M. de Boissieu

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.

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.

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.

Phason defects in Al-Pd-Mn approximant phases

Abstract Structural defects, observed by TEM, in Al-Pd-Mn approximant phases are identified as phason defects. Assuming their motion under an applied shear strain, it is shown that two approximant phases can be related between them by a phase transformation occurring through plastic deformations. Then, other approximant phases, experimentally observed, can be interpreted as intermediate states of such a phase transformation. Atomic motions corresponding to these phason shifts are partly examined on the basis of HREM observations and crystallographic data, obtained from a single-crystal X-ray study on one of these approximants. The description of this transformation in six-dimensional hyperspace is proposed in order to establish a relationship with the icosahedral quasicrystalline state. The possibility that a plastic deformation of the icosahedral phase, occurring without the strain-hardening effect, could only result in a motion of phason defects is briefly discussed.

The structure of the icosahedral AlPdMn quasicrystal

Abstract Neutron diffraction data were obtained from quasicrystals of the AlPdMn system and the isomorphic modifications AlPd(FeCr). From contrast variation effects, partial structure factors were determined. In the high-dimensional periodic description, the structure can be viewed as a six-dimensional cubic lattice belonging to the Pm space group, with a superstructure due to a chemical order which somewhat induces an F-type lattice.

Discussion on clusters, phasons and quasicrystal stabilisation

This paper summarises a two-hour discussion at the Ninth International Conference on Quasicrystals, including nearly 20 written comments sent afterwards, concerning (i) the meaning [if any] of clusters in quasicrystals; (ii) phason elasticity, and (iii) thermodynamic stabilisation of quasicrystals.

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.

Atomic structure of the icosahedral Al-Li-Cu quasicrystal

Using both powder and single crystal samples, neutron and X-ray diffraction data were obtained with quasicrystals of the AlLiCu system. Isotopic substitution on the Li and Cu atomic sites allowed amplitudes and phase shift of the partial structure factors to be determined. Using a high-dimensional crystallography approach results in the phases to be reconstructed and atomic densities were calculated. The six-dimensional periodic structure appeared as a primitive hypercubic lattice with mid-edge and vertex Al/Cu atomic surfaces plus a Li bodycentre site. The major drawbacks of the experimental approach are then bypassed by modelling details of the six-dimensional structure, still in agreement with diffraction data. The related three-dimensional quasiperiodic structure can be described in terms of connected clusters or, alternatively, families of atomic planes. Comparison with the structure of the crystalline R-phase is of interest.

Icosahedral crystals: neutron diffraction tells you where the atoms are

Neutron diffraction data were obtained from a single-phase icosahedral powder of the system Al74Si5Mn21 and its modification by isomorphous substitution on the Mn sites. Amplitudes and phase differences of the partial structure factors (FAl, FMn) were determined. From their Qperpendicular to -dependences within a strip-projection approach, phases were reconstructed. Atomic densities were then calculated in the physical space and in the six-dimensional periodic lattice, resulting in the first experimentally deduced decoration of the quasi-periodic network. The Mackay icosahedron no longer appears as the necessary basic structural unit. In six dimensions the structure has a simple CsCl-like space-group symmetry.

Phononic filter effect of rattling phonons in the thermoelectric clathrate Ba8Ge40+xNi6-x.

One of the key requirements for good thermoelectric materials is a low lattice thermal conductivity. Here we present a combined neutron scattering and theoretical investigation of the lattice dynamics in the type I clathrate system Ba-Ge-Ni, which fulfills this requirement. We observe a strong hybridization between phonons of the Ba guest atoms and acoustic phonons of the Ge-Ni host structure over a wide region of the Brillouin zone, which is in contrast with the frequently adopted picture of isolated Ba atoms in Ge-Ni host cages. It occurs without a strong decrease of the acoustic phonon lifetime, which contradicts the usual assumption of strong anharmonic phonon-phonon scattering processes. Within the framework of ab initio density-functional theory calculations we interpret these hybridizations as a series of anticrossings which act as a low-pass filter, preventing the propagation of acoustic phonons. To highlight the effect of such a phononic low-pass filter on the thermal transport, we compute the contribution of acoustic phonons to the thermal conductivity of Ba8Ge40Ni6 and compare it to those of pure Ge and a Ge-46 empty-cage model system.