Unknown Crystal Structures Research Articles

Extending the power of powder diffraction for structure determination

IN the modern techniques of high-resolution neutron and X-ray powder diffraction, an impressive amount of structural information may be obtained, allowing the refinement, using the Rietveld technique1, of structures containing more than 100 positional parameters. Despite these technical advances and the renewed popularity of the technique, powder diffraction suffers from the inevitable loss of information imposed by the collapse of three dimensions of diffraction data onto the one dimension of a powder pattern. This can seriously frustrate the determination of unknown crystal structures. As a consequence of accidental or exact reflection overlap, only relatively few reflections may have uniquely determined intensities. (For example, the cubic reflections 550, 710 and 543 exactly overlap.) Here I present a maximum-entropy algorithm (previously discussed theoretically2) that evaluates, from first principles, the intensities of overlapping reflections in powder diffraction profiles. Indeed, a full three-dimensional reconstruction of the image may be retrieved when only ∼20% of the reflections are uniquely determined. This precludes systems where the Patter-son group is not the holosymmetric group (for example, the 4/m symmetry where hkl and khl reflections are overlapping but not equivalent.) Nevertheless, for most crystal structures with unit cell volumes of less than 1,000 A3, this method should be useful.

Molecular conformation determination in unknown crystal structures by Patterson methods

A technique is described by which the conformation of a flexible molecular fragment can be obtained when some information is available on the orientation of part of the structure. Using calculations based on the reciprocal-space rotation function, it is found to be possible to determine the preferred conformation of the relevant group in an unknown crystal structure when merely orientational and not translational (positional) information is available. In structures where this conformation is the main interest, important chemical information is thus extracted.

A model for the non-molecular structures of the thiolates, MSR, of copper and silver

A model for the unknown crystal structures of copper (and silver) thiolates, MSR, is derived from the known crystal structure of Cu 8 (SCMe 2Et) 4(S 2CSCMe 2Et) 4 and other derivatives of MSR. The proposed structure is one-dimensionally non-molecular and tubular. Steric pressure between large substituents R contiguous along the chain could be accommodated with simple structural modifications, involving elongated secondary bonds and concomitant change of metal coordination from trigonal towards digonal. This results in either two intertwined infinite helical strands, or stacks of M 4(SR) 4 cycles along the chain, both of which are precedented structural functions.

The solution of unknown crystal structures from X-ray powder diffraction data. Technique and an example, ZrNaH(PO4)2

The solution of unknown crystal structures from X-ray powder diffraction data. Technique and an example, ZrNaH(PO₄)₂

A group refinement procedure in protein crystallography using Fourier transforms

A rigid-body refinement method and program for crystallography of macromolecules is described. Orientational and translational parameters are refined by fitting the molecular Fourier transforms to the observed structure-factor amplitudes. The range of convergence of the method has been tested on four examples with known crystal structure: PTI, chymotrypsinogen and two forms of α1 anti-trypsin. It was successfully applied in the structure solution of two unknown crystal structures: a third form of α1 anti-trypsin and C-phycocyanin.

Use of negative quartet cosine invariants as a phasing figure of merit: NQEST

Recent theoretical advances in the identification of those cosine invariants cos (ϕh + ϕk + ϕ1 + ϕm) which are probably negative suggest algorithms for the calculation of a figure of merit which is sensitive to the integrity of a phase set. The negative quartet figure of merit, NQEST, defined here is of particular utility in conjunction with fast multi-solution tangent formula techniques. Development of the methods and applications to both known and unknown crystal structures are presented.

ESR of Copper(II) Complexes in Magnetically Non-dilute Crystals. II. Polycrystals of Various Bis(amino acidato) copper(II) Complexes

Abstract The molecular g values of several bis(amino acidato) copper(II) complexes in crystals, whose crystal structures with two molecules per unit cell are known, have been estimated from the crystal g values by considering the effect of the spin-exchange interaction between the dissimilar copper(II) ions. All the crystal g values have been determined here from the powder K-band ESR spectra. Many other complexes with unknown crystal structures have also been dealt with in a similar way. The results have indicated that most of the complexes probably have a tetragonal or nearly tetragonal copper (II) ion environment in crystals, and a tendency for the estimated g⁄⁄ value to decrease with an increase in the energy of the visible absorption peak in crystals have been noted. A discussion about the correlation between an axial molecular g tensor and the two copper-ligand bond lengths of Cu–O and Cu–N has been given.

Applications of the Mössbauer effect to silicate mineralogy—II. Iron silicates of unknown and complex crystal structures

Measurements have been made of the Mössbauer spectra of howieite, deerite and two sapphirines, for which the crystal structures are unknown and zussmanite and the alkali amphibole crocidolite. Computer analyses of the spectral data for each silicate have yielded values for the chemical shift and quadrupole splitting for each doublet in the Mössbauer spectra. These parameters are correlated with those for iron ions in silicates of known crystal structures to give information on the oxidation state, electronic configuration, and co-ordination site of each iron atom in the structures. High spin iron is found in all minerals studied. All minerals except one sapphirine contain at least one structurally distinct type of Fe 2+ ion in sixfold co-ordination, while deerite contains Fe 2+ ions in fourfold co-ordination. Howieite, deerite, and crocidolite contain Fe 3+ in sixfold co-ordination, while sapphirines contain Fe 3+ in fourfold co-ordination. Computer calculated areas in the Mössbauer spectra have been used to estimate the fraction of each iron species in a structure giving rise to absorption, assuming that the area under a peak is directly proportional to the amount of iron in a site. The results for Fe 2+ and Fe 3+ containing minerals agree well with chemical analysis values. The area data has allowed Fe 2+ site populations to be determined in the crocidolite structure.

Interactive Graphics in Data Processing: Interactive aspects of crystal structure analysis

In demonstrating the advantageous use of graphics in a heuristic approach to problem solving, the deciphering of unknown crystal structures is used as an environment. The interactive graphic console lends concreteness to the crystallographer's abstract perception of three-dimensional structures. This paper describes how the crystallographer uses graphics in determining crystal structure by matching a known spatial molecular model with an experimental crystallographic model and by direct theoretical procedures when no model is available. Also presented are computer rendering techniques that make the man-machine relationship more productive. In conclusion, the author ponders the possibilities of more eficient and productive scientific research through the evolution of computer-aided data libraries.