Phase diagrams, general theory

To summarize we have reproduced the intricate structural properties of the Fe-Co, Fe-Ni and the Fe-Cu alloys by means of LMTO-ASA-CPA theory. We conclude that the phase diagram of especially the Fe-Ni alloys is heavily influenced by short range order effects. The general trend of a bcc-fcc phase transition at lower Fe concentrations is in accordance with simple band Ailing effects from canonical band theory. Due to this the structural stability of the Fe-Co alloys may be understood from VGA and canonical band calculations, since the common band model is appropriate below the Fermi energy for this system. However, for the Fe-Ni and the Fe-Cu system this simple picture breaks down. 

Some phenomenological features of a representative phase diagram (for C02) were previously described in Section 2.5. In the present section, we shall first review key topological features of the phase diagram for H20 from the perspective of the phase rule (Section 7.2.1). The general theory of phase boundaries will then be developed (Section 7.2.2) and illustrated (Section 7.2.3) for some simple elemental and molecular substances. These representative examples will serve to illustrate the bewildering multiplicity of phase forms and properties that are possible even in the simple c = 1 limit. 

Fig. 2.35).The synthesis and morphology of more complex trifunctional branched graft copolymers have recently been discussed. Gido et al. (1996) prepared PS2-PI-PS2 (H-shaped) and (PS-PI)PI(PS-PI) ( -shaped) copolymers (see Fig. 2.33). The observed morphology of these samples was compared to the theory of Milner, the comparison being facilitated by considering the H- and -shaped molecules to each be composed of two single graft copolymers. This generally produced a satisfactory mapping onto the phase diagram in Fig. 2.34.

More than 15 years after the discovery of high-Tc superconductivity in layered cuprates its mechanism is still under debate. This has to do with the asymmetry of physical properties between the electron-doped and hole-doped side of the complex phase diagram, temperature vs. doping, T(x), and with the fact that no consensus has been reached about the question what are the key experiments a theory of high-Tc superconductivity must be able to explain. In this paper we argue that the elementary excitations and their interdependence with spin excitations in the cuprates are of central interest in order to learn more about the correlations in general and, in particular, about the mechanism for Cooper-pairing in these systems. 

Figure 2.4. Corresponding states temperature versus density phase diagram for spherical molecules calculated from the generalized van der Waals theory of Longuet-Higgins and Widom [31],...

Rainwater and his co-workers have extended their work on heteronuclear hard dumbbells to the treatment of dipolar systems [267]. They have used a generalized van der Waals theory similar to that used for quadrupolar molecules [152,266] to calculate the phase diagram and have compared their results with experiment for methyl chloride. The theory correctly predicts the effect of the dipole moment on the stable crystal structure. 

Thus, there are four possible cases v = 1,/ = 3 v = 2,/ = 2 v = 3, / = 1 and v = 4,/ = 0. When v = 4 the system is completely determined and is represented by a point in phase-diagram space. The case V = 3 has already been discussed in the general theory of univariant systems (Sec. 9-2). The case v = 1 represents a homogeneous system and, therefore, does not require further discussion. The case v = 2 will now be discussed in some detail. In order to simplify the notation, we define the symbols... 

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