Derivatives, equilibrium phase diagrams

The production of corrosion-resistant materials hy alloying is well established, hut the mechanisms are noi lull) understood. It is known, of course, that elements like chromium, mckcl. titanium, and aluminum depend for their corrosion resistance upon a tenacious surface oxide layer (passive film). Alloying elements added for the purpose of passivation must be in solid solution. The potential of ion implantation is promising because restrictions deriving from equilibrium phase diagrams frequently do not applv li e., concentrations of elements beyond tile limits of equilibrium solid solubility might he incorporated). This can lead to heretofore unknown alloyed surfact-s which are very corrosion resistant... 

Of the generic aluminium alloys (see Chapter 1, Table 1.4), the 5000 series derives most of its strength from solution hardening. The Al-Mg phase diagram (Fig. 10.1) shows why at room temperature aluminium can dissolve up to 1.8 wt% magnesium at equilibrium. In practice, Al-Mg alloys can contain as much as 5.5 wt% Mg in solid solution at room temperature - a supersaturation of 5.5 - 1.8 = 3.7 wt%. In order to get this supersaturation the alloy is given the following schedule of heat treatments. 

Before comparing these predictions regarding the critical point with experimental results, we may profitably examine the binodial curve of the two-component phase diagram required by theory. The following useful approximate relationship between the composition V2 of the more dilute phase and the ratio y = V2/v2 of the compositions of the two phases may be derived (see Appendix A) by substituting Eq. (XII-26) on either side of the first of the equilibrium conditions (1), using the notation V2 for the volume fraction in the more dilute phase and V2 for that in the more concentrated phase, and similarly substituting Eq. (XII-32) for fX2 and y,2 in the second of these conditions ... 

Phase diagrams can be used to predict the reactions between refractories and various solid, liquid, and gaseous reactants. These diagrams are derived from phase equilibria of relatively simple pure compounds. Real systems, however, are highly complex and may contain a large number of minor impurities that significantly affect equilibria. Moreover, equilibrium between the reacting phases in real refractory systems may not be reached in actual service conditions. In fact, the successful performance of a refractory may rely on the existence of nonequilibrium conditions, eg, environment (15—19). 

Fig. 2. Phase diagram describing lateral phase separations in the plane of bilayer membranes for binary mixtures of dielaidoylphosphatidylcholine (DEPC) and dipalmitoyl-phosphatidylcholine (DPPC). The two-phase region (F+S) represents an equilibrium between a homogeneous fluid solution F (La phase) and a solid solution phase S presumably having monoclinic symmetry (P(J. phase) in multilayers. This phase diagram is discussed in Refs. 19, 18, 4. The phase diagram was derived from studies of spin-label binding to the membranes.

Minimization with respect to T], gives the equilibrium values. A study of the equilibrium values and their derivatives with respect to the coupling constants e, u gives then the phase diagram [18]. If temperature dependence needs to be studied, it can be done by making the coupling constants e, u temperature dependent. 

With these results in view of derived formulae (26)-(29) for free energies we can study the temperature dependence of hydrogen solubility in the PtHx. HX phases, define the equilibrium value of order parameter, investigate the phase transitions in considered system with increasing temperature, establish the conditions of their realization, evaluate the energetic constants of all components of chemical reaction (1), construct phase diagram of the system. Below we shall examine these problems. 

The value of x varies with the temperature, i.e., x decreases as the temperature increases. Wee Miller (1971) examined the phase equilibrium as a function of temperature. The results are shown in Figure 2.10. For temperatures below 35 °C the phase diagram is basically the same as the Flory theory while at higher temperatures, the curve deflects to a high concentration regime. This phenomenon was observed in a system of cellulose derivatives (Navard et al., 1981). 

In the light of the phase diagram derived earlier for a eonductive polymer blend (Figure 11.124), the energy dissipation meehanism by redispersion ean be understood. It is the energy input driven way baek, of the system from the equilibrium interfacial energy curve at the flocculation point to the fully dispersed, but still phase-separated boundary. 

Solozhenko (1988) [176] concluded that kinetic factors influenced the transformation significantly and that the true equilibrium line can only be determined by a thermodynamic approach. From data on heat capacities [177-189], relative enthalpies (heat contents) [190-199], enthalpies of formation data [177, 201-207], equations of state and thermal expansion data for all BN modifications, Solozhenko [176] derived a calculated new phase diagram which significantly differed from the Corrigan and Bimdy (1975) [174] version. An overview of somces of thermodynamic data is given in Table 15. A review of calorimetric studies was given by Gavrichev et al. (1994) [212]. Vaporization studies of boron nitride were made by [208-211]. 

Experimental work on the phase diagram of this system is meager. Some information on selected phase equilibria can be derived indirectly from work on the development of commercial materials in the Si-B-N system. Gugel et al. (1972) [223] suggested a tentative phase equilibrium diagram. Equilibria between silicon Sorides and silicon nitride were assumed. According to this result, silicon does not show an equilibrium with BN. Kato et al. [227]... 

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