Biomedical subjects

Lukás Palatinus

Publications and source records attributed to Lukás Palatinus.

8 recordsLinked to original sources

PubMed2006

Growth-induced incommensurability observed in the organic co-crystal hexamethylenetetramine resorcinol.

Co-crystals of hexamethylenetetramine and resorcinol were investigated by X-ray diffraction. The structure was refined in the superspace group Xmcm(0beta0)s0s, X=(1/2 1/2 0 1/2). In the average structure the resorcinol molecules are disordered between two orientations. The main effect of the modulation in the structure is a harmonic modulation of the occupation probabilities of the two orientations of the resorcinol molecule. However, the modulated order is not perfect and the resorcinol molecules remain partially disordered. Below 270 K the crystal undergoes a phase transition to a commensurately modulated structure with modulation vector q=(0 1/2 1/4) and superspace group X2/m(0betagamma)0s. The structure of the low-temperature phase could not be determined owing to the poor quality of the crystals affected by the reconstructive phase transition.

Crystallization↗

PubMed2006

The incommensurately and commensurately modulated crystal structures of chromium(II) diphosphate.

Chromium(II) diphosphate, Cr(2)P(2)O(7), has an incommensurately modulated structure at ambient conditions with a = 7.05, b = 8.41, c = 4.63 A, beta = 108.71 degrees and q = (-0.361, 0, 0.471). It undergoes a phase transition towards a commensurate structure with a commensurate q vector, q = (-1/3, 0, 1/2), at T(c) = 285 K. The incommensurate structure has been solved by the charge-flipping method, which yielded both the basic positions of the atoms and the shapes of their modulation functions. The structure model for the commensurate structure was derived directly from the incommensurate structure. The structure analysis shows that the modulation leads to a change of the coordination of the Cr(2+) ions from distorted octahedra in the average structure towards a sixfold coordination in the form of a more regular octahedron and a fivefold coordination in the form of a square pyramid. The fivefold and sixfold coordination polyhedra alternate along the lattice direction a with the pattern 5-6-5 5-6-5 in the commensurate structure. In the incommensurate structure this pattern is occasionally disturbed by a 5-6-5-5 motif. Both structures can be described in superspace using the same superspace group and a similar modulated structure model. The same superspace model can also be used for the low-temperature phases of other metal diphosphates with the thortveitite stucture type at high temperature. Their low-temperature structures can be obtained from the superspace model by varying the q vector and the origin in the internal dimension t(0).

Journal Article↗

PubMed2005

The twofold superstructure of titanium(III) oxybromide at T = 17.5 K.

The low-temperature (T = 17.5 K) structure of titanium(III) oxybromide, TiOBr, is reported as a twofold superstructure of the crystal structure at room temperature. Weak superlattice reflections were measured with synchrotron radiation X-rays and were analyzed by structure refinements employing superspace techniques. Both the low-temperature and the room-temperature structures of TiOBr are isostructural with the corresponding structures of TiOCl. The results indicate that at low temperatures TiOBr is in a spin-Peierls state, similar to that of TiOCl, but with the modulations and relevant interactions smaller than in the latter compound.

Journal Article↗

PubMed2005

The prior-derived F constraints in the maximum-entropy method.

The method of the prior-derived F constraints (PDC) enhances the quality of reconstructions of electron densities from X-ray diffraction data by the maximum-entropy method (MEM). The method concentrates on artifacts arising due to inaccurate extrapolation of non-measured data by the MEM. While these artifacts are unavoidable, when a flat prior is used, they can be effectively suppressed, if the prior information about the structure is known in the form of a procrystal prior electron density. The missing, usually high-angle, structure factors can be effectively substituted by the structure factors derived from the procrystal prior. This approach eliminates the occurrence of spurious peaks in the difference electron densities in the vicinity of the atomic positions. The method is illustrated with a simple one-dimensional example. Its use is then demonstrated on simulated data of oxalic acid dihydrate and on experimental data of sodium nitrite.

Journal Article↗

PubMed2004

Ab initio determination of incommensurately modulated structures by charge flipping in superspace.

The charge flipping algorithm proposed by Oszlányi & Suto [Acta Cryst. (2004), A60, 134-141] for ab initio reconstruction of crystal structures is generalized towards superspace. Its efficiency is demonstrated by successful reconstruction of eight known incommensurately modulated structures from experimental data. The output of the charge flipping algorithm is an electron density with symmetry P1. The symmetry of the structure is recovered by locating the positions of symmetry operators and averaging the density over the symmetry-related pixels. The reconstruction of a modulated structure by the charge flipping algorithm and the accuracy of the result is demonstrated in detail on the modulated structure of tetraphenylphosphonium hexabromotellurate(IV) bis[dibromoselenate(I)].

Journal Article↗

PubMed2004

Structure of incommensurate ammonium tetrafluoroberyllate studied by structure refinements and the maximum entropy method.

Incommensurately modulated ammonium tetrafluoroberyllate (AFB) occurs in a narrow temperature interval between the paraelectric room-temperature phase with space group Pnma (Ti = 178 K) and the ferroelectric low-temperature phase with space group Pna2(1) (Tc = 173 K). The structure is determined from accurate single-crystal X-ray diffraction data collected with synchrotron radiation at 175 K. The superspace group of the structure is Pnma(alpha00)0ss with alpha = 0.4796 (4). Both structure refinements and the maximum entropy method lead to the same structure model, which involves only single harmonic modulations. The building units of the structure are BeF4(2-) and NH4+ complex ions with approximately tetrahedral point symmetry. They are relatively rigid and the modulations consist mainly of translations of the tetrahedra and their rotations around a fixed axis. The modulation is related to changes in the network of the hydrogen bonds. The low-temperature superstructure can be described as a commensurately modulated structure with the same superspace symmetry. The first harmonic modulations of the low-temperature and incommensurate phases are related by a scale factor with a value of approximately two. In addition, the low-temperature phase exhibits a second harmonic modulation that is responsible for shifts along c and the ferroelectricity in this phase. The experimental data of the incommensurate phase do not contain any evidence for the presence of a second harmonic in the modulation functions. This suggests that the development of the second harmonic, i.e. the development of the spontaneous polarization, is responsible for the lock-in transition.

Journal Article↗

PubMed2003

The maximum-entropy method in superspace.

One of the applications of the maximum-entropy method (MEM) in crystallography is the reconstruction of the electron density from phased structure factors. Here the application of the MEM to incommensurately modulated crystals and incommensurate composite crystals is considered. The MEM is computed directly in superspace, where the electron density in the (3+d)-dimensional unit cell (d > 0) is determined from the scattering data of aperiodic crystals. Periodic crystals (d = 0) are treated as a special case of the general formalism. The use of symmetry in the MEM is discussed and an efficient algorithm is proposed for handling crystal symmetry. The method has been implemented into a computer program BayMEM and applications are presented to the electron density of the periodic crystal NaV(2)O(5) and the electron density of the incommensurate composite crystal (LaS)(1.14)NbS(2). The MEM in superspace is shown to provide a model-independent estimate of the shapes of the modulation functions of incommensurate crystals. The discrete character of the electron density is found to be the major source of error, limiting the accuracy of the reconstructed modulation functions to approximately 10% of the sizes of the pixels. MaxEnt optimization using the Cambridge and Sakata-Sato algorithms are compared. The Cambridge algorithm is found to perform better than the Sakata-Sato algorithm, being faster, always reaching convergence, and leading to more reliable density maps. Nevertheless, the Sakata-Sato algorithm leads to similar density maps, even in cases where it does not reach complete convergence.

Journal Article↗

PubMed2002

The generalized F constraint in the maximum-entropy method--a study on simulated data.

One of the classical problems in the application of the maximum-entropy method (MEM) to electron-density reconstructions is the uneven distribution of the normalized residuals of the structure factors [|F(obs)(H)|-|F(calc)(H)|]/sigma(H) of the resulting electron density. This distribution does not correspond to the expected Gaussian distribution and it leads to erroneous features in the MEM reconstructions. It is shown that the classical chi(2) constraint is only one of many possible constraints, and that it is too weak to restrict the resulting distribution to the expected Gaussian shape. It is proposed that constraints should be used that are based on the higher-order central moments of the distribution of the structure-factor residuals. In this work, the influence of different constraints on the quality of the MEM reconstruction is investigated. It is proposed that the use of a combined constraint on more than one central moment simultaneously would lead to again improved results. Oxalic acid dihydrate was chosen as model structure, from which several data sets with different resolutions and different levels of noise were calculated and subsequently used in the MEM. The results clearly show that the use of different constraints leads to significantly improved results.

Journal Article↗