Crystal structure determination and refinement

Thus, a fast experiment is routinely suitable for evaluation of the specimen and phase identification, i.e. qualitative analysis. When needed, it should be followed by a weekend experiment for a complete structural determination. An overnight experiment is required for indexing and accurate lattice parameters refinement, and a weekend-long experiment is needed for crystal structure determination and refinement. In some instances, e.g. when a specimen has exceptional quality and its crystal structure is known or very simple, all relevant parameters can be determined using data collected in an overnight experiment. Similarly, fast experiment(s) may be suitable for unit cell determination in addition to phase identification. In any case, one should use his/her own judgment and experience to assess both the suitability of the experimental data and the reliability of the result. 

Sir2004/CAOS S1R2004 an improved tool for crystal structure determination and refinement, M. C. Sir2004 CAOS... 

C. Giacovazzo, A. Guagliardi, A. G. G. Moliterni, G. Polidori and R. Spagna, J. Appl. Crystallogr., 1999, 32, 115 119 and SIR2004 an improved tool for crystal structure determination and refinement, M. C. Burla,... 

UppENBERG, J., Hansen, M.T., Patkar, S. and Jones, T.A. (1994) Sequence, crystal structure determination and refinement of two crystal forms of lipase B from Candida antarctica. Structure 2, 293-308... 

Crystal Structure Determination and Refinement of 2a. The data crystal used for X-ray investigation was as small as 0.03 x 0.07 x 0.42 mm. Data were collected at -110(l) C with an Enraf-Nonius CAD4 automatic counter diffractometer controlled by a Micro VAX II computer and fitted with a low-temperature apparatus. Ni-filtered CuKa (CuKa, X = 1.54178 A, l = 14.04 cm-i) was used. Fifty reflections with 33 >0>15 and CuKai wavelength (X = 1.54051 A) were used for lattice constants. A total of 4300 reflections with 1.0 < 20 <... 

Loris, R., Steyaert, J., Maes, D., Lisgarten, J., Pickersgill, R. and Wyns, L. 1993, Crystal structure determination and refinement at 2.3-A resolution of the lentil lectin. Biochemistry 32,8772-8781. 

Line intensity Phase abundance Chemical reaction kinetics Crystal-structure determination and refinement (whole pattern) Search/match (d-l) Space-group determination (20g-absent W Preferred orientation... 

Recent developments and prospects of these methods have been discussed in a chapter by Schneider et al. (2001). It was underlined that these methods are widely applied for the characterization of crystalline materials (phase identification, quantitative analysis, determination of structure imperfections, crystal structure determination and analysis of 3D microstructural properties). Phase identification was traditionally based on a comparison of observed data with interplanar spacings and relative intensities (d and T) listed for crystalline materials. More recent search-match procedures, based on digitized patterns, and Powder Diffraction File (International Centre for Diffraction Data, USA.) containing powder data for hundreds of thousands substances may result in a fast efficient qualitative analysis. The determination of the amounts of different phases present in a multi-component sample (quantitative analysis) is based on the so-called Rietveld method. Procedures for pattern indexing, structure solution and refinement of structure model are based on the same method. 

Diversity analysis and physical property calculation were performed by Ceris2 (4). HKL package was applied for X-ray data process (6) and the X-ray structure determination and refinement were carried out by CNX (4). X-ray co-crystal complex structures discussed in this chapter were deposited in PDB database with codes 205D, 2HWH, 2HWI, and 21 IK... 

Crystals and X-ray Data Collection. Detailed information concerning protein purification, crystallization, and X-ray data collection can be found in a previous report (Xu et al., 1991) and will be mentioned here in summary form. Recombinant murine apo-ALBP crystallizes in the orthorhombic space group P2j2i2i with the following unit cell dimensions a = 34.4 A, b = 54.8 A, and c = 76.3 A. The asymmetric unit contains one molecule with a molecular weight of 14,500. The entire diffraction data set was collected on one crystal. In the resolution range t -2.5 A, 5115 of the 5227 theoretically possible reflections were measured. Unless otherwise noted the diffraction data with intensities greater than 2a were used for structure determination and refinement. As can be seen in Table 8.2, this included about 96% of the measured data. 

Table I. Crystal Data and Details of the Structure Determination and Refinement for XeF5 AgF4"...

Figure 4.1. The flowchart illustrating common steps employed in a structural characterization of materials by using the powder diffraction method. It always begins with the sample preparation as a starting point, followed by a properly executed experiment both are considered in Chapter 3. Preliminary data processing and profile fitting are discussed in this chapter in addition to common issues related to phase identification and analysis. Unit cell determination, crystal structure solution and refinement are the subjects of Chapters 5,6, and 7, respectively. The flowchart shows the most typical applications for the three types of experiments, although any or all of the data processing steps may be applied to fast, overnight and weekend experiments when justified by their quality and characterization goals.

The Rietveld method is employed both to finalize the model of the crystal structure, when necessary, e.g. to locate a few missing atoms in the unit cell by coupling it with Fourier series calculations, and to confirm the crystal structure determination by refining positional and other relevant parameters of individual atoms together with profile variables. The fully refined... 

The simple model implies an infinite perfect crystal. The crystal specimen studied is necessarily finite (rarely more than 0.5 mm in size) and, if perfect by conventional criteria, would be utterly unsuitable for collection of intensity data of the kind required for ordinary structure determination and refinement. What is needed is an ideally imperfect crystal shot through with dislocations and intergrain boundaries so that it behaves, so far as diffraction is concerned, like a mosaic of perfect crystal blocks of the order of micrometers or tenths of micrometers in size, tilted with respect to one another by angles of the order of a few seconds of arc and scattering independently (incoherently) with respect to one another. The assumption of an ideally imperfect ... 

MSe2 crystals are very brittle and have a flat, layered, tabular appearance with shiny luster. A complete structure determination and refinement have been carried out on ErSe2 single crystals (see p. 314), Wang [6], Wang, Steinfink [5]. Line diagrams of LaSe 2 SmSe 2 given in Markovskii et al. [14]. 

In this section we will discuss perturbation methods suitable for high-energy electron diffraction. For simplicity, in this section we will be concerned with only periodic structures and a transmission diffraction geometry. In the context of electron diffraction theory, the perturbation method has been extensively used and developed. Applications have been made to take into account the effects of weak beams [44, 45] inelastic scattering [46] higher-order Laue zone diffraction [47] crystal structure determination [48] and crystal structure factors refinement [38, 49]. A formal mathematical expression for the first order partial derivatives of the scattering matrix has been derived by Speer et al. [50], and a formal second order perturbation theory has been developed by Peng [22,34],... 

X-Ray crystal structures of four 6-strand-templated active site inhibitors of thrombin, including compounds MOL-126 and MOL-174 (Section 12.10.15.2 ), have been determined and refined at about 2.1 A resolution to crystallographic R-values between 0.148 and 0.164 <1999JME1376>. 

The object of a crystal-structure determination is to ascertain the position of all of the atoms in the unit cell, or translational building block, of a presumed completely ordered three-dimensional structure. In some cases, additional quantities of physical interest, e.g.. the amplitudes of thermal motion, may also be derived from the experiment. The processes involved in such crystal-structure determinations may he divided conveniently into (I) collection of the data. (2) solution of the phase relations among the scattered x-rays (phase problem)—determination of a correct trial structure, and (3) refinement of this structure. 

Katz s two predictive techniques provided industry with acceptable predictions of mixture hydrate formation conditions, without the need for costly measurements. Subsequently, hydrate research centered on the determination of the hydrate crystal structure(s). Further refinements of the Kvsi values were determined by Katz and coworkers (especially Kobayashi) in Chapter 5 of the Handbook of Natural Gas Engineering (1959), by Robinson and coworkers (Jhaveri and Robinson, 1965 Robinson andNg, 1976), and by Poettmann (1984). 

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