Variable pressure phase diagrams

Hydrostatic pressure is a variable that obviously affects phase equilibria. Atmospheric pressure may generally be considered negligible and therefore neglected in 

30 and 2.31 show diagrams in which the state variable pressure is explicitly considered. Fig. 2.30 shows two typical one-component systems. In Fig. 2.31(a) and (b), on the other hand, the equilibria relevant to a simple two-component system are represented. 

As an example of more complex systems and descriptions, the Ni-Mg system is shown in Fig. 2.32 (adapted from Levinsky 1997). In (a) an isobaric section of the diagram is shown (a low pressure has been considered in order to have a certain extension of the gas phase which consists essentially of Mg vapour). In Fig 2.32(b) there is an isothermal section of the diagram at 700°C. Notice, for different values of pressure, the change in the sequence of phases stable at different compositions. A value of the pressure close to atmosphere is approached at the top of the figure. In Fig 2.32(c) the usual Tlx diagram is shown. This can be considered an isobaric phase diagram if pressure is relatively low but still higher than the sum of the equilibrium partial pressures of the components. 

For a discussion of the role of non-hydrostatic pressure in phase equilibria investigations, the effects of applied stress and their consequences in metallurgy, geology, etc. see Cahn (1989). 

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Although pressure and temperature are the common variables for phase diagrams in chemistry, volume can also be plotted on an axis in a phase diagram, as shown in Figure 6.10. There are also three-dimensional phase diagrams that plot pressure, volume, and temperature Figure 6.11 shows an example of that. 

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. 

Solid-Fluid Equilibria The phase diagrams of binai y mixtures in which the heavier component (tne solute) is normally a solid at the critical temperature of the light component (the solvent) include solid-liquid-vapor (SLV) cui ves which may or may not intersect the LV critical cui ve. The solubility of the solid is vei y sensitive to pressure and temperature in compressible regions where the solvent s density and solubility parameter are highly variable. In contrast, plots of the log of the solubility versus density at constant temperature exhibit fairly simple linear behavior. 

As yet, models for fluid membranes have mostly been used to investigate the conformations and shapes of single, isolated membranes, or vesicles [237,239-244], In vesicles, a pressure increment p between the vesicle s interior and exterior is often introduced as an additional relevant variable. An impressive variety of different shapes has been found, including branched polymer-like conformations, inflated vesicles, dumbbell-shaped vesicles, and even stomatocytes. Fig. 15 shows some typical configuration snapshots, and Fig. 16 the phase diagram for vesicles of size N = 247, as calculated by Gompper and Kroll [243]. 

In phase diagrams for two-component systems the composition is plotted vs. one of the variables of state (pressure or temperature), the other one having a constant value. Most common are plots of the composition vs. temperature at ambient pressure. Such phase diagrams differ depending on whether the components form solid solutions with each other or not or whether they combine to form compounds. 

Partial pressure as a variable. As mentioned in 2.1, many types of thermodynamic variables may be used in the construction of phase diagrams. The various rules of construction, based on the laws of chemical thermodynamics, which apply to the different types of phase diagrams have been discussed in several books and papers (for instance, Pelton and Schmalzried 1973, Okamoto 1991, Pelton 1991). Following a classification proposed by Pelton, the various, bidimensional, phase diagrams may be subdivided into three types as follows ... 

Temperature and pressure are the two variables that affect phase equilibria in a one-component system. The phase diagram in Figure 15.1 shows the equilibria between the solid, liquid, and vapour states of water where all three phases are in equilibrium at the triple point, 0.06 N/m2 and 273.3 K. The sublimation curve indicates the vapour pressure of ice, the vaporisation curve the vapour pressure of liquid water, and the fusion curve the effect of pressure on the melting point of ice. The fusion curve for ice is unusual in that, in most one component systems, increased pressure increases the melting point, whilst the opposite occurs here. 

The unary phase diagram is seldom used in solid state syntheses. However, the unary diagram forms the basis for the phase diagrams of multicomponent systems. Since there are no composition variables, the only externally controllable variables in a unary system are simply the temperature and pressure. For this... 

Ternary Phase Diagrams. In a ternary system, it is necessary to specify temperature, pressure, and two composition parameters to completely describe the system. Typically, pressure is fixed, so that there are three independent variables that are needed to fix the system temperature and two compositions. The third composition is, of course, fixed by the first two. We could create a three-dimensional plot with three mutually perpendicular axes, as is usually the case in mathematics however, it is more convenient, and graphically more appealing, to establish two compositional axes 60° apart from each other, with a third, redundant compositional axis, as in the form of an equilateral triangle (see Figure 2.14). The temperatme axis is then constructed perpendicular to the plane of the triangle, if desired. 

The usual environmental variables are temperature and pressure. However, one can imagine a system in which equilibrium is affected by some other variable (e.g., a magnetic field). Pressure is not considered to be a variable when equilibrium is described at a fixed total pressure (e.g., atmospheric). In general the number of environmental variables is designated as E. Most phase diagrams are at constant pressure so the only environmental variable is temperature. In this case E = 1. (If both variations in both temperature and pressure are considered, E = 2). 

The phase diagrams of aqueous surfactant systems provide information on the physical science of these systems which is both useful industrially and interesting academically (1). Phase information is thermodynamic in nature. It describes the range of system variables (composition, temperature, and pressure) wherein smooth variations occur in the thermodynamic density variables (enthalpy, free energy, etc.), for macroscopic systems at equilibrium. The boundaries in phase diagrams signify the loci of system variables where discontinuities in these thermodynamic variables exist (2). 

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