Acta Crystallographica Section A最新文献

Three models of charge-density distribution - Hansen-Coppens multipolar, virtual atom and kappa - of different complexities, different numbers of refined parameters, and with variable levels of restraints, were tested against theoretical and high-resolution X-ray diffraction structure factors for 2-methyl-4-nitro-1-phenyl-1H-imidazole-5-carbonitrile. The influence of the model, refinement strategy, multipole level and treatment of the H atoms on the dipole moment was investigated. The dipole moment turned out to be very sensitive to the refinement strategy. Also, small changes in H-atom treatment can greatly influence the calculated magnitude and orientation of the dipole moment. The best results were obtained when H atoms were kept in positions determined by neutron diffraction and anisotropic displacement parameters (obtained by SHADE, in this case) were used. Also, constraints on kappa values of H atoms were found to be superior to the free refinement of these parameters. It is also shown that the over-parametrization of the multipolar model, although possibly leading to better residuals, in general gives worse dipole moments.

A modified algorithm for X-ray dynamical diffraction theory is presented for curved boundary crystals and a detailed description of the numerical procedure is given. The simulated and experimental results both show an anomalous focusing behavior in a curved multi-plate crystal cavity of silicon under the (12,4,0) back-diffraction condition at a photon energy of 14.4388 keV. The focusing effects are analyzed, within the framework of the dynamical theory of X-ray diffraction, from the excitation of the dispersion surface and modification of the index of refraction with respect to the non-plane-parallel boundaries of a curved crystal cavity.

Various practical applications of the average (A) and difference (D) of Friedel opposites are described. Techniques based on the resonant-scattering contribution to Friedel differences are applied to see whether a crystal is centrosymmetric or not, and to determine the point group of the crystal. For the validation of a structural study, plots of A(obs) against A(model), and D(obs) against D(model) are used extensively. Moreover, it is useful to display both plots on the same graph. Intensity measurements on a crystal of NaClO(3) were made at three different speeds, with two different radiations and two different diffractometers, and treated with two different software packages and four different absorption corrections. The evaluation of these numerous data sets reveals underlying deficiencies. For comparison, plots of A(obs) against A(model), and D(obs) against D(model) are presented for two centrosymmetric crystals.

Structure-factor extractions in commonly used Rietveld refinement programs (FullProf, Jana2006 and GSAS) were examined with respect to subsequent calculation of electron-density distributions (EDDs) using the maximum entropy method (MEM). As a test case, 90 K synchrotron powder X-ray diffraction data were collected on the potential hydrogen storage material, NaGaH(4), at SPring-8, Japan. To support the model, neutron powder diffraction data were collected on the fully deuterated sample at PSI, Switzerland. Firstly, it was established whether the programs can produce observed structure factors, F(obs), corrected for anomalous dispersion and scaled to the scattering power of one unit cell. Secondly, different models for background and peak-shape description were investigated with respect to the extracted F(obs), and the effect on the subsequent MEM EDDs was analysed within the quantum theory of atoms in molecules. Substantial differences are observed in the estimated standard deviations, σ(obs), produced by the different programs. Since σ(obs) is a vital parameter in the calculation of MEM EDDs this leads to substantial variation between the MEM EDDs obtained with different Rietveld programs even in cases with similar F(obs). A new approach for selecting an optimized MEM EDD and thereby minimizing the effect of variation in σ(obs) is suggested.

The accuracy of electrostatic properties estimated from the Hansen-Coppens multipolar model was verified. Tests were carried out to determine whether the multipolar model is accurate enough to study changes of electrostatic properties under the influence of a crystal field. Perturbed and unperturbed electron densities of individual molecules of amino acids and dipeptides were obtained from cluster and perturbation theory calculations. This enabled the changes in electrostatic properties values caused by polarization of the electron density to be characterized. Multipolar models were then fitted to the subsequent theoretical electron densities. The study revealed that electrostatic properties obtained from the multipolar models are significantly different from those obtained directly from the theoretical densities. The electrostatic properties of isolated molecules are reproduced better by multipolar models than the electrostatic properties of molecules in a crystal. Changes of electrostatic properties caused by perturbation of electron density due to the crystal environment are barely described by the multipolar model. As a consequence, the electrostatic properties obtained from multipolar models fitted to the perturbed theoretical densities derived either from cluster or periodic calculations do not differ much from those estimated from multipolar models fitted to densities of isolated molecules. The main reason for this seems to be related to an inadequate description of electron-density polarization in the vicinity of the nuclei by the multipolar model.

Electron diffractive imaging (EDI) relies on combining information from the high-resolution transmission electron microscopy image of an isolated kinematically diffracting nano-particle with the corresponding nano-electron diffraction pattern. Phase-retrieval algorithms allow one to derive the phase, lost in the acquisition of the diffraction pattern, to visualize the actual atomic projected potential within the specimen at sub-ångström resolution, overcoming limitations due to the electron lens aberrations. Here the approach is generalized to study extended crystalline specimens. The new technique has been called keyhole electron diffractive imaging (KEDI) because it aims to investigate nano-regions of extended specimens at sub-ångström resolution by properly confining the illuminated area. Some basic issues of retrieving phase information from the EDI/KEDI measured diffracted amplitudes are discussed. By using the generalized Shannon sampling theorem it is shown that whenever suitable oversampling conditions are satisfied, EDI/KEDI diffraction patterns can contain enough information to lead to reliable phase retrieval of the unknown specimen electrostatic potential. Hence, the KEDI method has been demonstrated by simulations and experiments performed on an Si crystal cross section in the [112] zone-axis orientation, achieving a resolution of 71 pm.

It is shown that expectation values of Poisson-distributed random numbers exist not only for the well known positive integer powers but also for negative integer powers. A recursion formula for the calculation of expectation values of powers differing by one is given. This recursion formula helps to find an analytical representation for both positive and negative integer powers in terms of the hypergeometric function.

The generalized multicomponent short-range order (GM-SRO) parameter has been adapted for the characterization of short-range order within the highly chemically and spatially resolved three-dimensional atomistic images provided by the microscopy technique of atom-probe tomography (APT). It is demonstrated that, despite the experimental limitations of APT, in many cases the GM-SRO results derived from APT data can provide a highly representative description of the atomic scale chemical arrangement in the original specimen. Further, based upon a target set of the GM-SRO parameters, measured from APT experiments, a Monte Carlo algorithm was utilized to simulate statistically equivalent atomistic systems which, unlike APT data, are complete and lattice based. The simulations replicate solute structures that are statistically consistent with other correlation measures such as solute cluster distributions, enable more quantitative characterization of nanostructural phenomena in the original specimen and, significantly, can be incorporated directly into other models and simulations.

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.

A new Bravais-lattice determination algorithm is introduced herein. For error-stable Bravais-lattice determination, Andrews & Bernstein [Acta Cryst. (1988), A44, 1009-1018] proposed the use of operations to search for nearly Buerger-reduced cells. Although these operations play an essential role in their method, they increase the computation time, in particular when lattice parameters obtained in (powder) auto-indexing are supposed to contain large errors. The new algorithm requires only several permutation matrices in addition to the operations that are necessary when the lattice parameters have exact values. As a result, the computational efficiency of error-stable Bravais-lattice determination is improved considerably. Furthermore, the new method is proved to be error stable under a very general assumption. The detailed algorithms and the set of matrices sufficient for error-stable determination are presented.