M. Audier

A quasicrystal structure model for AI-Mn

Abstract A model is proposed for the atomic structure of the Al-Mn quasicrystal. Mn icosahedra are connected through their threefold axes, with a coordination number of seven and each bond defined by an octahedron. This Mn skeleton has icosahedral symmetry and its projections onto various planes have a self-similarity property based on the golden number, in agreement with TEM results. The filling up with A1 atoms determines a sublattice where empty Al icosahedra are connected by chains of three distorted octahedra. Two kinds of Mn-Al first-neighbour environments are distinguished, involving nine and ten Al atoms. Taking the ratio of the two Mn site numbers as equal to the golden number leads to a chemical composition in agreement with X-EDS analysis.

Neutron and X-ray single-crystal study of the AlPdMn icosahedral phase

Perfect single grains of the AlPdMn icosahedral phase have been used for structure determination by X-ray and neutron diffraction. Owing to the large difference between X-ray and neutron scattering factors, information is gained on the atomic positions of the three elements. A model is proposed as deduced from a six-dimensional (6D) Patterson analysis. Six different atomic hypersurfaces are located on node and body-centre sites of the 6D lattice. The superstructure that leads to a face-centred lattice is mainly due to a strong chemical ordering, all the palladium being on the even node and odd body centre of the 6D cube. The resulting 3D structure contains icosahedral clusters similar to the external shell of the Mackay icosahedron, with two kinds of chemical decoration. The structure may also be described via a quasi-periodic stacking of fivefold planes. Each set of planes is characterized by an average chemical composition and local order. This kind of description helps in the understanding of quasi-crystal growth, formation of dislocations and dynamic properties.

Morphology and crystalline order in catalytic carbons

Abstract The influence of temperature and of catalyst composition on the morphology and crystalline order has been studied for a series of catalytic carbons prepared by carbon monoxide disproportionation (2CO→CO2+C) over an iron-cobalt, an iron-nickel, and a nickel catalyst, and by methane decomposition (CH4→2H2+C) over a nickel catalyst. The morphology was studied by TEM in a bright field mode. The products are filamentous when prepared at low temperature and granular when prepared at high temperature. The ranges of temperature corresponding to each morphology depend both on the alloy composition and on the reacting gas. The structure of the catalytic carbons, as studied by TEM in SAD mode and by X-ray diffraction, is turbostratic (2D, i.e. biperiodic) when the carbons are prepared at low temperature and crystalline (3D, i.e. triperiodic) when prepared at high temperature. When the particle size is large, the temperature of transition is about 500°C, whatever the composition of the alloy and of the reacting gas are. However, small particles are always 2D. The carbon layers, as observed by TEM in lattice fringe mode, are short and curved for turbostratic, and large and stiff for crystalline phase. Biperiodic products are not graphitizable.

Al4Mn quasicrystal atomic structure, diffraction data and Penrose tiling

Abstract The modelling of the Al4Mn quasicrystal, recently proposed by Guyot and Audier (1985) on the basis of icosahedral atomic units characteristic of the crystalline phase α(AlFeSi) or α(AlMnSi), is analysed more deeply. After building the quasicrystal by connecting the basic structural units-double Al and Mn icosahedra with vacant centresm‐according to the rules previously described, it is found that the Mn and Al atoms lie in planes whose spacings are in agreement with X-ray or electron diffraction data. In terms of the three-dimensional Penrose tiling, two types of pairs of rhombohedral tiles are found: the first, with an edge length of 4·85 A, decorated by atoms, defines the primitive cells; the second, inflated by a ratio φ2 (φ is the golden number), is decorated by the basic icosahedral units, and their stacking into a rhombic triacontahedron may suggest the existence of icosahedral vacancy defects. A satisfying comparison with high-resolution transmission electron micrographs is also made.

Crystallographic orientations of catalytic particles in filamentous carbon; Case of simple conical particles

Abstract Filamentous catalytic carbons in the form of simple tubes with conical metal particles at one end have been selectively prepared by CO disproportionation (2 CO → CO 2 + C) catalysed by iron-cobalt and iron-nickel alloys of various compositions and structures: 6 iron-cobalt alloys with the bcc structure, 1 fcc iron-cobalt and 4 fcc iron-nickel. The crystallographic relations between the metal particles and their carbon tubes have been determined by CTEM. In the case of all the metal composites prepared from alloys of bcc structure, the metal particle is a single crystal with a [100] axis parallel to the axis of the carbon tube, and the basal faces of the truncated cone, which appear free of carbon, are (100) faces. In the case of all the metal composites prepared from alloys of fcc structure (FeCo and FeNi), the metal particles are not always single crystals as they present sometimes (111) twin planes. However, there is always a [110] axis parallel to the axis of the carbon tube and the carbon-free basal planes of the cones are always (111) faces.

Structure of quasicrystalline approximant phase in the Al[sbnd]Pd[sbnd]Mn system

Abstract The structure of an orthorhombic phase (ξ′ phase) with Al73·5Pd224Mn4·1 composition was solved by applying the direct methods and refined by a least-squares procedure. The space group is Pnma and the magnitudes of cell parameters are a = 23·541 A, b = 16·566 A and c = 12·339 A. The final reliability factor is R = 0·072 for 3419 independent reflections. The structure is made up of partial Mackay icosahedra in which the Pd atoms form icosahedra centred on Mn atoms. These central Mn atoms are located at the vertices of flattened hexagons arranged in quincunx. The ξ′ phase is nearly isomorphic to the Al3Pd structure and has a layer structure consisting of flat and puckered layers similar to what is found in Al3Mn and Al13Fe4.

An approach to the structure of quasicrystals: A single crystal X-ray and neutron diffraction study of the R-Al5CuLi3 phase

Abstract The structure of the R-Al5CuLi3 cubic phase, expected as being related to the icosahedral T2-Al6CuLi3 quasicrystal, has been determined by single crystal X-ray and neutron diffraction. This structure is discussed with respect to the one of (Al, Zn)49Mg32. A description is made in terms of successive polyhedral shells with two triacontahedra whose sizes are in the ratio of the golden mean τ = (√5 + 1) 2 .

The orthorhombic approximant phases of the decagonal phase

Abstract Two distinct orthorhombic phases form in the Al65Cu20Fe10Cr5 and Al63Cu17.5Co17.5Si2 alloys and represent an important class of approximant structures of the decagonal phase. Their structural units (convex pentagon, concave pentagon and rhombus) as revealed by high resolution electron microscopy (HREM) images can also be used to construct the Penrose tiling. We propose that one single orthorhombic phase may not be able to account for the transformation towards the high-temperature decagonal phase. For this transformation to be possible, the microcrystalline structure must satisfy a delicate balance among building blocks that is required to achieve a Penrose tiling. Two concepts are distinguished: the approximant phase and the approximation state. An analysis of the orientation relationships between a CsCl type of structure and orthorhombic phases suggests that such orthorhombic phases are three-dimensional superstruc-tures based on the CsCl unit cell. Furthermore, this relationship leads to the d...

A simple construction of the AlCuLi quasicrystalline structure related to the (Al, Zn)49 Mg32 cubic structure type

Abstract Both b.c.c. and icosahedral AlCuLi phases coexist following conventional ingot casting. Owing to a slight difference in their composition, they can be distinguished by a Z-contrast technique in a scanning electron microscope. Moreover, the existence of an orientation relationship between the b.c.c. and icosahedral (AlCuLi) phases is established by a transmission electron microscopic study of an ion-beam-thinned sample. It is therefore confirmed that a close structural relationship exists between both AlCuLi phases. A simple construction of the AlCuLi quasicrystalline structure is proposed on the basis of a modified illustration of the Bergman-Waugh-Pauling–type structure, Im3 (AlCuLi), isostructural with (Al,Zn)49Mg32, which reveals that triacontahedra—known to be the basic volume element of the three-dimensional Penrose tiling—exist in these cubic phases. A simple change of the coordination number between triacontahedra is considered to initiate the construction of the corresponding icosahedral ...

AlPdMn phase diagram in the region of quasicrystalline phases

Abstract We report results on a metallurgical investigation of the Al-Pd-Mn phase diagram in the region of the quasicrystalline phase field. Liquidus phase fields have been determined for icosahedral, decagonal and several periodic compounds which are approximant crystals of the quasicrystals. Structure analyses of these phases have been carried out by transmission electron microscopy. As defined from the linear phason strain field theory, the different crystal approximants can be distinguished as belonging either to the icosahedral phase or to the decagonal phase. An equilibrium between icosahedral and modulated icosahedral phases has also been identified. The modulations occur along the threefold icosahedral axes.