Crystal structure, determination from

Crystal structure determinations from very small samples have become possible due to the high intensities of the X-rays from a synchrotron. Very high pressures can be exerted on a small sample situated between two anvils made from diamond. In this way, our knowledge of the behavior of matter under high pressures has been widened considerably. Under pressure the elements of the fifth and sixth main groups exhibit rather unusual structures. A synopsis of the structures that occur is given in Fig. 11.9. 

Crystal structure determination from electron microscopy data... 

Fig. 2 Schematic diagram showing the sequence of stages involved in crystal structure determination from powder XRD data...

Peak positions. Shifts in the positions of the peaks in an experimental powder XRD pattern may arise due to a number of instrumental factors. Furthermore, comparison of powder XRD patterns recorded at different temperatures may show differences in appearance (particularly in regions with significant peak overlap) as a result of anisotropic thermal expansion/contraction. This issue is particularly relevant when an experimental powder XRD pattern recorded at ambient temperature is compared with simulated powder XRD patterns for known crystal structures determined from single-crystal XRD data at low temperature. 

As discussed in Sect. 3, the first stage of crystal structure determination from powder diffraction data involves determination of the unit cell by indexing the powder diffraction pattern. Clearly it is not possible to proceed with structure solution unless the correct unit cell has been found at this initial stage. Recognizing this issue, a technique employing a GA for indexing powder diffraction data has been reported [88]. The positions of the peaks in a powder diffraction pattern depend on the unit cell dimensions (lattice parameters) [a, b, c, a, ft, y], and the aim of indexing is to determine the correct lattice parameters from... 

Figure 6.1. The flowchart illustrating crystal structure determination from powder diffraction data. Preliminary processing and indexing are described in Chapters 4 and 5, respectively, and have been assumed accomplished at an earlier stage. Structure completion and Rietveld refinement are described in Chapter 7.

K.D.M. Harris, R.L. Johnston and B.M. Kariuki, The genetie algorithm Foundations and applications in structure solution from powder diffraction data, Acta Cryst. A54, 632 (1998) K. Shankland, B. David, and T. Csoka, Crystal structure determination from powder difffaetion data by the applieation of a genetie algorithm, Z. Kristallogr. 212, 550 (1997). 

K.D.M. Harris and M. Tremayne, Crystal structure determination from powder diffraction data, Chem. Mater. 8, 2554 (1996). 

We have seen this powder diffraction pattern several times throughout this text. The histogram collected from the nearly spherical LaNi4.85Sno.15 powder, produced by high pressure gas atomization from a melt, was used to illustrate both the quality of x-ray diffraction data and as one of the examples in the ab initio crystal structure solution. To demonstrate the Rietveld refinement of this crystal structure we will begin with the profile and unit cell parameters determined from Le Bail s algorithm Table 6.3) and the model of the crystal structure determined from sequential Fourier maps as described in section 6.9 and listed in Table 6.8. 

Criteria which have been drawn upon in classifying the compounds are based mainly on bond distances obtained from X-ray crystal structure determinations, from the stretching frequencies of both terminal and bridging fluorine bonds, and... 

To approximately locate the global minimum i.e., to obtain a good quality crystal structure solution) in a reasonable amount of time, grid search methods should be replaced by the stochastic ones, based on a random sampling of the parameter space. This technique, called Monte Carlo MC), has been widely used in other scientific fields to simulate the behavior of complex systems. Its application to crystal structure determination from powder diffraction data has been developed by many authors the main strategies are outlined below. 

C. Powder Indexing completes a comprehensive package of software modules for crystal structure determination from powder data. It is possible to establish unit cell and symmetry information, and use this to assist Rietveld refinement or crystal structure predictions. 

Water molecules are an essential aspect of protein structures. Without knowledge of the location of all tightly bound waters, many aspects of the structure, function, and stability of proteins cannot be properly studied. Unfortunately, waters are often abused in crystal structure determination. From the kinds of errors we detect, we assume that some crystallographers, shortly before they manually place waters in the density map, use software that places a water molecule close to each alpha carbon (in a well-determined structure there is about 1 bound water molecule visible per residue). Unfortunately, it regularly occurs that a few waters that are not moved to another position are forgotten, and remain part of the structure. 

The dye l,l, 3,3 -tetraethylimidazo[4,5-h]quinoxalinocyanine iodide (53) has had its crystal structure determined from single-crystal x-ray intensity data. It seems that steric interactions between the ethyl groups prevent the molecule from being planar. Nevertheless the bond lengths indicate that the cation is highly conjugated. 

Crystal structure prediction methods do not aim to replace experimental studies but are a complementary technique to experimental investigations. The roles that CSP can play in such investigations can fall into three categories to characterize an existing material, usually as an aid to crystal structure determination from... 

Crystal structure determination from X-ray powder diagrams generally consists of three steps ... 

Harris, K. D. M., Tremayne, M., Lightfoot, P., and Bruce, P. G., Crystal structure determination from powder diffiraaion methods by Monte Carlo methods, J. Am. Chem. Soc., 116,3543,1994. 

A. Le Bad, J. L. Fourquet, U. Bentmp t-AlF3 Crystal structure determination from X-ray powder diffraction data. A new MX3 comer-sharing octahedra 3D network, J. Solid State Chem. 199,151 (1992). 

The chlorine-poor isotypic series of nitride sulfide chlorides R6N3S4CI (R=La-Nd) were prepared by Lissner et al. (1996) from appropriate molar ratios of metal R, sulfur, NaN3 and RCI3 chloride at 850°C. Their orthorhombic (Pnma) crystal structure, determined from single crystal data of the lanthanum compound, exhibits two different chains of connected [NR4] tetrahedra, which are held together by the X-ray diffraction indistinguishable anions S " and Cl". 

---