Thermodynamics of Crystallization

Thermodynamics of Crystallization of Flexible-Chain Polymers Under Conditions of Molecular Orientation. 217... 

Flory, P. J. (1949). Thermodynamics of crystallization in high polymers. IV. A theory of crystalline states and fusion in polymers, copolymers, and their mixtures with diluents. 

In the planetary geochemical literature, there are also extensive discussions about the thermodynamics of crystallizing melts. Sophisticated programs have been developed to model the compositions of the minerals that crystallize from a cooling liquid as well as changes in the residual melt. 

The results of the discussion on the phenomenological thermodynamics of crystals can be summarized as follows. One can define chemical potentials, /jk, for components k (Eqn. (2.4)), for building units (Eqn. (2.11)), and for structure elements (Eqn, (2.31)). The lattice construction requires the introduction of structural units , which are the vacancies V,. Electroneutrality in a crystal composed of charged SE s requires the introduction of the electrical unit, e. The composition of an n component crystal is fixed by n- 1) independent mole fractions, Nk, of chemical components. (n-1) is also the number of conditions for the definition of the component potentials juk, as seen from Eqn. (2.4). For building units, we have (n — 1) independent composition variables and n-(K- 1) equilibria between sublattices x, so that the number of conditions is n-K-1, as required by the definition of the building element potential uk(Xy For structure elements, the actual number of constraints is larger than the number of constraints required by Eqn. (2.18), which defines nk(x.y This circumstance is responsible for the introduction of the concept of virtual chemical potentials of SE s. 

Flory, P.J. (1947) Thermodynamics of crystallization in high polymers. I. Crystallization induced by stretching, J. Chem. Phys. 15(6), 397-408... 

Thermodynamics of Crystals by D. C. Wallace, Dover Publications, Inc., Mineola New York, 1998. Wallace s chaps. 2-A give a thorough discussion of the material that has been sketched in the present chapter. 

Wallace DC (1972) Thermodynamics of Crystals. John Wiley and Sons, New York. 

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