isotropic displacement parameter
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2018 ◽  
Vol 74 (9) ◽  
pp. 1344-1357 ◽  
Author(s):  
Jan Fábry

A large number of structural determinations of compounds containing 2-hydroxy-3,5-dinitrobenzoic acid (I) and its various deprotonated forms, 2-hydroxy-3,5-dinitrobenzoate (II) or 2-carboxy-4,6-dinitrophenolate (III), are biased. The reason for the bias follows from incorrectly applied constraints or restraints on the bridging hydrogen, which is involved in the intramolecular hydrogen bond between the neighbouring carboxylic/carboxylate and oxo/hydroxy groups. This hydrogen bond belongs to the category of resonance-assisted hydrogen bonds. The present article suggests corrections for the following structure determinations that have been published in Acta Crystallographica: DUJZAK, JEVNAA, LUDFUL, NUQVEB, QIQJAD, SAFGUD, SEDKET, TIYZIM, TUJPEV, VABZIJ, WADXOR, YAXPOE [refcodes are taken from the Cambridge Structural Database [CSD; Groom et al. (2016). Acta Cryst. B72, 171–179]. The structural features of the title molecules in all the retrieved structures, together with structures that contain 3,5-dinitro-2-oxidobenzoate (IV), are discussed. Attention is paid to the localization of the above-mentioned bridging hydrogen, which can be situated closer to the O atom of the carboxylate/carboxylic group or that of the hydroxy/oxo group. In some cases, it is disordered between the two O atoms. The position of the bridging hydrogen seems to be dependent on the pK a (base) although with exceptions. A stronger basicity enhances the probability of the presence of a phenolate (III). The present article examines the problem of the refinement of such a bridging hydrogen as well as that of the hydrogen atoms involved in the hydroxy and primary and secondary amine groups. It appears that the best model, in many cases, is obtained by fixing the hydrogen-atom position found in the difference electron-density map while refining its isotropic displacement parameter.


Author(s):  
Kim V. Fendrich ◽  
Robert T. Downs ◽  
Marcus J. Origlieri

The crystal structure of ruizite, ideally Ca2Mn3+2[Si4O11(OH)2](OH)2·2H2O [dicalcium dimanganese(III) tetrasilicate tetrahydroxide dihydrate] was first determined in space groupA2 with an isotropic displacement parameter model (R= 5.6%) [Hawthorne (1984).Tschermaks Mineral. Petrogr. Mitt.33, 135–146]. A subsequent refinement in space groupC2/mwith anisotropic displacement parameters for non-H atoms converged withR= 8.4% [Mooreet al.(1985).Am. Mineral.70, 171–181]. The current study reports a redetermination of the ruizite structure by means of single-crystal X-ray diffraction data of a natural sample from the Wessels mine, Kalahari Manganese Field, Northern Cape Province, South Africa. Our data (R1= 3.0%) confirm that the space group of ruizite is that of the first study rather thanC2/m. This work improves upon the structure reported by Hawthorne (1984) in that all non-H atoms were refined with anisotropic displacement parameters and all hydrogen atoms were located. The crystal structure consists of [010] chains of edge-sharing MnO6octahedra flanked by finite [Si4O11(OH)2] chains. The Ca2+cations are situated in the cavities of this arrangement and exhibit a coordination number of seven.


2015 ◽  
Vol 71 (4) ◽  
pp. 467-470 ◽  
Author(s):  
Gunnar Thorkildsen ◽  
Helge B. Larsen

A simplified approach for calculating the equivalent isotropic displacement parameter is presented and the transformation property of the tensor representationUto point-group operations is analysed. Complete tables have been compiled for the restrictions imposed upon the tensor owing to the site symmetry associated with all special positions as listed in Hahn [(2011),International Tables for Crystallography, Vol. A,Space-group Symmetry, 5th revised ed. Chichester: John Wiley and Sons, Ltd].


Author(s):  
Sergey M. Aksenov ◽  
Ramiza K. Rastsvetaeva ◽  
Nikita V. Chukanov ◽  
Uwe Kolitsch

Calcinaksite, KNa[Ca(H2O)][Si4Ol0], a new natural member of the litidionite group, was found in a calcic xenolith from alkaline basalt of the Bellerberg volcano, Eastern Eifel region, Rhineland–Palatinate, Germany. The crystal structure has been studied based on single-crystal X-ray diffraction data. Triclinic unit-cell parameters are:a= 7.021 (2),b= 8.250 (3),c= 10.145 (2) Å, α = 102.23 (2), β = 100.34 (2), γ = 115.09 (3)°, space group P \bar 1. The structure model was determined by the `charge-flipping' method and refined toR= 0.0527 in anisotropic approximation using 3057I> 3σ(I). Calcinaksite is a hydrous calcium-dominant litidionite-group mineral. The crystal structure of calcinaksite (like other litidionite-group minerals and related compounds) is based on a heteropolyhedral framework and is characterized by the presence of several types of channels. Calcium forms distorted CaO5Ø (Ø = H2O) octahedra while Na forms NaO5square pyramids. Nine-coordinated K atoms are located in a channel extending along [010]. Water molecules occupy a channel running along the [100] direction and are characterized by a rather high equivalent isotropic displacement parameter of 0.053 (2) Å2. In calcinaksite, there are three short distances between the water molecule and oxygen atoms, Ow...O3 [2.844 (5) Å], Ow...O9 [2.736 (4) Å] and Ow...Ow[2.843 (7) Å]. These distances correspond to three hydrogen bonds detected by IR data (the bands at 3340, 3170 and 3540 cm−1).


2012 ◽  
Vol 45 (6) ◽  
pp. 1125-1135 ◽  
Author(s):  
Dubravka Šišak ◽  
Christian Baerlocher ◽  
Lynne B. McCusker ◽  
Christopher J. Gilmore

Over the past few years, the powder charge-flipping algorithm has proved to be a useful one for structure solution from powder diffraction data, so a semi-systematic study of the effect of the different input parameters on its success has been performed. Two data sets were studied in these tests: a zirconium phosphate framework material and D-ribose. TheSuperflipinput parameters tested were the reflection overlap factor, the intensity repartitioning frequency, the isotropic displacement parameter, the threshold for charge flipping and the number of cycles/runs. By varying the values of these parameters within sensible ranges, an optimized set could be found for the zirconium phosphate case, but no combination of parameters allowed the D-ribose structure to be solved. Reasoning that starting with nonrandom phases might help, an approximate (but incorrect) structure was generated using the direct-space global-optimization method implemented in the programFOX. This structure was then used to calculate initial phase sets forSuperflipby allowing the calculated phases to vary in a random fashion by a user-defined percentage. With such phases and reoptimized input parameters, some fully interpretable solutions with the correct symmetry could be produced, even with fairly low resolution data. Unfortunately, it was not possible to recognize these solutions using theSuperflip Rvalues, so other criteria were sought. Both cluster analyses and maximum entropy calculations of the solutions were performed, and the latter, in particular, look very promising. A set of guidelines derived from these two structures could be applied successfully to a further two inorganic and seven organic structures.


2012 ◽  
Vol 45 (2) ◽  
pp. 174-181 ◽  
Author(s):  
S. H. M. Ryding ◽  
F. Azough ◽  
R. Freer ◽  
R. J. Cernik ◽  
C. C. Tang ◽  
...  

Very high resolution powder diffraction structural studies of the potentially room temperature multiferroic Ga2−xFexO3solid solution series (x= 0.7–1.3, 0.1 steps) have been undertaken using a fixed angle of incidence geometry. The applied absorption correction was seen to improve the goodness of fit (χ2) of the Rietveld refinements from an average of 1.41 to 1.06. The correction also resulted in an increased mean isotropic displacement parameter from 0.5 to 0.65. The mean difference in the fractional coordinates of the atoms between the refined models from the corrected and uncorrected data was 0.0007 Å, compared with the mean fractional coordinate error of 0.0003 Å. It is concluded that the final crystal structures refined from the corrected and uncorrected data are not significantly different. The number of reflections in each data set was over 2700, and the average peak half-width was 0.018° with the data binned in 4 millidegree steps. The data quality allowed bond length and angle determinations of sufficiently high accuracy to measure significant metal site distortions to an average precision of ±0.007 Å. A lattice parameter nonlinearity was observed on either side of thex= 1 composition; this was attributed to local distortions, primarily of the Fe1 and Ga2 sites.


2011 ◽  
Vol 44 (3) ◽  
pp. 625-627 ◽  
Author(s):  
Jianglin Feng

A method is proposed for the initial identification of non-hydrogen atomic species in a crystal from X-ray diffraction intensities when the chemical composition is not available. When atom positions are determined, a portion of the scattering factor curve for each atom can be obtained by Fourier synthesis with reflections from concentric shells. From these curves, the atomic number and the isotropic displacement parameter for all non-H atoms, and the scaling constant of the structure factors, can be approximately determined.


1999 ◽  
Vol 32 (2) ◽  
pp. 309-321 ◽  
Author(s):  
R. Schreier ◽  
J. Kalus

The diffuse intensity distribution of X-rays scattered from a dipolar disordered single crystal of 2,3-dimethylnaphthalene (2,3-DMN) has been measured and was found to be nearly independent of temperature in some restricted regions of the reciprocal space. This behaviour was related to a static disorder of the crystal. Lattice parameters were determined between room temperature and 9 K and phase transitions at 227 K and 112 K were observed. The results of the data analysis at 298 K are: the equivalent isotropic displacement parameterUeqfor the thermal Debye–Waller factor is (0.18 Å)2; the displacement parameters describing the static disorder are U\raise.15em{_{xx}}\kern-.65em^C\le(0.05 Å)2, U\raise.15em{_{yy}}\kern-.65em^C=[0.22\,(2) Å]2and U_{zz}^C= [0.35\,(3) Å]2. The molecules show an orientational Gaussian distribution around thexaxis with a width of 5.0 (8)°. All these results refer to the molecular inertia system. Correlation coefficients characterizing the mean mutual orientation of neighbouring molecules were determined. The highest correlation coefficient was found along [010]: C=-0.231\pm 0.004.


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