Diffuse scattering and structural phase transitions

Abstract

O n the basis of numerous experiments using the mono-Laue method on the diffuse scattering of X-rays and electrons we have developed the Comes-Lambert-Guinier concept of the existence of co-operative thermal vibrations in perfect crystals in which one-dimensional or two-dimensional atomic objects, i.e. chains or planes of atoms, are moving in a double-well potential with conservation of coherence. For an approximate description of such a motion we have utilized the pseudospin king model approach which Is widely used in the theory of structural phase transitions. These ideas proved to be successful for the description of diffuse scattering patterns, and their temperature evolution in close connection with structural phase transitions.The developed theory gives the possibility through the observation of diffuse scattering at high temperatures and its analysis to predict the structural phase transition (and even the subsequent cascades of transitions) and to give the correct explanation for physical anomalies in the crystals, either with distortive (weak) or reconstructive (strong) transitions. A wide variety of crystallochemical situations and transitions in crystals of the perovskite family and in metals with a bcc lattice are analysed in detail. A number of new experimental diffuse scattering patterns from crystals of various types are obtained.KEY WORDS: mono-Laue method, crystal structure loose-packing, movable coherent extended objects, relrods and relplanes. I INTRODUCTIONIn this paper we shall consider only the spontaneous (occurring with temperature variation without outer interference) structural phase transitions of the displacement type. Two different types of such transitions are assumed to exist: distortive and reconstructive. Distortive transitions are weak structural phase transitions at which the structure is changed only slightly, and the atom displacements u are far less than the interatomic distances or lattice parameters, a so that u < a. Usually u/a % 10p2-10-3. At such a transition some symmetry elements of the initial phase vanish, but in such a way that the final and initial phases possess the subgroup relation: G, c Go. This is the fundamental relation for Landau theory and that is why the theory of such transitions is rather well developed. Among them one can find either second-order transitions or the so-called first-order transitions close to the secondorder ones. 89 Downloaded by [University of Cambridge] at 02:40 05 November 2014 90 F. A. KASSAN-OGLY, V. E. NAISH A N D I. V. SAGARADZEReconstructive transitions are strong first-order transitions at which a substantial crystal structure reconstruction with alteration of the actual structure type takes place, for example, bcc-fcc, bcc-hcp and so on. The displacements of atoms at these transitions are much greater (u i a) and the subgroup relation is absent completely; hence Landau theory in the usual way is not applicable to them. For this reason alone the theory of reconstructive transitions is far less developed.In the present paper, an...

Discovery of metastable tetragonal disordered phase upon phase transitions in the equiatomic nanostructured FePd alloy

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Microstructure of Mo – 47% Re – 0.4% Zr alloys after rolling at room temperature. II. Peculiarities of mechanical twinning and formation of high-angle boundaries between microbands

“…In this version, a direct (bcc→fcc, Fig. 5a) transformation, apart from cooperative displacements of atomic planes (110) along [110 ] and [110 ] not shown here (for details, see, e.g., [13,[15][16][17][18]), involves homogenous deformation transforming these planes into close-packed hcp-phases, in the case where the Nishiyama-Wassermann (N-W) relation is fulfilled.…”

“…Therefore, here we shall report but only briefly their potential to describe certain phenomena of plastic deformation and crystal-lattice reorientation, and present one of the atomic models of formation of reorientation bands (50-60)°<110> observed in an bcc-crystal in the present work. To develop the models, the authors of [7,[13][14][15][16][17] used the geometrical theory of martensitic (bcc →fcc and bcc→hcp) transformations (MT) [18], where atomic rearrangements represent combined cooperative atomic shears (shufflings) in close-packed planes of the bcc-lattice and homogeneous deformation of the Bein-type transformation.…”

Mechanisms of deformation localization and mechanical twinning under the conditions of phase instability of a crystal in stress fields

“…According to [21], a change of the system of the reverse α → γ transformation implies a change of the transformation plane. This type of transformation, resulting in a reorientation of the crystal lattice with the vector θ = 60° <110>, is exemplified in Fig.…”

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