Understanding Phase Diagrams

The equilibrium state of a system can be represented by a point in a (c + 2)-dimensional diagram. Phase diagrams are state diagrams for open systems, in which a particular state of equilibrium is specihed by the values of c + 2 independent state variables (the rest ate hxed dependent variables), with additional information on the phases present under various conditions. Although one typically sees phase diagrams with potentials (T) P, /a) chosen as the state variables, there are actually many possible ways to select the set of independent variables. 

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Some years ago in a continuing effort to understand phase diagrams, I had discovered [3] the following empirical rules among more than 300 binary phase diagrams reported in the literature (Hansen, Elliot Shunk) [4,5,6], The metallic radii, Ra, Rb, used are from INTERATOMIC DISTANCES (The Chemical Society, London, 1958) [7] and the structural notation follows that described in Handbook of Lattice Spacing and Structure of Metals (Pearson, 1958) [8]).. 

T. W. de Loos, "Understanding Phase Diagrams," in Supercritical Fluids Fundamentals for Applications, E. Kiran and J. M. H. Levelt Sengers (eds.), NATO ASI Series E, vol. 273, Kluwer Academic Publishers, Dordrecht, 1994, p. 65. 

Despite the fact, mentioned in 17.1.1, that phase diagrams are for the most part experimentally derived, they are controlled by and must conform to fundamental thermodynamic relationships. Understanding phase diagrams is enhanced by examining the relationships between the diagrams and the underlying thermodynamics. 

De Ix)os, Th. W. (1994) Understanding phase diagrams, in Kiran, i. and Ijevelt Sengers, J.M.H. (eds). Supercritical Fluids, Fundamentals for Application, Kluwer Academic Publishers, Dordrecht, pp. 65-89. 

Using Gibbs Energy to Understand Phase Diagrams... 

The example of a binary mixture is used to demonstrate the increased complexity of the phase diagram through the introduction of a second component in the system. Typical reservoir fluids contain hundreds of components, which makes the laboratory measurement or mathematical prediction of the phase behaviour more complex still. However, the principles established above will be useful in understanding the differences in phase behaviour for the main types of hydrocarbon identified. 

This last section allows you to test your understanding of the use of phase diagrams. 

We must start with fluid behavior to understand the basic concepts of unified chromatography. We must forget most of what we know from common experience about liquid and gas behavior since this experience is tied with ambient conditions. Instead, we must embrace the new possibilities afforded by temperatures and pressures that are different from ambient. This new view requires phase diagrams (17, 18). 

To understand what a phase diagram implies, consider first the curves AB and AC, and the line AD in Figure 9.5. Each of these lines shows the pressures and temperatures at which two adjacent phases are at equilibrium. 

In the three areas of the phase diagram labeled solid, liquid, and vapor, only one phase is present. To understand this, consider what happens to an equilibrium mixture of two phases when the pressure or temperature is changed. Suppose we start at the point on AB... 

The chemistry and the structures in this report have been organized by the main-group/chalcogen building block units (Fig. 14.1). At the start of 2000, we were beginning to understand aspects of the chemistry of chalcophosphates both as selenophosphates and thiophosphates. The thesis of Dr. Carl Evenson [14] and his subsequent papers discuss the composition phase diagrams of Y,... 

Eiven though this phase diagram is complicated, it is easy to understand. 

This work was of value in constructing that part of the phase diagram involving solutions in water. Of greater value in understanding cement formulations were the results obtained in the earlier study (Sorrell Armstrong, 1976) for the MgO-rich portion of the phase diagram. 

Though it is impossible to apply this phase diagram quantitatively to real polymers, we can understand the easiness of phase separation qualitatively. For example, it may be presumed that SD in PE is probably more difficult than that in PET the normalized density of PE is pw = 0.685 [4] which is quite far from the critical point of pw = 0.53 and so SD would occur at considerably... 

The importance of temperature-controlled scanning calorimetry for measurements of heat capacity and of scanning transitiometry for simultaneous caloric and pVT analysis has been demonstrated for polymorphic systems [9]. This approach was used to study an enantiotropic system characterized by multiphase (and hindered) transitions, the role of heat capacity as a means to understand homogeneous nucleation, and the creation of (p, T) phase diagrams. The methodology was shown to possess distinct advantages over the more commonly used combination of characterization techniques. 

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