Crystallization Gibbs free energy

As in the qualitative discussion above, let 7 be the Gibbs free energy per unit area of the interface between the crystal and the surrounding hquid. This is undoubtedly different for the edges of the plate than for its faces, but we... 

The change in Gibbs free energy, AG, in the formation of FCC and ECC, depending on the drawing ratio of the melt ft and the crystallization temperature, is given by14 ... 

Fig. 6. Gibbs free energy vs. degree of crystallinity a, / 1 0.4,2 0.5 and 3 0.6. Crystallization temperature...

Which component of Gibbs free energy (entropy or enthalpy) drives crystal formation in a polymer How ... 

The papers of Wagner and Schottky contained the first statistical treatment of defect-containing crystals. The point defects were assumed to form an ideal solution in the sense that they are supposed not to interact with each other. The equilibrium number of intrinsic point defects was found by minimizing the Gibbs free energy with respect to the numbers of defects at constant pressure, temperature, and chemical composition. The equilibrium between the crystal of a binary compound and its components was recognized to be a statistical one instead of being uniquely fixed. 

In these equations gv is the change in Gibbs free energy on taking one atom from a normal lattice site to the surface of the crystal and (gt + gv) the change when an atom is taken from a normal lattice site to an interstitial site, both at constant temperature and pressure. cr denotes a site fraction of species r on its sublattice, and is the chemical potential of a normal lattice ion in the defect-free crystal. 

G is the total Gibbs free energy of the crystal. The condition for equilibrium is that the Gibbs free energy is a minimum,... 

In considering the equilibrium of the crystal with a second phase the Gibbs chemical potentials are required and we therefore express these in terms of the defect chemical potentials so far discussed. The Gibbs free energy of the system is given by... 

We consider first the activity coefficients. The contribution of the defects, N cation vacancies and N divalent ions, to the Gibbs free energy of the doped crystal is... 

Table 2.4 Crystal Ionic Radii and Standard Molar Gibbs Free Energies of Flydration of Ions... 

The capability of evaluating with sufficient accuracy the Gibbs free energy of a silicate melt in various P-T-Xconditions has obvious petrogenetic implications, besides those already outlined. For instance, the P-T loci of equilibrium of a given crystal with the melt can be determined with good approximation. Let us consider, for example, the equilibrium... 

The Gibbs free energy of phase y is represented by a straight line connecting the standard state potentials of the two end-members in the mixture. Because we use the term mixture, it is evident that the standard state of both end-members is the same and is that of pure component. The two components are totally immiscible in any proportion and the aggregate is a mechanical mixture of the two components crystallized in form y ... 

At Ty, the Gibbs free energy of phase a (i.e., melt) at all compositions is lower than that of mechanical mixture y + y" phase a is then stable over the whole compositional range. At T2, the chemical potential of component 1 in a is identical to the chemical potential of the same component in y . Moreover, the equahty condition is reached at the standard state condition of the pure component T2 is thus the temperature of incipient crystallization of y. At T, the Gibbs free energy of a intersects mechanical mixture y + y" on the component 1-rich side of the diagram and touches it at the condition of pure component 2. Applying the prin-... 

At the melt is absent and 7 and 7" coexist stably in a mechanical mixture of bulk composition C. The crystallization process in a closed system is thus completely defined at all T (and P) conditions by the Gibbs free energy properties of the various phases that may form in the compositional field of interest. 

Figure 7J Gibbs free energy curves and T-X phase stability relations between a phase with complete miscibility of components (silicate melt L) and a binary solid mixture with partial miscibility of components (crystals ]8). 

Figure 7,8 Gibbs free energy curves and T-X phase relations for an intermediate compound (C), totally immiscible with pure components. Column 1 Gibbs free energy relations leading to formation of two eutectic minima separated by a thermal barrier. Column 2 energy relations of a peritectic reaction (incongruent melting). To facilitate interpretation of phase stability fields, pure crystals of components 1 and 2 coexisting with crystals C are labeled y and y", respectively, in T-X diagrams same notation identifies mechanical mixtures 2-C and C-1 in G-X plots.

All of our analysis of the Cu crystal structure has been based on the reasonable idea that the crystal structure with the lowest energy is the structure preferred by nature. This idea is correct, but we need to be careful about how we define a materials energy to make it precise. To be precise, the preferred crystal structure is the one with the lowest Gibbs free energy, G G(P, T). The Gibbs free... 

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