Stable and Metastable Equilibrium

In position (b), it is possible to imagine the ball balanced and unmoving, so that the first part of the definition would be fulfilled, and this is sometimes referred to as a third type of equilibrium, admittedly a trivial case, called unstable equilibrium. However, it does not survive the second part of the definition, so we are left with only two types of equilibrium, stable and metastable. 

This true or idealized energy minimum is also sometimes referred to as the equilibrium state, stable or metastable, and discussions can become confused unless the distinction between the macroscopic, practical kind of equilibrium that we have defined and the more idealized, conceivable kind of equilibrium state is made clear. 

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Figure 7.17. Predicted phase diagiam for the system (CiiInSe2)i-x(ZnSe)2i (a) stable and metastable equilibrium between dialcopyrite (CH) and zinc-blende (ZB) phases using volume-dependent interaction parameters (b) using a hierarchy of less accurate tqiproximations (<)sorio el al. 1993).

In this section we use the simple mechanical analogy in 1.3 to distinguish between stable and metastable equilibrium. This explanation is satisfactory for an intuitive understanding, but we return to this subject for a better theoretical understanding in 4.9.1. 

Rodebush has also implied that the accuracy with which very low temperatures can be measured is restricted by the uncertainty principle and by the nature of the substance under investigation. However, the accuracy of a temperature measurement is not limited in a serious way by the uncertainty principle for energy, inasmuch as the relation between the uncertainty in temperature and the length of time involved in the measurement depends on the size of the thermometer, and the uncertainty in temperature can be made arbitrarily small by sufficiently increasing the size of the thermometer we assume as the temperature of the substance the temperature of the surrounding thermostat with which it is in either stable or metastable equilibrium, provided that thermal equilibrium effective for the time of the investigation is reached. 

It is assumed that in this experiment (58), stable or metastable equilibrium had been reached between the aqueous solution and a surface layer of the apatite particles. 

A number of computer programs for generating potential -pH diagrams have been described (49, 50 51). Helgeson (52) describes a method often used within geosciences whereBy compositional changes, mass transfers and the order of appearance of stable and metastable phases are determined in tracing reaction paths from an initial set of conditions to a final state of equilibrium. 

Note 3 For a two-component mixture, a necessary and sufficient condition for stable or metastable equilibrium of a homogeneous single phase is... 

In the first discussion of equilibrium (Ch. 5) we recognized that there may be states of a system that are actually metastable with respect to other states of the system but which appear to be stable and in equilibrium over a time period. Let us consider, then, a pure substance that can exist in two crystalline states, a and p, and let the a phase be metastable with respect to the p phase at normal temperatures and pressures. We assume that, on cooling the a. phase to the lowest experimental temperature, equilibrium can be maintained within the sample, so that on extrapolation the value of the entropy function becomes zero. If, now, it is possible to cool the p phase under the conditions of maintaining equilibrium with no conversion to the a phase, such that all molecules of the phase attain the same quantum state excluding the lattice vibrations, then the value of the entropy function of the p phase also becomes zero on the extrapolation. The molar absolute entropy of the a phase and of the p phase at the equilibrium transition temperature, Tlr, for the chosen... 

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. 

It should be noted that both stable and metastable compounds may occur in reaction couples. Analysis of the available experimental data shows that the growth of metastable compound layers is observed relatively rarely. The possibility of formation of metastable compounds is usually mentioned in the explanatory text accompanying the equilibrium phase diagram of any binary system. For certain systems, diagrams of both stable and metastable equilibria have been proposed.142145193 215-225... 

Ohman, L.-O. (1988). Equilibrium and structural studies of silicon(IV) and alu-minum(III) in aqueous solution, 17 Stable and metastable complexes in the system H -AP+—citric acid. Inorg. Chem. 27, 2565-2570. 

Thermodynamics allows us to calculate the energy differences between equilibrium states of all kinds, stable and metastable, for all kinds of substances. If that is all it does, and natural systems are not at equilibrium, how can it be useful ... 

Univariant Systems.—Equilibrium between liquid and vapour. Vaporisation curve. Upper limit of vaporisation curve. Theorems of van t Hoff and of Le Chatelier. The Clausius-Clapeyron equation. Presence of complex molecules. Equilibrium between solid and vapour. Sublimation curve. Equilibrium between solid and liquid. Curve of fusion. Equilibrium between solid, liquid, and vapour. The triple point. Complexity of the solid state. Theory of allotropy. Bivariant systems. Changes at the triple point. Polymorphism. Triple point Sj—Sg— V. Transition point. Transition curve. Enantiotropy and monotropy. Enantiotropy combined with monotropy. Suspended transformation. Metastable equilibria. Pressure-temperature relations between stable and metastable forms. Velocity of transformation of metastable systems. Metastability in metals produced by mechanical stress. Law of successive reactions. 

Thermodynamic Stability In colloid sdence, the terms thermodynamically stable and metastable mean that a system is in a state of equilibrium... 

The laboratory studies were designed to examine in detail the composition of aluminum species in dilute solutions having values of r between 0.5 and 4.0, after various periods of aging. The behavior of OH boimd to aluminum was examined by kinetic methods, precipitated solids were identified by the electron microscope and x-ray diffractometer, and equilibrium solubilities were calculated for stable and metastable aluminum hydroxides. 

Phase diagrams determined exclusively by DTA/DSC measurements are correct only in those rare cases when equilibrium is attained sufficiently rapidly compared with the heating rate applied. In most case both the stable and metastable lines are jointly traced in a different magnitude and it is up to the investigator again to separate them. The most convenient way is to look for the extrapolated lines of metastable phases, see Fig. 3, viewing thus e.g. the complex peritectic... 

In recent pharmaceutical literature, the terms equilibrium solubility and kinetic or apparent solubility are often used for the systems with stable and metastable equilibria, respectively (Lipinski et al. 2001 Huang and Tong 2004). 

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