Phase stable

Figure A2.5.1. Schematic phase diagram (pressure p versus temperature 7) for a typical one-component substance. The full lines mark the transitions from one phase to another (g, gas liquid s, solid). The liquid-gas line (the vapour pressure curve) ends at a critical point (c). The dotted line is a constant pressure line. The dashed lines represent metastable extensions of the stable phases.

R is the gas constant per mole, while K is the temperature unit Kelvin). The dashed lines represent metastable extensions of the stable phases beyond the transition temperatures. 

Since zeolites are metastable crystallization products tliey are subject to Ostwald s mle which states tliat metastable phases are initially foniied and gradually transfonii into tlie tlieniiodynaniically most stable product. The least stable zeolitic phase (tliat witli tlie lowest framework density) is tlierefore foniied first and consumed with furtlier syntliesis time at tlie expense of a more stable phase due to a continuous crystallization/redissolution equilibrium. 

Unlike melting and the solid-solid phase transitions discussed in the next section, these phase changes are not reversible processes they occur because the crystal stmcture of the nanocrystal is metastable. For example, titania made in the nanophase always adopts the anatase stmcture. At higher temperatures the material spontaneously transfonns to the mtile bulk stable phase [211, 212 and 213]. The role of grain size in these metastable-stable transitions is not well established the issue is complicated by the fact that the transition is accompanied by grain growth which clouds the inteiyDretation of size-dependent data [214, 215 and 216]. In situ TEM studies, however, indicate that the surface chemistry of the nanocrystals play a cmcial role in the transition temperatures [217, 218]. 

Tripolyphosphates. The most commercially important tripolyphosphate salt is sodium tripolyphosphate (STP), Na P O Q. Three distinct crystalline forms are known two are anhydrous (STP-I and STP-II) the other is the hexahydrate [15091 -98-2] Na P O Q 6H20. Sodium tripolyphosphate anhydrous Form I is the high temperature, thermodynamically stable phase sodium tripolyphosphate anhydrous Form II is the lower temperature form which can be readily converted to STP-I by heating to above 417 8° C, the transition temperature. However, the reverse reaction is extremely slow below 417°C. Both anhydrous forms of sodium tripolyphosphate are therefore stable enough to coexist at room temperature. 

There are 16 SiO units per unit cell the space group is C2/c. Coesite persists as a basically stranded phase at atmospheric pressure and is a stable phase at... 

Increased pressures can lower the temperature at which crystallisation occurs. Experiments performed using Spectrosil (Thermal Syndicate Ltd.) and G.E. Type 204 (General Electric Company) fused siUcas (see Eig. 2) show that at pressures above 2.5 GPa (<25, 000 atm), devitrification occurs at temperatures as low as 500°C and that at 4 GPa (<40, 000 atm), it occurs at as low as 450°C (107). Although the temperatures and pressures were in the coesite-phase field, both coesite and quarts were observed. Both the devitrification rate and the formation of the stable phase (coesite) were enhanced by the presence of water. In the 1000—1700°C region at 500—4000 MPa (<5, 000-40,000 atm), a- and p-quarts were the primary phases. Crystal growth rates... 

The relationships between condensed phases ia the B2O3—H2O system are shown ia Figure 1 (42). There is no evidence for stable phases other than those shown. B2O3 melts and glasses containing less than 50 mol % water have mechanical and spectroscopic properties consistent with mixtures of HBO2 and vitreous B2O3. 

The water solubiUty of kernite is shown in Figure 5 and in Table 9. Kernite is the stable phase in contact with its solutions from 58.2°C to ca 95°C (71). Its rate of crystallisation is, however, much slower than that of the pentahydrate. Large kernite crystals can be grown slowly by seeding saturated borax solutions. 

Although hydration under hydrothermal conditions may be rapid, metastable iatermediate phases tend to form, and final equiUbria may not be reached for months at 100—200°C, or weeks at even higher temperatures. Hence, the temperatures of formation given ia Table 6 iadicate the conditions under saturated steam pressure that may be expected to yield appreciable quantities of the compound, although it may not be the most stable phase at the given temperature. The compounds are Hsted ia order of decreasiag basicity, or lime/siHca ratio. Reaction mixtures having ratios C S = 1 yield xonotHte at 150—400°C. Intermediate phases of C—S—H (I), C—S—H (II), and crystalline tobermorite ate formed ia succession. Tobermorite (1.13 nm) appears to persist indefinitely under hydrothermal conditions at 110—140°C it is a principal part of the biader ia many autoclaved cement—silica and lime—silica products. 

Figure 1.11 The formation of metal clusters during the nucleation of a new phase. The co-ordination is first tetrahedral, leading to 5-fold symmetry, until the 13-atom icosahedron is formed which transforms into the cubic icosahedron of the stable phase...

Taking as the reference system an unsheared monolayer (o. = 0), the thermodynamic integration procedure in Eqs. (107) permits one to construct the plot shown in Fig. 17. For = 0, A = 0 vanishes for the monolayer as expected. As increases, A rises, indicating that the sheared mono-layer is increasingly less stable. A bilayer film, on the other hand, becomes increasingly stable as > 0.5, eventually intersecting the monolayer curve at As increases from 0.0 up to the monolayer is the thermodynamically stable phase because its A is smallest for the bilayer... 

In this review we consider several systems in detail, ranging from idealized models for adsorbates with purely repulsive interactions to the adsorption of spherical particles (noble gases) and/or (nearly) ellipsoidal molecules (N2, CO). Of particular interest are the stable phases in monolayers and the phase transitions between these phases when the coverage and temperature in the system are varied. Most of the phase transitions in these systems occur at fairly low temperatures, and for many aspects of the behavior quantum effects need to be considered. For several other theoretical studies of adsorbed layer phenomena see Refs. 59-89. 

The sulfides have been less thoroughly examined than the oxides but it is clear that a number of stable phases can be produced and nonstoichiometry is again prevalent (p. 679). The most important are the disulfides, which are semiconductors with metallic lustre. TiS2 and ZrS2 have the Cdl2 structure (p. 1211) in which the cations occupy the octahedral sites between alternate layers of hep anions. 

In this example of the corrosion of zinc in a reducing acid of pH = 4, the corrosion product is Zn (aq.), but at higher pHs the thermodynamically stable phase will be Zn(OH)j and the equilibrium activity of Zn will be governed by the solubility product of Zn(OH)j and the pH of the solution at still higher pHs ZnOj-anions will become the stable phase and both Zn and Zn(OH)2 will become unstable. However, a similar thermodynamic approach may be adopted to that shown in this example. 

As with all determinations of thermodynamic stability, we comihehce by defining all stable phases possible, and their standard, chemical, potentials. For inost, metals there are many such phases, including oxides, hydroxides and dissolved ions. For brevity, here, only the minimum number of phases is Considered. The siriiplest system is a metal, ilf, which can oxidise lo form a stable dissolved pro,duct, (qorrpsipn), or to form a stable oxide MO (passivation), lit aqueous environments thfbe equilibria Can thereby be... 

Fig. 1.43 Schematic potential/pH diagram for a metal M in equilibrium with water in the absence of complexing species. Line a represents equations 1.117 and 1.122. Line b represents equations 1.118 and 1.123. Line c represents equations 1.119 and 1.124. The stable phases are marked in bold. The metastable phase is in parentheses. The broken line is an extrapolation of equation 1.123 and indicates possible metastable passivity...

Extensive studies have been carried out by Giggins and Pettit and by Vasantasree and Hocking on a range of nickel chromium alloys with up to 50% alloying addition. Generally the principles outlined above can be used to interpret the experimental observations, where the thermodynamics of the reaction are a major factor determining the rate of attack, depending upon whether oxide or sulphide is the stable phase. 

Fig. 7.46 The stable phases in the Al-O-S system in molten Na2S04 at 1 000°C as a function of acidity and oxygen activity (after Goebel and Pettit )...

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