A. Letoublon

Phason elastic constants of the icosahedral Al-Pd-Mn phase derived from diffuse scattering measurements

The diffuse scattering in the diffraction pattern of the icosahedral Al-Pd-Mn quasicrystalline phase has been measured on an absolute scale by X-ray and neutron scattering on single-grain samples. Most of the diffuse scattering can be interpreted in the framework of the elasticity theory of icosahedral quasicrystals considering only phason fluctuations. At room temperature the absolute values of the K1/kBT and K2/kB T phason elastic constants are of the order of 0.06 and 0.031atom-1. The amount of diffuse scattering intensity is insensitive to the sample annealing treatment.

Reversible transformation between an icosahedral Al-Pd-Mn phase and a modulated structure of cubic symmetry

Abstract A new Al-Pd-Mn phase, called F2M, and its reversible transformation into an icosahedral structure at high temperatures were studied by transmission electron microscopy (TEM) and by in-situ X-ray diffraction using synchrotron light sources. The phase F2M appears to be closely related to the F2 super-ordered icosahedral phase identified by Ishimasa and Mori (1992, Phil. Mag. Lett., 71, 65) and has almost the same chemical composition. As identified by TEM, its structure is of cubic symmetry and non-periodic. An overall icosahedral symmetry results with crystallographic orientational relationships between domains of cubic symmetry. The room-temperature X-ray diffraction pattern presents first- and second-order satellite reflections around the main and superstructure Bragg peaks of the F2 phase. They are located along directions parallel to threefold axes with a wave-vector equal to a quarter of a six-dimensional reciprocal-lattice vector of the icosahedral Al-Pd-Mn lattice. In a first approximation,...

Dynamics of long-wavelength phason fluctuations in the i-Al-Pd-Mn quasicrystal.

We report on the dynamics of phason modes in the i-Al–Pd–Mn icosahedral quasicrystal, measured between room temperature and 650°C, using the X-ray intensity fluctuation spectroscopy (XIFS) technique. Up to 500°C, the autocorrelation function, ℑ(q, t), displays almost no time evolution as expected for frozen-in phason fluctuations at low temperature. At higher temperatures, ℑ(q, t) follows a single exponential time decay from which the characteristic time τ c(q) is extracted. These results are compared to the expected shape of ℑ(q, t) as derived from the expressions of the eigenvalues and eigenvectors of the C ⊥ ⊥(q) phason dynamical matrix. In agreement with the hydrodynamic theory of quasicrystals, which predicts phasons with diffusive character, we find that τ c(q) varies linearly with q −2 at 650°C. The corresponding diffusion coefficient is 2.2(±0.5) × 10−18 m2 s−1 and the activation energy is estimated around 2.3(±1) eV.

Superlattice ordering of cubic symmetry in an icosahedral Al-Pd-Mn phase

Abstract A new Al-Pd-Mn phase, called F2M, and its reversible transformation with an icosahedral structure at high temperature have been identified in a previous synchrotron X-ray diffraction study (de Boissieu et al. 1998, Phil. Mag. A, 78, 305). From the present results of a transmission electron microscopy study, it is shown that such a phase exhibits a cubic symmetry with local cubic approximant arrangements of huge cell parameter (a = 294 ± 1.5 A). The microstructure of the F2M phase is multidomains with crystallographic orientational relationships between domains imparting an overall icosahedral symmetry. An interpretation in terms of a superlattice ordering of cubic symmetry in a super-ordered icosahedral phase (i.e. the F2 phase described by Ishimasa (1995, Phil. Mag. Lett., 71, 65) is proposed on the basis of an analysis of the peculiar sandwich structure observed along (111) threefold axes of the F2M structure. A crystallographic space group for local cubic arrangements is also proposed.

Degree of structural perfection of icosahedral quasicrystalline grains investigated by synchrotron X-ray diffractometry and imaging techniques

A study of the structural perfection of icosahedral quasicrystalline grains of various alloys (Al-Pd-Mn, Zn-Mg-RE (RE L rare earth) and Al-Cu-Fe), grown by different slow solidification techniques (Czochralski, Bridgman, flux and annealing) was performed using high-resolution diffraction, including recording rocking curves combined with X-ray topography and phase contrast radiography, at a third-generation synchrotron radiation source (European Synchrotron Radiation Facility, Grenoble, France). For Al-Pd-Mn, additional coherent diffraction and diffuse scattering measurements were also carried out. After evaluating the potentialities of the techniques used, in the light of the criteria defined for crystals, it is shown that the structural perfection of icosahedral quasicrystals is quite comparable with that of metallic crystals but is considerably influenced by either uniform phason strains which can destroy the quasiperiodic long-range order, or by long-wavelength phason fluctuations leading to diffuse scattering. The structural perfection was also found to be extremely variable across the as-grown quasicrystalline grains and to be dependent on the presence and characteristics of inhomogeneities (pores and precipitates) often included in the quasicrystalline matrix. Regarding the grains that we used, it has been impossible to distinguish a clear influence of either the type of alloy or the growth method. It has, however, been noticed that Al-Pd-Mn and Al-Cu-Fe grains appeared less defective than Zn-Mg-RE grains and that the microstructure of these latter grains looks like that of crystals grown by the same technique. Annealing and mechanical polishing effects have also been analysed in the case of Al-Pd-Mn grains. It appeared that annealing improves the quasicrystalline lattice perfection by lowering phason strains insofar as no precipitates are nucleated. Mechanical polishing can introduce defects, located at the external surfaces, having the shape of bands.

Magnetic domain fluctuations observed by coherent X-ray scattering

Abstract Coherent X-ray-scattering measurements were performed in the type-I antiferromagnetic phase of UAs at the M IV uranium absorption edge. Speckle patterns from a magnetic reflection were followed up through the magnetic transition. The origin of the speckles is discussed in terms of antiferromagnetic domain configuration and fluctuations.

Stability of the F2-(Al-Pd-Mn) phase

The stability of the F2-(Al-Pd-Mn) phase has been studied by in-situ neutron diffraction on a single quasicrystal with composition Al69.8Pd21.4Mn8.8. We find that the F2 phase is not stable and corresponds to a transient state in the process of the transformation of the icosahedral phase to the F2M phase. The icosahedral-to-F2Mphase transition occurs at around 715oC. In the F2 phase a large amount of diffuse scattering is located close to the icosahedral Bragg reflection in place of the S 1 superstructure reflections characteristic of the F2m phase.

Formation conditions of two quasiperiodic modifications of Al-Pd-Mn icosahedral phase studied by annealing method

Abstract Formation conditions of F-phase, F2-phase and F2 M -phase were systematically studied at alloy composition of Al 71 Pd 21 Mn 8 by annealing and succeeding quenching method. The results indicated that the transformation from the F-phase to the F2 M -phase occurs in two steps between 734 and 743°C; in the first step the F-phase is transformed to the F2-phase, in the second step the F2-phase is transformed to the F2 M -phase. It was reconfirmed that the F-phase is a high-temperature phase stable above approximately 748°C, and the F2 M -phase is a low-temperature phase stable below approximately 743°C. The present experiment also indicated that the F2-phase is a transient state between the F-phase and the F2 M -phase.

High resolution X-ray and neutron diffraction of super- and disorder in decagonal Al–Co–Ni

Abstract Synchrotron measurements at DESY and ESRF of decagonal quasicrystals with the nominal composition Al 70 Co 15 Ni 15 and Al 72 Co 16 Ni 12 , show that Bragg reflections with high |H i ∗ | values are surrounded by up to four weak subsidiary peaks. The positions of these additional peaks depend solely on the position of the Bragg reflection in the reciprocal perpendicular subspace and can be explained by a linear phason strain model. This model sheds new light on the current superorder models [K. Hradil et al. Phil. Mag. A 79 (1999) 1963] and is a further step towards an understanding of the real structures of decagonal quasicrystals.

Phason elastic constants and diffuse scattering in the i-AlPdMn phase

Abstract The diffuse scattering in the diffraction pattern of the i-AlPdMn phase has been measured on an absolute scale by X-ray and neutron scattering on single grain samples. Most of its intensity is due to long wave length phason fluctuations, interpreted as pretransitional fluctuations. The phason elastic constants have been extracted by comparison of the results with the elasticity theory of quasicrystals: we found that they are of the same order of magnitude for neutron and X-ray data. A precise comparison shows that they are independent of the thermal history of the sample.