Thermodynamic metastability

Amorphous alloys are in a thermodynamically metastable state, and hence essentially they are chemically more reactive than corresponding thermodynamically stable crystalline alloyIf an amorphous alloy crystallises to a single phase having the same composition as the amorphous phase, crystallisation results in a decrease in the activity of the alloy related to the active dissolution rate of the alloy . 

The physical origin of this structural flexibility of the FeO overlayer is still unclear, the more so since no clear trend is observable in the sequence of lattice parameters of the coincidence structures. The FeO(l 11) phase forming up to coverages of 2-3 ML is clearly stabilized by the interactions with the Pt substrate since FeO is thermodynamically metastable with respect to the higher iron oxides [106,114], FeO has the rock salt structure and the (111) plane yields a polar surface with a high surface energy [115], which requires stabilization by internal reconstruction or external compensation. The structural relaxation observed in the form of the reduced Fe—O... 

Shortly after, we recognized that ScCu4Ga2 (Im3) [70] might also be tuned to a QC, but the correct stoichiometry and reaction conditions were not achieved in our limited experiments. Recently, Honma and Ishimasa [71] have reported that i-QC phase forms almost exclusively from a rapidly quenched ScisCu48Ga34 composition, emphasizing a very narrow phase width and its thermodynamic metastability at room temperature. However, the failure turned us to other Ga intermetallics, which led to the pseudogap tuning concepts that follow. 

The formation of bulk cobalt carbide is quite a slow process since it requires the diffusion of carbon into the cobalt bulk. It was reported that the full conversion of unsupported and reduced Co to Co2C only occurred after 500 h of exposure to pure CO at 230°C. Increasing the reaction temperature resulted in a faster rate of carburization.81 Bulk cobalt carbides are considered to be thermodynamically metastable species, and therefore Co2C will decompose to hep cobalt and graphite, while Co3C will decompose to fee cobalt and methane. Thermal decomposition of bulk carbides under an inert atmosphere is believed to occur at 400°C.81 Hydrogenation of the bulk carbides is believed to be a fast process and occurs around 200°C.82 83... 

The synthesis of chalcogenides such as those of the rare earth elements has traditionally been performed through the reaction of rare earth metals or oxides with a molten or vaporous chalcogen source in a high-temperature environment. Soft synthetic methods utilizing lower temperature conditions, such as hydrothermal or flux syntheses, can allow access also to thermodynamically metastable phases. Flux syntheses of R chalcogenides via an alkali poly-chalcogenide flux have been shown to be extremely versatile for the preparation of many new structures, some of which cannot be obtained by direct synthesis from the elements. 

The stability of films, even in thermodynamically metastable states, may be tested by stopping the barrier drive at intervals during compression of the film. If there is no drop in film pressure after several minutes, it is unlikely that the it-A relationships up to that point will be dependent on the compression rate. Figure 12 shows... 

Note 4 If a mixture is thermodynamically metastable, it will demix if suitably nucleated (see Definition 2.5). If a mixture is thermodynamically unstable, it will demix by spinodal decomposition or by nucleation and growth if suitably nucleated, provided there is minimal kinetic hindrance. 

Since the additional electron enters an antibonding n orbital, the bond order of 0-0 in O is 1.25 and the bond length increases. Ionic ozonides such as KO3 are thermodynamically metastable and extremely sensitive to moisture... 

Fig. 7 Electron micrographs of two different virgin UHMW-PE samples, (a) commercially synthesized Z-N (grade B) and (b) laboratory-synthesized Z-N (grade A). The samples were annealed in the hexagonal phase, at 1500 bars, 190 °C for 30 minutes. Under these conditions the samples were in the thermodynamically metastable hexagonal phase. (For details see references [27,28])...

Based on the extension by the repetition of three kinds of C-C bonds to infinite molecules, we may define carbon families, consisting of diamond, graphite, fullerenes, and carbynes [1], In each family, the structure shows characteristic diversities representative structures are listed in Figure 2.2. The detailed diversity in structure will be explained in the following sections for each family. Most structures in each family are thermodynamically metastable, and the family is represented by the allotrope name. In Figure 2.2, some possibilities to accept foreign species are also illustrated. 

Fumed silica is always found to be amorphous, and therefore does not cause silicosis. The respective AI2O3 is crystalline and consists of the thermodynamically metastable S form instead of the stable a form. It can be transformed to the a-AI203 phase by heating to i200°C. This conversion is associated with a loss of surface area and an increase of hardness and abrasiveness. In the commercial Ti02 obtained by flame hydrolysis, the thermodynamically metastable modification anatase is the main phase, with about 30% rutile. The lattice transformation towards higher amounts of rutile becomes notable at temperatures above 700 °C. It is also associated with a decrease of... 

The only "normal" phase state for polymers, known from the physics of small molecules, is the liquid state, though even here polymers show special properties, like viscoelasticity. The typical states of polymers are the glassy, the rubbery and the semi-crystalline state, all of which are thermodynamically metastable. 

In fact, most mesoporous adsorbents possess complex networks of pores of different size. It is therefore unlikely that the condensation-evaporation processes can occur independently in each pore. The complexity of capillary condensation in porous materials is illustrated by the recent Monte Carlo computer simulation studies of Page and Monson (1996) and Gelb and Gubbins (1998). The well-defined hysteresis loops observed in the simulation results of both studies were attributed to the presence of thermodynamically metastable states and not to kinetic effects. However, it appears that the extent of die hysteresis was associated with the overall heterogeneity of the adsorbent structure and not simply due to capillary condensation within individual pores. 

Dependence of the lifetime of foam bilayers on the concentration of dissolved surfactant. The stability of foam, emulsion and membrane bilayers can be characterised by their mean lifetime r which is the time elapsing form the moment of formation of a bilayer with a given radius until the moment of its rupture. Obviously, this is a kinetic characteristic of the bilayer stability and can only be applied to thermodynamically metastable bilayers. 

Anatase, brookite and rutile are three polymorphs of titanium dioxide. Anatase is a kind of thermodynamically metastable form while rutile is a kind of stable one. Anatase can transform irreversibly to rutile at elevated temperatures ranged from 400 to 1200 °C according to particle size, morphology and additives. The solid-state phase transformation behavior has been widely investigated while the phase evolution between anatase and rutile under hydrothermal condition has been little paid attention to so far [5]. In this work, the structural evolution from anatase to rutile under milder hydrothermal conditions is proposed as well [7, 10]. 

When the lamella between two droplets thins and breaks, the droplets on either side coalesce into a single, larger droplet (41,72). Continuation of this backward" process eventually leads to the disappearance of the dispersion, if it is not balanced by the forward" mechanisms of snap-off and division. Lamellae are thermodynamically metastable, and there are many mechanisms by which static and moving thin films can rupture. These mechanisms also depend on the molecular packing in the film and, thus, on the surfactant structure and locations of the dispersed and dispersing phases in the phase diagram. The stability and rupture of thin films is described in greater detail in Chapter 7. 

Crystals form in supersaturated solutions in which the solute concentration exceeds its solution solubility. Supersaturation is usually expressed as either of the ratios dc or (c — c )lc, where c is the concentration of solute before crystallization and is the solute equilibrium saturation concentration. Supersaturated solutions are thermodynamically metastable. Equilibrium can be restored by reducing the solute concentration through precipitation or formation of nuclei and subsequent crystal growth. The super saturation requirements for nucleation and... 

The standard method of solving the problem by the equilibrium constant approach is to use linearized matrix inversion. Convergence assumes, of course, that the solution not only exists but that it is unique. If a system can have several thermodynamically metastable states (local minima in the Gibbs function) then several nonunique solutions are possible. 

Insofar as small crystals of nonreducible oxides dispersed on the internal interfaces of the basic structural units (platelets) will stabilize the active catalyst surface Fe(lll), the paracrystallinity hypothesis will probably hold true. But the assumption that this will happen on a molecular level on each basic structural unit is not true. The unique texture and anisotropy of the ammonia catalyst is a thermodynamically metastable state. Impurity stabilization (structural promotion) kinetically prevents the transformation of platelet iron into isotropic crystals by Ostwald ripening [154]. Thus the primary function of alumina is to prevent sintering by acting as a spacer, and in part it may also contribute to stabilizing the Fe(lll) faces [155], [156], [298],... 

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