), [Co(dca)(2)(bpa)] (3), [Zn(dca)(2)(bpa)] (4), and [Ni(dca)(bpa)(2)]dca·6H(2)O (5), with dca = dicyanamide and bpa = 1,2-bis(4-pyridyl)ethane, has been synthesized. These compounds have been characterized by single crystal (1, 2, 4, and 5) and powder X-ray diffraction (3), by Fourier transform infrared (FTIR), UV-vis, and electron paramagnetic resonance (EPR) spectroscopies, and by magnetic measurements. Compound 1 crystallizes in the monoclinic C2/c space group, Z = 4, with a = 16.757(6), b = 9.692(3), and c = 13.073(4) Å, and β = 123.02(2)°; Compound 2 crystallizes in the monoclinic C2/c space group, Z = 4, with a = 16.588(5), b = 9.661(3), c = 12.970(5) Å, and β = 123.16(3)°; Compound 4 crystallizes in the monoclinic C2/c space group, Z = 4, with a = 16.519(2), b = 9.643(2), c = 12.943(2) Å, and β = 123.15(1)°; Compound 5 crystallizes in the monoclinic C2/c space group, Z = 4, with a = 18.504(4), b = 19.802(3), and c = 8.6570(18) Å, and β = 99.74(2)°. The compounds 1-4 are isostructural and show a one dimensional (1D) disposition, with the metal(II) ions bridged by double μ(1,5) dca ligands and unusually by a third bridge consisting of the bpa ligand, which adopts a very low torsion angle to accommodate in the structure. This kind of structure is unusual, even considering the voluminous bpa bridge. The compound 5 shows a 3D structure with layers of Ni-bpa joined by single dca bridges. Magnetic susceptibility measurements show antiferromagnetic couplings, increasing for 1-3. Compound 5 shows very slight antiferromagnetic interactions.

Diffraction symmetry of incommensurate structures

The symmetry of the diffusion pattern for an incommensurate displacive structure is analysed in a general context. The rotational symmetry and systematic extinctions in the diffraction diagram of this type of structure are shown to be directly based on a particular transformation property of the amplitudes of the atomic modulation waves intervening in the distortion for a subgroup of the basic structure space group. Hence a general three-dimensional framework can be established, where diffraction symmetry can straight-forwardly be used to restrict and relate the amplitudes corresponding to the atomic modulation waves of the distortion. It is shown how a full direct exploitation of diffraction symmetry can therefore be accomplished to determine the characteristics of the incommensurate distortion, without referring to the superspace group formalism. The equivalence of the present simpler approach with the latter is then demonstrated. Finally a concept of atomic scattering modulation factors is proposed to reduce the expression of the structure factor for these phases to a very simple form analogous to those used in commensurate cases.

Molybdates of aromatic heterocyclic compounds. Synthesis and structure of an octamolybdate containing coordinately bound pyrazole: [(C3H4N2)2(Mo8O26)]4−

Abstract Molybdenum trioxide reacts with pyrazole to give the octamolybdate: (C3H4N2H)4[(C3H4N2)2(Mo8O26)]. The anion [(C3H4N2)2(Mo8O26)]4−, is built of two C3H4N2MoO5 and six MoO6 edge-sharing octahedra. The MoNNC3H4 bond length is 2.243(4) A, giving a bond strength of 0.35.

X-ray diffraction study of the phase transitions of (CH3)4NCdCl3 between 293 and 80 K: a quantitative analysis of the ferroelastic domains distribution below 118 K

X-ray diffraction patterns of [N(CH3)4][CdCl3], tetramethylammonium trichlorocadmate(II), have been investigated in the temperature range 80-293 K, which includes two phase transitions at 118 and 104 K, respectively. The main interest in this compound is to establish the mechanism of the structural phase transitions common to other members of the isostructural family [(CH3)4N][MX3]. It is supposed to be related to the ordering of the organic part together with some small distortion of the inorganic chains. The origin of the order-disorder mechanism would be the orientationally disordered distribution of the tetramethylammonium tetrahedra at room temperature. Maximum Entropy Methods suggest that the most probable distribution of the organic groups can be described through the so-called two-well model, in which one threefold axis of the tetramethylammonium tetrahedron coincides with the crystallographic threefold axis of the structure. Below 118 K the reflections are split. However, the splitting cannot be fully explained by the ferroelastic domains expected to appear after the phase transitions. Recent NMR results [Mulla-Osman et al. (1998). J. Phys. Condensed Matter, 10, 2465-2476] corroborate the existence of more domains than expected from symmetry considerations. A model of ferroelastic domains which is in agreement with both X-ray diffraction diagram and NMR measurements is proposed.

Crystal structure, spectroscopic and magnetic properties of two unusual compounds: [Cu(terpy)(N3)Cl] and [{Cu0.75Ni0.25(terpy)(N3)2}2]·2H2O (terpy = 2,2′ : 6′,2″-terpyridine)

The crystal structures of two unusual complexes [Cu(terpy)(N3)Cl]1 and [(Cu0.75Ni0.25(terpy)-(N3)2}2]·2H2O 2(terpy = 2,2′:6′,2″-terpyridine) have been determined at room temperature: 1. space group P21c. a= 10.586(5), b= 8.572(1), c= 16.396(3)A, β= 100.69(3)°, Z = 4, R=R′= 0.036, for 2818 reflections with I 3σ(I); 2, space group P21/c, a= 10.195(5), b= 9.996(3), c= 15.866(8)A, β= 91.10(5)°, Z= 4, R=R′= 0.055 for 3134 reflections with I 3σ(I). Complex 1 possesses the first known co-ordination polyhedron including both halide (Cl) and pseudohalide (N3) ligands. It shows a square-pyramidal topology for the copper(II), with the three nitrogen atoms of the terpy ligand and one terminal nitrogen atom of the azide group in the basal positions while the chloride atom is in the apical one. Compound 2 contains 25% of [{Ni(terpy)(N3)2}2]·2H2O and 75% of [{Cu-(terpy)(N3)2}2]·2H2O enclosed in the global lattice. It possesses (end-on) azide bridges and terminal azide ligands. The co-ordination polyhedron of the metal ion is a slightly distorted octahedron with the nitrogen atoms of the terpy ligand and a nitrogen atom of one of the azide bridging groups in the equatorial positions, while the nitrogen atoms of both the bridge and terminal azide groups occupy the axial positions. The pure copper phase related to compound 2 exhibits a discrete molecular topology; however, the pure nickel phase shows the same dimeric structure, which is useful for comparison. The magnetic properties of compound 2 can be explained by contributions from the isolated Cu2 and Ni2 entities, giving rise to global ferromagnetic interactions characterised by the parameters J= 20.1 cm–1, D=–12.5 cm–1, gNi= 2.26 and ρ= 0.76 corresponding to the copper proportion. The EPR measurements for both compounds reveal rhombic symmetries for the g tensors. Single-crystal EPR measurements on 2 show the presence of two magnetically different copper entities, with an antiferrodistortive ordering, in the lattice.

Structure of the incommensurate phase of BCCD at 130 K

Abstract The incommensurate structure of BCCD at 130 K with q = 0.296c∗ has been determined in the superspace-group P(Pnma):(1, s, −1) by means of single crystal X-ray diffraction data including main and first-order satellite reflections. Only zero and first-order harmonics have been considered in the modulation functions. The final agreement factors are R = 0.048, Ro = 0.042 and R1 =0.067, for all, main and first-order satellite reflections respectively. Only the atomic modulations of the betaine molecule could be interpreted in terms of rigid-body modulated motions. The symmetry of the structure is in accordance with a single A3 soft-mode model for the phase transition sequence.

Revision of pyrrhotite structures within a common superspace model

The structure of pyrrhotite (Fe(1 - x)S with 0.05 < or = x < or = 0.125) has been reinvestigated in the framework of the superspace formalism. A common model with a centrosymmetric superspace group is proposed for the whole family. The atomic domains in the internal space representing the Fe atoms are parametrized as crenel functions that fulfil the closeness condition. The proposed model explains the x-dependent space groups observed and the basic features of the structures reported up to now. Our model yields for any x value a well defined ordered distribution of Fe vacancies in contrast to some of the structural models proposed in the literature. A new (3 + 1)-dimensional refinement of Fe(0.91)S using the deposited dataset [Yamamoto & Nakazawa (1982). Acta Cryst. A38, 79-86] has been performed as a benchmark of the model. The consistency of the proposed superspace symmetry and its validity for other compositions has been further checked by means of ab initio calculations of both atomic forces and equilibrium atomic positions in non-relaxed and relaxed structures, respectively.

Quantitative analysis of δ′ precipitation kinetics in Al–Li alloys

The Rietveld method has been applied to X-ray spectra in order to study the precipitated mass fraction of δ′ and δ in Al–Li alloys. The method allows us to obtain quantitatively the δ′ and δ precipitate mass fractions, and their evolution with aging time. Furthermore, this method also gives directly the cell parameter evolution of the matrix phase and indirectly the mean half radius of δ′ precipitates through an appropriate calibration curve. Experimentally, this calibration has been approached by previously studying the evolution of the mean half radius of δ′ by transmission electron microscopy (TEM). Thermoelectric power has also been shown to be a powerful technique to study the microstructural evolution of Al–Li alloys, being sensitive to the different stages of precipitation associated to the δ′ and δ phases. The comparison of the different experimental results allow us to stablish a clear difference between the precipitation kinetics and the hardening kinetics.