Yoshie Matsuo

The structure of Al3Mn: Close relationship to decagonal quasicrystais

Abstract The crystal structure of the Al3Mn phase, considered to be closely related to that of decagonal auasicrystais, has been determined by a combination of single-crystal X-ray analysis and high-resolution electron microscopy. The atomic model, obtained from a Patterson synthesis and high-resolution electron microscopy, was refined by the least-sauares methods with the Unics III system to a final R value of 0.066. There are 156 atoms in an orthorhombic unit cell with the lattice parameters a=1.483 nm, b=1.243 nm and c=1.251 nm, and the space group is Pnma (No. 62). Based on the structure of Al3Mn, an atomie arrangement for the Al-Pd-Mn decagonal quasicrystal is discussed.

Formation of Decagonal Quasicrystal in the Al-Pd-Mn System and Its Structure

Formation of a decagonal quasicrystal in Al70Pd30-xMnx alloys (x=8-20) and its structure were examined by X-ray powder diffraction, electron diffraction and high-resolution electron microscopy. The decagonal quasicrystal is formed as a coexisting phase with an icosahedral phase in the composition range of x=10-15, and as a single phase at a composition of x about 20. The structure of the decagonal phase is a mixture of decagonal quasicrystalline regions with some linear phason strain and microcrystalline regions. We propose that the structure of Al-Pd-Mn decagonal quasicrystal may be interpreted as a tiling formed by atom cluster linkages, which are different to those reported in Al-Ni-Co and Al-Cu-Co decagonal quasicrystals.

The structure of Al3Pd: Close relationship to decagonal quasicrystals

Abstract The crystal structure of the Al3Pd phase, considered to be a closely related structure to decagonal quasicrystals with a period of about 1.6nm, has been determined by a combination of single-crystal X-ray analysis and high-resolution electron microscopy. The atomic model, which has about 280 atoms in an orthorhombic unit cell with parameters a = 2.336 nm, b = 1.232 nm and c = 1.659 nm and has the space group Pna21 (No. 33), was refined by a least-squares method with the Unics III system to a final R of 0.072 for 2348 unique reflections. The structure can be characterized as a two-dimensional arrangement of decagonal atom columns.

The structure of an Al-Pd decagonal quasicrystal studied by high-resolution electron microscopy

Abstract The structure of a decagonal quasicrystal with 1.6nm periodicity, formed in a rapidly solidified Al3Pd alloy, was examined by high-resolution electron microscopy, with the aid of the structure of an Al3Pd crystalline phase. Its structure is characterized as a two-dimensional arrangement formed by sharing a side of decagonal atom columns. A two-dimensional tiling constructed by connecting the atom columns by lines is compared with the Penrose tilings obtained from the projection of hypercubic lattices in the five-dimensional space to the two-dimensional space.

Atomic Short-Range Order in an Al72Ni20Co8 Decagonal Quasicrystal by Anomalous-X-Ray Scattering

By anomalous-X-ray scattering, the diffuse scattering around Bragg reflections was observed in a single decagonal quasicrystal of Al72Ni20Co8, which has no phason strain. The diffuse scattering is distributed around the center of the superstructure points. Intensity modulations of the diffuse scattering occur at each incident wavelength. The contrast of diffuse scattering shows the presence of atomic short-range order (SRO) in three kinds of pair correlation functions: between Al and Ni, between Ni and Co and between Co and Al. The correlation length of the diffuse scattering is estimated to be 22.5 A.

Diffuse scattering from an Al72Ni20Co8 decagonal quasicrystal on an order–disorder transformation

Non-uniform distortion induced by superstructure domains has been observed during the ordering process of an order–disorder transformation in a single decagonal quasicrystal of Al72Ni20Co8. The full width at half maximum (FWHM) of the fundamental reflections increased below the transformation temperature, Tc. At the same time, the integrated intensity of the fundamental reflections varied drastically at Tc. A small hysteresis was also observed in the temperature dependences of both the FWHM and the integrated intensity of the fundamental reflections. Peak broadening of the fundamental reflections is predominantly dependent on |G∥ | below Tc. In addition, the weak dependence of the peak broadening with |G⊥ | is extracted from the observed FWHM of the fundamental reflections. After deconvolution, the FWHM of the fundamental reflections appears to be a linear combination of |G∥ | and |G⊥ |. Coexistence of the non-uniform distortion and of the random phason strain contributes to the ordering process below Tc. The diffuse scattering from atomic short-range order (SRO) was distributed around the ideal positions of the superstructure reflections. The SRO diffuse scattering disappeared completely above Tc + 10 K. In addition, a small hysteresis of the SRO diffuse scattering was found in the temperature cycle.

Investigation of phason strains in decagonal Al-Pd-Mn single quasicrystals by means of x-ray diffraction

A careful examination of the peak profiles, peak shifts and peak separations of Bragg reflections, which are inherent in the disordering of quasicrystal, is carried out using an x-ray diffraction method for decagonal Al-Pd-Mn single quasicrystals. The full widths at half-maximum (FWHM) of the Bragg reflections along the longitudinal direction (L) have no or -dependence whereas those for both transverse directions, which are perpendicular to the L direction in an aperiodic plane and with a periodic axis, have linear -dependence. Notable peak shifts and separations of Bragg reflections are observed. The absolute values of the shifts are found to be proportional to . The peak shifts and separations are analysed in terms of linear phason strains.

X-ray study of the electron density distributions for hexagonal and

The electron density distributions of and , which include icosahedral clusters, have been studied by a single-crystal x-ray diffraction method. The maximum-entropy method (MEM) is used to construct the electron density distribution (EDD). In the EDD maps, strongly covalent bonds between Al atoms and transition metal (TM) atoms are visible. As regards the chemical bonding, has an icosahedral bonding environment, whereas does not. The number of electrons belonging to each atom and the charge transfer from Al atoms to TM atoms have been derived from the EDD maps. The negative valences were estimated to be -1.25 and -1.26 for Co atoms and -1.00 for a Mn atom. These negative valences can be understood to be the charge transfer due to the covalent bond with strongly ionic character. These results were compared with pair-potential calculations and band-structure calculations.

Anomalous X-ray Scattering Associated with Short-Range Order in an Al70Ni15Co15 Decagonal Quasicrystal

Abstract The diffuse scattering around Bragg reflections was observed in a single decagonal quasicrystal of Al 70 Ni 15 Co 15 using anomalous-X-ray scattering. The intensities of diffuse scattering vary with the three incident X-ray wavelengths, near the Co K-edge and the Ni K-edge and between them. The contrast of diffuse scattering shows the existence of atomic short-range order (SRO) between Ni and Co. The distributions of diffuse scattering are anisotropically modulated and the diffuse shapes vary from one reciprocal lattice point to another. In quasicrystals, anisotropic diffuse shapes derive from phason strain. It is concluded that both SRO and phason strains exist in Al 70 Ni 15 Co 15 . In addition, as the first neighbor of Ni, Ni is preferred to Co statistically, since SRO intensities appear about zone-centers, i.e. there is local clustering of these species.

X-ray study of the electron density distribution for Al6Mn

The electron density distribution of Al6 Mn has been studied by a single-crystal x-ray diffraction method. The maximum-entropy method (MEM) is used to construct the electron density distribution (EDD). In the EDD maps, strong covalent bonds between Al atoms and Mn atoms are visible. The number of electrons belonging to each atom and the charge transfer from Al atoms to an Mn atom have been derived from the EDD maps. The negative valence was estimated to be -1.46 for an Mn atom. This negative valence can be understood to be the charge transfer due to the covalent bond with a strong ionic character. These results were compared with pair-potential calculations and band-structure calculations.