Case studies in phase diagrams

So far we have discussed the basic concept of non-stoichiometry without showing real examples. Here we shall consider case studies in order to understand the non-stoichiometry appearing in various kinds of substances. To construct phase diagrams which contain non-stoichiometric compounds, it is indispensable to know the relationship between the deviation from stoichiometry <5, the partial pressure of coexisted gas, (for diatomic gases),... 

CASE STUDIES IN LYSOZYME AND THE GENERIC PROTEIN PHASE DIAGRAM... 

Due to its ability to distinguish between (strongly or weakly) first-order and second-order transitions, high-resolution calorimetry is a powerful technique for studies of phase diagrams near critical points. It probes the evolution of the latent heat in the regime of first-order transitions via the mismatch between the ac and relaxation runs. In the case of a continuous or gradual evolution, the two modes of operation yield identical anomalies. 

Remark The above reasoning is very much simplified. It is incorrect to conclude that increasing the amount of solute (e.g., salt) allows to continuously depress the freezing point. For instance in the case of NaCl we can only get down to about -21.1 °C. At lower temperatures ice and solid salt coexist. What this means we discuss in the next chapter, where we study simple phase diagrams (in particular liquid-solid coexistence in binary systems starting on p. 160). 

Each chapter is designed to provide the content of a 50-minute lecture. Each block of four or so chapters is backed up by a set of Case Studies, which illustrate and consolidate the material they contain. There are special sections on design, and on such materials as wood, cement and concrete. And there are problems for the student at the end of each chapter for which worked solutions can be obtained separately, from the publisher. In order to ease the teaching of phase diagrams (often a difficult topic for engineering students) we have included a programmed-learning text which has proved helpful for our own students. 

The process involved in the incident is concerned with the separation of crude into three phases. The crude is pumped into a two stage separation process where it is divided into three phases oil, gas, and water. The water is cleaned up and dumped to drain. The remaining mixture of oil and gas is then pumped into the main oil line where it is metered and sent on for further processing. A simplified process diagram is shown in Figure 7.1. The case study described here is centered on a flange leak in one of the oil pipeline pumps (pump A) and its associated pressure relief valve piping. 

The phase diagrams we have shown are based upon the fact that A and B form solid mutually soluble solid state solutions. If they do not, i.e.- they are not mutually soluble in the solid state, then the phase diagram becomes more complicated. As an example, consider the following, which is the case of limited solid solubility between A and B. (N.B.- study the following diagrams carefully)"... 

The information available on aqueous polymer blends is qualitative in nature because of the lack of a suitable theory to interpret the experimental observations. Mixed gels can be comprised of an interpenetrating network, a coupled network (as discussed above), or a phase-separated network [2]. The latter is the most common as the blends have a tendency to form two phases during gelation. In such cases the miscibility and thermodynamic stability have to be empirically investigated and proper conditions for miscible blends identified. This involves a phase diagram study as is described in [3]. 

As a case study an acetic acid process has been given. Acetic acid is produced by a liquid-phase methanol carbonylation. Acetic acid is formed by the reaction between methanol and carbon monoxide which is catalysed by rhodium iodocarbonyl catalyst. The process diagram is shown in Figure 7. 

As an example for the specific case of vanadium alloys with palladium, the trend of the average atomic volume of the alloys is shown in Fig. 4.20 and compared with the phase diagram. These data were obtained by Ellner (2004) who studied the solid solutions of several metals (Ti, V, Cr, Mn, Fe, Co and Ni) in palladium. The alloys were heat treated at 800°C and water-quenched. From the unit cell parameters measured by X-ray diffraction methods, the average atomic volume was obtained Vat = c 14 (see Table 4.3). These data together with those of the literature were reported in a graph, and the partial molar (atomic) value of the vanadium volume in Pd solid solution (Fv)... 

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