Quasicrystal formation

The dependence of anion exclusion volume on particle thickness in the infinite-plane model arises solely from the geometric decrease in exclusion-specific surface area with an increase in particle thickness via quasicrystal formation [Eq. (13)]. Thus, on the infinite-plane model, the anion exclusion volume simply has an inverse relation to particle thickness. Reduction of the anion exclusion volume from an increase in particle thickness is, however, more complicated and more significant on the disk model (Fig. 6). An increase in particle thickness (or the number of unit layers... 

The evidence for quasicrystal formation in suspensions of mono-valent-ion-saturated montmorillonites [23,58] indicates that wav for Na-montmorillonite should lie between 1.0 and 2.0. The viscosity data in Fig. 11 in fact lead to wav = 1.3 if the ratio of hD-values [from Eq. (30)] for Na-montmorillonite and Li-montmorillonite is equated to their ratio of av values, with av = 1.0 for Li-montmorillonite. Similarly, if the ratio of mp-values taken from Eq. (31) is equated to a ratio of av values (i.e., mp = wo wav, where wo is the mass of a unit-layer particle), then av = 1.4 0.3 on the basis of the data in Fig. 11, along with other published data on light transmission by dilute Li- and Na-montmorillonite suspensions [23]. 

Fig. 3.38. Basic principles of quasicrystal formation by a solid-state reaction...

QUASICRYSTAL FORMATION. The mixing together of Na- and Ca-montmorillonite suspensions to produce an overall charge fraction of Na" on the clay particles below 0.1 results in a very rapid (less than 1 min) formation of quasicrystals from conversion of the Na-montmorillonite particles.This rapid conversion is necessarily mediated by a redistribu- tion of the exchangeable cations such that Na ions are relocated, as required, to the external surfaces of already-formed quasicrystals that contain Ca ions on their internal surfaces. The relocation probably involves replacement by Na of Ca " already on external surfaces since the latter ions are likely to have a higher mobility than Ca " adsorbed inside a quasicrystal. 

These characteristics of quasicrystal formation and breakdown are consistent with the trends in Fig. 6.2. When Enh is less than 0.1, for example, the properties of a mixed Na/Ca-montmorillonite do not differ much from those of Ca-montmorillonite and the quasicrystal should remain a stable entity. When Ens is larger than 0.6, however, the mixed Na/Ca-montmorillonite exhibits properties that are indistinguishable from those of a Na-montmorillonite and a quasicrystal should be an inherently unstable structural unit. 

H. Tanaka, Roles of local icosahedral chemical ordering in glass and quasicrystal formation in metallic glass formers. J. Phys. Condens. Matter , L491-L498 (2003). 

Types of quasicrystals and examples of alloy systems showing their formation. A short description of the main types of quasicrystals and of their occurrence is given here below (Kelton 1995, Steurer 1996). 

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). 

Note that the low-temperature structure is neither a quasicrystal nor an icosahedral glass. Given the molecular symmetry, one might have predicted the latter, whereas icosahedral quasicrystals require two distinct structural units to satisfy space filling. While the precise energetic requirements for crystal versus icosahedral glass formation are not understood, it seems likely that the structural order at low T is driven both by a preference for close packing and,by local orientational order. 

Formation of Quasicrystals and Milling-Induced Phase Transitions... 

Molecular quantum potential and non-local interaction depend on molecular size and the nature of intramolecular cohesion. Macromolecular assemblies such as polymers, biopolymers, liquids, glasses, crystals and quasicrystals are different forms of condensed matter with characteristic quanmm potentials. The one property they have in common is non-local long-range interaction, albeit of different intensity. Without enquiring into the mechanism of their formation, various forms of condensed matter are considered to have well-defined electronic potential energies that depend on the nuclear framework. A regular array of nuclei in a structure such as diamond maximizes cohesive interaction between nuclei and electrons, precisely balanced by the quantum potential, almost as in an atom. 

Koster, U. Meinhardt, J. (1994). Crystallization of highly undercooled metallic melts and metallic glasses around the glass-transition temperature. Materials Science and Engineering A, Vol. 178, No. 1-2, (April 1994), pp. 271-278, ISSN 0921-5093 Koster, U. Meinhardt, J. Roos, S. Liebertz, H. (1996). Formation of quasicrystals in bulk glass forming Zr-Cu-Ni-Al alloys. Applied Physics Eetters, Vol. 69, No. 2, (July 1996), pp. 179-181, ISSN 0003-6951... 

There have been few reports to date on quasicrystaUine structure foimatimi from BCPs. Hayashida et al. obtained a 2D quasicrystaUine structure, a tUing pattern with 12-fold symmetry, from an ABC star BCP and homopolymer blend (see Fig. 3) [34]. The Bates group at the University of Minnesota generated a 3D dodecagonal quasicrystal from diblock and tetrablock copolymers [33]. These unique structures are mediated by macromolecular packing frustration. However, a substantial number of unanswered questions about the stmcture formation await further in-depth studies of these interesting morphologies. 

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