Electronic structure of complex Hume-Rothery phases and quasicrystals in transition metal aluminides

https://iopscience.iop.org/article/10.1088/1468-6996/9/1/013008/pdf

Icosahedral clusters, icosaheral order and stability of quasicrystals—a view of metallurgy*

A six-dimensional cluster model of icosahedral Al-Pd-Mn $(i\ensuremath{-}\mathrm{Al}\ensuremath{-}\mathrm{Pd}\ensuremath{-}\mathrm{Mn})$ quasicrystals used in the recent structure refinement is described in detail. This model is based on five kinds of clusters located at vertices, edge centers of the inflated three-dimensional Penrose pattern (3DPP) with an edge length of about 20 \AA{}, and two body-diagonal positions of each acute rhombohedron. Two kinds of 20 \AA{} clusters, one of which is seen in $\ensuremath{\beta}\ensuremath{-}\mathrm{Al}\ensuremath{-}\mathrm{Pd}\ensuremath{-}\mathrm{Mn}\ensuremath{-}\mathrm{Si},$ are located at even- and odd-parity 12-fold vertices of the inflated 3DPP. This is proved to give small R factors ${(R}_{w}=0.055,R=0.049)$ for 493 independent reflections and leads to the 1/1 and 2/1 approximant structures of $i\ensuremath{-}\mathrm{Al}\ensuremath{-}\mathrm{Pd}\ensuremath{-}\mathrm{Mn}$ $(\ensuremath{\alpha}\ensuremath{-}$ and $\ensuremath{\beta}\ensuremath{-}\mathrm{Al}\ensuremath{-}\mathrm{Pd}\ensuremath{-}\mathrm{Mn}\ensuremath{-}\mathrm{Si})$ by introducing appropriate cubic phason strains and taking a three-dimensional cut.

Six-dimensional model of icosahedral Al-Pd-Mn quasicrystals

Investigation of pre-existing particles in Al 5083 alloys

Effects of Mo and Mn microadditions on strengthening and over-aging resistance of nanoprecipitation-strengthened Al-Zr-Sc-Er-Si alloys

The structure of a cubic A1 69.5 Pd 23.0 Mn 6.2 Si 1.3 phase, which is referred as a 2/1 approximant of an icosahedral phase, was determined by means of single crystal X-ray structural analysis: space group Pm3 (No. 200), a = 20.211(2) A, V = 8255.9(14) A 3 , MoK a (λ = 0.71069 A); refined as A1 69.6 Pd 24.3 Mn 6.1 , atom/cell = 512.83, F(000) = 11154.6, μ = 8.72 mm -1 , D calc = 4.95 Mgm- 3 , R(wR2) = 0.0623(0.1691) for 2597 reflections with I > 2.0σ(J) and goodness of fit S = 1.096 for 165 variables. In the cubic 2/1 approximant structure, an atom cluster with about 20 A in diameter locates at the origin of the unit cell. This large cluster can be described by nine atomic shells with icosahedral symmetry, where the atomic arrangements similar to the Bergman or double Mackay clusters are clearly identified together with the τ-inflated relationships in their sizes. The icosahedral quasicrystals in Al-Pd-Mn system are considered to be realized by a quasi-periodic arrangement of the similar atom clusters.

Crystal structure of a cubic Al70Pd23Mn6Si; a 2/1 rational approximant of an icosahedral phase

Crystals of the α-(AlMnSi) (aluminium manganese silicon alloy, Al4Mn1.01Si0.74) cubic 1/1 approximant phase for the icosahedral quasi-crystal were prepared from an Al72Mn16Si12 alloy under an argon atmosphere. The structure is reproduced by the connection of two large atom clusters with icosahedral symmetry (a Mackay icosahedron and double-Mackay icosahedron) [Yang (1988). Phil. Mag. B58, 47–57]. Si and Mn atoms are suggested to constitute icosahedral arrangements in the atom clusters. The crystal structure of α-(AlMnSi) was determined previously by Cooper & Robinson [Acta Cryst. (1966), 20, 614–617].

Re‐Refinement of α‐(AlMnSi)

The structure of a cubic Al 67.4 Pd 11.4 Mn 14.4 S 6.8 phase, which is referred as an 1/1 rational approximant of an icosahedral phase, was determined by means of single crystal X-ray structural analysis: space group Pm3 (No. 200), a = 12.281(1)A, V = 1852.0(3) A 3 , MoK a (λ = 0.71069 A); refined as Al 66.3 Pd 12.0 Mn 14.7 Si 7.0 , atom/ cell = 122.72, F(000) = 2305, p = 7.54 mm -1 , D calc = 4.47 Mgm -3 , R = 0.0319 for the observed 703 reflections with I > 2.0σ(1). An atom cluster with about 13 A in diameter is found at the origin of a unit cell and the cubic arrangement of these clusters through the shared edges can reproduce the present 1/1 approximant structure. This atom cluster is ranked into five atomic shells, where the atomic arrangement analogous to the Bergman cluster is clearly identified. The clusters of Bergman's derivation are suggested to be one of the most essential cluster units for the face-centered icosahedral quasicrystals.

Nobutaka Kaji

Papers

Crystal structure of a cubic Al70Pd23Mn6Si; a 2/1 rational approximant of an icosahedral phase

Re‐Refinement of α‐(AlMnSi)

Crystal structure of a cubic Al67Pd11Mn14Si7; a new 1/1 rational approximant for the Al-Pd-Mn icosahedral phase

Crystal structure of rhombohedral λ-AlFeSi

Re-Refinement of α-(AlMnSi).