Metastable liquids addition

In Sections III and IV, the principles of nucleation and growth were discussed separately. Now the crystallization process as a whole will be considered. In any practical application of crystallization, a stable solid phase must first be formed from the metastable liquid phase, and then additional molecules are deposited on the nucleus to form the macroscopic crystalline solid. Since nucleation and growth are taking place simultaneously, the theoretical principles discussed earlier are difficult to apply quantitatively to crystallization practice. Consequently, empirical expressions are still generally used in the design of equipment and prediction of its operation. 

In addition to the aforementioned conventional liquid organic solvents, two other types of molecular liquids have attracted much interest as supplementary or alternative media for synthesis and processing, namely supercritical fluids (sc-fluids) [209] and metastable liquids [210]. 

It was shown that this remarkable phase behaviour could be understood on the basis of the sensitivity to the form of the pair potential of the phase diagram of small attractive colloidal particles [268-270]. Moreover, it was soon realized that successful protein crystallization depends on the location (protein concentration and temperature) in the phase diagram [271-275]. Control of protein crystal nucleation around the metastable liquid-liquid phase boundary appears key to the development of systematic crystallization strategies (for a concise review see [276]). This phase boundary can be manipulated by depletion interactions through the addition of non-adsorbing polymers such as polyethylene glycol. 

Ice I is one of at least nine polymorphic forms of ice. Ices II to VII are crystalline modifications of various types, formed at high pressures ice VIII is a low-temperature modification of ice VII. Many of these polymorphs exist metastably at liquid nitrogen temperature and atmospheric pressure, and hence it has been possible to study their structures without undue difficulty. In addition to these crystalline polymorphs, so-called vitreous ice has been found within the low-temperature field of ice I. It is not a polymorph, however, since it is a glass, i.e. a highly supercooled liquid. It is formed when water vapour condenses on surfaces cooled to below — 160°C. 

Figure 6.1. Gibbs free energy curves for Ti (a) a, j9 and liquid segments corresponding to the stable regions of each phase (b) extrapolated extensions into metastable regions (c) characterisation from Kaufinan (1959a) using equation (6.2) and (d) addition of the G curves for u and f.c.c. structures (from Miodownik...

In addition to the melting point of the P phase and the a/P allotropic transfonnation temperature in Fig. 6.1(b), there is a fluther intersection between the Gibbs energy of a and liquid phases. This corresponds to the metastable melting point of the a phase. A linear model will then dictate that the entropy of melting for a is defined by the entropies of melting and transformation at the two other critical points (Ardell 1963),... 

SUPERCOOLING. The cooling of a liquid below its freezing point without the separation of the solid phase. This is a condition of metastable equilibrium, as is shown by solidification of the supercooled liquid upon the addition of the solid phase, or the application of certain stresses, or simply upon prolonged standing. 

Besides water for hydrothermal reactions, liquid ammonia (bp, 78°C Tc, 132°C Pc, 113 atm) is also used for the solvothermal synthesis of nitrides. Metastable or otherwise unobtainable nitride materials were reported to be formed by this rnethod. " Ammonium and amide (NH2) ions are the strongest acid and base, respectively, for the liquid ammonia system, and therefore ammonium salt acts as the acid mineralizer, while amide ion can be prepared by addition of alkali metals to the solvent. Since ammonia has a low boiling point, the reaction pressure is usually quite high. 

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