Agreement diagram

Fig. 3. Graphical displays of the agreements agreement diagram) between Set 1 and Set 2 (The sets shown in Figure 2). (Figure drawn using PO correlation)...

The ternary diagrams shown in Figure 22 and the selectivi-ties and distribution coefficients shown in Figure 23 indicate very good correlation of the ternary data with the UNIQUAC equation. More important, however, Table 5 shows calculated and experimental quarternary tie-line compositions for five of Henty s twenty measurements. The root-mean-squared deviations for all twenty measurements show excellent agreement between calculated and predicted quarternary equilibria. 

We will focus on one experimental study here. Monovoukas and Cast studied polystyrene particles witli a = 61 nm in potassium chloride solutions [86]. They obtained a very good agreement between tlieir observations and tire predicted Yukawa phase diagram (see figure C2.6.9). In order to make tire comparison tliey rescaled the particle charges according to Alexander et al [43] (see also [82]). At high electrolyte concentrations, tire particle interactions tend to hard-sphere behaviour (see section C2.6.4) and tire phase transition shifts to volume fractions around 0.5 [88]. 

Colloidal crystals . At the end of Section 2.1.4, there is a brief account of regular, crystal-like structures formed spontaneously by two differently sized populations of hard (polymeric) spheres, typically near 0.5 nm in diameter, depositing out of a colloidal solution. Binary superlattices of composition AB2 and ABn are found. Experiment has allowed phase diagrams to be constructed, showing the crystal structures formed for a fixed radius ratio of the two populations but for variable volume fractions in solution of the two populations, and a computer simulation (Eldridge et al. 1995) has been used to examine how nearly theory and experiment match up. The agreement is not bad, but there are some unexpected differences from which lessons were learned. 

Correlation diagrams can be constructed in an analogous fashion for the disrotatory and conrotatory modes for interconversion of hexatriene and cyclohexadiene. They lead to the prediction that the disrotatory mode is an allowed process whereas the conrotatory reaction is forbidden. This is in agreement with the experimental results on this reaction. Other electrocyclizations can be analyzed by the same method. Substituted derivatives of polyenes obey the orbital symmetry rules, even in cases in which the substitution pattern does not correspond in symmetiy to the orbital system. It is the symmetry of the participating orbitals, not of the molecule as a whole, that is crucial to the analysis. 

Phase transitions in adsorbed layers often take place at low temperatures where quantum effects are important. A method suitable for the study of phase transitions in such systems is PIMC (see Sec. IV D). Next we study the gas-liquid transition of a model fluid with internal quantum states. The model [193,293-300] is intended to mimic an adsorbate in the limit of strong binding and small corrugation. No attempt is made to model any real adsorbate realistically. Despite the crudeness of the model, it has been shown by various previous investigations [193,297-300] that it captures the essential features also observed in real adsorbates. For example, the quite complex phase diagram of the model is in qualitative agreement with that of real substances. The Hamiltonian is given by... 

The phase diagrams for assoeiating fluids evaluated by using the Johnson and Gubbins approaeh [114] are in good agreement with eomputer simulation. 

Fig. 2. For the case of global reconstruction of the surface, the phase diagram retains a dicontinuous IPX of first order at the critical point 0.5235 0.0005, i.e., a value very close to but slightly smaller than that of the standard ZGB model given by F2A — 0.525 60 0.00001 [31]. Also, the second-order IPX of the standard ZGB model is no longer observed, in qualitative agreement with experiment, e.g.. Fig. 3.

In summary, we have demonstrated the possibility of calculating the phase stability of a magnetic random alloy from first principles by means of LMTO-CPA theory. Our calculated phase diagram is in good agreement with experiment and shows a transition from the partially ordered a phase to an hep random alloy at 85% Co concentration. 

The fact that the structure that I formulated for this alloy from chemical arguments with no knowledge about the X-ray diffraction diagram was found later to agree quantitatively with that diagram has convinced me that the structure is correct. I emphasize that I formulated only one structure, and that the X-ray diagram was not involved in any way in its formulation. The probability of chance agreement of the lattice constant to 0,1 A and of adherence to the selection rules for intensities is surely less than 1 in 1,000. 

The entire Ba-Cu system has been examined a partial study (0-50 at% Ba) has also been carried out. Where comparable the two sets of data are in agreement consequently, the recommended phase diagram is that in ref. 1. Two compounds exist in the system BaCu (570°C) melts congruently, whereas BaCujj (670°C) is formed in a peritectic reaction. Further evidence for BaCu has come from a structural study. ... 

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