D. Gratias

Indexing of icosahedral quasiperiodic crystals

Since the definition of quasiperiodicity is intimately connected to the indexing of a Fourier transform, for the case of an icosahedral solid, the step necessary to prove, using diffraction, that an object is quasiperiodic, is described. Various coordinate systems are discussed and reasons are given for choosing one aligned with a set of three orthogonal two-fold axes. Based on this coordinate system, the main crystallographic projections are presented and several analyzed single-crystal electron diffraction patterns are demonstrated. The extinction rules for three of the five icosahedral Bravais quasilattices are compared, and some simple relationships with the six-dimensional cut and projection crystallography are derived. This analysis leads to a simple application for indexing powder diffraction patterns.

About the AlCuFe icosahedral phase formation

Abstract In the present work, results obtained by differential thermal analysis (DTA) and X-ray diffraction (XRD) confirm [5, 8] that the icosahedral phase (i-phase) is formed by a peritectic reaction. A single i-phase can be obtained after annealing around the compositions Al64Cu24Fe12Al61.75Cu25.5Fe12.75. For the composition Al62Cu25.5Fe12.5, the XRD lines of the i-phase are narrow whatever the annealing temperature (800 °C or 600 °C). Thus, this result establishes that there exists a single phase domain where the i-phase is perfect (without phasons) and remains stable at 600 °C. A provisional vertical section along the line Al70Cu20Fe10Al64Cu24Fe12Al58CuPin28Fe14 is proposed and shows the phases that exist equilibrium at various temperatures in this range of compositions.

The phase diagram and structures of the ternary AlCuFe system in the vicinity of the icosahedral region

Abstract The phase diagram of the ternary system (Al, Cu, Fe) has been systematically studied around the icosahedral region. At 680°C, the i-region extends approximately over a triangle with vertices of Al, Cu and Fe composition of respectively 62.4-24.4-13.2, 65-23-12 and 61-28.4-10.6. This region splits schematically into 3 fields: (i) the perfect icosahedral phase which is stable down to the lowest possible annealing temperature where atomic diffusion is active in a tiny region of composition close to Al62.3Cu24.9Fe12.8; (ii) a well defined periodic phase with rhombohedral lattice which transforms reversibly into ico near 710°C in the lower part of the triangle; (iii) a complex region characterized by additional diffraction effects (peak broadening, lineshapes, etc.) which may correspond to various approximant structures closely related to the i-phase.

On the determination of the Burgers vector of quasicrystal dislocations by transmission electron microscopy

Abstract The contrast of dislocations in icosahedral quasicrystals observed by transmission electron microscopy is discussed in the framework of the kinematical theory of electron diffraction. It is found that, owing to the special structural features of dislocations in quasiperiodic lattices, there are two basically different imaging conditions for which the contrast can vanish. The conditions are established for contrast experiments in which the direction of the Burgers vector components can be determined in physical and orthogonal space. Provided that the dislocation displacement field fulfils certain requirements, contrast experiments employing both extinction conditions permit the defect to be characterized by the direction of a Burgers vector in the six-dimensional reference space of icosahedral quasicrystals.

Antiphase domains in icosahedral Al-Cu-Fe alloy

Abstract Electron microscopy observations of the newly discovered icosahedral phase in the Al‐Cu‐Fe ternary system show a domain structure as expected from a group‐subgroup formal decomposition from a primitive six-dimensional (6D) hypercubic unit cell to a face‐centred one with twice the lattice parameter, as suggested by Ebalard and Spaepen. The structure of Al65Cu20Fe15 can be seen as an ordered F superstructure of the usual primitive quasilattice with, at least, two motifs in the 6D representation. The smoothness of the observed antiphase boundaries and the relative weak intensities of the superstructure reflections suggest that the ordered motifs should share many geometrical features. A possibility could be that at least one of the orbits of a given atomic species arranges in space according to a 6D primitive skeleton and chemical ordering occurs on the remaining orbits.

Crystallographic description of coincidence‐site lattice interfaces in homogeneous crystals

Coincidence-site lattice interfaces (CSLI) are frequently observed in crystals where a rigid framework remains invariant on both sides of the interface. They also seem to minimize the interface energy, for example, in metals where, empirically, the greater the density of the coincidence-site lattice the more stable the grain boundary becomes. Group-theory considerations allow the determination of all the possible interface operations which leave a given sublattice invariant. A classification of these CSLI with respect to the number of equivalent sublattices they leave invariant is a guide for the prediction of the most stable type of interfaces with respect to the sublattice considered. Examples from different types of crystals illustrate the method, which also applies for translation boundaries, twins and grain boundaries.

Characterization of two different types of long‐period ordered alloys by high‐resolution electron microscopy

High-resolution electron microscopy can be used to differentiate between two structural models of long-period ordered alloys. These models differ in the nature of the disorder as seen in the stacking irregularities which can have planar boundaries as exemplified by Ag3Mg or wavy boundaries as in AuCu II. In the composition range 22-27 at. % Mg, Ag3Mg is built up with a regular arrangement of two kinds of structural layers, 1 or 2 LI 2 cells in thickness. Some stacking disorder exists, but this alloy can be locally described using a space-group notation and has the character of being an infinitely adaptative structure. High-resolution images have been used to show the perfect planarity of the boundaries in Ag3Mg, thus demonstrating the way in which disorder is accommodated in this alloy.

Dislocation climb in icosahedral quasicrystals

Abstract We discuss here some arguments in favor of climb being the dominant mode of dislocation motion responsible for the plastic deformation of icosahedral quasicrystals.

Dislocation motions in 5-fold planes of icosahedral Al-Pd- Mn

Dislocations moving in 5-fold planes of icosahedral AlPdMn have been observed in in situ heating TEM experiments. Similar dislocations forming a deformation band in the as-grown material have been analyzed in bright field and in LACBED conditions. Their Burgers vectors are translations of the 6-dimensional hyperlattice, with components in the physical space along 2-fold directions out of the plane of motion. Dislocations have accordingly moved by climb, presumably with a difficult jog-pair nucleation.

Etude des phases ordonnées à longue période irrationelle. Les alliages AuCu II et AuCu–Zn

It is shown, by electron diffraction and high-resolution microscopy, that AuCu II is a typical example of an irrational long-period alloy, contrary to Ag3Mg, for instance, which is a typical rational long-period alloy. Antiphase boundaries are not planar (as is the case for Ag3Mg) but rather fluctuating around a mean position, as shown by high-resolution images; this structure is well described by Jehanno & Perios model [J. Phys. (1964), 25, 966-974], which always involves some disorder localized in the boundaries themselves. The long period is always the result of an average of domains of different lengths, thus giving a statistical meaning to the irrationality. This structural behaviour is not confined to alloys with large values of the mean length of domains, as is demonstrated by the study of AuCu-Zn.