Phase transition metastability

Unlike melting and the solid-solid phase transitions discussed in the next section, these phase changes are not reversible processes they occur because the crystal stmcture of the nanocrystal is metastable. For example, titania made in the nanophase always adopts the anatase stmcture. At higher temperatures the material spontaneously transfonns to the mtile bulk stable phase [211, 212 and 213]. The role of grain size in these metastable-stable transitions is not well established the issue is complicated by the fact that the transition is accompanied by grain growth which clouds the inteiyDretation of size-dependent data [214, 215 and 216]. In situ TEM studies, however, indicate that the surface chemistry of the nanocrystals play a cmcial role in the transition temperatures [217, 218]. 

FIG. 4 Qualitative phase diagram close to a first-order irreversible phase transition. The solid line shows the dependence of the coverage of A species ( a) on the partial pressure (Ta). Just at the critical point F2a one has a discontinuity in (dashed line) which indicates coexistence between a reactive state with no large A clusters and an A rich phase (hkely a large A cluster). The dotted fine shows a metastability loop where Fas and F s are the upper and lower spinodal points, respectively. Between F2A and Fas the reactive state is unstable and is displaced by the A rich phase. In contrast, between F s and F2A the reactive state displaces the A rich phase. 

Pressure-induced phase transitions in the titanium dioxide system provide an understanding of crystal structure and mineral stability in planets interior and thus are of major geophysical interest. Moderate pressures transform either of the three stable polymorphs into the a-Pb02 (columbite)-type structure, while further pressure increase creates the monoclinic baddeleyite-type structure. Recent high-pressure studies indicate that columbite can be formed only within a limited range of pressures/temperatures, although it is a metastable phase that can be preserved unchanged for years after pressure release Combined Raman spectroscopy and X-ray diffraction studies 6-8,10 ave established that rutile transforms to columbite structure at 10 GPa, while anatase and brookite transform to columbite at approximately 4-5 GPa. 

When the bulk transition is of first order, the above mentioned arguments based on dimensionality do not apply and the would be roughening transition temperature T j may be larger than the bulk transition temperature T, in which case there is simply no roughening transition. The situation is further complicated by the wetting phenomena. When we approach T from below, the disordered phase becomes metastable and may wet the interface a large layer of disordered phase develops in between the two ordered domains. 

Figure 4.7 Heat capacity and phase transitions in phosphine. The same entropy at point (a) is obtained by going the stable (lower) route or by going the metastable (upper) route. Point (b) is the normal boiling temperature.

Similar considerations apply to chemical or physicochemical equilibria such as encountered in phase transitions. A chilled salt solution may be stable (at or below saturation), metastable (supercooled to an extent not allowing nucle-ation), or unstable (cooled sufficiently to nucleate spontaneously). In the case of a solid, S, dispersed in a binary liquid, Li + L2, instability at the instant of formation gives way to a neutral or metastable condition wherein three types of contacts are established ... 

Cp is the specific heat at constant pressure, k is the compressibility at constant temperature. The conversion process of a second-order phase transition can extend over a certain temperature range. If it is linked with a change of the structure (which usually is the case), this is a continuous structural change. There is no hysteresis and no metastable phases occur. A transformation that almost proceeds in a second-order manner (very small discontinuity of volume or entropy) is sometimes called weakly first order . 

The hydration equilibria and phase transformations associated with a cytotoxic drug, BBR3576, have been studied [72]. The initially hydrated form could be made to undergo a phase transition where it lost approximately half of its water content, but the hemidesolvated product could be easily rehydrated to regenerate the starting material. If however, the original sample was completely dehydrated, the substance first formed a metastable anhydrate phase that underwent an irreversible exothermic transition to a new anhydrate crystal form. The hydration of this latter anhydrate form yielded a new hydrate phase whose structure was different from that of the initial material. 

A given phase may persist beyond the point at which transition to another phase should properly occur. On the T5 isotherm, for instance, it is possible to compress the vapour in clean conditions beyond point V, as shown by the dots, without condensation occurring. This vapour is supercooled, and Pv > Pl- When disturbed, the supercooled vapour condenses at once. In the same way, clean liquid may be superheated without boiling, in which case Pl > Pv Supercooled or superheated phases are metastable. They appear to be stable, but are thermodynamically unstable, since another state of lower chemical potential exists. 

On heating from a crystalline phase, DOBAMBC melts to form a SmC phase, which exists as the thermodynamic minimum structure between 76 and 95°C. At 95°C a thermotropic transition to the SmA phase occurs. Finally, the system clears to the isotropic liquid phase at 117°C. On cooling, the SmC phase supercools into the temperature range where the crystalline solid is more stable (a common occurrence). In fact, at 63°C a new smectic phase (the SmF) appears. This phase is metastable with respect to the crystalline solid such phases are termed monotropic, while thermodynamically stable phases are termed enantiotropic. The kinetic stability of monotropic LC phases is dependent upon purity of the sample and other conditions such as the cooling rate. However, the appearance of monotropic phases is typically reproducible and is often reported in the phase sequence on cooling. It is assumed that phases appearing on heating a sample are enantiotropic. 

Another spectral change was found w hen a cast film of C AzoCgN+Br was annealed and then moistened (Figure 13). The type I spectrum of the as-cast film changed to the type V spectrum (the broken-line spectrum in Figure 13) after heating above its phase transition (115°C[22]), and then immediately shifted to the type III spectrum within 30 sec in a 75% humidity condition at room temperature. The type III state seemed to be another metastable state in the annealed film because the moisture induced isothermal transition from the type III to the type I required a long period (e.g. 13 hours even at 75% humidity). 

Structural polymorphism has been already reported as a peculiar solid-solid phase transition with a large spectral shift in the cast film of CgAzoCioN+ Br (chapter 4). The type 1 spectrum was thermally transformed to the type VI spectrum and then backed to the type I by the isothermal moisture treatment. The reversible spectral change between the type I and VI is a good experimental evidence of Okuyama s prediction on the molecular packing. Since the type VI state is assumed to be a metastable state, the isothermal phase transition to the type I state is expected to be induced by some external stimuli. Water molecules adsorbed to cast bilayer films might act as an accelerator of the phase transition. 

To summarize, in the present scenario pure hadronic stars having a central pressure larger than the static transition pressure for the formation of the Q -phase are metastable to the decay (conversion) to a more compact stellar configuration in which deconfined quark matter is present (i. e., HyS or SS). These metastable HS have a mean-life time which is related to the nucleation time to form the first critical-size drop of deconfined matter in their interior (the actual mean-life time of the HS will depend on the mass accretion or on the spin-down rate which modifies the nucleation time via an explicit time dependence of the stellar central pressure). We define as critical mass Mcr of the metastable HS, the value of the gravitational mass for which the nucleation time is equal to one year Mcr = Miis t = lyr). Pure hadronic stars with Mh > Mcr are very unlikely to be observed. Mcr plays the role of an effective maximum mass for the hadronic branch of compact stars. While the Oppenheimer-Volkov maximum mass Mhs,max (Oppenheimer Volkov 1939) is determined by the overall stiffness of the EOS for hadronic matter, the value of Mcr will depend in addition on the bulk properties of the EOS for quark matter and on the properties at the interface between the confined and deconfined phases of matter (e.g., the surface tension a). 

The explosive phenomena produced by contact of liquefied gases with water were studied. Chlorodifluoromethane produced explosions when the liquid-water temperature differential exceeded 92°C, and propene did so at differentials of 96-109°C. Liquid propane did, but ethylene did not, produce explosions under the conditions studied [1], The previous literature on superheated vapour explosions has been critically reviewed, and new experimental work shows the phenomenon to be more widespread than had been thought previously. The explosions may be quite violent, and mixtures of liquefied gases may produce overpressures above 7 bar [2], Alternative explanations involve detonation driven by phase changes [3,4] and do not involve chemical reactions. Explosive phase transitions from superheated liquid to vapour have also been induced in chlorodifluoromethane by 1.0 J pulsed ruby laser irradiation. Metastable superheated states (of 25°C) achieved lasted some 50 ms, the expected detonation pressure being 4-5 bar [5], See LIQUEFIED NATURAL GAS, SUPERHEATED LIQUIDS, VAPOUR EXPLOSIONS... 

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