Metastability description

Figure A3.3.2 A schematic phase diagram for a typical binary mixture showmg stable, unstable and metastable regions according to a van der Waals mean field description. The coexistence curve (outer curve) and the spinodal curve (iimer curve) meet at the (upper) critical pomt. A critical quench corresponds to a sudden decrease in temperature along a constant order parameter (concentration) path passing through the critical point. Other constant order parameter paths ending within tire coexistence curve are called off-critical quenches.

If 5v //v /coex is not small, the simple description Eq. (14) in terms of bulk and surface terms no longer holds. But one can find AF from Eq. (5) by looking for a marginally stable non-uniform spherically symmetric solution v /(p) which leads to an extremum of Eq. (5) and satisfies the boundary condition v /(p oo) = v(/ . Near the spinodal curve i = v /sp = Vcoex /a/3 (at this stability limit of the metastable states both and S(0) diverge) one finds "... 

Finally, we have considered an example of metastable state without potential barrier exponential approximation with the MFPT of the point d for kT = 1 (Fig. 13). It is seen that even for such an example the exponential approximation [with the mean decay time (6.5)] gives an adequate description of the probability evolution and that this approximation works better for larger noise intensity. 

Since the large majority of metalloid clusters E Rthis section is divided in two parts, including the few clusters for In hitherto known. For many of the metalloid clusters discussed in this section (for a definition of metalloid cf. Section 2.3.1, Introduction) the technique of cryochemistry is essential, i.e., trapping of a high-temperature species together with an excess of a suitable solvent in order to obtain a metastable solution. Detailed descriptions and discussions of this technique have been presented recently [7-12],... 

In this chapter, general aspects and structural properties of crystalline solid phases are described, and a short introduction is given to modulated and quasicrystal structures (quasi-periodic crystals). Elements of structure systematics with the description of a number of structure types are presented in the subsequent Chapter 7. Finally, both in this chapter and in Chapter 6, dedicated to preparation techniques, characteristic features of typical metastable phases are considered with attention to amorphous and glassy alloys. 

Several descriptions of the process of addition of the electrophile X" " to aromatic substrates, based on kinetic and other evidence have been given and most versions agree that the potential energy surface does not consist of a simple barrier, but involves details relating to metastable intermediates. 

Particular care has been devoted to establishing a qualitatively correct description of the metastable anion state that arises. 

Berry, L. G., B. Mason, and R. V. Dietrich (1983). Mineralogy Concepts, Descriptions, Determinations, 2nd ed. W. H. Freeman, San Francisco. Blander, M., H. N. Planner, K. Keil, L. S. Nelson, and N. L. Richardson (1956). The origin of chondrales experimental investigation of metastable liquids in the system Mg2Si04Si02- Geochem. Cosmochem. Acta 40 889-896. 

In this section, a brief description of the necessary experiments to identify the kinetic parameters of a seeded naphthalene-toluene batch crystallization system is presented. Details about the experimental apparatus and procedure are given by Witkowski (12). Operating conditions are selected so that the supersaturation level is kept within the metastable region to prevent homogeneous nucleation. To enhance the probability of secondary nucleation, sieved naphthalene seed particles are introduced into the system at time zero. 

Solids undergoing martensitic phase transformations are currently a subject of intense interest in mechanics. In spite of recent progress in understanding the absolute stability of elastic phases under applied loads, the presence of metastable configurations remains a major puzzle. In this overview we presented the simplest possible discussion of nucleation and growth phenomena in the framework of the dynamical theory of elastic rods. We argue that the resolution of an apparent nonuniqueness at the continuum level requires "dehomogenization" of the main system of equations and the detailed description of the processes at micro scale. 

The radiative transitions of the previous descriptions have all been spontaneous Relaxation from the excited state to the ground state and emission of photons occur without external aid. In contrast, a stimulated emission occurs when the half-life of the excited state is relatively long, and relaxation can occur only through the aid of a stimulating photon. In stimulated emission, the emitted photon has the same direction as, and is in phase with, the stimulating photon. The example of Cr +-doped AI2O3 that we utilized earlier for our description of the color of ruby works equally well for a description of stimulated emission. Recall that the presence of chromium in alumina alters the electronic structure, creating a metastable state between the valence and conduction bands. Absorption of a blue-violet photon results in the excitation of an electron from... 

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