Metastable states thermodynamic

Here the nucleation barrier AO is the excess thermodynamic potential needed to form the critical embryo within the uniform metastable state, while the prefactor Jq is determined by the kinetic characteristics for the embryo diffusion in the space of its size a. Expressions for both AO and Jo given by Zeldovich include a number of phenomenological parameters. 

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 . 

Melting point, 193, 203, 528 Meslin s theorem, 229 Metastable states, 181 Mixed liquids, 380 Mixture rule, 263 Mobile equilibrium, 304, 340 Model, thermodynamic, 240 Mol, 20, 135... 

The reason for the formation of anatase phase at such a high temperature might be explained as following. The as-prqiared ultrafine titania particles are liquefied at sufficimtly high temperature because melting point of nanoparticlra are lower than that of bulk titania (1850 C). The liquid titania particles are supercooled and became metastable states. The residence time in the flame is only in the order of miU-second so that the metastable phase has no time to become thermodynamically stable phase, rutile. 

This effect is called subcooling or supercooling. During subcooling, the PCM is in a metastable state, which means it is not in thermodynamic equilibrium. Subcooling is typical for many inorganic PCM. To reduce or... 

The temperature dependences of the isothermal elastic moduli of aluminium are given in Figure 5.2 [10]. Here the dashed lines represent extrapolations for T> 7fus. Tallon and Wolfenden found that the shear modulus of A1 would vanish at T = 1.677fus and interpreted this as the upper limit for the onset of instability of metastable superheated aluminium [10]. Experimental observations of the extent of superheating typically give 1.1 Tfus as the maximum temperature where a crystalline metallic element can be retained as a metastable state [11], This is considerably lower than the instability limits predicted from the thermodynamic arguments above. 

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... 

The ratio of the instantaneous solute concentration c to the solute s solubility s, where the latter is the solute concentration in equihbrium with its crystalline or precipitated phase. Hence, RS = c/s, and a supersaturated solution experiences a thermodynamic driving force (AG = RT ln[RS]). A supersaturated solution will remain as a metastable state, because crystallization or precipitation requires a mechanism for relieving the supersaturated condition (eg., nucleation or addition of crystallite/precipitate). See Biomineralization... 

It should be realized, at the outset, that colloidal solutions (unlike true solutions) will almost always be in a metastable state. That is, an electrostatic repulsion prevents the particles from combining into their most thermodynamically stable state, of aggregation into the macroscopic form, from which the colloidal dispersion was (artificially) created in the first place. On drying, colloidal particles will often remain separated by these repulsive forces, as illustrated by Figure 1.1, which shows a scanning electron microscope picture of mono-disperse silica colloids. 

Yet this description is not entirely correct, because even when the system is at a site in Da, and even inside Aai there is still a probability, however small, for a giant fluctuation to occur, which takes it across into Dc. It will then move to the neighborhood of c until a similar giant fluctuation takes it back to Da. Thus a mesostate represented by a probability peak in Aa does not survive forever its probability is slowly depleted in favor of a peak near (f)c. Although a is a stable solution of the macroscopic equation, the related mesostate is not strictly stable but merely long-lived, and may be called metastable. Indeed, a metastable state in thermodynamics, such as supersaturated vapor, also exists because it is stable with respect to small fluctuations, but an improbable giant fluctuation may carry it into a macro-scopically different thermodynamic state. 

It is also known that a rod structure is generated in compact DNA under some conditions. However, it was not clear whether the rod-like structure is a thermodynamically stable state or a kinetically trapped metastable state (Chattoraj et al., 1978 Eickbush and Moudrianakis, 1978 Grosberg, 1979 Arscott et al., 1990 Plum etal., 1990 Perales et al., 1994). 

In Chap. 3 (Sect. 3.6), we discussed limitations of the FREZCHEM model that were broadly grouped under Pitzer-equation parameterization and mathematical modeling. There exists another limitation related to equilibrium principles. The foundations of the FREZCHEM model rest on chemical thermodynamic equilibrium principles (Chap. 2). Thermodynamic equilibrium refers to a state of absolute rest from which a system has no tendency to depart. These stable states are what the FREZCHEM model predicts. But in the real world, unstable (also known as disequilibrium or metastable) states may persist indefinitely. Life depends on disequilibrium processes (Gaidos et al. 1999 Schulze-Makuch and Irwin 2004). As we point out in Chap. 6, if the Universe were ever to reach a state of chemical thermodynamic equilibrium, entropic death would terminate life. These nonequilibrium states are related to reaction kinetics that may be fast or slow or driven by either or both abiotic and biotic factors. Below are four examples of nonequilibrium thermodynamics and how we can cope, in some cases, with these unstable chemistries using existing equilibrium models. 

In colloid science, the terms thermodynamically stable and metastable mean that a system is in a state of equilibrium corresponding to a local minimum of free energy (Ref. [978]). If several states of energy are accessible, the lowest is referred to as the stable state and the others are referred to as metastable states unstable states are not at a local minimum. Most colloidal systems are metastable or unstable with respect to the separate bulk phases. See also Colloid Stability, Kinetic Stability. 

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