Niels K. Hansen

The modulated structure of Ba0.39Sr0.61Nb2O6. I. Harmonic solution

The structure of a crystal of Sr(0.61)Ba(0.39)Nb(2)O(6) has been solved and refined as an incommensurate structure in five-dimensional superspace. The structure is tetragonal, superspace group P4bm(pp1/2,p - p1/2), unit-cell parameters a = 12.4566 (9), c = 7.8698 (6) A, modulation vectors q(1) = 0.3075 (6) (a* + b*), q(2) = 0.3075 (6) (a* - b*). The data collection was performed on a KUMA-CCD diffractometer and allowed the integration of weak first-order satellite reflections. The structure was refined from 2569 reflections to a final value of R = 0.0479. The modulation affects mainly the positions of the O atoms, which are displaced by as much as 0.5 A, and the site 4c that is occupied by Sr and Ba atoms. Only a simplified model, in which this atomic position is occupied by an effective atom Sr/Ba, could be refined from the data set. The modulation of displacement parameters has been used to account for the modulated distribution of Sr and Ba. The whole refinement uses only first-order modulation waves, but there are strong indications that for a complete solution the use of higher-order satellites and a more complicated model is necessary.

The Phase Problem in the Analysis of X-ray Diffraction Data in Terms of Electron-Density Distributions

The refinement of electron-density distributions for non-centrosymmetric crystals from X-ray diffraction data may lead to a very good fit between model and data but to totally meaningless electron densities. This is to a large extent because varying certain parameters, or combination of parameters, in the model mainly leads to a change in the phases of the structure factors. A formal analysis of why this happens, when using multipole models, is given as well as specific examples using real data: the contributions of odd-order multipoles, which are invariant under crystal-class symmetry operations, are poorly determined. The importance of applying constraints on the models is stressed. The conclusions of this analysis can be carried over to refinements of anharmonic atomic vibrations.

Electron Density Distribution in LiB3O5 at 293 K

The electron density distribution in lithium triborate LiB3O5 has been studied at room temperature by X-ray diffraction using Ag K\alpha radiation up to 1.02 A−1 [1439 unique reflections with I > 3\sigma(I)]. Conventional refinements with a free-atom model yield R(F) = 0.0223, wR(F) = 0.0299, S = 1.632. Atom charge refinements show that the lithium should be considered a monovalent ion. Multipolar refinements were undertaken up to fourth order, imposing local non-crystallographic symmetry constraints in order to avoid phase problems leading to meaningless multipole populations due to the non-centrosymmetry of the structure (space group: Pna21). The residual indices decreased to: R(F) = 0.0147, wR(F) = 0.0193, S = 1.106. The net charges are in good agreement with what can be expected in borate chemistry. Deformation density maps are analysed in terms of \sigma and \pi bonding. The experimental electron distribution in the pz orbitals of triangular B atoms and surrounding O atoms has been analysed by introducing idealized hybridized states. In parallel, the electron density has been determined from ab initio Hartree–Fock calculations on fragments of the structure. Agreement with the X-ray determination is very good and confirms the nature of bonding in the crystal. The amount of transfer of \pi electrons from the oxygen to the triangular B atoms is estimated to be 0.22 electrons by theory.

Studies of electric field induced structural and electron‐density modifications by X‐ray diffraction

During the last two decades, a number of X-ray diffraction studies on the response of a crystal to an applied electric field have been carried out. In a few cases, the electron-density polarizations could be determined. The analysis of the induced variations of the structural properties on an atomic scale are of prime importance in order to acquire a better understanding of physical properties like the piezoelectric and dielectric properties of crystals. This article reviews the experimental technique used and the modelling methods of the Bragg scattering variations induced by the field. Some noteworthy results are presented that illustrate the possibility of detecting subtle structural changes, for example as small as 0.1 degrees in bond angles arising from applying a strong field, 10-40 kV cm(-1), as well as the pitfalls of such an approach for clarifying the relevance of the structural properties in physical mechanisms.

The piezoelectric tensor element d33 of KTiOPO4 determined by single crystal X-ray diffraction

The d33 piezoelectric constant of KTiOPO4 (potassium titanium orthophosphate, KTP) has been determined for two different samples and at temperatures between 100 and 220 K, using high-resolution X-ray diffraction of a single-crystal in an electric field. The observed value of 15 (2) \times 10−12 m V−1 is between the two values of 10.4 and 25.8 \times 10−12 m V−1 found in the literature. The value of d33 is shown to be constant over the temperature range 100–220 K and no anomaly was observed at the conductor–insulator transition at 150 K. The results obtained are believed to be sample-independent, since the same value was obtained for two different crystals, measured at different sources.

Electron density of CaNi2Si2 studied using synchrotron x-ray diffraction and first-principles calculations

The electron-density distribution in CaNi2 Si2 has been analysed by means of x-ray diffraction measurements and a full-potential augmented-plane-wave band-structure calculation. The agreement between experiment and theory is good, considering the difficulty of the experiment. A Si-Si bonding interaction is clearly observed in the valence electron distribution as well as a preferred occupation of the Ni 3d orbitals.

Electric properties of KTiOPO4 and NaTiOPO4 from temperature-dependent X-ray diffraction

Single crystals of KTiOPO4 (KTP) and NaTiOPO4 (NaTP) show pronounced pyroelectric behaviour. In order to determine the origin of this property on an atomic scale, X-ray diffraction measurements have been carried out at several temperatures between 100 and 600 K. Modelling of the electron density and the evolution of the structure as a function of temperature has enabled the determination of values for the spontaneous polarization of the compounds and the pyroelectric coefficient of KTP, principally due to the alkaline-ion displacements with a value of 2.0 nC cm−2 K−1. Structure modifications, compared with NaTiOPO4, and the calculation of the electrostatic potential explain the anisotropic behaviour of ionic conductivity of KTP single crystals.

Structure analysis and the existence of light-induced long-lived metastable states in Xn[Fe(CN)5NO] with inorganic and organic cations: Xn = Pb, (H3O+CH6N+), (C2N2H7)2 and (C16H36N)2

Abstract The crystal structures of four compounds Xn[Fe(CN)5NO] with the different inorganic and organic cations Xn = Pb, (H3O+CH6N+), (C2N2H7)2 and (C16H36N)2 were determined. (H3O+CH6N+)[Fe(CN)5NO] and (C2N2H7)2[Fe(CN)5NO] crystallize in the non-centrosymmetric space groups Cmc21 and Pca21, respectively. Two metastable states can be excited by irradiation with light in each of these two compounds. Pb[Fe(CN)5NO] and (C16H36N)2[Fe(CN)5NO] crystallize in the centrosymmetric space groups Pnma and P21/n, respectively, but only one metastable state can be obtained at 110 K. In (H3O+CH6N+)[Fe(CN)5NO] and (C2N2H7)2[Fe(CN)5NO] the cations are disordered. The disorder is produced by symmetry related hydrogen bonds. The hydrogen bonds are established for all organic cations, but they are weak in (C16H36N)2[Fe(CN)5NO]. The donor-acceptor relation is fulfilled between the hydrogen atoms of the cations and the nitrogen atoms of the cyanide ligands. The light-induced metastable states, created by irradiation with light in the spectral range Δλ = 410–500 nm at 110 K, were investigated by Differential Scanning Calorimetry. The isothermal measurements show that the decay of the metastable states is purely exponential. From the dynamical measurements of heat flow versus temperature the activations energies and frequency factors of the metastable states are obtained.

X-ray diffraction from α quartz crystals under electric fields

The aim of our work is to analyze by diffraction techniques the correlations between structural and physical properties of crystals onto which an electric field is applied. In the laboratory in Nancy we have, based on the ideas of previous work [1], build a device using a field switching technique. It consists of a high voltage supply, the electronics for switching the field, and synchronous counting on four chains combined with a control for stepscanning the diffraction profiles [2]. By using this stroboscopic technique, it is possible to measure very small changes in the Bragg angles due to the strain resulting from the converse piezoelectric effect, and also to measure minute changes in the Bragg intensities due to polarisations of atomic structure and electron density. A first measure was carried out at LURE with the 4-circle diffractometer WDIF-4C on α-quartz, since perfect crystal samples can easily be obtained. Furthermore, quartz is a well-characterised piezo-electric material. Electrodes were vapour deposited onto the (1 1 0) extended faces of a crystal plate of dimensions 5x5x0.5 mm. Our measurements reproduce the known piezo-electric coefficients of α-quartz. We have measured changes in Bragg intensities for 27 reflections, 21 unique. Different atomic models have been investigated in search for an explanation of the origin of piezoelectric effect. Our conclusions are compared with a previous study with a similar technique [3]. [1]A. Paturle, H. Graafsma, H. -S. Sheu, P. Coppens & P. Becker (1991) Phys. Rev. B43, 14683-14691. [2] R. Guillot, P. Allé, P. Fertey, N. K. Hansen & E. Elkaïm ( 2002) J. Appl. Cryst. in print. [3] U. Pietch, J. Stahn, J. Davaasambuu & A. Pucher (2001) J. of Physics and Chemistry of Solids 62, 2129-2133.

Electron Deformation Density of Metal Carbyne Complexes

The carbynic complexes have been discovered in 1973 by E. O. Fischer1 . Their originality consists in a triple bond between a transition metal and a carbon atom, which makes them very unstable, sensitive to moisture, air and temperature. In relation with this very specific structural character, the chemical bonding in this family of compounds requires special attention in order to understand a new and important area of organometallic chemistry. As a matter of fact, carbyne complexes have been recognized as precursors in the synthesis of organometallic products which take part into catalytic reactions2. Our goal was to investigate the electronic deformation density of two members of this family: the trans- chlorotetracarbonyl phenylcarbyne chromium (I) and its methylic analog (II). The present paper is designed to show that a joint experimental and theoretical study combining the multipole model refinement and the ab initio CASSCF calculations can lead to informations of interest to the chemist on topics such as backdonation, conjugation or hyperconjugation effects.