Phase fraction diagram

Numerous thermodynamic calculations of phase equilibria in the Si-C-N system have been published but only few experimental investigations are documented. Calculated isothermal sections [117, 234-237], isopleths [117, 234], different types of potential phase diagrams [234,235,238-244] and phase fraction diagrams [234, 239] were presented. Additional information is provided by [245]. No or very low solid solubilities between SiC and Si3N4 could be detected by X-ray diffraction up to 2500 K [246, 247]. Also the nitrogen solubility in SiC is low. For more experimental information see [248, 249]. 

Fig. 19. Calculated phase fraction diagrams in the Si-C-N system for PHMS-derived ceramics (C Si < 1) [234, 237]...

The phase fraction diagram for the high temperature stable PHBS(p)-derived ceramic (composition indicated in Fig. 25) was calculated and is shown in Fig. 27. 

Fig. 27. Phase fraction diagram for Si-B-C-N ceramics derived from PHBS(p) precursor [273]...

In a first phase, the diagram for processing oil fractions features the addition of complementary units that enable the production of unleaded gasoline such as ... 

Figures 10.8S(a,b) show phase fraction plots for inclusions 1 and 2 in Table 10.4. These are plotted in such a way as to show the cumulative amount of all phases as well as their individual amounts. A quasi-ternary diagram was then plotted for an ideal inclusion with a fixed level of Al2O3=20.4wt% and MgO = 8.2wt% (Fig. 10.86). From this it can be seen that a slight increase in Si02 reduces the liquidus...

Figure C.6 Free energy vs. mole fraction diagram, showing a shift of chemical potentials with pressure in the (3 phase.

Binary liquid-liquid equilibria are usually represented as temperature-vol-ume fraction diagrams. These diagrams give the mutual solubilities in the two coexisting liquid phases, as functions of temperature. Figure 2F-3 illustrates six types of phase behavior that have been observed in binary LLE. A horizontal line intersects the phase boundary curve at two points which give the compositions of the two phases in equilibrium at the corresponding temperature. 

The specified variables are the final temperature and pressure, T2 and P2- The dependent variables are the vapor fraction, t /, the liquid and vapor compositions, X, and the total enthalpy of the two phases, /Z2 + H, and the heat duty, Q. The term isothermal should not be interpreted to imply that the transition from initial conditions to final conditions is at constant temperature is, in general, different from T. It simply means that within the flash drum the temperature, as well as the pressure, is fixed. The heat duty required to bring about the final conditions is equal to the enthalpy change, Q = (Hj + 2) - i> where is the enthalpy at and P,. Isothermal flash conditions may be represented by a point ( 2, P2) on tbs phase envelope diagram. It is clearly possible that this point may fall either within the phase envelope or outside it, in which case the system would be all vapor or all liquid (or dense phase). A flash drum operating at such conditions would have a single product and no phase separation would take place. In a single-phase situation, the dependent variables are the properties of the vapor or liquid product. The liquid or vapor composition is, of course, identical to the feed or overall composition, Z,. Note that any set of temperature and pressure specifications is feasible. 

Figure 7.31. An example of a two-dimensional LC/MS analysis of yeast proteome using cation-exchange (SCX) for fractionation and reversed-phase LC/MS/MS of the collected fractions. Diagram courtesy of Andy Alpert of Poly LC from data originated by S. Gygi and Junmin Peng of Harvard Medical School.

Figure 15.4 shows a phase equilibrium diagram for a somewhat more complex case when an azeotrope is formed. At the azeotropic composition, the mole fraction of both components is identical (for equilibrium) in both the vapor and the liquid, and the dew point and bubble point tempera-... 

Step 3. Apply the lever rule to the equilateral triangular phase equilibrium diagram. Letting x, be the mass fraction of species i in the raffinate stream j and y, the mass fraction of species / in extract stream /. 

INTERMETALLIC PHASES AND COMPOUNDS 3.3.1 Potential versus mole fraction diagrams... 

Figure /. Equilibrium volume phase transition diagram for the gel The polymer volume fraction (f> is represented as a function of Flory s interaction parameterX-...

Figure 3 presents the Phase Volume Diagram for the oil/chemical slug/formation brine combination used in the flow experiments discussed above. In the upper part of the diagram we plot phase volume fractions observed at equilibrium as a function of the amount of chemical slug replaced by formation brine in each sample tube. The points plotted at X = 0,5,10,15,20,30,40,50 and 60 show phase volume fractions observed for the oil/chemical slug/formation brine set of overall compositions 30/70/0, 30/65/5, 30/60/10, etc. 

The addition of xanthan gum polymer did not affect phase behavior. This was evidenced by the close match between the volume fraction diagrams for a surfactant solution (4% sodium dihexyl sulfosuccinate, 8% IPA) with 500 mg/1 xanthan gum polymer and without polymer as shown in Figure 2. As shown in Figure 4, the viscosity of the surfactant solution is increased by the addition of polymer. All samples with polymer were observed to coalesce to microemulsions in less than 20 hours, which is still fast enough to be acceptable based upon subsequent column floods. 

Figure 2.5. Generalized phase continuity diagram, of polymer blends, as controlled by viscosity, 17, and weight fraction, w, for polymers 1 and 2. At equal viscosities and weight fractions (marked point), or along idealized curve, some aspects of dual phase continuity may be initiated.

Figure 1 shows the gas phase fractional abundance of certain species included in the model as a function of time. It can be seen from the diagram that there is a very steep fall in the abundances as accretion dominates. The effect is exaggerated over that determined for quiescent clouds because, in a free-fall collapse, the density rises rapidly in the latter stages, and the accretion timescale, proportional to 1/n, becomes very short. Magnetic fields and turbulence caused by rotation may slow the collapse. We have modelled cases in which the collapse is slowed by factors of 10 and 100 and found no qualitative difference from the results presented here. As already mentioned, the inclusion of accretion means that... 

Illian et al. [81] observed a closed loop re-entrant N-SmA phase boundary in a temperature-mole fraction diagram at atmospheric pressure. At higher pressures the SmA region of existence decreases until at... 

Illian et al. [82] studied the pressure effect on the phase transition behavior of binary mixtures of terminally polar and nonpolar components which exhibit induced SmA phases. The re-entrant N phase is stabilized by increasing pressure and at about 101 MPa the SmA-re-entrant N phase boundary meets the N-SmA one. At higher pressures a nematic gap appears and finally the SmA phase on the polar side of the temperature-mole fraction diagram (175 MPa) disappears. 

One of the first experimental phase equilibrium diagrams was obtained by Miller et al. [14] for solutions of PEG in dimethylformamide (DMF). This diagram is shown in Fig. 2.7, which indicates that the transition from the narrow concentration corridor to the broad two-phase region, where the concentration of polymer in the isotropic phase is very low and the concentration of the anisotropic phase is within the limits of 0.70-0.85 vol. fractions of polymer, takes place at a temperature below 15°C. With an increase in the temperature (correspondingly, with a decrease in %) beyond 15 C, the coexisting isotropic and anisotropic phases differ relatively little with respect to the concentration of polymer, i.e., V2 /v2 is close to 1.5, as Flory theoretically calculated. It has not... 

Fig. 9. The diagram calculated by pressing the phase fraction button. The curves show the amount of phase as function of the temperature at a given composition the mole-fraction of copper is set to 0.71.

Figure 3.8. Phase state diagrams of PVC - n - oxyethylene-dimetacrylate blends. Numbers on curves correspond to n value. 92 is the volume fraction of...

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