Phase transition variable composition

Fig. XVII-8.—Phase equilibrium diagram for the system Cu-Zn, in which a number of phases of variable composition arc formed, mixtures of the phases being stable between the regions of stability of the pure phases. The phase a is face centered cubic, as Cu is, j8 is body centered, 7 is a complicated structure, e and r) are hexagonal. The transition between and /S is an order-disorder transition, /3 being disordered, and /8 ordered, as discussed in the following chapter.

Phase transitions in binary systems, nomially measured at constant pressure and composition, usually do not take place entirely at a single temperature, but rather extend over a finite but nonzero temperature range. Figure A2.5.3 shows a temperature-mole fraction T, x) phase diagram for one of the simplest of such examples, vaporization of an ideal liquid mixture to an ideal gas mixture, all at a fixed pressure, (e.g. 1 atm). Because there is an additional composition variable, the sample path shown in tlie figure is not only at constant pressure, but also at a constant total mole fraction, here chosen to be v = 1/2. 

Transition elements, for which variable valency is energetically feasible, frequently show non-stoichiometric behaviour (variable composition) in their oxides, sulfides and related binary compounds. For small deviations from stoichiometry a thermodynamic approach is instructive, but for larger deviations structural considerations supervene, and the possibility of thermodynamically unstable but kinetically isolable phases must be considered. These ideas will be expanded in the following paragraphs but more detailed treatment must be sought elsewhere. " ... 

Some gels were synthesized which underwent the phase transition twice as the solvent composition was monotonically varied from 0% to 100%. Figure 30 shows the swelling behaviors of NIPA (open circles) and acrylamide (solid circles) gels in a mixture of dimethylsulfoxide (DMSO) and water [24]. When the DMSO concentration was lower than 33%, the NIPA gel was slightly swollen. Above 33% DMSO, a discrete transition to a collapsed state occurred. However, the gel showed a discontinuous re-swelling at 90%. Such reentrant behavior has also been observed when temperature or pH were used as variables. 

This section covers some other heterometallic rare earth oxides, including Al, Ti, Zr, Sn, Mo, W, Mn, Fe, Co, Ni, and Cu complex oxides, while certain well-known oxysalts, Y-Ba-Cu-O, for example, will not be specifically discussed. For these heterometallic compounds, due to their relatively complex compositions, it is usually difficult to obtain phase-pure products, especially when some dopant ions are added. At elevated temperatures, some of these oxides undergo phase transitions, which may significantly change their physical and chemical properties such as thermal expansion coefficient and ionic conductivity. And for fhose oxides with variable metal valencies, different nonstoichiometric compositions may also result in distinct functionalities in magnetism and catalysis. 

Finally, it is clear that many more solid solutions must be examined for minerals and mineral analogs in order to achieve a fundamental understanding of compositionally induced phase transitions. Currently it is not possible to predict how transition temperatures will change when a particular impurity substitutes in a mineral structure, nor can we predict the interaction length for that impurity in the mineral. Landau-Ginzburg analysis provides an ideal framework for comparing the character of phase transitions that are activated by different variables (temperature, pressure, composition), and future studies of this type will lay an empirical foundation from which the detailed character of morphotropic transitions in minerals may be inferred. 

Natural tridymite and cristobalite often, if not invariably, contain appreciable concentrations of foreign ions, particularly of the alkali and alkaline-earth metals,suggesting that they may have been deposited as the stable phases at femperatures well below the respective transition points. The variable composition of these minerals is presumably the reason for wide ranges of temperatures recorded for the Q-j3 transition points. The origin of the high-temperature tridymite studied by Gibbs is not known but it appears that the monoclinic form stable at room... 

High-resolution in situ STM as well as phase transition dynamics of nucleobases on Au(lll) and other low-index electrode surfaces supported by infrared spectroscopy have been reviewed recently by Nichols and coworkers [142] and Wandlowski and coworkers [143]. We refer to these reviews for details and note instead another aspect of single-molecule dynamics of DNA-based molecules. The observed electronic conductivity of oligonucleotides of variable length and variable base composition has opened almost a Pandora s box of novel DNA-based electronic properties. These include particularly photochemical and interfacial electrochemical ET. We refer to other recent reviews [144, 145] for this, still far from settled, issue but note the following STM-based studies that illuminate the conductivity issue at the single-molecule level (Figure 2.4). 

The computer-aided procedure, unless automated by the program, requires running a series of liquid-liquid equilibrium calculations (the equivalent of vapor-hquid flash calculations) at constant temperature and pressure. The composition is varied around the equilibrium curve, and the transition points from one phase to two, or vice versa, are noted. As many points as needed are obtained this way to generate the entire equilibrium curve. Also, each time an equilibrium calculation is done in the two-phase region, the compositions of the two phases are recorded. Each pair of data points thus obtained defines a tie line. The data obtained at one temperature and pressure generate one triangular diagram. If so desired, the procedure is repeated at other temperatures and pressures to determine the effect of these variables. 

Other properties of fatty acid monolayers such as the phase transition temperature are consistent with the field strength theory stearic acid monolayers formed rigid films on alkaline earth subphases (17, 35). The temperature of the phase transition from rigid to fluid monolayers, estimated by the Devaux talc test, was a function of pH and buffer composition (Figure 17). Thus transition temperature at pH 6 decreased in a weak field sequence (I in Table III) while transition temperatures at pH 8 decreased in an intermediate field sequence (III or IV in Table III). Since variables such as tt are not controlled in these experiments, it is surprising that transition temperature data followed these sequences. 

When melts of some metal mixtures solidify, the alloy formed may possess a definite lattice type that is difierent from those of the pure metals. Such systems are classified as intermetallic compounds, e.g. 3-brass, CuZn. At 298 K, Cu has a ccp lattice and Zn has a structure related to an hep array, but 3-brass adopts a bcc structure. The relative proportions of the two metals are crucial to the alloy being described as an intermetallic compound. Alloys labelled brass may have variable compositions, and the a-phase is a substitutional alloy possessing the ccp structure of Cu with Zn functioning as the solute. 3-Brass exists with Cu Zn stoichiometries around 1 1, but increasing the percentage of Zn leads to a phase transition to y-brass (sometimes written as Cu5Zng, although the composition is not fixed), followed by a transition to... 

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