Phase diagrams experimental examples

The use of an ideal-solution model meant that there were a number of instances where calculated and experimental results were quantitatively at variance. However, the approach very successfully predicted the general form of most of the phase diagrams, for example whether they were peritectic or eutectic, and accounted for the appearance of intermediate phases in systems such as Cr-Rh. That the approach could do this using such simple and internally self-consistent models is a demonstration of the inherent power of CALPHAD methods. The importance of this first step therefore cannot be overestimated, although its significance was not... 

It takes a finite time for the process to be completed the composition o slowly changes to the coexistent compositions (t>a and b- The process is illustrated by the horizontal arrow in Fig. 10.28. Kinetics of phase separation in a blend has recently gained considerable interest from both a theoretical and experimental point of view. Several experimental examinations were carried out to determine the concentration fluctuation during the phase-separation process taking PS/PVME as a model, which exhibits a LCST phase diagram. For example, Larbi et al. [168] observed fluorescence emission of anthracene-labeled PS in PS/PVME to investigate kinetics of both spinodal decomposition and nucleation growth. 

Indeed, the experimentally observed phase behavior differs substantially from the mean-field phase diagram. An example is shown in Fig. 6. The Lifshitz point is destroyed, the three phase coexistence region between the... 

Wev] Wever, F., Heinzel, A., Two Examples of Ternary Iron Systems with Closed -y-Loop (in German), Mitt. K.-W.-Inst. Eisenforschung, 13,193-197 (1931) (Phase Diagram, Experimental,, , 14)... 

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]. 

Phase transitions in two-dimensional layers often have very interesting and surprising features. The phase diagram of the multicomponent Widom-Rowhnson model with purely repulsive interactions contains a nontrivial phase where only one of the sublattices is preferentially occupied. Fluids and molecules adsorbed on substrate surfaces often have phase transitions at low temperatures where quantum effects have to be considered. Examples are molecular layers of H2, D2, N2 and CO molecules on graphite substrates. We review the path integral Monte Carlo (PIMC) approach to such phenomena, clarify certain experimentally observed anomalies in H2 and D2 layers, and give predictions for the order of the N2 herringbone transition. Dynamical quantum phenomena in fluids are analyzed via PIMC as well. Comparisons with the results of approximate analytical theories demonstrate the importance of the PIMC approach to phase transitions where quantum effects play a role. 

Figure 8.23 (Solid + liquid) phase diagram for (. 1CCI4 +. yiCHjCN), an example of a system with large positive deviations from ideal solution behavior. The solid line represents the experimental results and the dashed line is the ideal solution prediction. Solid-phase transitions (represented by horizontal lines) are present in both CCI4 and CH3CN. The CH3CN transition occurs at a temperature lower than the eutectic temperature. It is shown as a dashed line that intersects the ideal CH3CN (solid + liquid) equilibrium line.

An example of an early paper on a binary system is the work of Spencer and Putland (1973) on Fe-V. This combined a review of the thermodynamics and phase diagram of the Fe-V system with new, selective experimental thermodynamic... 

The example above illustrates how constructing a phase diagram is relatively straightforward once a list of candidate structures has been specified. At the same time, the complexity of the surface oxide structure in Fig. 7.6 is an excellent example of why generating the relevant candidate structures is often far from straightforward. The structure shown in Fig. 7.6 was based on the best experimental data available on this ordered surface phase that were available at the time of Li, Stampfl, and Scheffler s1 calculations. Since then, however, additional experiments and DFT calculations have indicated that the structure of the true surface oxide is somewhat different than the one shown in Fig. 7.6 and, moreover, other surface oxide phases with similar stabilities also exist. 

Note that the above considerations establish only the number of independent chemical variations c, not which species should be chosen as variables in the phase diagram, the latter choice being purely a matter of convenience. Note also from the final problem (f) that the question of effective chemical variability c can be addressed experimentally, based on the active chemistry of the actual system (rather than, for example, abstract theoretical... 

Physical measurements are directly input to the statistical thermodynamics theory. For example three-phase hydrate formation data, and spectroscopic (Raman, NMR, and diffraction) data were used to determine optimum molecular potential parameters (e,o,a) for each guest, which could be used in all cavities. By fitting only a eight pure components, the theory enables predictions of engineering accuracy for an infinite number of mixtures in all regions of the phase diagram. This facility enables a substantial savings in experimental effort. 

As a typical example from industrial practice we consider the simulation of a process with the reaction of methylphosphinic acid and butanol to methylphosphinic acid butyl ester and water, which was modeled by Gordana Hofmann-Jovic at InfraServ Knapsack [C28]. Because of the lack of experimental data for the binary systems with phosphorous compounds, COSMO-RS was used for the prediction of the binary activity coefficients. Then the results were fitted by an NRTL equation and the entire process was modeled by a commercial process simulator. The resulting phase diagrams were in close agreement with experimental measurements obtained later (Fig. 8.2). 

---