Shape of phase diagram

If a substance is allotropic this will affect the shape of phase diagrams for systems involving the substance. Consider a system which involves two allotropic substances, A and B. The following figure shows one of the possible diagrams which involve allotropic substances. The point e in the diagram is called the eutectoidpoint, and the eutectoid reaction is... 

The lines of phase boundary aty= 150s and>>= 189s are drawn arbitrarily because the shape of phase diagram is not clear at present... 

In the same way, we can construct the profile of the free energy of mixing, as (AG B)mix is a function of composition. As a rule, which follows from the shape of phase diagram curve, the miscibility of two polymers is always higher at small fractions of one of the components. 

Thus, it is clear that changing the position and shape of phase diagrams of poljmier alloys in the presence of filler should be taken into account when selecting condition of production of composite materials on their basis. 

In Chapter 5 we will attempt to make sense of the wide variety of shapes and sizes of phase diagrams for various petroleum mixtures. 

Rottman C. and Wortis M., Statistical Mechanics of Equilibrium Crystal Shapes Interfacial Phase Diagrams and Phase Transitions, Phys. Rep. 103, 59 (1984). 

The previous sections dealt with various types of phase diagrams and their interpretations. What has been glossed over, however, is what determines their shape. In principle, the answer is simple the phase or combination of phases for which the free energy of the system is lowest is by definition the equilibrium state. However, to say that a phase transformation occurs because it lowers the free energy of the system is a tautology, since it would not be observed otherwise — thermodynamics forbids it. The more... 

The effect of a second component in the phase structure is treated in this chapter in several stages. First, it was assumed that both components were of identical size and behaved ideally, i.e., they do not interact. Assuming further that there is no cocrystallization, the typical eutectic phase diagram of Fig. 2.27 results. The discussion of the experimental evaluation of phase diagrams indicated the effect of formation of solid solutions, as seen in Fig. 7.2. The deviation from an ideal solution can be treated by introduction of an activity as in Fig. 7.3. Next, in Sect. 7.1.2 the shape-difference of two components was treated using the free-volume argument of Hildebrandt, and finally, the interaction parameter % was introduced to treat real solutions in Fig. 7.4-6. The examples treated in Sects. 7.1.3-5 dealt then with components that were isolated molecules. 

The calculations physical properties of antiferroelectrics based on the Kittel model (i.e. with respect to antiparallel alignment of sublattices polarization vectors) can be done within the formalism of Chap. 1. The numerical calculations of phase diagrams of nanosized antiferroelectric systems of different shapes were carried out in Ref. [68] without consideration of either external or internal electric fields. Corresponding analytical calculations had been carried out in Ref. [69], However, the model used for calculations in [69] did not take into account both mechanical strains and surface piezoeffect generating built-in field. The consistent account for latter effects in Ref. [70] show that they are playing a decisive role in transformation of antiferroelectric phase into ferroelectric one in sufficiently thin Aims. With respect to the latter, the subsequent consideration will be done according to Ref. [70]. 

In polymer solutions and polymer blends, LCST, UCST, combined UCST and LCST, hourglass, and closed-loop shaped phase diagrams have been found experimentally. These five types of phase diagrams are the most commonly observed phase diagrams in polymer systems. An important role is played by temperature in the phase diagrams according to the equation ... 

Figure 9.1 shows a typical phase diagram for a pure (one-component) substance. The three phase boundary lines (liquid-solid, liquid-gas, and solid-gas) meet at the triple point (the one temperature and pressure where all three phases coexist). The liquid-gas boundary line terminates at the critical point. These phase boundaries indicate how the coexistence pressure between two phases changes as the temperature changes. In this section, we will examine how we can use thermodynamics to predict the shape of phase coexistence curves for pure substances. For mixtures, more complicated phase diagrams can be constructed that indicate the dependence of the coexistence pressure and temperature upon the composition of the various phases. Phase diagrams for mixtures are discussed in Sections 9.2 and 9.3. 

All geometric elements of phase diagrams, their reactions and shapes (but not the combinations of these elements) can be illustrated by existing experimental examples. 

Similar results have been reported in recent theoretical analyses [17, 36], where the authors analyzed a liquidus-soHdus phase diagram for a binary system with full mutual solubility of the components. The well-known lens-type shape of a diagram on the temperature-composition surface is shifted to lower temperatures. Thereby, the dependence of the melting temperature on the partide size has been found to obey Equation 13.3 ... 

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