Metastable conditions

Rapidly quenching to room temperature retains a maximum amount of alloying element (Cu) in soHd solution. The cooling rate required varies considerably with different alloys. For some alloys, air cooling is sufficiently rapid, whereas other alloys require water-quenching. After cooling, the alloy is in a relatively soft metastable condition referred to as the solution-treated condition. 

Although vitreous silica is nominally a homogeneous isotropic amorphous material, and should normally remain so during its service life, it is in fact in a metastable condition. The tendency to revert to crystalline forms with attendant deterioration in mechanical durability places severe limitations on the range of applications. Figure 18.2 illustrates the polymorphic forms of silica, and the dimensional changes accompanying each transition. 

Mre = Y, all Ln (except La, Ce) claimed to exist under metastable conditions, no lattice parameters available yet ErRh4B4, 3 MANOS4B4 Man 13 13... 

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 ... 

Reaction can create metastable conditions directly. This is an attractive option when the reaction to produce the desired product and the separation can be carried out simultaneously. 

Periodic adjustment of metastable condition, usually due to lack of nucleation sites... 

The stability of the fee 8-plutonium, which is malleable and easily shaped, is important because of its uses (in nuclear weapons, etc.). This phase may be retained, either in stable or metastable conditions, down to room temperature by the addition of gallium or aluminium. In a way, the two versions of the phase diagram may now be reconciled. The diagram in Fig 5.16 (a) is adequate for practical applications... 

Solvent viscosity vs, concentration plots for cellulose dissolved in TFA-CH2CI2 (70/30, v/v) do not exhibit a maximum (1I,S1) in contrast to the typicid behavior of polymer liquid crystal solutions. This same behavior is exhibited by other cellulose-solvent systems (52,fiQ). Conio et al. (59) si gest that due to the close proximity of the cholesteric mesophase to its solubility limit, it is only observed in a metastable condition. 

If the product of the concentrations of the ionic species exceeds the Ksp value then either precipitation occurs or a metastable condition of supersaturation develops. When reporting solubility products, the temperature should always be provided. Examples of a few relevant Ksp values (at 25°C) are given below. 

A metastable condition in which the amount of a dissolved substance is greater than the condition in which the dissolved molecular entity is in equilibrium with the undissolved sohd. See Biomineralization... 

The determination of individual binary equilibrium diagrams usually only involves the characterisation of a limited number of phases, and it is possible to obtain some experimental thermodynamic data on each of these phases. However, when handling multi-component systems or/and metastable conditions there is a need to characterise the Gibbs energy of many phases, some of which may be metastable over much of the composition space. 

A graph of Eq. (44) is shown in Fig. 15. The peak is of great interest, for this represents the metastable condition. Clusters of this size, R0, are stable as long as they do not change in radius. However if the radius were to decrease slightly, say because of the loss of one molecule, the cluster would collapse with an accompanying decrease in free energy. 

Fig. 23. Graph of equation of state, such as Van der Waals expression, showing metastable conditions.

ANNEALING. The process of holding a solid material at an elevated temperature for a specified length of time in order that any metastable condition, such as frozen-in stains, dislocations, and vacancies may go into thermodynamic equilibrium. This may result in re-crystallization and polygonization of cold-worked materials. 

The foregoing is the original version of the famous Heat Theorem proposed by Walther Nernst in 1906. One must be quite careful in the application of Eq. (1.21.8) because in some special cases either AS cannot be computed, or else, a nonattainment of equilibrium states interferes. These matters were already discussed earlier, but should be supplemented here. One cannot assume AS - 0 for any process wherein the system passes from a metastable state to an equilibrium state because metastable conditions are nonaccessible to equilibrium theories, so that corresponding changes do not fall within the scope of Eq. (1.21.8). 

Metastability is difficult to treat by the conventional methods of thermodynamics. The essential requirement of a metastable condition... 

For example, at 10 atm, 50% of the CO should have transformed to CH at 590 K, but this reaction is very slow in the absence of catalysts and so CO may instead disproportionate to CO2 and elemental carbon. This reaction should be 50% complete at 520 K. It yields carbynes rather than graphite, if a chromite catalyst is present. At 400 K, clays form from anhydrous silicates, catalyzing hydrogenation of CO to complex organic cxrmpounds. The dashed line shows the temperatures at which 1 % of the CO transforms to a typical alkane, C20H42, under metastable conditions (the lines for most other alkanes, from CjHg upward, are very similar). 

Uranium Sulphate, U(S0j)3.nH20.—The anhydrous uranous sulphate has not been prepared, but an extraordinarily large number of hydrates is known. Salts containing 1, 2, 3, 4, 5, 6, 7, 8, and 9 molecules of w-ater have been described, and of these the di-, tetra-, octa-, and nona-hydrates are stable. The actual relation of these hydrates to one another is difficult to determine, as they undergo hydrolysis to a considerable extent when in solution, and the tetra-and octa-hydrates, at least, show a marked tendency to remain in a metastable condition at temperatures far removed from the transition-point between the two phases. Solubility determinations indicate that this transition-point is in the neighbourhood of 20° C., but it has been shown that the octahydrate wffien heated in absence of air changes into the tetrahydrate at 68° to 87° C. w hen the former hydrate is in a state of metastable equilibrium. 

The tetra-, oeta-, and nona-hydrates are isomorphous with the corresponding hydrates of thorium sulphate, and the relation between the uranium salts is probably similar to that between the sulphates of thorium, which are not so subject to hjffirolysis and do not remain in the metastable condition to any extent. ... 

If a saturated solution is cooled, the solubility of the solute generally decreases in order for the cooled solution to return to equilibrium, some solute must come out of solution as solid crystals. The crystallization rate may be slow, however, so that a metastable condition can exist in which the concentration of the solute is higher than the equilibrium value at the solution temperature. Under such conditions, the solution is said to be supersaturated and the difference between actual and equilibrium concentrations is referred to as supersaturation. Ail problems involving solid-liquid separations in this text assume that equilibrium exists between the solid and liquid phases, so that supersaturation need not be considered. 

B when its temperature is Ti. Further heating brings the solution to C. At this point the solution is supersaturated at a temperature of T2. It is in a metastable condition and precipitation can be expected. As heating is continued, precipitation reduces the salt concentration till it falls onto the solubility curve at temperature T3. 

Figure 6.11 Stability relations among the calcium-magnesium carbonates at 25 C and 1 bar total pressure as a function of the mCa VmMg ratio and CO2 pressure. The stippled field is that of ordered, well-crystallized dolomite. The plot shows that when dolomite is kinetically inhibited from precipitating, nesquehonite, hydromagnesite, or brucite can coexist with calcite under metastable conditions. Huntite (not shown) is stable relative to crystalline dolomite for mCa VmMg < 10 . From D. Langmuir, Physical and chemical characteristics of carbonate water. In Guide to the hydrology of carbonate rocks, P. E. La-moreaux, B. M. Wilson, and B. A. Memeon, eds. 1984 by UNESCO. Used by permission.

During crystal growth, a metastable condition exists such that spontaneous detonation can occur [19], One should refer to the discussion in Chapter 2, Volume 1. 

As a conclusion, we can say that the method developed by us is a promising tool to estimate the liquid-vapour stability limit of various liquids. The required data are measurable under stable liquid condition in this way this is the only method which does not require any measurement under metastable conditions to estimate the spinodal. The most important advantage of this method, that it can be used for any liquid. It is even applicable for liquid mixtures however for the mechanical stability and not for the difihsion stability. 

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