Crystal instability

CRYSTAL INSTABILITY PEIERLS TRANSITION, CHARGE-DENSITY WAVES AND SPIN DENSITY WAVES... 

However, there should be some limit to T. in this treatment, since the larger the effective volume, the more dispersed BEDT-TTF molecules will be in a unit cell, which makes the crystal unstable. If one can control the band filling of organic superconductors of low molecular weight, just like a doped polymer or an inorganic oxide superconductor, may increase with small N without increasing the crystal instability. 

Interesting pattern formations also occur in surfactants spreading on water due to a hydrodynamic instability [52]. The spreading velocity from a crystal may vary with direction, depending on the contour and crystal facet. There may be sufficient imbalance to cause the solid particle to move around rapidly, as does camphor when placed on a clean water surface. The many such effects have been reviewed by Stemling and Scriven [53]. 

A second case to be considered is that of mixtures witli a small size ratio, <0.2. For a long time it was believed tliat such mixtures would not show any instability in tire fluid phase, but such an instability was predicted by Biben and Flansen [109]. This can be understood to be as a result of depletion interactions, exerted on the large spheres by tire small spheres (see section C2.6.4.3). Experimentally, such mixtures were indeed found to display an instability [110]. The gas-liquid transition does, however, seem to be metastable witli respect to tire fluid-crystal transition [111, 112]. This was confinned by computer simulations [113]. 

Boyer L L 1985 Theory of melting based on lattice instabilities Phase Trans. 5 1 Cotteril R M J 1980 The physics of melting J. Crystal Growth 48 582... 

Chemical conversion of compounds to intermediates of known absolute configuration is a method routinely used to determine absolute configuration (86). This is necessary because x-ray analysis is not always possible suitable crystals are required and deterrnination of the absolute configuration of many crystalline molecules caimot be done because of poor resolution. Such poor resolution is usually a function of either molecular instability or the complex nature of the molecule. For example, the relative configuration of the macroHde immunosuppressant FK-506 (105) (Fig. 8), which contains 14 stereocenters, was determined by x-ray crystallographic studies. However, the absolute configuration could only be elucidated by chemical degradation and isolation of L-pipecoUc acid (110) (80). 

In addition to these direct long-range forces there may also exist effective long-range forces, produced by some medium or substrate. An especially drastic effect is expected for epitaxial growth on a semiconductor. If adsorbate atoms are different from the substrate, the adsorbed layers have a lattice constant different from that of the substrate. In the case of thick adsorbate layers, an instability then appears on the surface of the crystal such that the surface undergoes wavy deformation, which might even lead to... 

Figure 14.6 Structure and key dimensions of (a) the complex [(Fh3P)2EihCI( -02)]2 and (b) the complex [Pt(02)(PPh3)2]. The data in (b) arc of poor quality because of the difficulty of growing suitable crystals and their instability in the X-ray beam (distances 5 pm angles 2 ).

Anhydrous NaC102 crystallizes from aqueous solutions above 37.4° but below this temperature the trihydrate is obtained. The commercial product contains about 80% NaC102. The anhydrous salt forms colourless deliquescent crystals which decompose when heated to 175-200° the reaction is predominantly a disproportionation to C103 and Cl but about 5% of molecular O2 is also released (based on the C102 consumed). Neutral and alkaline aqueous solutions of NaC102 are stable at room temperature (despite their thermodynamic instability towards disproportionation as evidenced by the reduction potentials on p. 854). This is a kinetic activation-energy effect and, when the solutions are heated near to boiling, slow disproportionation occurs ... 

The linear instability theory of the behavior of a system near the bifurcation point can be successfully applied to many self-organization problems, such as thermal convection in hydrodynamics4 and crystal growth in solution.5 In these theories, various initial fluctuations play important roles. Occasionally the fluctuations arise from the thermal motion of atoms or molecules. If a system reaches an unstable mode over... 

Similarly, we can pick another example in crystal growth in melt. In this case, the growth occurs at the interface between the melt and a substrate that is kept at a constant temperature that is lower than the critical temperature for crystallization. The morphology characteristic of the instability is formed by the coupling of the heat flux and the surface-form fluctuation. This problem was first theoretically analyzed by Mullins and Sekerka.57-62... 

Cyclobutadiene owes its observed instability much to the kinetic property. Cyclobutadiene dimerizes in the argon matrix above 35 K [69] and only exists for 2-10 ms under low pressure [70, 71], However, cyclobutadiene is stabilized by bulky substituents (Scheme 30). The ferf-butyl derivative was quantitatively prepared even at a high temperature (130 °C) [72]. Yellow crystals of the cyclobutadiene fused by two seven-membered rings did not decompose below 240 °C [73]. 

There is no ready explanation for the relative instability of the alkyl-substituted cyclopentadienylthallium(I) compounds. The change in the hydrocarbon substrate, which results from introduction of an alkyl group, is likely to be small and insufficient to account for the dramatic stability differences [in the case of 9-R-substituted fluorenes, for example, where R = H, CHj, C2H5, or terf-butyl, the maximum difference in p. units between any two compounds is only 1.6 (9)]. The change in orbital overlap caused by introduction of an alkyl group is also likely to be small the l,T-dialkylferrocenes, for example, are stable compounds 137). At present, the only plausible explanation appears to be that the relative stabilities of the crystal lattices vary markedly 169). 

A difiiculty with this mechanism is the small nucleation rate predicted (1). Surfaces of a crystal with low vapor pressure have very few clusters and two-dimensional nucleation is almost impossible. Indeed, dislocation-free crystals can often remain in a metastable equilibrium with a supersaturated vapor for long periods of time. Nucleation can be induced by resorting to a vapor with a very large supersaturation, but this often has undesirable side effects. Instabilities in the interface shape result in a degradation of the quality and uniformity of crystalline material. 

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