Curve liquid-solid

In the two-phase region of ice and liquid water, the border line is inclined to the ordinate. The curve has a negative slope. This is an exceptional behavior that is exhibited by water, and a few other substances only, e.g., glass ceramics [2] and organic polymers. 

For most other compounds the solid - liquid curve has a positive slope. A consequence of this negative slope is the exceptional behavior of water, i.e., ice has a smaller density than liquid water, so ice swims on water. This is highly important for the development of life. If ice would be heavier than liquid water, ice would sink down, making the oceans full of ice. 

The phase diagram of water as shown in Fig. 7.1 is not complete. It has been found out that at higher pressures there are further modifications of ice besides of 

In the contrary to the critical point in the case of the liquid - gas equilibrium, in the case of the solid - liquid equilibrium a critical point has never been observed at all. It is suspected, however, that there should be a critical point also for the solid - liquid equilibrium. At very high pressures, it is believed that the matter will be converted into a metallic state. 

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At p = 140 MPa (Figure 14.20d) the (liquid + liquid) equilibrium region has moved to the acetonitrile side of the eutectic. Increasing the pressure further decreases the (liquid + liquid) region, until at p= 175 MPa (Figure 14.20e), the (liquid + liquid) region has disappeared under a (solid + liquid) curve that shows significant positive deviations from ideal solution behavior. 

This triple point is the point of intersection of the three univariant systems solid— vapour (curve FD), liquid— vapour (curve DE), solid— liquid (curve DI). The values of the vapour pressures of solid and of liquid violet phosphorus are given in the tables on pp. 60 and 61. The curve DE will end abruptly at the critical point of liquid phosphorus. The critical temperature was found by W. A. Wahl to lie at 695° C. and from the course of the vapour-pressure curve, Smits and Bokhorst have calculated that at this temperature the pressure (critical pressure) would be 82 2 atm. According to Marckwald and Helmholz, the critical temperature is 720 6 . 

Figure 12.11 shows that lowering the vapor pressure of the solution shifts the solid-liquid curve to the left. Consequently, this line intersects the horizontal line at a temperature lower than the freezing point of water. The freezing point depression (ATf) is defined as the freezing point of the pure solvent (TJ) minus the freezing point of the solution (Tf) ... 

However, AF depends strongly on T andp because depends strongly on T and p. The slope of the liquid-gas curve is small compared with that of the solid-liquid curve ... 

In most substances the solid-liquid curve has a positive slope too, for the same reason given above. Water is anomalous as can be seen from Fig. 1.17 the slope of the solid-liquid curve is negative. This means that AH and AV have different signs. This is an important observation. We shall discuss its molecular implications in the next chapter. 

Let us now turn to the ice-water equilibrium. The negative slope of the solid-liquid curve means that the melting point of... 

This function is represented by a coexistence curve in the phase diagram. Figure 1.4 shows a solid-vapor curve, a solid-liquid curve, and a liquid-vapor curve. The equilibrium pressure when a liquid phase or a solid phase is equilibrated with a vapor (gas) phase is called the vapor pressure of that phase. Figure 5.2 shows the equilibrium vapor pressure of liquid water as a function of temperature. 

This gives the rigorously correct slope of the liquid-solid curve at 32 F on a P-T diagram. Here we use P instead of p because neither phase is a gas, so this is not a vapor pressure. If we further assume that the solid-liquid curve is a straight line, which is equivalent to assuming that Ah/ T Av) is a constant over the region of interest, then we can estimate the pressure at 22°C = —7.6°F by... 

Corrosion protection of metals can take many fonns, one of which is passivation. As mentioned above, passivation is the fonnation of a thin protective film (most commonly oxide or hydrated oxide) on a metallic surface. Certain metals that are prone to passivation will fonn a thin oxide film that displaces the electrode potential of the metal by +0.5-2.0 V. The film severely hinders the difflision rate of metal ions from the electrode to tire solid-gas or solid-liquid interface, thus providing corrosion resistance. This decreased corrosion rate is best illustrated by anodic polarization curves, which are constructed by measuring the net current from an electrode into solution (the corrosion current) under an applied voltage. For passivable metals, the current will increase steadily with increasing voltage in the so-called active region until the passivating film fonns, at which point the current will rapidly decrease. This behaviour is characteristic of metals that are susceptible to passivation. 

To understand the conditions which control sublimation, it is necessary to study the solid - liquid - vapour equilibria. In Fig. 1,19, 1 (compare Fig. 1,10, 1) the curve T IF is the vapour pressure curve of the liquid (i.e., it represents the conditions of equilibrium, temperature and pressure, for a system of liquid and vapour), and TS is the vapour pressure curve of the solid (i.e., the conditions under which the vapour and solid are in equili-hrium). The two curves intersect at T at this point, known as the triple point, solid, liquid and vapour coexist. The curve TV represents the... 

S. Coriell, R. Boisvert, R. Rehm, R. Sekerka. Lateral solute segregation during unidirectional solidification of a binary alloy with a curved solid-liquid interface. J Cryst Growth 54 167, 1981. 

Similar results, to the Fe-Zn system were obtained in the Ti,j,-Al(,) and Ti(j)-Al, ) system where, in the solid-liquid couples some of the expected surface layer phases were not formed, whereas in the solid-vapour system it was possible to obtain all the phases and predict from the AG -concen-tration curves the compositions at the different layer phase boundaries. 

Systems in which the saturated vapor pressure curve cuts a three-phase line of liquid + liquid + gas at a second quaternary point (solid + liquid + liquid + gas). Such systems have the first (or normal) quaternary point (solid + solid + liquid + gas) at lower temperatures and pressures (Fig. 13). Examples, ethane +... 

Solid gas boundary curves, 87 Solid liquid boundary curves, 87 Solubility, in a compressed gas, 92 of a solid in a liquid, 86 of quartz, 99... 

Figure 8.21 gives the ideal solution prediction equation (8.36) of the effect of pressure on the (solid + liquid) phase diagram for. yiC6H6 + xj 1,4-C6H4(CH3)2. The curves for p — OA MPa are the same as those shown in Figure 8.20. As... 

FIGURE 8.10 The liquid-vapor boundary curve is a plot of the vapor pressure of the liquid (in this case, water) as a function of temperature. The liquid and its vapor are in equilibrium at each point on the curve. At each point on the solid liquid boundary curve (for which the slope is slightly exaggerated), the solid and liquid are in equilibrium. 

The differences between the two curves can be explained by the sulfonate (the most adsorbed surfactant) monomer concentrations at equilibrium, which were reached in both cases, considering the amounts of surfactants, liquid and solid present. Figure 4 shows a distinct evolution of monomer concentrations for the two solid/liquid ratios considered. 

Fig. 3 Liquid-liquid demixing curves (dashed lines denoted by T ) and liquid-solid transition curves (solid lines denoted by Tm) of polymer solutions with variable energy parameter sets [denoted by T(EV/EC, B/Ec)]. The solution system is made of 32-mers in a 32-sized cubic box. a Theoretical curves b simulation results in the optimized approach [14]...

Similarly to classical PTC reaction conditions, under solid-liquid PTC conditions with use of microwaves the role of catalyst is very important. On several occasions it has been found that in the absence of a catalyst the reaction proceeds very slowly or not at all. The need to use a phase-transfer catalyst implies also the application of at least one liquid component (i.e. the electrophilic reagent or solvent). It has been shown [9] that ion-pair exchange between the catalyst and nucleophilic anions proceeds efficiently only in the presence of a liquid phase. During investigation of the formation of tetrabutylammonium benzoate from potassium benzoate and tetrabu-tylammonium bromide, and the thermal effects related to it under the action of microwave irradiation, it was shown that potassium benzoate did not absorb micro-waves significantly (Fig. 5.1, curves a and b). Even in the presence of tetrabutylammonium bromide (TBAB) the temperature increase for solid potassium benzoate... 

Figure 26 shows the ternary phase diagrams (solubility isotherms) for three types of solid solution. The solubilities of the pure enantiomers are equal to SA, and the solid-liquid equilibria are represented by the curves ArA. The point r represents the equilibrium for the pseudoracemate, R, whose solubility is equal to 2Sd. In Fig. 26a the pseudoracemate has the same solubility as the enantiomers, that is, 2Sd = SA, and the solubility curve AA is a straight line parallel to the base of the triangle. In Figs. 26b and c, the solid solutions including the pseudoracemate are, respectively, more and less soluble than the enantiomers. 

The purpose of this chapter is to introduce the effect of surfaces and interfaces on the thermodynamics of materials. While interface is a general term used for solid-solid, solid-liquid, liquid-liquid, solid-gas and liquid-gas boundaries, surface is the term normally used for the two latter types of phase boundary. The thermodynamic theory of interfaces between isotropic phases were first formulated by Gibbs [1], The treatment of such systems is based on the definition of an isotropic surface tension, cr, which is an excess surface stress per unit surface area. The Gibbs surface model for fluid surfaces is presented in Section 6.1 along with the derivation of the equilibrium conditions for curved interfaces, the Laplace equation. 

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