Anna Crespi

A direct phasing method based on the origin-free modulus sum function and the FFT algorithm. XII.

An alternative way of refining phases with the origin-free modulus sum function S is shown that, instead of applying the tangent formula in sequential mode [Rius (1993). Acta Cryst. A49, 406-409], applies it in parallel mode with the help of the fast Fourier transform (FFT) algorithm. The test calculations performed on intensity data of small crystal structures at atomic resolution prove the convergence and hence the viability of the procedure. This new procedure called S-FFT is valid for all space groups and especially competitive for low-symmetry ones. It works well when the charge-density peaks in the crystal structure have the same sign, i.e. either positive or negative.

Capabilities of through-the-substrate microdiffraction: application of Patterson-function direct methods to synchrotron data from polished thin sections

Some theoretical and practical aspects of the application of transmission microdiffraction (µXRD) to thin sections (≤30 µm thickness) of samples fixed or deposited on substrates are discussed. The principal characteristic of this technique is that the analysed micro-sized region of the thin section is illuminated through the substrate (tts-µXRD). Fields that can benefit from this are mineralogy, petrology and materials sciences since they often require in situ lateral studies to follow the evolution of crystalline phases or to determine new crystal structures in the case of phase transitions. The capability of tts-µXRD for performing structural studies with synchrotron radiation is shown by two examples. The first example is a test case in which tts-µXRD intensity data of pure aerinite are processed using Patterson-function direct methods to directly solve the crystal structure. In the second example, tts-µXRD is used to study the transformation of laumonite into a new aluminosilicate for which a crystal structure model is proposed.

Application of synchrotron through-the-substrate microdiffraction to crystals in polished thin sections.

The synchrotron through-the-substrate X-ray microdiffraction technique is applied to the structural study of microvolumes of randomly oriented crystals embedded in polished thin sections. The whole procedure is discussed in detail with the help of examples from petrology, and possible future developments are envisaged.

Crystal-structure refinement of Fe3+-rich aerinite from synchrotron powder diffraction and Mössbauer data

Pale-blue fibres of an Fe 3+ -rich variety of aerinite from Tartareu (Catalunya, Spain) were studied by synchrotron powder diffraction. Crystal data and composition are: a = b = 16.9161(1), c = 5.2289(1) A, V = 1296 A 3 , space group P 3 c 1, D calc = 2.46 g cm 3 ; (Ca 4.31 , Na 0.07 ) (Al 5.25 , Si 0.43 , Mg 0.33 ) (Fe 1.36 , 3+ Fe 0.64 2.5+ ) (Fe 1.2 3+ , Mg 0.5 , Al 0.3 ) [Si 12 O 36 (OH) 12 ] [(CO 3 ) 0.75 (SO 3 ) 0.25 (H 2 O) 11.1 ], Z = 1. The oxidation states of Fe in these fibres were determined from Mossbauer spectroscopy. The model of the structure was refined with the Rietveld method to the residual value R wp = 0.036 (χ 2 = 1.73). The unit cell of aerinite contains two similar basic building units (columns) formed by three pyroxene chains pointing inwards producing two different cation sites (M1a,b) at the centres of the resulting face-sharing octahedra. The composition of M1a is 68 % Fe 3+ and 32 % mixed-valence iron (Fe 2.5+ ) and the composition of M1b is 60 % Fe 3+ , 25 % Mg 2+ and 15 % Al 3+ . The presence of mixed-valence iron provides an explanation for the observed blue colour of aerinite. According to the electron-microprobe analysis, 0.43 Si 4+ can not be hosted in the pyroxene chains and most probably occupy M2 positions. However, due to the small amount that it represents, i.e. 6 % of the M2 sites, these positions have been refined as Al 3+ assuming an octahedral coordination (final M2–O average bond length of 1.92(6) A). The large “channel” includes 0.75 CO 3 2− and 0.25 sulphur atoms, probably as sulphite groups, stacked along one threefold axis. Inspection of a polished thin section of the same Tartareu specimen from which the studied aerinite fibres were taken shows the presence of an additional deeper blue phase forming a stripe of approximately 0.2–0.3 mm thickness between the pale-blue aerinite and the laumontite substrate. The electron-microprobe analysis of this new phase indicates that it is related to aerinite but Si-richer and Fe- and Ca-poorer. Both phases also display a different optical behaviour under transmitted polarised light.

Increasing data completeness in synchrotron tts-microdiffraction experiments for δ-recycling phasing of low-symmetry compounds

Abstract Successful phasing of synchrotron through-the-substrate microdiffraction data by δ-recycling direct-methods largely depends on the number of missing intensities caused by the limited sample rotation range [J. Rius, Direct phasing from Patterson syntheses by δ recycling. Acta Cryst. A 2012, 68, 77–81]. Particularly, for the unfavorable triclinic system, dataset completeness resulting from a single series of consecutive ϕ-scans covering a total ϕ interval of ±35° is around 41%. This value is not enough for the routinary solution of a crystal structure by δ-recycling but can be increased by ~29% by applying the orthogonal χ strategy consisting of merging the information of two series of orthogonal ϕ-scans collected at the same microvolume of the polished thin section. Test calculations using simulated and experimental tts-data of the triclinic mineral axinite confirm that, with the help of the orthogonal χ strategy, crystal structures can be solved routinely. Since data in the ±35 ϕ-interval are normally accessible even for relatively thick glass-substrates (1–1.5 mm), a crystal structure can be determined from a single microvolume. For high-symmetry phases, due to the Laue symmetry redundancy, a single series of ϕ-scans normally suffices for the application of δ-recycling. However, when for experimental causes this series is incomplete, the orthogonal χ strategy also provides a simple way to increase the completeness which besides allowing solving the structure, is also beneficial for the subsequent refinement.

Use of TALP with laboratory powder diffraction data from 2D detectors

The viability of the direct-space strategy TALP (Vallcorba et al. , 2012b) to solve crystal structures of molecular compounds from laboratory powder diffraction data is shown. The procedure exploits the accurate metric refined from a ‘Bragg-Brentano’ powder pattern to extract later the intensity data from a second ‘texture-free’ powder pattern with the DAJUST software (Vallcorba et al. , 2012a). The experimental setup for collecting this second pattern consists of a circularly collimated X-ray beam and a 2D detector. The sample is placed between two thin Mylar ® foils, which reduces or even eliminates preferred orientation. With the combination of the DAJUST and TALP software a preliminary but rigorous structural study of organic compounds can be carried out at the laboratory level. In addition, the time-consuming filling of capillaries with diameters thinner than 0.3mm is avoided.