Marianne Quiquandon

Atomic structure of the (Al,Si)CuFe cubic approxi­mant phase

The structure of the alpha-(Al,Si)CuFe approximant phase is determined by a single-crystal X-ray diffraction study and compared to the ideal structure obtained by the perpendicular shear method of the parent icosahedral phase. It is shown that the local environments (typical atomic clusters) of the two phases are similar and expand significantly farther than the size of the unit cell of the approximant. The orbit Al(2) issuing from the theoretical icosahedral model corresponding to the inner dodecahedron of the Mackay-type cluster is not found in the approximant and is replaced by a partially occupied inner icosahedron with an unusually large Debye-Waller factor.

Atomic clusters and atomic surfaces in icosahedral quasicrystals.

This paper presents the basic tools commonly used to describe the atomic structures of quasicrystals with a specific focus on the icosahedral phases. After a brief recall of the main properties of quasiperiodic objects, two simple physical rules are discussed that lead one to eventually obtain a surprisingly small number of atomic structures as ideal quasiperiodic models for real quasicrystals. This is due to the fact that the atomic surfaces (ASs) used to describe all known icosahedral phases are located on high-symmetry special points in six-dimensional space. The first rule is maximizing the density using simple polyhedral ASs that leads to two possible sets of ASs according to the value of the six-dimensional lattice parameter A between 0.63 and 0.79 nm. The second rule is maximizing the number of complete orbits of high symmetry to construct as large as possible atomic clusters similar to those observed in complex intermetallic structures and approximant phases. The practical use of these two rules together is demonstrated on two typical examples of icosahedral phases, i-AlMnSi and i-CdRE (RE = Gd, Ho, Tm).

Geometry of metadislocations in approximants of quasicrystals

We propose a simple geometrical definition of metadislocations based on the N-dim description of quasicrystals and their approximants, as being the traces of quasicrystalline dislocations with a non-zero component of their N-dim Burgers vector in the perpendicular space of the approximant. Examples are given in the octagonal canonical tiling.

Structures of quasicrystals : where are the atoms

This paper is an attempt to present a chronological review of the structural concepts that have been developed to characterize quasicrystals, starting from the experimental discovery of D. Shechtman and the concomitant theoretical definition of quasicrystal as proposed by D. Levine and P. Steinhardt, up to the present research in the field. The largest part of the paper is a discussion of the specific points that make the atomic structure determination of quasicrystals an original and difficult scientific challenge. We finally discuss the soundness of our knowledge of the actual atomic structure in quasicrystals: we do have quite a solid idea of where the atoms are but we are not sure about the distribution of the chemical species.

Atomic structure of the cubic 1/1 approximant α-(Al,Si)CuFe

Abstract A X-ray diffraction structural analysis has been performed on single crystals of the α-(Al, Si)CuFe cubic 1/1 approximant of the parent icosahedral phase i-AlCuFe. It shows that the atomic clusters in the cubic phase are similar to those of the icosahedral phase but connect differently in agreement with the model of approximant obtained by the perpendicular shear method of the parent quasicrystal.

About the chemistry of the terminating 5f-planes in i-AlPdMn : A comparison between models and surface studies

Structural arguments are proposed that support the hypothesis that the equilibrium 5f-surfaces of i-AlPdMn icosahedral alloys are actual cuts of the bulk structure with almost pure Al termination planes [1, 2] corresponding to actual bulk properties with no need for possible Al segregation on the surface. Most of the 5f termination planes in i-AlPdMn are made of two close planes containing essentially Al at the upper one and Al and Pd at the second one (see for instance [3]). Here, perfect unrelaxed structural models that differ only in the chemical distribution of the atomic species are devised, close to the description proposed in [4]. Once compared to experimental X-rays data [5], the calculations show that although the chemical decoration has a rather limited influence on the global R-factor, there is a clear tendency toward favoring models with almost pure Al on the atomic surface located on the node n, in excellent agreement with the surface studies.

Study of quasicrystals obtained from a structural model of icosahedral phases of type F AlPdMn/AlCuFe

Abstract A recent structural model [1] for the F-type icosahedral phases i-AlPdMn and i-AlCuFe based on the KG cell decomposition [2] of the Mackay clusters has shown that they both enter in an unique model of general composition Al61.8(Pd Ι Cu)21.35(Mn Ι Fe)8.29(Al Ι Fe Ι Mn)4.28(Al Ι Cu)4.28 where (X Ι Y) means X or Y species. Three new alloys satisfying this composition rule, two ternaries Al66.08Cu21.35Mn12.57 and Al70.36Pd21.35Fe8.29 and one quaternary Al66.08Cu21.35Mn8.29Fe4.28 have been prepared by rapid quenching and annealing and studied by X-ray diffraction and electron microscopy. All three phases are quasicrystalline after quench: Al66.08Cu21.35Mn12.57 is decagonal, and the two others are F-icosahedral phases. After annealing, the quaternary alloy transforms into a decagonal phase. The present results are compared to those of previous studies in the litterature of samples with close compositions.

Simulations of High Resolution Electron Microscopy Images of Icosahedral Quasicrystals

We apply the scattering matrix formulation for calculating the images of high-resolution electron microscopy (HREM) images of quasiperiodic crystals and discuss their basic properties. The main feature in the image formation comes from the truncation effects of the q-basis, especially the perpendicular components which must be numerous enough for properly reproducing quasiperiodicity. A comparison between two types of atomic structural model is presented that illustrates the difficulties of differentiating the models from the HREM observations.

Z-module defects in intermetallic alloys

We analyze what kind of new defects could appear in crystalline structures where the positions of the atoms and the unit cell belong to a same Z-module, i. e. are irrationnal projections of a N > 3 dim (N-D) lattice Λ as in the case of quasicrystals. Beyond coherent irrationally oriented twins already discussed in a previous paper (M. Quiquandon et al. 2016), new 2D translational defects are expected, the translation vectors of which, being projections of nodes of Λ, have irrational coordinates with respect to the unit cell reference frame. Partial dislocations, called here module dislocations, are the linear defects bounding these translation faults. A specific case arises when the Burgers vector B is the projection of a non-zero vector of Λ that is perpendicular to the physical space. We call this new kind of dislocation a scalar dislocation since, because its Burgers vector in physical space is zero, it generates no displacement field and has no interaction with external stress fields and others dislocations.

Group Theory Considerations in Quasicrystal to Crystal Transformations

We first discuss several aspects of group theory for reformulating the group-subgroup re-lations in quasicrystals to crystals transformations based on the original approach proposed by D.Mermin and his group on indiscernability groups. In the second part of the paper, we discuss ways ofdetermining the possible space-groups of approximants of quasicrystals as generated by the perpen-dicular shear technique.