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ABSTRACT: Crystal structure analyses of the layered compounds La(n)(Ti(1-x)Fe(x))(n)O(3n+2), with nominal compositions x = 0.2 for n = 5 and x = 0.33 for n = 6, show that the iron is concentrated at the centers of the slabs. The spatial arrangements of the iron ions can be approximated by two-dimensional square lattices with strong magnetic interactions between neighboring sites, albeit with fractional occupancies of the sites of an average of 0.67 magnetic ions in n = 6 and 0.42 magnetic ions in n = 5 compounds. A previously described (Lichtenberg et al 2008 Prog. Solid State Chem. 36 253) crossover of magnetic behavior of n = 6 at room temperature is explained by the formation of two-dimensional, ferromagnetically organized magnetic clusters with an average size of 52 Fe(3+) ions. The absence of long-range magnetic order follows from the fractional occupancy of the sites by the magnetic ions. The lower concentration of magnetic ions in n = 5 explains why crossover behavior is not found and clusters do not form in that compound.
Journal of Physics Condensed Matter 01/2013; 25(7):076003. · 2.55 Impact Factor
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ABSTRACT: It is shown that the dynamic electron density corresponding to a structure model can be computed by inverse Fourier transform of accurately calculated structure factors, employing the method of fast Fourier transform. Maps free of series-termination effects are obtained for resolutions better than 0.04 Å in direct space, corresponding to resolutions larger than 6 Å(-1) in reciprocal space. Multipole (MP) models of α-glycine and D,L-serine at different temperatures have been determined by refinement against X-ray diffraction data obtained from the scientific literature. The successful construction of dynamic electron densities is demonstrated by their topological properties, which indicate local maxima and bond-critical points (BCPs) at positions expected on the basis of the corresponding static electron densities, while non-atomic maxima have not been found. Density values near atomic maxima are much smaller in dynamic than in static electron densities. Static and low-temperature (∼20 K) dynamic electron-density maps are found to be surprisingly similar in the low-density regions. Especially at BCPs, values of the ∼20 K dynamic density maps are only slightly smaller than values of the corresponding static density maps. The major effect of these zero-point vibrations is a modification of the second derivatives of the density, which is most pronounced for values at the BCPs of polar C-O bonds. Nevertheless, dynamic MP electron densities provide an estimate of reasonable accuracy for the topological properties at BCPs of the corresponding static electron densities. The difference between static and dynamic electron densities increases with increasing temperature. These differences might provide information on temperature-dependent molecular or solid-state properties like chemical stability and reactivity. In regions of still lower densities, like in hydrogen bonds, static and dynamic electron densities have similar appearances within the complete range of temperatures that have been considered (20-298 K), providing similar values of both the density and its Laplacian at BCPs in static and dynamic electron densities at all temperatures.
Acta crystallographica. Section A, Foundations of crystallography 09/2012; 68(Pt 5):568-81. · 49.93 Impact Factor
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ABSTRACT: A new probe, 3-[(3-benzyloxypyridin-2-ylimino)methyl]-2-hydroxy-5-methylbenzaldehyde (1-H) behaves as a highly selective fluorescent pH sensor in a Britton-Robinson buffer at 25 °C. The pH titrations show a 250-fold increase in fluorescence intensity within the pH range of 4.2 to 8.3 with a pK(a) value of 6.63 which is valuable for studying many of the biological organelles.
Organic Letters 08/2011; 13(17):4510-3. · 5.86 Impact Factor
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ABSTRACT: Crystal structures of TiI(3) were determined at selected temperatures between 4 and 340 K. On heating, thermal expansion is found to increase abruptly at the phase transition at T(c) = 323 K. Most prominently, linear thermal expansion is highly anisotropic and small along c (i.e. along chains of Ti atoms) in the low-temperature phase, while above T(c) it is much larger along c. An order parameter is defined by the ratio between the long and the short Ti-Ti distances on the metal chains. The temperature dependence of the order parameter indicates the transition to be of first order.
Zeitschrift für Kristallographie 08/2011; 226(8):640-645. · 0.95 Impact Factor
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ABSTRACT: A combination of structure refinements, analysis of the superspace MEM density and interpretation of difference-Fourier maps has been used to characterize the incommensurate modulation of rubidium tetrachlorozincate, Rb(2)ZnCl(4), at a temperature of T = 196 K, close to the lock-in transition at T(lock-in) = 192 K. The modulation is found to consist of a combination of displacement modulation functions, modulated atomic displacement parameters (ADPs) and modulated third-order anharmonic ADPs. Up to fifth-order Fourier coefficients could be refined against diffraction data containing up to fifth-order satellite reflections. The center-of-charge of the atomic basins of the MEM density and the displacive modulation functions of the structure model provide equivalent descriptions of the displacive modulation. Modulations of the ADPs and anharmonic ADPs are visible in the MEM density, but extracting quantitative information about these modulations appears to be difficult. In the structure refinements the modulation parameters of the ADPs form a dependent set, and ad hoc restrictions had to be introduced in the refinements. It is suggested that modulated harmonic ADPs and modulated third-order anharmonic ADPs form an intrinsic part, however small, of incommensurately modulated structures in general. Refinements of alternate models with and without parameters for modulated ADPs lead to significant differences between the parameters of the displacement modulation in these two types of models, thus showing the modulation of ADPs to be important for a correct description of the displacive modulation. The resulting functions do not provide evidence for an interpretation of the modulation by a soliton model.
Acta crystallographica. Section B, Structural science 06/2011; 67(Pt 3):205-17. · 1.80 Impact Factor
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ABSTRACT: The incommensurately modulated structure of a natural nepheline of composition K(0.54)Na(3.24)Ca(0.03)Al(3.84)Si(4.16)O(16) has been determined in superspace. The compound crystallizes in the trigonal centered superspace group X3(00γ)0 with γ = 0.2048 (10), X = (0, 0, 0, 0), (1/3, 2/3, 0, 2/3), (2/3, 1/3, 0, 1/3), a = 17.2889 (8) and c = 8.3622 (10) Å. The structure is characterized by a framework of corner-connected (Al,Si)O(4) tetrahedra. The additional cations are incorporated in two different types of channels of the framework. All atoms in the structure are displacively modulated with amplitudes below 0.1 Å. The modulation can be well described taking into account harmonics of first order only. Atomic positions in the smaller channels of the framework are fully occupied by Na(+). Cationic positions in the larger channel are occupationally modulated, yet the variation of electron density as a function of the internal coordinate t is very small and indicates that the incorporation of different types of cations (K(+), Na(+), Ca(2+)) and vacancies is realised in a highly disordered way. Average T-O distances indicate a nearly complete Al/Si ordering in the tetrahedral framework. A large part of the O atoms are approximated by split-atom positions, which are additionally affected by occupational modulation resulting in a high degree of disorder in the modulated structure. Occupational probabilities for the split-atom positions are complementary. Occupational modulations of the cations in the larger channels and the O atoms of the tetrahedral framework are coupled and correlations between occupational and displacive modulations exist.
Acta crystallographica. Section B, Structural science 02/2011; 67(Pt 1):18-29. · 1.80 Impact Factor
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ABSTRACT: Crystal structures of TiI3 were determined and refined at selected temperatures between 4 and 340 K against neutron powder diffraction data. On heating, thermal expansion is found to increase abruptly at the phase transition at Tc = 323 K. Most prominently, linear thermal expansion is highly anisotropic and small along c (i.e. along chains of Ti atoms) in the low-temperature phase, while above Tc it is much larger along c. An order parameter is defined by the ratio between the long and the short Ti—Ti distances on the metal chains. The temperature dependence of the order parameter indicates the transition to be of first order.
Zeitschrift für Kristallographie 226 (2011) 640–645. 01/2011; 226:640-645.
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Swastik Mondal, Sander van Smaalen,
Andreas Schönleber,
Yaroslav Filinchuk,
Dmitry Chernyshov,
Sergey I Simak,
Arkady S Mikhaylushkin,
Igor A Abrikosov,
Evgeniya Zarechnaya,
Leonid Dubrovinsky,
Natalia Dubrovinskaia
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ABSTRACT: The peculiar bonding situation in γ boron is characterized on the basis of an experimental electron-density distribution which is obtained by multipole refinement against low-temperature single-crystal x-ray diffraction data. A topological analysis of the electron-density distribution reveals one-electron-two-center bonds connecting neighboring icosahedral B(12) clusters. A unique polar-covalent two-electron-three-center bond between a pair of atoms of an icosahedral cluster and one atom of the interstitial B(12) dumbbell explains the observed charge separation in this high-pressure high-temperature polymorph of boron.
Physical Review Letters 01/2011; 106(21):215502. · 7.37 Impact Factor
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Swastik Mondal, Sander van Smaalen,
Andreas Schoenleber,
Yaroslav Filinchuk,
Dmitry Chernyshov,
Sergey I. Simak,
Arkady S. Mikhaylushkin,
Igor A. Abrikosov,
Evgeniya Zarechnaya,
Leonid Dubrovinsky,
Natalia Dubrovinskaia
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ABSTRACT: The peculiar bonding situation in gamma boron is characterized on the basis of an experimental electron-density distribution which is obtained by multipole refinement against low-temperature single-crystal x-ray diffraction data. A topological analysis of the electron-density distribution reveals one-electron-two-center bonds connecting neighboring icosahedral B(12) clusters. A unique polar-covalent two-electron-three-center bond between a pair of atoms of an icosahedral cluster and one atom of the interstitial B(2) dumbbell explains the observed charge separation in this high-pressure high-temperature polymorph of boron.
Phys Rev Lett. 01/2011; 106(21).
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ABSTRACT: Temperature-dependent x-ray diffraction on SmNiC2 has shown that the orthorhombic lattice symmetry of this compound persist down to a temperature of at least 9 K, i.e., into the charge-density-wave (CDW) state below TCDW=148 K and in the ferromagnetically ordered state below TC=17.7 K. The modulated crystal structure has been determined for the incommensurate CDW state with qCDW=(0.5,0.516,0) at T=60 K. The observed atomic modulation displacements indicate that the CDW should be considered as a commensurate CDW centered on chains of Ni atoms along a. Frustrated interchain coupling is responsible for the incommensurability of the three-dimensionally ordered CDW state.
Phys. Rev. B. 08/2010; 82(5).
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ABSTRACT: In a systematic approach, the ability of the Maximum Entropy Method (MEM) to reconstruct the most probable electron density of highly disordered crystal structures from X-ray powder diffraction data was evaluated. As a case study, the ambient temperature crystal structures of disordered alpha-Rb(2)[C(2)O(4)] and alpha-Rb(2)[CO(3)] and ordered delta-K(2)[C(2)O(4)] were investigated in detail with the aim of revealing the ;true' nature of the apparent disorder. Different combinations of F (based on phased structure factors) and G constraints (based on structure-factor amplitudes) from different sources were applied in MEM calculations. In particular, a new combination of the MEM with the recently developed charge-flipping algorithm with histogram matching for powder diffraction data (pCF) was successfully introduced to avoid the inevitable bias of the phases of the structure-factor amplitudes by the Rietveld model. Completely ab initio electron-density distributions have been obtained with the MEM applied to a combination of structure-factor amplitudes from Le Bail fits with phases derived from pCF. All features of the crystal structures, in particular the disorder of the oxalate and carbonate anions, and the displacements of the cations, are clearly obtained. This approach bears the potential of a fast method of electron-density determination, even for highly disordered materials. All the MEM maps obtained in this work were compared with the MEM map derived from the best Rietveld refined model. In general, the phased observed structure factors obtained from Rietveld refinement (applying F and G constraints) were found to give the closest description of the experimental data and thus lead to the most accurate image of the actual disorder.
Acta crystallographica. Section B, Structural science 04/2010; 66(Pt 2):184-95. · 1.80 Impact Factor
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ABSTRACT: The crystal structure of Lambda-(1,3,6,8,10,13,16,19-octaazabicyclo[6.6.6]eicosane)cobalt(III) trinitrate, [Co(C(12)H(30)N(8))](NO(3))(3), consists of a sepulchrate moiety that serves as a macrobicyclic nitrogen cage for the Co(3+) cation, which is six-coordinated by N atoms, and three nitrate anions. The Co-sepulchrate group lies on a threefold axis (site symmetry 32), as do two symmetry-related and ordered nitrate groups (site symmetry 3), with which it is connected via N-H...O hydrogen bonds [Co-N = 5.1452 (12) A]. The third nitrate group is disordered as a result of symmetry requirements around the origin (site symmetry 32), and is further away from the Co-sepulchrate cage [Co-N = 6.3160 (8) A]. The structure is described by applying orientational disorder over six equivalent orientations for the disordered nitrate group, which is considered as an ideal planar molecule of regular trigonal geometry with its molecular plane rotated out of the ab plane and the molecular centre of gravity slightly shifted away from the origin. This new model for disorder clearly improves a previous crystal structure determination.
Acta crystallographica. Section C, Crystal structure communications 04/2010; 66(Pt 4):m107-9. · 0.78 Impact Factor
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ABSTRACT: The maximum entropy method (MEM) has been used to determine electron density in superspace of incommensurately modulated chromium pyrophosphate from X-ray diffraction data measured by Palatinus et al. [(2006), Acta Cryst. B62, 556-566]. Chromium pyrophosphate, Cr(2)P(2)O(7), contains ordered regions (83% of the volume) and regions with disorder. Analysis of the MEM density has allowed the determination of the displacive modulation functions within ordered regions. The disordered regions can be described as the alternate occupation of two conformations of the pyrophosphate group and two positions of the chromium atom, with occupational probabilities that depend continuously on the phase of modulation t. A structure model based on the interpretation of the MEM density provides a fit to the diffraction data of the same quality as the model given by Palatinus et al. (2006). The failure to find a model that better fits the data is attributed to the intrinsic inaccuracy of approximately 0.01 A for positions derived from the MEM and to the difficulties in constructing an appropriate model for the anharmonic ADPs and their modulation functions from electron densities.
Acta crystallographica. Section B, Structural science 04/2010; 66(Pt 2):130-40. · 1.80 Impact Factor
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ABSTRACT: Rb(1.3711)MnO(2) (Rb(11)Mn(8)O(16)) has been synthesized via the azide/nitrate route from a stoichiometric mixture of the precursors Mn(2)O(3), RbNO(3) and RbN(3). The structure of this extremely air- and moisture-sensitive compound can best be described in terms of an incommensurate composite structure, built up by a honeycomb-like framework of Rb ions, as one subsystem and by a second subsystem of chains, consisting of edge-sharing MnO(4/2) tetrahedra. These two composite substructures interpenetrate in such a way that the manganate chain polyanions centre the channels of the Rb-honeycomb framework. Crystals transform by an aging process into Rb(1.3636)MnO(2) (Rb(15)Mn(11)O(22)), which has a similar structure but a different commensurate modulation. Two reasons can be established for the origin of the modulations: the charge ordering of Mn(2+)/Mn(3+) on one hand, and the incompatibility of the Mn-Mn and Rb-Rb separations on the other.
Acta crystallographica. Section B, Structural science 02/2010; 66(Pt 1):27-33. · 1.80 Impact Factor
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ABSTRACT: A general discussion is given of the Maximum Entropy Method (MEM) as a method to determine the electron density in superspace from X-ray diffraction data. The MEM has been used to determine the electron density in superspace of incommensurately modulated chromium pyrophosphate from X-ray diffraction data published by Palatinus et al. [Acta Crystallogr. B 62, 556]. Chromium pyrophosphate, Cr(2)P(2)O(7), contains ordered regions (83% of the volume) and regions with disorder. Analysis of the MEM density has allowed us to determine the displacive modulation functions within the ordered regions. The disordered regions can be described as the alternate occupation of two conformations of the pyrophosphate unit and two positions of the chromium atom. Both the conformations and the occupational probabilities of them depend continuously on the phase of modulation t.
Journal of Physics Conference Series 01/2010; 226(1):012012.
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ABSTRACT: We studied the crystal structure of TiOCl up to pressures of p = 25 GPa at room temperature by x-ray powder-diffraction measurements. Two pressure-induced structural phase transitions are observed: at p(c1) approx 15 GPa emerges an 2a times 2b times c superstructure with b-axis unique monoclinic symmetry (space group P21/m). At p(c2) approx 22 GPa, all lattice parameters of the monoclinic phase show a pronounced anomaly. A fraction of the sample persists in the ambient orthorhombic phase (space group Pmmn) over the whole pressure range.
Physical Review B 01/2010; 82(13):134117. · 3.69 Impact Factor
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Helvetica Chimica Acta 12/2009; 92(12):2675 - 2697. · 1.48 Impact Factor
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ABSTRACT: Charge densities have been determined by the Maximum Entropy Method (MEM) from the high-resolution, low-temperature (T approximately 20 K) X-ray diffraction data of six different crystals of amino acids and peptides. A comparison of dynamic deformation densities of the MEM with static and dynamic deformation densities of multipole models shows that the MEM may lead to a better description of the electron density in hydrogen bonds in cases where the multipole model has been restricted to isotropic displacement parameters and low-order multipoles (l(max) = 1) for the H atoms. Topological properties at bond critical points (BCPs) are found to depend systematically on the bond length, but with different functions for covalent C-C, C-N and C-O bonds, and for hydrogen bonds together with covalent C-H and N-H bonds. Similar dependencies are known for AIM properties derived from static multipole densities. The ratio of potential and kinetic energy densities |V(BCP)|/G(BCP) is successfully used for a classification of hydrogen bonds according to their distance d(H...O) between the H atom and the acceptor atom. The classification based on MEM densities coincides with the usual classification of hydrogen bonds as strong, intermediate and weak [Jeffrey (1997). An Introduction to Hydrogen Bonding. Oxford University Press]. MEM and procrystal densities lead to similar values of the densities at the BCPs of hydrogen bonds, but differences are shown to prevail, such that it is found that only the true charge density, represented by MEM densities, the multipole model or some other method can lead to the correct characterization of chemical bonding. Our results do not confirm suggestions in the literature that the promolecule density might be sufficient for a characterization of hydrogen bonds.
Acta crystallographica. Section B, Structural science 10/2009; 65(Pt 5):624-38. · 1.80 Impact Factor
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ABSTRACT: The maximum entropy method (MEM) can be used to determine the electron density in the unit cell from phased x-ray diffraction data. A critical discussion is given of the possibilities and limitations of the MEM for the determination of accurate electron densities in chemical bonds. An overview is given of the principles of the MEM, and recent extensions and modifications are discussed, as they are required for a successful application of the MEM in accurate charge-density studies. The quantitative interpretation of MEM electron densities according to Bader's atoms-in-molecules (AIM) theory is discussed, and it is compared to AIM properties of densities obtained from multipole refinements. Applications are presented concerning the analysis of covalent bonds and hydrogen bonds in molecular crystals.
Physica Scripta 04/2009; 79(4):048304. · 1.20 Impact Factor
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ABSTRACT: The maximum entropy method (MEM) can be used to determine the electron density in the unit cell of periodic crystals from phased x-ray diffraction data. As a straightforward extension of this method, the MEM formalism can be applied to the generalized electron density in the unit cell of superspace describing the structures of aperiodic crystals. The principles of the MEM are discussed as they need to be modified for the application of the MEM to generalised electron densities in (3+d)-dimensional superspace (d is an integer). A critical discussion is given of the potential of the MEM for the determination of modulation functions of incommensurately modulated crystals and composite crystals as well as for the determination of atomic occupation domains of quasicrystals.
Physica Scripta 04/2009; 79(4):048305. · 1.20 Impact Factor
