ASTRA– a program package for accurate structure analysis by the intermeasurement minimization method

Abstract

ASTRA2.0 is a program package for single‐crystal structure research using different experimental conditions and radiation of different types (X‐rays, neutrons and electrons). The package includes programs for data collection optimization, data reduction, structural parameter refinement and electron density plotting. The expression that is responsible for minimization of the difference between reduced measurements is included in the goal function of the refinement program. The refinement program is based on an adaptive nonlinear least‐squares method. The crystal structure is described by a detailed model for electron density analysis. ASTRA uses a multipole model up to eighth order for the aspherical electron density description, an anharmonic model up to sixth order for the description of atom displacement and a model of mixed atomic positions for the description of atomic replacement. Refinement of the structural parameters using data of precession electron diffraction and the Bloch‐wave method to account for multiwave scattering is realized. Tools for refinement automation are included in ASTRA.

Crystal-structure refinement of Sr3Ga2Ge4O14

“…The SGG structure is characterized by the presence of two mixed cation sites, which is accompanied by the anharmonic motion of the cat ions in the 3e, 3f, and 2d sites and two oxygen atoms in general positions. The unit cell parameter а of SGG is smaller than that of STGS, whereas the Sr polyhedron in SGG for is more elongated along the twofold axis, which correlates with an increase in the piesoelectric coefficient d 11 …”

“…1 In both experiments the data were collected over almost the full sphere of reciprocal space for the reso lution used (sinθ/λ| max ≈ 1.33 Å -1 ). The X ray diffrac tion data were processed according to the procedure described in [9], where new versions of the ASTRA program [10,11] were employed. The correction for thermal diffuse scattering was applied as described in [12] using elastic constants [3].…”

Software for HUBER-5042 diffractometer with Displex DE-202 helium cryostat

“…The importance of the anharmonic model is verified by constructing a probability density function for finding electrons in a given volume of space and computing Fourier difference maps. The valence electron density distribution was described using the multipole Hansen-Coppens model [20] with corrections [8]. The main refinement results are indicative of the high quality of collected experimental data: sp.…”

“…We used the following data processing techniques (ASTRA program [8]): integration of peaks, introduction of thermal diffuse scattering correction (according to [13]) with elastic constants [14], and consideration of the extinction effect [15,16]. The structural model of CaF 2 was refined using F 2 ; the atomic scattering curves were taken from [17].…”

“…We also developed some new programs and modified existing ones for the following steps: preliminary stage of diffraction experiment, planning and carrying out data collection (with the possibility of measuring high-angle reflections and speeding up collection), a profile analysis of peaks with instrumental drift correction, etc. The programs of the software package can be divided into two groups: programs for controlling the diffractometer, which are written on the C-like SPEC language [1], and programs of the ASTRA package [8] for auxiliary calculations and processing experimental data.…”