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Author(s):  
Ted Janssen ◽  
Gervais Chapuis ◽  
Marc de Boissieu

The law of rational indices to describe crystal faces was one of the most fundamental law of crystallography and is strongly linked to the three-dimensional periodicity of solids. This chapter describes how this fundamental law has to be revised and generalized in order to include the structures of aperiodic crystals. The generalization consists in using for each face a number of integers, with the number corresponding to the rank of the structure, that is, the number of integer indices necessary to characterize each of the diffracted intensities generated by the aperiodic system. A series of examples including incommensurate multiferroics, icosahedral crystals, and decagonal quaiscrystals illustrates this topic. Aperiodicity is also encountered in surfaces where the same generalization can be applied. The chapter discusses aperiodic crystal morphology, including icosahedral quasicrystal morphology, decagonal quasicrystal morphology, and aperiodic crystal surfaces; magnetic quasiperiodic systems; aperiodic photonic crystals; mesoscopic quasicrystals, and the mineral calaverite.

Author(s):  
Wang Rong ◽  
Ma Lina ◽  
K.H. Kuo

Up to now, decagonal quasicrystals have been found in the alloys of whole Al-Pt group metals [1,2]. The present paper is concerned with the TEM study of a hitherto unreported hexagonal phase in rapidly solidified Al-Ir, Al-Pd and Al-Pt alloys.The ribbons of Al5Ir, Al5Pd and Al5Pt were obtained by spun-quenching. Specimens cut from the ribbons were ion thinned and examined in a JEM 100CX electron microscope. In both rapidly solidified Al5Ir and Al5Pd alloys, the decagonal quasicrystal, with rosette or dendritic morphologies can be easily identified by its electron diffraction patterns(EDPs). The EDPs of the decagonal phase for the two alloys are quite similar. However, the existance of decagonal quasicrystal in the Al-Pt alloy has not been verified by our TEM study. It is probably for the reason that the cooling rate is not great enough for the Al5Pt alloy to form the decagonal phase. During the TEM study, a metastable hexagonal phase has been observed in the Al5Ir, Al5Pd and Al5Pt alloys. The lattic parameters calculated from the X-ray powder data of this phase are a=1.229 and c=2.647nm(Al-Pd) and a=1.231 and c=2.623nm(Al-Ir). The composition of this phase was determined by EDS analysis as Al4(Ir, Pd or Pt). It coexists with the decagonal phase in the alloys and transformed to other stable crystalline phases on heating to high temperature. A comparison between the EDPs of the hexagonal and the decagonal phase are shown in Fig.l. Fig. 1(a) is the EDPs of the decagonal phase in various orientions and the EDPs of the hexagonal phase are shown in Fig.1(b), in a similar arrangement as Fig.1(a). It can be clearly seen that the EDPs of the hexagonal phase, especially the distribution of strong spots, are quite similar to their partners of the decagonal quasicrystal in Fig.1(a). All the angles, shown in Fig.l, between two corresponding EDPs are very close to each other. All of these seem strongly to point out that a close structural relationshipexists between these two phases:[110]//d10 [001]//d2(D) //d2 (P)The structure of α-AlFeSi is well known [3] and the 54-atom Mackay icosahedron with double icosahedral shells in the α-AlFeSi structure [4] have been used to model the icosahedral quasicrystal structure. Fig.2(a) and (b) show, respectively, the [110] and [001] projections of the crystal structure of α- AlFeSi, and decagon-pentagons can easily be identified in the former and hexagons in the latter. In addition, the optical transforms of these projections show clearly decagons and hexagons of strong spots, quite similar to those in [110] and [001] EDPs in Fig.1(b). This not only proves the Al(Ir, Pt, Pd) metastable phase being icostructural with the α-AlFeSi phase but also explains the orientation relationship mentioned above.


2005 ◽  
Vol 13 (7) ◽  
pp. 2370 ◽  
Author(s):  
Peng Yao ◽  
Garrett J. Schneider ◽  
Dennis W. Prather ◽  
Eric D. Wetzel ◽  
Daniel J. O'Brien

2005 ◽  
Vol 87 (9) ◽  
pp. 091117 ◽  
Author(s):  
Dennis McPhail ◽  
Martin Straub ◽  
Min Gu

2006 ◽  
Vol 532-533 ◽  
pp. 568-571
Author(s):  
Ming Zhou ◽  
Hai Feng Yang ◽  
Li Peng Liu ◽  
Lan Cai

The photo-polymerization induced by Two-Photon Absorption (TPA) is tightly confined in the focus because the efficiency of TPA is proportional to the square of intensity. Three-dimensional (3D) micro-fabrication can be achieved by controlling the movement of the focus. Based on this theory, a system for 3D-micro-fabrication with femtosecond laser is proposed. The system consists of a laser system, a microscope system, a real-time detection system and a 3D-movement system, etc. The precision of micro-machining reaches a level down to 700nm linewidth. The line width was inversely proportional to the fabrication speed, but proportional to laser power and NA. The experiment results were simulated, beam waist of 0.413μm and TPA cross section of 2×10-54cm4s was obtained. While we tried to optimize parameters, we also did some research about its applications. With TPA photo-polymerization by means of our experimental system, 3D photonic crystal of wood-pile structure twelve layers and photonic crystal fiber are manufactured. These results proved that the micro-fabrication system of TPA can not only obtain the resolution down to sub-micron level, but also realize real 3D micro-fabrication.


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