Problem crystal structures

By necessity, then, I limit my remarks on the topic of problem crystal structures to selected examples that hopefully will illustrate a few, but surely far from all, of the problems that can befall both the aware and the unaware. 

The purpose of this paper is to inform nonspecialists about those features of a completed structure determination that lead one to view the answers with suspicion. While many criteria may be employed in such an evaluation, some of which have been discussed in preceding papers, the ultimate criterion is one s own chemical intuition. Such intuition must be used with caution, however, or one may overlook subtle, genuine chemical effects that might be of importance. With this in mind, let us pass along through a Rogue s Gallery of Problem Crystal Structures. ... 

This has been an abbreviated tour through a Rogue s Gallery of Problem Crystal Structures. The overall morals include the following (1) If you don t believe the results, know enough to detect the false steps in experiment or calculation that are involved (2) whereas problems in diffraction studies are minimized by a healthy observation-to-parameter ratio, it is still possible to make mistakes (3) when all else fails, believe your chemical intuition and that warm, happy feeling and don t be impressed by elegant models, or low R indices. 

The integrand in this expression will have a large value at a point r if p(r) and p(r+s) are both large, and P s) will be large if this condition is satisfied systematically over all space. It is therefore a self- or autocorrelation fiinction of p(r). If p(r) is periodic, as m a crystal, F(s) will also be periodic, with a large peak when s is a vector of the lattice and also will have a peak when s is a vector between any two atomic positions. The fiinction F(s) is known as the Patterson function, after A L Patterson [14], who introduced its application to the problem of crystal structure detemiination. 

A Classic Optimisation Problem Predicting Crystal Structures... 

An additional problem is encountered when the isolated solid is non-stoichiometric. For example, precipitating Mn + as Mn(OH)2, followed by heating to produce the oxide, frequently produces a solid with a stoichiometry of MnO ) where x varies between 1 and 2. In this case the nonstoichiometric product results from the formation of a mixture of several oxides that differ in the oxidation state of manganese. Other nonstoichiometric compounds form as a result of lattice defects in the crystal structure. ... 

Syntheses, crystallization, structural identification, and chemical characterization of high nuclearity clusters can be exceedingly difficult. Usually, several different clusters are formed in any given synthetic procedure, and each compound must be extracted and identified. The problem may be compounded by the instabiUty of a particular molecule. In 1962 the stmcture of the first high nuclearity carbide complex formulated as Fe (CO) C [11087-47-1] was characterized (40,41) see stmcture (12). This complex was originally prepared in an extremely low yield of 0.5%. This molecule was the first carbide complex isolated and became the foremnner of a whole family of carbide complexes of square pyramidal stmcture and a total of 74-valence electrons (see also Carbides, survey). 

In order to answer these questions as directly as possible we begin by looking at diffusive and displacive transformations in pure iron (once we understand how pure iron transforms we will have no problem in generalising to iron-carbon alloys). Now, as we saw in Chapter 2, iron has different crystal structures at different temperatures. Below 914°C the stable structure is b.c.c., but above 914°C it is f.c.c. If f.c.c. iron is cooled below 914°C the structure becomes thermodynamically unstable, and it tries to change back to b.c.c. This f.c.c. b.c.c. transformation usually takes place by a diffusive mechanism. But in exceptional conditions it can occur by a displacive mechanism instead. To understand how iron can transform displacively we must first look at the details of how it transforms by diffusion. 

Most materials scientists at an early stage in their university courses learn some elementary aspects of what is still miscalled strength of materials . This field incorporates elementary treatments of problems such as the elastic response of beams to continuous or localised loading, the distribution of torque across a shaft under torsion, or the elastic stresses in the components of a simple girder. Materials come into it only insofar as the specific elastic properties of a particular metal or timber determine the numerical values for some of the symbols in the algebraic treatment. This kind of simple theory is an example of continuum mechanics, and its derivation does not require any knowledge of the crystal structure or crystal properties of simple materials or of the microstructure of more complex materials. The specific aim is to design simple structures that will not exceed their elastic limit under load. 

There is a lively controversy concerning the interpretation of these and other properties, and cogent arguments have been advanced both for the presence of hydride ions H" and for the presence of protons H+ in the d-block and f-block hydride phases.These difficulties emphasize again the problems attending any classification based on presumed bond type, and a phenomenological approach which describes the observed properties is a sounder initial basis for discussion. Thus the predominantly ionic nature of a phase cannot safely be inferred either from crystal structure or from calculated lattice energies since many metallic alloys adopt the NaCl-type or CsCl-type structures (e.g. LaBi, )S-brass) and enthalpy calculations are notoriously insensitive to bond type. 

Figure 6.4 Crystal structure of ar-tetragonal boron. This was originally thought to be B50 (4Bi2 + 2B) but is now known to be either B50C2 or B50N2 in which the 2C (or 2N) occupy the 2(b) positions the remaining 2B are distributed statistically at other vacant sites in the lattice. Note that this reformulation solves three problems which attended the description of the or-tetragonal phase as a crystalline modification of pure B ...

Similar problems arise with the four isomeric dibenzazepines 4-7. since only 5//-dibenz-[6,d]azepine (4) and 5//-dibenz[/>,./]azepine (7) can be drawn as fully benzenoid ring structures. Even so, 5//-dibenz[/ ,t/]azepines are rare and are known only as the 7-oxo derivatives.4 In contrast, 5//-dibenz[6,e azepine (5) and 6//-dibenz[r,t>]azepine (6) exist only as the 11//- 5a and 5H- 6a isomers, respectively. In fact, there is no chemical or spectrosopic evidence for the isomerization of 5//-dibenz[e,e]azepine,5 or its 6-oxide,6 to the 6//-dibenz[r, e]azcpinc isomer (6). In addition, an X-ray crystal structure of 7-methoxy-5//-dibenz[e,e]azepine supports unequivocally the benzenoid rather than the quinonoid form.7 9//-Tribenz[6,d /]azepine (8) has only recently been prepared.8... 

X-Ray diffraction from single crystals is the most direct and powerful experimental tool available to determine molecular structures and intermolecular interactions at atomic resolution. Monochromatic CuKa radiation of wavelength (X) 1.5418 A is commonly used to collect the X-ray intensities diffracted by the electrons in the crystal. The structure amplitudes, whose squares are the intensities of the reflections, coupled with their appropriate phases, are the basic ingredients to locate atomic positions. Because phases cannot be experimentally recorded, the phase problem has to be resolved by one of the well-known techniques the heavy-atom method, the direct method, anomalous dispersion, and isomorphous replacement.1 Once approximate phases of some strong reflections are obtained, the electron-density maps computed by Fourier summation, which requires both amplitudes and phases, lead to a partial solution of the crystal structure. Phases based on this initial structure can be used to include previously omitted reflections so that in a couple of trials, the entire structure is traced at a high resolution. Difference Fourier maps at this stage are helpful to locate ions and solvent molecules. Subsequent refinement of the crystal structure by well-known least-squares methods ensures reliable atomic coordinates and thermal parameters. 

We have already dlsussed structure factors and symmetry as they relate to the problem of defining a cubic unit-cell and find that still another factor exists if one is to completely define crystal structure of solids. This turns out to be that of the individual arrangement of atoms within the unit-cell. This then gives us a total of three (3) factors are needed to define a given lattice. These can be stipulated as follows ... 

Hydrocolloid stabilizers are vitally important in the manufacture of sherbet and ices. The absence of larger amounts of milk colloids and the presence of larger amounts of water emphasize the need for proper stabilization. Stabilizers help to maintain a Arm body and smooth texture during manufacture, storage, and distribution. Bleeding and surface sugar crystallization are two problems related to crystal structure in sherbet and ices and are very closely associated with the use of the proper hydrocolloid stabilizer. 

However, in the case of multimetallic catalysts, the problem of the stability of the surface layer is cmcial. Preferential dissolution of one metal is possible, leading to a modification of the nature and therefore the properties of the electrocatalyst. Changes in the size and crystal structure of nanoparticles are also possible, and should be checked. All these problems of ageing are crucial for applications in fuel cells. 

There is great interest in the development of methods that allow the identification of a reasonably good structure with which to start the simulation of dense atomistically detailed polymer systems. The problem of generating dense polymer systems is formidable due to the high density and the connectivity of polymer systems. For crystal structures this can be systematically achieved [33,34] for amorphous structures, however, there is no generally satisfactory method available. Two recent developments in methods for generating amorphous packing (Santos, Suter) are reviewed in Section 3. 

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