Equilibrium metastable, unstable

A system may be in a stable, metastable, unstable, or neutral equilibrium state. In a stable system, a perturbation causes small departures from the original conditions, which are restorable. In an unstable equilibrium, even a small perturbation causes large irreversible changes. A metastable system may be stable or unstable according to the level and direction of perturbation. All thermodynamic equilibria are stable or metastable, but not unstable. This means that all natural processes evolve toward an equilibrium state, which is a global attractor. 

Stable A term describing a system in a state of equilibrium corresponding to a local minimum of the appropriate thermodynamic potential for the specified constraints on the system. Stability cannot be defined in an absolute sense, but if several states are in principle accessible to the system under given conditions, that with the lowest potential is called the stable state, while the other states are described as metastable. Unstable states are not at a local minimum. Transitions between metastable and stable states occur at rates that depend on the magnitude of the appropriate activation energy barriers that separate them. 

Polymer composite systems usually exist in a metastable (unstable) state of mechanical equilibrium. This is because a mixture of mutually insoluble components separates extremely slowly due to the very low diffusion coefficients of the polymer matrix of the ingredients. This state of polymer systems is sometimes defined as kinetic compatibility [28]. 

For the first-order phase transition, there are multiple solutions that need to be calculated, corresponding to the stable (equilibrium), metastable and unstable branches. Fig. 2(a) shows a representation of these solutions. 

There may be situations when pjquations 7 and 9 are realized while Equations 8 and 10 are not realized, i.c. the system is stable toward infinitely small perturbations while being unstable toward finite ones (a local maximum of entropy or a minimum of internal energy with at least one additional extremum). In such cases it is generally agreed to speak of a metastable equilibrium (metastable state) of the system. Conditions 8 and 10 define a stable equilibrium. When simultaneously breaking conditions 7 10, the system proves to be absolutely unstable. 

To start with, it is sufficient to replace the terms stable ( equilibrium ), metastable , and unstable by the terms stationary , metastationary , and non-stationary . Thus, with the aid of such a primitive glossary, a complete analogy in description of linear and non-linear phenomena may be attained including even the methods of description and the criteria of first- and second-order (in Landau s sense) phase transitions. 

Unless other statements were made by the authors, it is assumed that the substances concerned are homogeneous and in a state of equilibrium. Where the state of equilibrium has not been attained or where metastable, unstable, martensitic or heterogeneous substances are being considered, this is referred to in the second last column under Weitere Angaben (=further information) or in an additional footnote on the formula. 

FIGURE 1.5 Mechanical models of stable, metastable, unstable, and neutral equilibrium. 

Systems involving an interface are often metastable, that is, essentially in equilibrium in some aspects although in principle evolving slowly to a final state of global equilibrium. The solid-vapor interface is a good example of this. We can have adsorption equilibrium and calculate various thermodynamic quantities for the adsorption process yet the particles of a solid are unstable toward a drift to the final equilibrium condition of a single, perfect crystal. Much of Chapters IX and XVII are thus thermodynamic in content. 

A homogeneous metastable phase is always stable with respect to the fonnation of infinitesimal droplets, provided the surface tension a is positive. Between this extreme and the other thennodynamic equilibrium state, which is inhomogeneous and consists of two coexisting phases, a critical size droplet state exists, which is in unstable equilibrium. In the classical theory, one makes the capillarity approxunation the critical droplet is assumed homogeneous up to the boundary separating it from the metastable background and is assumed to be the same as the new phase in the bulk. Then the work of fonnation W R) of such a droplet of arbitrary radius R is the sum of the... 

Another kinetic jjhenomenon where Calm s critical waves can possibly be visualized and studied is the replication of interphase boundaries (IPB) illustrated in Figs. 8-10. Similarly to the replication of APBs. it can arise after a two-step quench of an initially uniform disordered alloy. First the alloy is quenched and annealed at temperature T in some two-phase state that can be either metastable or spinodally unstable with respect to phase separation. Varying the annealing time one can grow here precipitates ("droplets ) of a suitable size /. For sufficiently large /, the concentration c(r) within A-riched droplets is close to the equilibrium binodal value C(,(T ) (thin curve in Fig. 9). 

The unstable position, B, does not remain in equilibrium long enough to represent the state of any dispersion except at the instant of its preparation or during the transition of a dispersion from a metastable to a stable condition. Of chief interest here are conditions A and D, for they are the mechanical... 

Stable, metastable and unstable states a simple analogy. A simple mechanical model is shown in Fig. 2.37 a block on a stand may be in different equilibrium states. In A and C the centre of gravity (G) of the block is lower than... 

Figure 2.37. A simple mechanical system and its equilibrium states. Different positions of a block on a stand and the corresponding values of the gravitation potential energy are shown. Point G is the centre of gravity of the block. In A there is stable equilibrium, in C metastable, in B unstable.

Figure 2. Eh-pH diagram of dissolved Mo speciation in the system M0-H2O-S. ZMo = 10 M ES = 10 M. Modified after Manheim and Landergren (1974), using molybdate protonation constants from Baes and Mesmer (1986). H2M0O4 is related to Mo(OH)g by addition of two water molecules (see text). MoO +, included in earlier Eh-pH diagrams, is omitted because this and other Mo(V) species are typically unstable except as dimers (e.g., Mo20/ ) at higher EMo than common in natiwe. Speciation at Eh below fiie SO/ - H2S ftansition is not well characterized and is commonly out of equilibrium. The boundary between MoS/ and MoO/ is based on Erickson and Helz (2000) intermediate oxythiomolybdates are metastable and hence not indicted.

An unstable equilibrium state (or configuration) that is at maximal potential energy. A metastable state is at equilibrium, and its potential energy [written here as U(x)] is such that any displacement (dx) from Xequiiibnum will result in the loss of potential energy. 

Networks of steps, seen in STM observations of vicinal surfaces on Au and Pt (110), are analyzed. A simple model is introduced for the calculation of the free energy of the networks as function of the slope parameters, valid at low step densities. It predicts that the networks are unstable, or at least metastable, against faceting and gives an equilibrium crystal shape with sharp edges either between the (110) facet and rounded regions or between two rounded regions. Experimental observations of the equilibrium shapes of Au or Pt crystals at sufficiently low temperatures, i.e. below the deconstruction temperature of the (110) facet, could check the validity of these predictions. 

Metastability of Hydrolyzed Iron (III) Solutions The low solubility of ferric hydroxide has been alluded to in the Introduction. Feitknecht and Michaelis (29) have observed that aU ferric perchlorate solutions to which base has been added are unstable with respect to eventual precipitation of various forms of hydrated ferric oxides. In 3 M NaC104 at 25° C the two phase system reaches an apparent equilibrium after 200 hours, according to Biedermann and Schindler (6), who obtained a reproducible solubility product constant for ferric hydroxide at varying degrees of hydrolysis. It appears that many of the solutions used in the equilibrium studies of Hedstrom (9) and Biedermann (22) were metastable, and should eventually have produced precipitates. Nevertheless, since the measured potentials were reversible, the conclusions reached about the species present in solution remain valid. 

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