Quasicrystals phases

Structural relations between quasicrystals and other intermetallic phases. As discussed in several sections of the review published by Kelton (1995) on quasicrystals and related structures, numerous studies and observations indicate structural similarities between non-periodic quasicrystal phases with crystalline phases and also, on the other hand, with amorphous, glassy and liquid phases. 

Rapid solidification of TaioFe2oAl7o gives rise to a quasicrystal phase with icosahedral symmetry [1988Tsa, 1989Sri, 1993Kel], and it has a quasilattice constant of a = 460 pm [1989Sri]. 

A pecuhar sohd phase, which has been discovered not too long ago [172], is the quasi-crystalline phase. Quasi-crystals are characterized by a fivefold or icosahedral symmetry which is not of crystallographic type and therefore was assumed to be forbidden. In addition to dislocations which also exist in normal crystals, quasi-crystals show new types of defects called phasons. Computer simulations of the growth of quasicrystals [173] are still somewhat scarce, but an increasing number of quasi-crystalline details are studied by simulations, including dislocations and phasons, anomalous self-diffusion, and crack propagation [174,175]. 

Clustering in Condensed Lithium Ternary Phases A Way Towards Quasicrystals I 143... 

In this second edition the text has been revised and new scientific findings have been taken into consideration. For example, many recently discovered modifications of the elements have been included, most of which occur at high pressures. The treatment of symmetry has been shifted to the third chapter and the aspect of symmetry is given more attention in the following chapters. New sections deal with quasicrystals and other not strictly crystalline solids, with phase transitions and with the electron localization function. There is a new chapter on nanostructures. Nearly all figures have been redrawn. 

Jassen T, Chapuis G, de Boissieu M eds (2007) Aperiodic crystals from modulated phases to quasicrystals. Oxford University Press, New York... 

Another characteristic point is the special attention that in intermetallic science, as in several fields of chemistry, needs to be dedicated to the structural aspects and to the description of the phases. The structure of intermetallic alloys in their different states, liquid, amorphous (glassy), quasi-crystalline and fully, three-dimensionally (3D) periodic crystalline are closely related to the different properties shown by these substances. Two chapters are therefore dedicated to selected aspects of intermetallic structural chemistry. Particular attention is dedicated to the solid state, in which a very large variety of properties and structures can be found. Solid intermetallic phases, generally non-molecular by nature, are characterized by their 3D crystal (or quasicrystal) structure. A great many crystal structures (often complex or very complex) have been elucidated, and intermetallic crystallochemistry is a fundamental topic of reference. A great number of papers have been published containing results obtained by powder and single crystal X-ray diffractometry and by neutron and electron diffraction methods. A characteristic nomenclature and several symbols and representations have been developed for the description, classification and identification of these phases. 

In this chapter, general aspects and structural properties of crystalline solid phases are described, and a short introduction is given to modulated and quasicrystal structures (quasi-periodic crystals). Elements of structure systematics with the description of a number of structure types are presented in the subsequent Chapter 7. Finally, both in this chapter and in Chapter 6, dedicated to preparation techniques, characteristic features of typical metastable phases are considered with attention to amorphous and glassy alloys. 

Icosahedral quasicrystals. Many icosahedral phases (both stable and metastable) have been identified in several systems, mainly Al-based but also Mg-based, Ti-based, etc. 

Crystal approximants. Several crystalline phases contain more or less closely packed atomic assemblies (polyhedra, clusters) which have been considered fundamental constituents of several quasicrystals, metal glasses and liquids. Such crystalline phases (crystal approximants), as reported in the previous paragraph, are often observed in the same (or similar) systems, as those corresponding to the formation of quasicrystals and under similar preparation conditions. Crystalline phases closely related to the quasicrystals (containing similar building blocks) have generally complex structures as approximants to the ico-quasicrystals we may, for instance, mention the Frank-Kasper phases (previously described in 3.9.3.1). 

Figure 3.50. The Yb-Cd binary phase diagram. The congruently melting compound YbCd57 is the first stable binary quasicrystal identified.

We have reconstructed the 3D structure of a complex quasicrystal approximant v-AlCrFe (P6 m, a = 40.687 and c = 12.546 A) (Zou et al, 2004). Due to the huge unit cell, it was necessary to combine crystallographic data from 13 projections to resolve the atoms. Electron microscopy images containing both amplitude and phase information were combined with amplitudes from electron diffraction patterns. 124 of the 129 unique atoms (1176 in the unit cell) were found in the remarkably clean calculated potential maps. This investigation demonstrates that inorganic crystals of any complexity can be solved by electron crystallography. 

The basic modem data describing the atomic stmcture of matter have been obtained by the using of diffraction methods - X-ray, neutron and electron diffraction. All three radiations are used not only for the stmcture analysis of various natural and synthetic crystals - inorganic, metallic, organic, biological crystals but also for the analysis of other condensed states of matter - quasicrystals, incommensurate phases, and partly disordered system, namely, for high-molecular polymers, liquid crystals, amorphous substances and liquids, and isolated molecules in vapours or gases. This tremendous... 

The coating is applied by using flame, supersonic, and plasma-arc spraying. The deposited material consists of a mixture of quasiciystals and crystalline phases. The quasicrystal content of the surface ranges from 30-70%. 

Aperiodic crystals from modulated phases to quasicrystals... 

Some stable ternary intermetallic phases have been found that are quasiperi-odic in two dimensions and periodic in the third. These are from the systems Al—Ni—Co, Al—Cu—Co, and Al—Mn—Pd. They contain decagonally packed groups of atoms (local tenfold rotational symmetry). It should be noted that there are also known metastable quasicrystals with local eightfold rotational symmetry (octagonal) and 12-fold rotational symmetry (dodecagonal) as well. The dodecahedron is also one of the five Platonic solids (Lalena and Cleary, 2005). 

Figure 1-12) [30], This pattern was extended by Alan Mackay into the third dimension and he even produced a simulated diffraction pattern that showed 10-foldedness (Figure 1-13) [31], It was about the same time that Dan Shechtman was experimenting with metallic phases of various alloys cooled with different speeds and observed 10-foldedness in an actual electron diffraction experiment (Figure 1-14) for the first time. The discovery of quasicrystals has added new perspective to crystallography and the utilization of symmetry considerations. 

A. Csanady, K. Papp, M. Dobosy, M. Bauer, Direct Observation of the Phase Transformation of quasicrystals to Al6Mn Crystals. Symmetry 1990, 1, 75-79. 

Pauling countered the claim of Schechtman et al. that the x-ray powder diffraction pattern of the icosahedral phase of MnAle could not be indexed with any Bravais lattice by showing that the patterns of the quasicrystals could be explained by twinning [80-94]. Pauling s explanation was based on the idea that the truncated icosahedron shown in Figure 8 is the basic structural unit of the icosahedral phase of MnAl6. According to him,... 

L. Pauling, Icosahedral quasicrystals are twins of cubic crystals containing large icosa-hedral clusters of atoms The 1012-atom primitive cubic structure of Al6CuLi3, the C-phase of Al37Cu3Li2iMg3, and GaMg2Zn3. Proc. Natl. Acad. Sd. (USA) 85, 3666-3669 (1988). 

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