MODELLING OF IRREGULAR INTERSTRATIFIED STRUCTURES OF SINGLE CRYSTALS WITH CHEMICAL INHOMOGENEITY

T.I. Ivanova1, O.V. Frank-Kamenetskaya1 and V.A. Drits2

1St. Petersburg State University, University emb. 7/9, 199034 St.Petersburg, Russia
2Geological Institute RAS, Pyzhevsky per. 7, 109017 Moscow, Russia

Keywords: X-ray diffraction, aperiodic crystals, irregular interstratified structures, simulation of diffractograms

The possibilities of modelling of irregular interstratified structures of single crystals with chemical inhomogeneity are discussed: the theoretical basis, the requirements to the X-ray experiment, the accuracy and reproducibility of the diffraction data, the reliability of the suggested models. The examples of the successful application of the approach to the study and description of the real structures of single crystals belonging to different structural types are considered. Three general types of irregular interstratified structures differing in the nature of chemical inhomogeneity as well as in the peculiarities of their diffraction patterns are distinguished.

One of the wide-spread types of structural inhomogeneity of crystals is so-called interstratified or mixed-layered structures [1] with any proportion of two-dimensional modules (layers) differing in chemical composition as well as in crystal structure stacked in a more or less ordered sequence. The irregular alternation of layers, having the identical or fairly different two-dimensional cell in the layer plane that allows them to coexist within a coherent domain, perturbs the perfect periodicity of the whole structure in the direction perpendicular to the layer plane. The distinct features of the diffraction patterns of crystals with irregular interstratified structures is that basal reflections form irrational series and usually display broadening and asymmetry of their profiles.

For the quantitative description of real structure of single crystals with chemical inhomogeneity we proposed [2] the use of the statistical model of irregular interstratified structures [1] with probabilistic parameters which characterise a proportion of layers and a motif of their distribution along a certain direction in a coherent domain. The approach is based on the analysis of profiles of basal peaks using the theory of X-ray diffraction by disordered lamellar structures [1]. It permits to reveal some structural peculiarities of single crystals consisting of layers with different composition, which are invisible for commonly used X-ray structural analysis.

Depending on the size and the shape of the samples the measurements of their X-ray diffraction patterns were carried out by q-2q scanning along a certain direction in either conventional powder or four-circle autodiffractometer both supplied with monochromators. The special attention was paid to the collimation of the beam.

The study of the number of single crystals [2-5] (various perovskite-like high-temperature superconductors (HTSC); edenite, a representative of calcium amfiboles; natural grandite garnets, the intermediate members of grossular - andradite series) and LB-films [6] proved that their structural inhomogeneity along certain directions could be described in terms of two-component irregular interstratified structures with different nature of admixture layers, their proportion and character of distribution within the crystal. It has been shown that the statistical parameters of these structures, varying from one crystal to another, determined the degree and the scale of inhomogeneity and correlate with the formation conditions of crystals and their physical properties.

Thus, broad and stepwise transitions to superconducting state of HTSC crystals obtained in different conditions were associated with their interstratified structures [5]. Based on the correlation "formation conditions - structure - SC properties" the techniques of the synthesis and postgrowth treatment conditions of homogeneous YBa2Cu3Ox single crystals with high Tc values and narrow transitions to SC-state have been developed [7].

It has been established for grandite garnets [8] that the drastic change of the structural characteristics from sample to sample going along with the change of their optical patterns showed the correlation between the fine and superfine oscillating zonality. The self-affinity of zoning at different scales testify to the possible origin of the zonality due to the non-linear dynamics at the growth front. The wide variation of the layer compositions revealed by the simulation of the X-ray diffraction patterns seems to contradict the hypothesis of unmixing in grandites.

The restrictions of the approach originate from the use of method of trials and errors while simulating the diffraction patterns of the crystals. This allows rejection of the incorrect models but inevitably leads to the multivariant results. The reliability of models can be essentially increased on the basis of the data on crystal structural chemistry brought in agreement with the data of detailed chemical analysis of the samples. It is also expedient to combine the modelling with the other techniques such as high-resolution electron microscopy and electron diffraction.

This work was supported by RFBR grant N 96-05-65579.

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