Thermodynamically stable phase

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. 

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 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. 

Steam-Moderated Process. The basic idea behind this approach is to limit the extent of conversion of the methanation reaction, Reaction 1, by adding steam to the feed gases. This process simultaneously provides for (46) elimination of the CO shift, Reaction 2, to get a 3 1 H2 CO ratio from the make-up gas ratio of about 1.5 1 and avoidance of carbon laydown by operation under conditions in which carbon is not a thermodynamically stable phase (see Chemistry and Thermodynamics section above). 

The new phases were discovered by the combination of exploratory synthesis and a phase compatibility study. As commonly practised, the new studies were initially made through the chemical modification of a known phase. Inclusion of salt in some cases is incidental, and the formation of mixed-framework structures can be considered a result of phase segregation (for the lack of a better term) between chemically dissimilar covalent oxide lattices and space-filling, charge-compensating salts. Limited-phase compatibility studies were performed around the region where thermodynamically stable phases were discovered. Thus far, we have enjoyed much success in isolating new salt-inclusion solids via exploratory synthesis. 

The reason for the formation of anatase phase at such a high temperature might be explained as following. The as-prqiared ultrafine titania particles are liquefied at sufficimtly high temperature because melting point of nanoparticlra are lower than that of bulk titania (1850 C). The liquid titania particles are supercooled and became metastable states. The residence time in the flame is only in the order of miU-second so that the metastable phase has no time to become thermodynamically stable phase, rutile. 

On heating from a crystalline phase, DOBAMBC melts to form a SmC phase, which exists as the thermodynamic minimum structure between 76 and 95°C. At 95°C a thermotropic transition to the SmA phase occurs. Finally, the system clears to the isotropic liquid phase at 117°C. On cooling, the SmC phase supercools into the temperature range where the crystalline solid is more stable (a common occurrence). In fact, at 63°C a new smectic phase (the SmF) appears. This phase is metastable with respect to the crystalline solid such phases are termed monotropic, while thermodynamically stable phases are termed enantiotropic. The kinetic stability of monotropic LC phases is dependent upon purity of the sample and other conditions such as the cooling rate. However, the appearance of monotropic phases is typically reproducible and is often reported in the phase sequence on cooling. It is assumed that phases appearing on heating a sample are enantiotropic. 

Coagulation The irreversible formation of the thermodynamically stable phase in bulk quantities The precipitation of crystals... 

It is worth noting that a monotropic polymorphic system offers the potential of annealing the substance to achieve the preferred form of the thermodynamically stable phase. The use of the most stable form is ordinarily preferred to avoid the inexorable tendency of a metastable system to move toward the thermodynamic form. This is especially important especially if someone elects to use a metastable phase of an excipient as part of a tablet coating, since physical changes in the properties of the coating can take place after it has been made. Use of the most stable form avoids any solid-solid transition that could... 

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. 

In the case of the graphite-to-diamond transformation, thermodynamic results predict that graphite is the stable allotrope at a fixed temperature at all pressures below the transition pressure and that diamond is the stable aUotrope at all pressures above the transition pressure. But diamond is not converted to graphite at low pressures for kinetic reasons. Similarly, at conditions at which diamond is the thermodynamically stable phase, diamond can be obtained from graphite only in a narrow temperature range just below the transition temperature, and then only with a catalyst or at a pressure sufficiently high that the transition temperature is about 2000 K. 

Recently we published a short review of the single source precursor concept in chemical vapor deposition (CVD) and in the sol/gel process [1]. hi this article we described in which way several constituent elements of a targeted material can be assembled in a precursor molecule and how this assembly has an effect on the properties of the hnal material. Three types of precursors have been distinguished (1) Precursors which contain the correct ratio of metallic elements (SSP-I), (2) precursors which besides the correct ratio of metallic elements also have ligands which interact with one another to form only few side-products (SSP-II), and (3) precursors with a surplus of one metallic element compared to a thermodynamically stable phase and which form biphasic mixed-materials on a nanometer scale (SSP-III) [1],... 

If the electrostatic forces between charged surfactant head groups are sufficiently high, vesicles can also be a thermodynamically stable phase and be... 

Classical BCS theory dictated that superconductors with the highest Tc s would not be thermodynamically stable phases. Softening the phonons would raise Tc but would ultimately lead to structural instabilities. Increasing the density of states at the Fermi level would raise Tc but would eventually lead to an electronic instability. 

We do not need to regard YBa2Cus07 as a solid solution, but it is not a thermodynamically stable phase at any temperature/pressure condition (11). Thermodynamic stability exists in the YBa2Cus06+x system in a certain region of temperature and oxygen pressure, but only for values of x between zero and about 0.6. Even these compositions appear not to be thermodynamically stable at room temperature and below. 

Secondary phases predicted by thermochemical models may not form in weathered ash materials due to kinetic constraints or non-equilibrium conditions. It is therefore incorrect to assume that equilibrium concentrations of elements predicted by geochemical models always represent maximum leachate concentrations that will be generated from the wastes, as stated by Rai et al. (1987a, b 1988) and often repeated by other authors. In weathering systems, kinetic constraints commonly prevent the precipitation of the most stable solid phase for many elements, leading to increasing concentrations of these elements in natural solutions and precipitation of metastable amorphous phases. Over time, the metastable phases convert to thermodynamically stable phases by a process explained by the Guy-Lussac-Ostwald (GLO) step rule, also known as Ostwald ripening (Steefel Van Cappellen 1990). The importance of time (i.e., kinetics) is often overlooked due to a lack of kinetic data for mineral dissolution/... 

Propene to acrolein. Hildenbrand and Lintz87,88 have used solid electrolyte potentiometry to study the effect of the phase composition of a copper oxide catalyst on the selectivity and yield of acrolein during the partial oxidation of propene in the temperature range of 420-510°C. Potentiometric techniques were used to determine the catalyst oxygen activity, and hence the stable copper phase, under working conditions. Hildenbrand and Lintz used kinetic measurements to confirm that the thermodynamically stable phase had been formed (it is known that propene is totally oxidised over CuO but partially oxidised over ). 

Figure 4. Plot of e vs. pH for the system C-H-O-N (incomplete) at 25°C. and 1 atm., showing stability and decomposition relations for various C-H-O-N compounds. H , H20, CHh, C, and C02 represent thermodynamically stable phases...

The presence of arsenic at the interface implies that surface states within the band gap will be introduced (see Fig. 1). We associate the high surface recombination velocity with the presence of arsenic. The formation of elemental As on the GaAs surface explains the difference in behavior of InP and of GaAs. In InP the thermodynamically stable phase that results from oxidation of the surface is colorless InP04 which straddles the band gap. In GaAs it is Ga203 and small band gap As. 

Lipid-water gel phases were previously regarded as metastable structures that are formed before separation of water and lipid crystals when the corresponding lamellar liquid crystal is cooled. New information on gel phases (see below) reveals that they can form thermodynamically stable phases with very special structural properties. This characteristic makes them as interesting as the lamellar liquid crystals from a biological point of view. 

A binary mixture of methane + ethane, which are both si hydrate formers, can form sll hydrate as the thermodynamically stable phase (Subramanian et al., 2000). 

Figure 1 shows changes in the system phase behavior as its HLB value is systematically adjusted. The left side of the diagram represents a two-phase system with micellar-solubilized oil in equilibrium with an excess oil phase (Winsor Type I) (Winsor 1954). The right side of the diagram represents a different two-phase system with reversed micellar-solubilized water. In-between these two systems a third phase coemerges which contains enriched surfactant with solubilized water and oil. This new thermodynamically stable phase is known as a Winsor Type HI middle phase microemulsion. 

There is an abundance of experimental gas partial pressures for gas hydrate equilibria across a broad range of temperatures (Fig. 3.10 Sloan 1998). The lower temperature limit in our model database for these systems is 180 K (Fig. 3.10) because this is the lower limit of our model s ability to estimate aw (Fig. 3.1, Eq. 3.11), which is needed to calculate the solubility product of gas hydrates (Eq. 3.36). In our model, the upper temperature limit for methane hydrate is at 298 K (25 °C), which is the upper temperature limit for FREZCHEM the upper temperature limit for carbon dioxide hydrate is at 283K (10 °C), which is the temperature where liquid C02(l) becomes the thermodynamically stable phase. 

This figure is known as the phase diagram of a substance. It shows the thermodynamically stable phases at different pressures and temperatures. The lines... 

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