Phase crystal structure problem

The most spectacular successes of X-ray methods, however, are in molecular and crystal structure analysis. Examples are the structures of insulin [130], hemoglobin (131], and vitamin B 2 [132]. Today, single-crystal X-ray structure analyses of relatively complex compounds (up to ca. 40-200 nonhydrogen atoms) are performed with computer-controlled diffractometers whose computers can be used simultaneously to solve the phase and structure problem within a few days or just a few hours.. The method has gained parity in investigation time with spectroscopic methods... 

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 ...

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. 

They have been prepared with several anions,332-335 the tetrafluoroborate salt exhibits SA and Sc phases332,333 but the triflate shows a nematic phase 334 One of the problems in studying these complexes was the very high temperatures at which the phases existed and the fact that decomposition was often observed in the upper reaches of the SA phases. Reduction of these temperatures was achieved by changing the small anions for dodecyl sulfate that also make that more materials exhibit nematic SA and Sc phases, and another more viscous phase appeared, named cubic phase So- With the anion octyl sulfate336 the crystal structure of one of the complex with 4-metoxystilbazole could be achieved (20), with this anion the cubic phase was not present. 

The problem of phase determination is the fundamental one in any crystal structure analysis. Classically protein crystallography has depended on the method of multiple isomorphous replacement (MIR) in structure determination. However lack of strict isomorphism between the native and derivative crystals and the existence of multiple or disordered sites limit the resolution to which useful phases may be calculated. 

Nowadays computers are so absurdly fast that the phase problem can be solved by recursive computation the newly proposed charge-flipping algorithm [14] performs in absence of any information on the target crystal structure not even the molecular composition or the crystal symmetry is needed. The procedure starts with... 

Methylene difluorocyclopropanes are relatively rare and their rearrangement chemistry has been reviewed recently [14]. In addition, electron deficient alkenes such as sesquiterpenoid methylene lactones may be competent substrates. Two crystal structures of compounds prepared in this way were reported recently [15,16]. Other relatively recent methods use dibromodifluoromethane, a relatively inexpensive and liquid precursor. Dolbier and co-workers described a simple zinc-mediated protocol [17], while Balcerzak and Jonczyk described a useful reproducible phase transfer catalysed procedure (Eq. 6) using bromo-form and dibromodifluoromethane [18]. The only problem here appears to be in separating cyclopropane products from alkene starting material (the authors recommend titration with bromine which is not particularly amenable for small scale use). Schlosser and co-workers have also described a mild ylide-based approach using dibromodifluoromethane [19] which reacts particularly well with highly nucleophilic alkenes such as enol ethers [20], and remarkably, with alkynes [21] to afford labile difluorocyclopropenes (Eq. 7). 

The complexity and volume of. available diffraction data requires that other than manual tediniques be used to match unknown to known spectra. Available computer programs have indeed simplified the problem of identifying an unknown substance (Refs 9,15,16,21 22). The work of Abel and Kemmey (Ref 16) in this area is worthy of note. Data taken from this report is presented as Table 4. The authors use values of 26 (<90°) to identify phase location instead of values of d in A. Major computer programs of this type endeavor to identify the crystal structure of an. unknown and cite a general factor of certainty to support the credibility of the analysis interpretation... 

Zeolite crystallization represents one of the most complex structural chemical problems in crystallization phenomena. Formation under conditions of high metastability leads to a dependence of the specific zeolite phase crystallizing on a large number of variables in addition to the classical ones of reactant composition, temperature, and pressure found under equilibrium phase conditions. These variables (e.g., pH, nature of reactant materials, agitation during reaction, time of reaction, etc.) have been enumerated by previous reviewers (1,2, 22). Crystallization of admixtures of several zeolite phases is common. Reactions involved in zeolite crystallization include polymerization-depolymerization, solution-precipitation, nucleation-crystallization, and complex phenomena encountered in aqueous colloidal dispersions. The large number of known and hypo-... 

Chemists and physicists must always formulate correctly the constraints which crystal structure and symmetry impose on their thermodynamic derivations. Gibbs encountered this problem when he constructed the component chemical potentials of non-hydrostatically stressed crystals. He distinguished between mobile and immobile components of a solid. The conceptual difficulties became critical when, following the classical paper of Wagner and Schottky on ordered mixed phases as discussed in chapter 1, chemical potentials of statistically relevant SE s of the crystal lattice were introduced. As with the definition of chemical potentials of ions in electrolytes, it turned out that not all the mathematical operations (9G/9n.) could be performed for SE s of kind i without violating the structural conditions of the crystal lattice. The origin of this difficulty lies in the fact that lattice sites are not the analogue of chemical species (components). 

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. 

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