Melting line

TABLE 2-357 Thermodynamic Properties of Water Substance along the Melting Line... 

Line db in Figure 8.1 represents the equilibrium melting line for C02. Note that the equilibrium pressure is very nearly a linear function of T in the (p, T) range shown in this portion of the graph, and that the slope of the line, (d/ /d7 )s ], is positive and very steep, with a magnitude of approximately 5 MPa-K-1. These observations can be explained using the Clapeyron equation. For the process... 

The sign of the slope of the melting line is governed by the signs of the two quantities, Afus5m and Afus Vm. Since for most substances AfusSm > 0 for solid... 

Figure 8.9 is the phase diagram for Sn, a system that shows (solid + solid) phase transitions." Solid II is the form of tin stable at ambient conditions, and it is the shiny, metallic element that we are used to observing. Line ab is the melting line for solid II. Points on this line represent the values of p and T for which... 

At high pressures, solid II can be converted (slowly) to solid III. Solid III has a body-centered cubic crystal structure. Line bd is the equilibrium line between solid II and solid III, while line be is the melting line for solid III.P A triple point is present between solid II, solid III, and liquid at point b. Two other triple points are present in this system, but they are at too low a pressure to show on the phase diagram. One involves solid II, liquid, and vapor while the other has solid I, solid II, and vapor in equilibrium. 

Figure 5.12 (a) The p-T phase diagram of Si. The melting lines for the low-pressure polymorph of Si and the liquid-liquid phase transition are calculated by using the two-state model and the parameters given in Table 5.2. (b) Iso-concentration lines for species B in the p-T plane, (c)) The fraction of species B as a function of temperature at constant pressure p = 2 GPa. 

We are now able to use this model for the Gibbs energy of the liquid to calculate the melting line for four-coordinated Si by using the Clapeyron equation (eq. 2.10) ... 

The densities of liquid and solid helium are different thus, AVm of Equation (8.9) is not zero. Yet the horizontal slope of the melting line of the phase diagram shows that dP/dT is zero near 0 K. Hence, it is clear that A5m of Equation (8.9) must be zero at 0 K, that is, that 5m,ok is zero for liquid He as well as for solid He. 

The limiting factor in the temperature effect is the slope of the melting line. 

Incomplete miscibility at room temperature or above is rare with non-polar liquids. Only Snl4, molten phosphorus and molten sulphur, all with a very high specific cohesion, are exceptions to this statement. With increasing cohesion of the second substance, for example of sulphur with benzene, naphthalene and anthracene, respectively, the critical solubility temperature falls below the melting line but the partial miscibility is still present in the metastable state (Kruyt, Kete-laar and Jibben). ... 

Figure 11.15. Neglecting the existence of a high-melting line compound (AS) in the phase equilibria calculations (left) can result in a largely erroneous liquidus or solidus in an extrapolated phase diagram (right).

Figure 7 (a) Phase diagram of carbon. (Reproduced by permission ofElsevier from F.P. Bundy, P/ty /ca, 1989, A156,169) (b) Aportion of the phase diagram including the melting line of pure Ni, the Ni-graphite eutectic, and the diamond synthesis zone. (Reproduced by permission of Decker from F.P. Bimdy. )... 

B. L. Holian and D. J. Evans, Shear Viscosities away from the Melting Line, J. Chem. Phys., 78 (1983), 5147-5150. 

It is still uncertain whether or not the solid-hquid equihbrium Hne terminates at a critical point. Munster has recently given theoretical reasons for behoving that all first-order transitions possess a critical point, but this conclusion is contrary to that reached by Domb, j"j whose theory predicts the absence of a solid-fluid critical point. The experimental work of Simon and his co-workers on the melting line of hehum shows no evidence for a critical point up to a pressure of 9,000 atm. and a temperature of 56° K. Alder and Jura have, however, made calculations which suggest that a soHd-fluid critical point should... 

The silicon melting line has been determined using a coexistence simulation292 and is able to predict a decrease in Tm with increase in pressure, consistent with experiment. Vega et al.2S9 carry out Gibbs-Duhem integration to determine the coexistence line of water, and the change in the coexistence line... 

The values in these tables were generated from the NIST REFPROP software (Lemmon, E.W., McLinden, M.O., and Huber, M.L., NIST Standard Reference Database 23 Reference Fluid Thermodynamic and Transport Properties—REFPROP, National Institute of Standards and Technology, Standard Reference Data Program, Gaithersburg, Md., 2002, Version 7.1). The primary source for the thermodynamic properties is Buecker, D., and Wagner, W, A Reference Equation of State forthe Thermodynamic Properties of Ethane for Temperatures from the Melting Line to 675 K and Pressures up to 900 MPa, J. Phys. Chem. Ref. Data, 35(1) 205-206, 2006. The source for viscosity and thermal conductivity is Friend, D.G., Ingham, H., and Ely, J.E, Thermophysical Properties of Ethane, /. Phys. Chem. R. Data, 35(l) 205-266, 2006. 

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