Calculated and experimental phase

To illustrate, predictions were first made for a ternary system of type II, using binary data only. Figure 14 compares calculated and experimental phase behavior for the system 2,2,4-trimethylpentane-furfural-cyclohexane. UNIQUAC parameters are given in Table 4. As expected for a type II system, agreement is good. 

Figure 1 shows a comparison of calculated and experimental phase compositions at 40 , 50 , and 60 C. The fit of phase compositions for the L1L2G equilibrium at 60 C and 12.2 MPa is very good, while the fit of the L1L2L3 phase ecjuilibrium at 40 C and 8.4 MPa is semi-quantitative, at best. Since the three phases at 40 C correspond to a different three-phase equilibrium than the L1L2G equilibrium at 50 C, which was used to fit binary interaction parameters, the poorer fit at 40 C is not unexpected. Indeed, these results show that L1L2L3 ecjuilibrium can be predicted with parameters obtained from an entirely different three-phase region. 

From the comparison of the calculated and experimental phase diagrams, it follows that the thermodynamic model of silicate melts is suitable for the description of the phase equilibrium also in titania-bearing silicate systems and provides deeper information on the behavior of Ti(IV) atoms. It was, however, shown that Ti(IV) atoms behave in silicate melts as network formers, except in the region of its high concentration, and in highly basic melts. 

Figure 14. Calculated and experimental phase diagrams for the C-Re-W (Ref. 1) and C-Re-Mo (Refs. 12,13) systems.

Using UNIQUAC, Table 2 summarizes vapor-liquid equilibrium predictions for several representative ternary mixtures and one quaternary mixture. Agreement is good between calculated and experimental pressures (or temperatures) and vapor-phase compositions. ... 

Figure 12.6. (a) Calculated (a + a) phase boundary for Fe-V together with experimental boundaries (After Spencer and Putland 1973). (b) Comparison between calculated and experimental values of the concentration of Al, V and Fe in the two phases in Ti-6AMV alloy (after Saunders and... 

It is seen that by taking a mean value for the slope, there is very little divergence between the calculated and experimental values. Consequently, the methylene groups can, indeed, be taken as a reference group for assessing the effect of molecular structure on solute retention. The concept will now be applied to a simple n-alkanes series as discussed above, the data for which was obtained on the stationary phase n-heptadecane. 

While the dilated van Laar model gives a reliable representation of constant-pressure activity coefficients for nonpolar systems, the good agreement between calculated and experimental high-pressure phase behavior shown in Fig. 14 is primarily a result of good representation of the partial molar volumes, as discussed in Section IV. The essential part of any thermodynamic description of high-pressure vapor-liquid equilibria must depend,... 

Various pc electrode models have been tested.827 Using the independent diffuse layer electrode model74,262 the value of E n = -0.88 V (SCE) can be simulated for Cd + Pb alloys with 63% Pb if bulk and surface compositions coincide. However, large deviations of calculated and experimental C,E curves are observed at a 0. Better correspondence between experimental and calculated C,E curves was obtained with the common diffuse-layer electrode model,262 if the Pb percentage in the solid phase is taken as 20%. However, the calculated C, at a Ois noticeably lower than the experimental one. It has been concluded that Pb is the surface-active component in Cd + Pb alloys, but there are noticeable deviations from electrical double-layer models for composite electrodes.827... 

The details of the specific features of the heat transfer coefficient, and pressure drop estimation have been covered throughout the previous chapters. The objective of this chapter is to summarize important theoretical solutions, results of numerical calculations and experimental correlations that are common in micro-channel devices. These results are assessed from the practical point of view so that they provide a sound basis and guidelines for the evaluation of heat transfer and pressure drop characteristics of single-phase gas-liquid and steam-liquid flows. 

It is difficult to decide whether the discrepancy between the calculated and experimental data is due to a different conformational preference of the thietane dioxides in the liquid and the solid phase, or to the crude approximations included in the Karplus-Barfield equation. However, the relationship between vicinal coupling constants and dihedral angles appears qualitatively valid in thietane oxides and dioxides, particularly if trends instead of exact values are discussed . At any rate thietane dioxides, 1,3-dithietane dioxides and tetroxides maintain either planarity or a slightly distorted average vibrating conformation with a low barrier to ring planarity . 

The excellent correlation between calculated and experimental log P values was obtained by vast investigations of the partitioning of simple chemicals in different mutually immiscible two-phase liquid systems by means of universal model based on the MOD theory [23] ... 

The preferred conformations of methoxy groups attached to aromatic rings in the phenethylamines have recently been investigated using theoretical approaches, gas phase experimental methods, and nuclear magnetic resonance (NMR) techniques for the molecules in aqueous solution. Ab initio theoretical calculations and experimental gas phase results have indicated that when two... 

Because a few errors were found in the original article complete expressions for activity coefficients are given in the appendix. BEUTIER took H, K, Aaa parameter from the earlier EDWARDS et al. (2) work. A new treatment of ternary data is presented u-sing H, K, Aaa parameters from the newer EDWARDS et al. (10) work. All parameters necessary in the calculation are listed in tables 2. a, b, c. Numerical results and comparison of calculated and experimental partial pressures are given in tables 3. a, b for a few typical data sets. In this work deviations to ideality in the vapor phase are calculated according to NOTHNAGEL et al. (5). 

The calculated and experimental gaseous and liquid phase compositions are shown in Figures 1 and 2 respectively. 

Nitrogen - Water System. The interaction parameters for the nitrogen - water system have been evaluated using the data of Wiebe and Gaddy (10), Paratella and Sagramora (Vj ), Rigby and Prausnitz (12)and O Sullivan and Smith (13). As with the two previous systems, only one constant interaction parameter was necessary to correlate the vapor phase composition while the interaction parameter for the aqueous liquid phase increased monotonically with temperature. A comparison of the calculated and experimental vapor phase and aqueous liquid phase compositions is given in Table I. 

Figure 6 illustrates the calculated and experimental equilibrium phase compositions at 220°F for this binary system. 

A comparison of calculated and experimental values of vapour pressure and saturated liquid and vapour volumes at various temperatures is shown in Table 2. The water composition in the liquid phase and the corresponding degree of association,... 

Stemming from a comparison between calculated and experimental methods, the proposed calculations appear quite precise and thus open up new perspectives in polarization calculations for natural crystalline phases. As we will see in chapter 4, polarization energy is of fundamental importance in the evaluation of defect equilibria and consequent properties. 

To appreciate the predictive properties of Kieffer s model, it is sufficient to compare calculated and experimental entropy values for several phases of geochemical interest in table 3.1, which also lists entropy values obtained through apphcation of Debye s and Einstein s models. One advantage of Kieffer s model with respect to the two preceding formulations is its wider T range of applicability (Debye s model is appropriate to low frequencies and hence to low T, whereas Einstein s model is appropriate to high frequencies and hence to high T). 

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... 

Figure 10.20 Comparison between calculated and experimental values for the concentration of Al, V and Fe in the a and 0 phase in Ti-6At-4V alloys.

Figure 10.40 (>>mparison between calculated and experimentally observed % of austenite in digtlex stainless steels. (Data fiom Longbottom and Hayes (1991) represent dual phase steels.). 

Figure 10.43 Comparison between calculated and experimental values (Wisell 1991) for the concen-tration of Cr, Mo, W, V and Fe in (a) the MC, (b) the M C and (c) MjC phases of high-speed steels.

---