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Icosahedral clusters, icosaheral order and stability of quasicrystals-a view of metallurgy - PubMed

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

An Pang Tsai. Sci Technol Adv Mater. .

Abstract

We review the stability of various icosahedral quasicrystals (iQc) from a metallurgical viewpoint. The stability of stable iQcs is well interpreted in terms of Hume-Rothery rules, i.e. atomic size factor and valence electron concentration, e/a. For metastable iQcs, we discuss the role of phason disorder introduced by rapid solidification, in structural stability and its interplay with chemical order and composition.

Keywords: icosahedral order; isodahedral cluster; phason disorder; stable quasicrystal; valence concentration.

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Figures

Figure 1
Figure 1

The projection method with different slopes of the strip for different sequences: (a) the Fibonacci sequence projected from a strip with slope of formula image , (b) the LLS periodic sequence projected from a strip with slope of formula image , (c) a random sequence projected from a random work strip with overall slope close to formula image . Electron diffraction patterns: (a) twofold from the stable Zn80Mg5Sc15 iQc, (b) (100) from the In44Ag41Yb15 2/1 approximant, (c) twofold from the metastable Al75Cu15V10 iQc. The line profiles obtained along twofold axes indicated with white lines are shown on the right-hand side.

Figure 2
Figure 2

Twofold diffraction patterns of (a) P-type and (b) F-type iQcs.

Figure 3
Figure 3

Concentric structures of three types of icosahedral clusters derived from three 1/1 approximants of quasicrystals. (a) The Al–Mn–Si class or Mackay icosahedral cluster: the center is vacant, the 1st shell is an Al/Si icosahedron, the 2nd shell is a Mn icosahedron, and the 3rd shell is an Al/Si icosidodecahedron. (b) The Zn–Mg–Al class or Bergman cluster: an example is R-AlLiCu: the center is vacant, the 1st shell is an Al/Cu icosahedron, the 2nd shell is a Li dodecahedron, the 3rd shell is a larger Al/Cu icosahedron. (c) The Cd–Yb class: the center is a Cd tetrahedron, the 1st shell is a Cd dodecahedron, the 2nd shell is a Yb icosahedron, and the 3rd shell is a Cd icosidodecahedron.

Figure 4
Figure 4

Bright-field image and electron diffraction patterns along fivefold axis obtained from different areas encircled in the image for melt-quenched Al72Pd25Cr3.

Figure 5
Figure 5

(a) Bright-field image and (b)–(d) electron diffraction patterns taken from the same area along two-, three-, fivefold axes.

Figure 6
Figure 6

Powder x-ray diffraction patterns as a function of Q (Q=4πsin θ/λ) of as-quenched state and annealed state for Al75Cu15V10 and Al53Si27Mn20 alloys.

Figure 7
Figure 7

Evolution of crystallization to the iQc for the Al75Cu15V10 amorphous phase.

Figure 8
Figure 8

(a) Bright-field image and (b)–(d) electron diffraction patterns for the iQc crystallized from the amorphous Al53Si27Mn20 alloy.

Figure 9
Figure 9

(a) High resolution image and (b) the corresponding electron diffraction pattern, taken along a fivefold axis from the Al75Cu15V10 iQc. (c) Illustration of tiling traced from (a).

Figure 10
Figure 10

Selected electron diffraction and convergent-beam electron diffraction patterns taken along a fivefold axis from the Al75Cu15V10 iQc.

Figure 11
Figure 11

G⊥ dependence of peak widths for the Al75Cu15V10 and Al53Si27Mn20 iQcs.

Figure 12
Figure 12

Powder x-ray pattern of iQcs in the as-quenched state (dotted lines) and annealed state (solid lines) for (a) Al70Pd20Mn10 and (b) Al63Cu25Fe12 iQcs.

Figure 13
Figure 13

G⊥ dependence of peak widths for the as-quenched and annealed Al70Pd20Mn10 iQcs.

Figure 14
Figure 14

Crystallization of melt-quenched Al74Pd17Mn9 annealed at 1503 K for 24 h.

Figure 15
Figure 15

Bright-field images and fivefold diffraction patterns before and after annealing for melt-quenched Al74Pd17Mn9.

Figure 16
Figure 16

Schematic of free-energy composition for the iQc and crystalline compounds. Metastable iQc shown by broken line represents the region of the melt-quenched iQc.

Figure 17
Figure 17

Formation of stable iQc in the Al–Cu–TM and the Al–Pd–TM systems.

Figure 18
Figure 18

(a) Binary Cd–Yb phase diagram and (b) pseudobinary In–Ag–Yb phase diagram involving iQc.

Figure 19
Figure 19

(a) Cooling curves for electostatically levitated droplet of Ti–Zr–Ni as a function of temperature. (b) X-ray diffraction pattern as a function of q vector (formula image) for undercooled Ti–Zr–Ni alloy at different temperatures corresponding to (a). [73] Courtesy of K Kelton.

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