Azeotropy rules

When the types of all boundary SPs and their topological indexes are established by means of Table 5.2, one should use the rule of azeotropy (5.18). In the case of terpolymerization this rule can be written as ... 

When P > 0, using Table 5.5 one can immediately point out the type of the inner azeotrope, and when p < 0, only the node (N) and saddle (S) in this table are replaced with the focus (F) and saddle-focus (SF), respectively. The sign of Ind (X ) of this azeotrope is opposite to the sign of a3 and is determined by indexes of the boundary SPs (see Table 5.6) in accordance with the rule of azeotropy (5.18) which in the case of tetrapolymerization yields ... 

Solid-fluid phase diagrams of binary hard sphere mixtures have been studied quite extensively using MC simulations. Kranendonk and Frenkel [202-205] and Kofke [206] have studied the solid-fluid equilibrium for binary hard sphere mixtures for the case of substitutionally disordered solid solutions. Several interesting features emerge from these studies. Azeotropy and solid-solid immiscibility appear very quickly in the phase diagram as the size ratio is changed from unity. This is primarily a consequence of the nonideality in the solid phase. Another aspect of these results concerns the empirical Hume-Rothery rule, developed in the context of metal alloy phase equilibrium, that mixtures of spherical molecules with diameter ratios below about 0.85 should exhibit only limited solubility in the solid phase [207]. The simulation results for hard sphere tend to be consistent with this rule. However, it should be noted that the Hume-Rothery rule was formulated in terms of the ratio of nearest neighbor distances in the pure metals rather than hard sphere diameters. Thus, this observation should be interpreted as an indication that molecular size effects are important in metal alloy equilibria rather than as a quantitative confirmation of the Hume-Rothery rule. 

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