Systematics generalized phase diagrams

Figure 5.10. The generalized phase diagram, at atmospheric pressure, for trivalent (not Eu and Yb) intra-lanthanide alloys. The so-called systematization number is shown according to Gschneidner and Calderwood (1986). Notice that, in principle, the same behaviour should be expected for every mixture of any two trivalent lanthanides as long as the same (averaged) systematization number is calculated (see the text).

In connection with these generalized phase diagrams as a function of pressure, the phase boundary of the bcc phase is clearly established and follows systematics as has been discussed earlier in section 3.2. 

A systematic analysis of structure and stability of binary and ternary Laves phases, or Friauf-Laves phases, has been performed by Stein et al. (2004, 2005). By reviewing a large number of experimentally determined phase diagrams with Laves phases, a number of general conclusions have been obtained. These may be summarized in the following points ... 

Table 5.17. Systematization numbers of a few characteristic points in the generalized rare earth phase diagram (according to Gschneidner and Calderwood 1986) (see Fig. 5.10).

However interesting and significant the results mentioned above may be, most of them are somewhat lacking of generality since they were derived from experiments limited to some microemulsion compositions. With this in mind, the authors of the present study decided to perform systematic conductivity and permittivity determinations over the entire transparent isotropic water-in-oil type solubilization area of the phase diagram of some microemulsion systems, with a view to gain as thorough as possible information about the structural behavior of the systems. 

The generalized K-S model is designed to capture the vesicle flow behavior for non-spherical shapes sufficiently far from a sphere. For quasi-spherical vesicles, a derivation of the equations of motion by a systematic expansion in the undulation amplitudes gives quantitatively more reliable results. An expansion to third order results in a phase diagram [200, 201], which agrees very well with Fig. 28. 

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