Experimental Phase Diagrams

SmA phases, and SmA and SmC phases, meet tlie line of discontinuous transitions between tire N and SmC phase. The latter transition is first order due to fluctuations of SmC order, which are continuously degenerate, being concentrated on two rings in reciprocal space ratlier tlian two points in tire case of tire N-SmA transition [18,19 and 20], Because tire NAC point corresponds to the meeting of lines of continuous and discontinuous transitions it is an example of a Lifshitz point (a precise definition of tliis critical point is provided in [18,19 and 20]). The NAC point and associated transitions between tire tliree phases are described by tire Chen-Lubensky model [97], which is able to account for tire topology of tire experimental phase diagram. In tire vicinity of tire NAC point, universal behaviour is predicted and observed experimentally [20]. 

Monovoukas Y and Cast A P 1989 The experimental phase diagram of charged colloidal suspensions J. Colloid Interface Sol. 128 533-48... 

Imhof A and Dhont J K G 1995 Experimental phase diagram of a binary oolloidal hard-sphere mixture with a large size ratio Phys. Rev. Lett. 75 1662-5... 

For recent reviews on experimental phase diagrams of amphiphilic systems see K. V. Schubert. Ber Bunsenges Phys Chemie 700 190-205, 1996 R. S. Strey. Curr Opin Coll Interf Sci 7 402-410, 1996. 

It turns out that for some systems the GPM yields the pair interactions, particularly those between first neighbors, which do not correspond to experimental phase diagrams. It is the purpose of the present work to show some of these cases and make a comparison with results obtained by other methods, particularly by the CWIS. 

We have found that for some alloys (e.g. Pt-Rh and Ni-Pt), the GPM yields pair interactions which are incorrect, because their values are either too large and would lead to overestimated transition temperatures (Ni-Pt), or they have even opposite sign than that expected from the experimental phase diagram and predicted by other theoretical methods (Pt-Rh). Various explanations of these discrepancies are conceivable ... 

Data at two temperatures were obtained from Zeck and Knapp (1986) for the nitrogen-ethane system. The implicit LS estimates of the binary interaction parameters are ka=0, kb=0, kc=0 and kd=0.0460. The standard deviation of kd was found to be equai to 0.0040. The vapor liquid phase equilibrium was computed and the fit was found to be excellent (Englezos et al. 1993). Subsequently, implicit ML calculations were performed and a parameter value of kd=0.0493 with a standard deviation equal to 0.0070 was computed. Figure 14.2 shows the experimental phase diagram as well as the calculated one using the implicit ML parameter estimate. 

Fig. 13. (a) Experimental phase diagram for H adsorbed on Pd(lOO). Crosses denote the points where the LEED intensities have dropped to one-half of their low-temperature values. Dashed curve is a theoretic phase diagram obtained from ° for R, = - 1/2. (b) LEED intensities plotted versus... 

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/maximum transition temperature, but fail to reproduce the apparent widening of the ordered phase regime at lower temperatures. 

Experimental phase diagrams of CO2 with ethyl acetate [37] and alkyl carbonates [38] are also available. Molecular simulations that describe the binary phases diagrams of many organic solvents with CO2 were also recently published [39], Binary phase diagrams of methanol with fluoroform are also available [40], At any given pressure and temperature, fluoroform is more miscible with methanol than CO2. Ternary phase diagrams for a number of systems are also available, such as methanol/H20/C02 [41] acetonitrile/H20/C02, and methanol/H20/fluoroform [40]. 

Figure 3.4. Experimental phase diagrams in the micelle volume fraction volume fraction (f>...

F. Leal-Calderon, J. Bibette, and J. Biais Experimental Phase Diagrams of Polymer and Colloid Mixtures. Europhys. Lett. 23, 653 (1993). 

Hume-Rothery was to prove a fair, if demanding, editor, and the result was an important review on the stability of metallic phases as seen from the CALPHAD viewpoint (Kaufman 1969). The relevant correspondence provides a fascinating insight into his reservations concerning the emerging framework fiiat Kaufman had in mind. Hume-Rothery had spent most of his life on the accurate determination of experimental phase diagrams and was, in his words (Hume-Rothery 1968), ... not unsympathetic to any theory which promises reasonably accurate calculations of phase boundaries, and saves the immense amount of work which their experimental determination involves . 

Figure 7.6. Comparison of (a) experimental phase diagram for the Cu-Au system (Hansen 1958) with (b) predictions for the Cu-Au system calculated using the tetrahedron approximation but including asymmetric four-body interactions (de Fontaine and Kikuchi 1978).

Fig. 6. Experimental phase diagram for [EMIMJCl/AlCls- Reproduced with permission from Fannin et al. (8).

In this chapter we show a large part of the experimental phase diagram and thermodynamic data for the Ga-In-Sb and Hg-Cd-Te systems along with calculated values for these data obtained from a simultaneous, quantita-... 

In the preceding discussion, QOtas treated as a uniform substance undergoing a phase transition a from the gas critical point is deLnedfkjyandTc. Above the critical point, that is, fqj > Pc... 

Figure 2.3. Experimental phase diagrams of the system (A) CaC03-MnC03 from 325-625°C, and (B) CaC03-FeC03 from 300-900°C. The regions under the curves are those in which a two-carbonate assemblage was observed. Elsewhere homogeneous solid solutions were obtained. (After Goldsmith, 1983, and Goldsmith et al., 1962.)...

Figure 23.4 Form of the experimental phase diagram for two normal substances (a) iodine (l2) and (b) carbon dioxide (C02).

A typical experimental phase diagram for the system toluene-benzene is sketched in Figure 34.4 from which it can be seen that this diagram corresponds exactly in form to a superposition of the liquid and vapour curves derived in Figures 34.2 and... 

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