From melts phase equilibria

The interpretation of the viscosity-temperature behavior of these complex systems is difficult since many aspects of the melt conditions must be simultaneously considered. These include the chemical composition of the melt to establish the nature of the polymeric network including the amphoteric behavior of species like AI2O3 and Fe2O3> as well as the acid/base behavior of mixed valence constituents such as iron oxides, and the formation of immiscible liquid phases sometimes associated with the existence of several types of stable anions of significantly different size or charge in the system the nature of the container since some of it may dissolve and affect the composition of the melt the existence of a solid phase to establish the effect on the composition of the residual liquid phase (the solid phase may not be the one expected from related phase equilibrium studies) the relative amount of the liquid and solid phases to establish the composition of the liquid phase (this composition changes as the solid crystallizes out of... 

Three different approaches have been used. Firstly, the distribution of the major elements between mineral phases and a coexisting silicate melt may be calculated from experimental phase equilibrium data using regression techniques. Secondly, mineral-melt equilibria can be determined from mineral-melt distribution coefficients. A third, less empirical and more complex, approach is to use equilibrium thermodynamic models for magmatic systems. These require a thermodynamically valid mixing model for the liquid and an internally consistent set of solid-liquid thermodiemical data. 

The fusion free energy of both chain ends can be calculated from the equilibrium condition Z = 1 in Eq. 4 by setting the chain length r = 2 in the melt phase. The additional contribution is thus given by... 

Let us call the melt phase a and the solid phase with complete immiscibility of components y. P is constant and fluids are absent. The Gibbs free energy relationships at the various T for the two phases at equilibrium are those shown in figure 7.2, with T decreasing downward from Ty to Tg. The G-X relationships observed at the various T are then translated into a T-X stability diagram in the lower part of the figure. 

Figure 9,13 Relationship between activity of H2O in gaseous phase and molar amount of H2O in melt at equilibrium. Experimental data from Burnham and Davis (1974) ( ) Fraser (1975b) ( ) Kurkjian and Russel (1958) ( ). Reprinted from B. J. Wood and D. G. Fraser, Elementary Thermodynamics for Geologists, 1976, by permission of Oxford University Press.

During mantle partial melting, the partition coefficients of Th, Pa, and Ra are different from that of U. Assuming the melt and the mantle residue as a whole maintains secular equilibrium, if the melting process is slow, there is chemical equilibrium between the phases, which means each phase (such as the melt phase) is out of secular equilibrium because of different partition coefficients (McKenzie, 1985). 

Frequently, growth of crystals from melt involves more than one component, such as impurities, intentionally added dopants, etc., in addition to the major component. In these cases, it is essential to know the distribution of the second component between the growing crystal and the melt. This distribution occurs according to the phase diagram relating the equilibrium solubilities of the second component (impurity) in the liquid and the solid phases. 

Comparison between the various condis crystals shows that large variations in the amount of conformational disorder and motion is possible even in similar molecules. The tritriacontane in the condis state possesses about 3 gauche conformations per 100 carbon atoms. For cyclodocosane which is in its transition behavior similar to the tetracosane of Fig. 23, one estimates about 16 gauche conformations per 100 carbon atoms, and for the high pressure phase of polyethylene (see Sect. 5.3.2), one expects 37 gauche conformations per 100 carbon atoms 171). The concentration of gauche conformations in cyclodocosane and polyethylene condis crystals are close to the equilibrium concentration in the melt, while the linear short chain paraffin condis crystals are still far from the conformational equilibrium of the melt. 

In the first section, up to Uhlmann s paper, we arc concerned with polymer melts in equilibrium. In dilute solution, the dominant restriction on randomness, apart from the very fact that the polymer molecule is a chain, is self-exclusion, and Paul Flory taught us how to cope with that many years ago. In the interior (and I emphasize interior) of the pure amorphous phase, mutual exclusion has a large effect on the total entropy, but its effect on molecular conformations is the relatively minor one of virtually cancelling the effects of self-exclusion. That knowledge we also owe to Flory. Hence a limited number of parameters suffice both to describe and explain the conformations in this case. Uhlmann s paper dismisses for us the aberrant nodular structures which have been proposed there only remains to ask how in certain circumstances the appearance of nodular structure can be produced. 

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