Contemporary Diffraction Methods in Study of Polycrystals

Abstract

Diffraction in the polycrystal/crystalline powder is one of the most powerful techniques in study of microstructure and crystal structure of solids. This technique enables, in synergy with microscopic, spectroscopic and other physical techniques, a complete analysis of onephase and multi-phase substances, that are important in scientific and technological fields. Information on microstructure and crystal structure of a substance is stored in its diffraction pattern; in order to reveal this information, the diffraction pattern should be decoded by application of adequate mathematical and physical procedures which may often be rather complex. During the last decades, diffraction techniques in the polycrystal are developing rapidly due to the introduction of sophisticated instrumentation, powerful computers and by application of synchrotron radiation. This advance enables the collection and interpretation of diffraction data in a short real time as well as the study of time-resolved dynamic processes in the crystalline substance. Possibilities of diffraction techniques in the polycrystal are concisely described and illustrated by examples of authors' scientific studies.Keywords: X-ray diffraction, microstructure, crystal structure, recent advancement in diffraction. DIFFRACTION IN THE POLYCRYSTALIFFRACTION is a phenomenon in which the beam of X-rays, electrons or neutrons, by passing through a single crystal or a polycrystal, deviates from the initial direction due to the scattering on the structural motifs (atoms, ions, molecules) in the crystal. The scattered waves give rise to diffraction maxima in a set of discrete space directions due to their mutual constructive interference. These directions strongly depend on the periodicity and symmetry of the crystal. The set of diffraction maxima represent the diffraction pattern of the single crystal / polycrystal. The intensities of diffraction maxima depend on the nature of structural motifs and their mutual space arrangement. Therefore, diffraction techniques are ideal in the study of the crystal structure and microstructure: space periodicity in the crystal, unit-cell parameters (unit-cell edges a, b and c and angles among them, α, β and γ), symmetry elements which determine the space group, space periodical arrangement of structural motifs, identification of particular atoms and their coordinates, definition of the nature and length of their mutual chemical bonds, the angles among the chemical bonds, the size and shape of crystallites, distribution of crystallite sizes, the nature of the crystallite / grain boundary, stresses and strains inside the crystallite, point, planar and volume defects inside the crystallite, phase transitions in a given substance and the definition of its phase diagram, etc.In determination of the crystal structure, diffraction in the single crystal has an advantage in relation to the diffraction in the polycrystal. That is a consequence of the fact that the 3D data, obtained by diffraction in the single crystal, are transferred ...

Quantitative Phase Analysis by X-ray Diffraction—Doping Methods and Applications

“…The doping methods have been applied in a series of author's studies, among others, in the study of the phase transition in titanium dioxide [18,19], biomineralization processes in the oyster Ostrea edulis [20,21], crystalline phases in intermetallic oxides [22][23][24][25][26][27], precipitation processes in Al-Zn alloys [11][12][13]19].…”

“…Therefore, one can find the molar fractions of the phases R and A by comparison of the measured intensities and the intensities of diffraction lines calculated on the basis of the crystal structure of R and A, for instance, of the R diffraction line 110, and of the A diffraction line 101, according to R ⁄ A = 1.25 I110R ⁄I101A. At several temperatures, the molar ratio was also checked at RT by the doping method, after quenching the sample to RT [18,19]. [19].…”

“…At several temperatures, the molar ratio was also checked at RT by the doping method, after quenching the sample to RT [18,19]. [19].…”

“…An extensive study of Al-Zn alloys, with the molar zinc content, x(Zn), up to 0.62 by XRD, TEM, and DTA resulted in many new information on the microstructure of the alloys (unit-cell parameters, crystallite size and shape, strains, phase fractions, thermal expansion, etc. ), in dependence on the initial composition, applied thermal treatment, and temperature [12,13,19]. Essential points from References [12,19] are given here.…”

“…), in dependence on the initial composition, applied thermal treatment, and temperature [12,13,19]. Essential points from References [12,19] are given here. The alloys rapidly quenched from a temperature, T t , higher than the solid-solution temperature, T ss , to RT are supersaturated solid solutions.…”