Crystal growth metastable phases

Under equiUbrium vapor pressure of water, the crystalline tfihydroxides, Al(OH)2 convert to oxide—hydroxides at above 100°C (9,10). Below 280°—300°C, boehmite is the prevailing phase, unless diaspore seed is present. Although spontaneous nucleation of diaspore requires temperatures in excess of 300 °C and 20 MPa (200 bar) pressure, growth on seed crystals occurs at temperatures as low as 180 °C. For this reason it has been suggested that boehmite is the metastable phase although its formation is kinetically favored at lower temperatures and pressures. The ultimate conversion of the hydroxides to comndum [1302-74-5] AI2O2, the final oxide form, occurs above 360°C and 20 MPa. 

Precipitation can occur if a water is supersaturated with respect to a solid phase however, if the growth of a thermodynamically stable phase is slow, a metastable phase may form. Disordered, amorphous phases such as ferric hydroxide, aluminum hydroxide, and allophane are thermodynamically unstable with respect to crystalline phases nonetheless, these disordered phases are frequently found in nature. The rates of crystallization of these phases are strongly controlled by the presence of adsorbed ions on the surfaces of precipitates (99). Zawacki et al. (Chapter 32) present evidence that adsorption of alkaline earth ions greatly influences the formation and growth of calcium phosphates. While hydroxyapatite was the thermodynamically stable phase under the conditions studied by these authors, it is shown that several different metastable phases may form, depending upon the degree of supersaturation and the initiating surface phase. 

Calcium phosphate precipitation may also be involved in the fixation of phosphate fertilizer in soils. Studies of the uptake of phosphate on calcium carbonate surfaces at low phosphate concentrations typical of those in soils, reveal that the threshold concentration for the precipitation of the calcium phosphate phases from solution is considerably increased in the pH range 8.5 -9.0 (3). It was concluded that the presence of carbonate ion from the calcite inhibits the nucleation of calcium phosphate phases under these conditions. A recent study of the seeded crystal growth of calcite from metastable supersaturated solutions of calcium carbonate, has shown that the presence of orthophosphate ion at a concentration as low as 10-6 mol L" and a pH of 8.5 has a remarkable inhibiting influence on the rate of crystallization (4). A seeded growth study of the influence of carbonate on hydroxyapatite crystallization has also shown an appreciable inhibiting influence of carbonate ion.(5). 

All crystal growth takes place in low-temperature, low-pressure aqueous solution (at 1 atmospheric pressure and room temperature). This suggests a higher probability of formation of an amorphous state, phases of low crystallinity, and metastable phases as precursors, and therefore subsequent transformation to stable or metastable phases. 

Crystallization, by definition, implies that the initial structure be a glass, followed by the nucleation and growth of a crystalline phase, be it the equilibrium one or a metastable phase. The process is a first-order transformation and involves atomic diffusion, or at least atomic shuttles. Types of crystallization reactions that occur include polymorphous crystallization, which is a composition invariant transformation such as that in Fe-B, and eutectic crystallization, T, in FeNiPB glass, where line lamellae of iron-nickel austenite and mclastable (FeNiJj PB phases grow cooperatively. 

Thus far, two types of solvent-assisted solid-to-solid transformations of a kinetically formed metastable crystalline phase into a thermodynamically stable one in a process of crystal growth, relevant to the occurrence of Preferential Enrichment, have been observed One is a relatively fast polymorphic transition noted in the case of ( )-NNMe3,18 and the other is a slow one in the case of ( )-NPMe3.18,26... 

Fig. 14 Binary phase diagram for C246H494 in octacosane. The top curve shows the equilibrium liquidus for extended-chain crystals, and the bottom line the metastable liquidus for once-folded crystals. Experimental dissolution temperatures are fitted to the Flory-Huggins equation with / = 0.15 (solid lines). Vertical dotted lines (a) and (b) indicate the concentrations at which the growth rates were determined as a function of Tc in [29]. Horizontal dotted lines indicate the temperatures at which the rates were determined in [45] as a function of concentration. G(c) at Tc = 106.3 °C, measured along line (c), is shown in Fig. 12. The shading indicates schematically the crystal growth rate (black = fast), and the dashed line the position of the growth rate minimum...

It is instructive to consider the free-energy hierarchy and the metastable phase equilibria when crystallization of an amorphous material is discussed. Koster and Herold [56] discussed these aspects of crystallization and showed that crystallization reactions of amorphous alloys can be classified into the following three types polymorphic, primary and eutectic crystallization reactions. Among these three types, the slowest crystal growth process is expected for primary crystallization and thus, primary crystallization is ideal for tailoring fine microstructures upon decomposition of amorphous alloys. 

The process of crystallization from solution is generally understood in terms of three interdependent conditions supersaturation, nucleation and growth. For crystallization from the melt or the gas phase, supersaturation is simply interpreted as undercooling. Of the essence is a metastable phase, at chemical potential higher than that of the crystalline phase under the same conditions. The transition from the metastable state to the state of equilibrium between phases corresponds to nucleation. 

To circumvent such seemingly insurmountable difficulties, approximations and simplifications can often be made. For example, even though the formation of a solid from a saturated solution can involve several successive reactions, one may judiciously select for analysis or prediction the one that presents the slowest rate. The so-called Oswald s phase rule states that a supersaturated solution that undeigoes a sudden alteration that takes it out of such a state will produce a metastable solid (instead of the expected thermodynamically stable solid). It is a very useful rule, although it is not always obeyed. Three limiting cases are shown in Figure 5.8 for different values of the overall crystallization rate (nucleation -1- crystal growth), v. 

Gel dissolution Zeolite nucleation Crystal growth of the zeolite nuclei Dissolution/recrystallization of metastable phases (Oswald s Law of successive transformations)... 

Numerous kinetic studies have been made of the spontaneous precipitation of calcium phosphates from solutions containing concentrations of lattice ions considerably in excess of the solubility values (33, 34). Although attempts, are usually made to control the mixing of reagent solutions, it is difficult to obtain reproducible results from such experiments since chance nucleation of solid phases may take place on foreign particles in the solution. Many of these difficulties can be avoided by studying the crystal growth of well-characterized seed crystals in metastable supersaturated solutions of calcium phos.phate. 

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