Ordering models diagram calculations

The contour diagrams for this model are shown in figure 9.18a. It is clear that deviations from the first-order model are at their greatest when x = X2 = 0.5 and the level of component is zero. We continue to look at the calculated deviation from the purely first-order model, along the line representing equal amounts of components 1 and 2 (a = X2), but with steadily increasing amount of component 3. The model predicts a very rapid decrease on the part of the effect bi2XiX2 as the proportion of Xj increases. 

FIG. 13 Phase diagram of a vector lattice model for a balanced ternary amphiphilic system in the temperature vs surfactant concentration plane. W -I- O denotes a region of coexistence between oil- and water-rich phases, D a disordered phase, Lj an ordered phase which consists of alternating oil, amphiphile, water, and again amphi-phile sheets, and L/r an incommensurate lamellar phase (not present in mean field calculations). The data points are based on simulations at various system sizes on an fee lattice. (From Matsen and Sullivan [182]. Copyright 1994 APS.)... 

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. 

Fig. 7.3. Deformation zone as calculated from the Dugdale-Barenblatt-model (Eq. 7.2). In order to magnify the displacements, E/cry = 7 was assumed for the diagram, whereas, in reality the ratio is about 38 (Tables 5.1 and 6.1)...

While in this system the lattice gas model is believed to be a good approximation of reality, the fact that the maximum transition temperature occurs for 0.48 instead of 0 = 1/2 shows that a model with strictly pairwise interaction is not adequate. Calculations with a reasonable value for the strength of the trio-interaction in Fig. 1 (/ , = (pt/experimental phase diagram at temperatures near the maximum transition temperature, but fail to reproduce the apparent widening of the ordered phase regime at lower temperatures. 

FIGURE 4. Scatter diagrams of bond length data (a) calculated for H2n-m X+mO molecules and (b) observed for main group cations vs the bond order parameter p. The expression R(X—O) = 1.39p-2/9 serves to model both sets of data equally well... 

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