Phase Diagrams closed system

Given the chemical data for natural mineral compositions, it should be possible to construct a phase diagram including those phases that are likely to occur with sepiolite and palygorskite in a system where the mass of the components is an extensive variable of the system (a closed system). 

Since alkalis enter into the structure of these two minerals in only small quantities, these variables can be ignored in a first approximation. The associations of alkali-rich and alkali-poor systems will be discussed later. 

M = montmorillonites I illite Chi chlorite Pa = palygorskite Sep = sepiolite ppt = zone of silicate precipitation. 

Let us look more closely at the various environments in which these minerals are found so that we can attempt to establish the chemical system influencing the paragenesis of the clays in each geological environment. 

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The state of the art has been summarized by Colinet (2003) who reported a description of the ab initio calculation methods of energies of formation for intermetallic compounds and a review of the aluminium-based compounds studied. In its conclusions, this paper underlined that the complete ab initio calculation of complex phase diagrams is not close at hand. However, calculation of phase diagrams in systems, where experimental data are missing, could, in the future, be performed by combination of CALPHAD routines and ab initio calculations of formation energies or mixing energies. 

Figure 2 Schematic phase diagram close to a quantum critical point for systems having an ordered phase at nonzero temperature. The solid line is the finite-temperature phase boundary while the dashed lines are crossover lines separating different regions within the disordered phase. QCP denotes the quantum critical point.

Figure A2.5.31. Calculated TIT, 0 2 phase diagram in the vicmity of the tricritical point for binary mixtures of ethane n = 2) witii a higher hydrocarbon of contmuous n. The system is in a sealed tube at fixed tricritical density and composition. The tricritical point is at the confluence of the four lines. Because of the fixing of the density and the composition, the system does not pass tiirough critical end points if the critical end-point lines were shown, the three-phase region would be larger. An experiment increasing the temperature in a closed tube would be represented by a vertical line on this diagram. Reproduced from [40], figure 8, by pennission of the American Institute of Physics.

Fig. 2. The phase diagrams and terminology of a microemulsion system close to its two critical end points, where the middle phase and one of the binodals...

Carbon steels as received "off the shelf" have been worked at high temperature (usually by rolling) and have then been cooled slowly to room temperature ("normalised"). The room-temperature microstructure should then be close to equilibrium and can be inferred from the Fe-C phase diagram (Fig. 11.1) which we have already come across in the Phase Diagrams course (p. 342). Table 11.1 lists the phases in the Fe-FejC system and Table 11.2 gives details of the composite eutectoid and eutectic structures that occur during slow cooling. 

The curves in Fig. 10 were drawn for the particular instance of a volatile solute dissolved in a volatile solvent, such as would exist for the acetone-chloroform system (whose diagram is very nearly like that of Fig. 10B). For many nonvolatile solutes, it not possible to trace smooth partial pressure curves across the entire range of mole fractions. This is especially true for aqueous salt solutions, where at a certain concentration of solute the solution becomes saturated. Any further addition of crystalline solute to the system does not change the mole fraction in the liquid phase, and the partial pressure of water thereafter remains constant, in accord with the phase rule. This phenomenon permits the use of saturated salt solutions as media to establish fixed relative humidity values in closed systems [12],... 

Phase diagrams show coexistent phases in equilibrium. We have seen in Chapter 1 that the conditions for equilibrium in a heterogeneous closed system at constant pressure and temperature can be expressed in terms of the chemical potential of the components of the phases in equilibrium ... 

Figure 2.30. Typical one-component systems (a) Room temperature, room pressure region of the well-known PIT phase diagram of water (notice the logarithmic scale of pressure), (b) P-T phase diagram of elemental Fe. The fields of existence of the different forms of Fe are shown a (body-centred cubic Fe), (face-centred cubic), 6 (body-centred cubic, high-temperature form isostructural with a), e (hexagonal close packed), L (liquid Fe). The gas phase field, owing to the pressure scale and the not very high temperatures considered, should be represented by a very narrow region close to the T axis.

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. 

Figure 4.17. The binary phase diagrams of the magnesium alloy systems with the divalent metals ytterbium and calcium (Ca is a typical alkaline earth metal and Yb one of the divalent lanthanides). Notice, for this pair of metals, the close similarity of their alloy systems with Mg. The compounds YbMg2 and CaMg2 are isostructural, hexagonal hP12-MgZn2 type.

For the niobium-copper system different phase diagrams of the simple eutectic type (with the eutectic point very close to Cu) have been proposed, either with an S-shaped near horizontal liquidus line or with a monotectic equilibrium. It was stated that the presence of about 0.3 at.% O can induce the monotectic reaction to occur, whereas if a lesser amount of oxygen is present no immiscibility gap is observed in the liquid. 

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