Stressed mobile components

Chemists and physicists must always formulate correctly the constraints which crystal structure and symmetry impose on their thermodynamic derivations. Gibbs encountered this problem when he constructed the component chemical potentials of non-hydrostatically stressed crystals. He distinguished between mobile and immobile components of a solid. The conceptual difficulties became critical when, following the classical paper of Wagner and Schottky on ordered mixed phases as discussed in chapter 1, chemical potentials of statistically relevant SE s of the crystal lattice were introduced. As with the definition of chemical potentials of ions in electrolytes, it turned out that not all the mathematical operations (9G/9n.) could be performed for SE s of kind i without violating the structural conditions of the crystal lattice. The origin of this difficulty lies in the fact that lattice sites are not the analogue of chemical species (components). 

Figure 21 Changes in component ratio for metallocene (filled symbols) and Ziegler films (open symbols) (A) Mobile, (B) intermediate and (C) rigid amorphous components. The shaded area indicates the plateau stress region.

Sternstein and Ongchin (28) considered that if cavitation occurs in crazes the criterion for crazing initiation should include the dilative stress component. They proposed the criterion to fit the experimental data for surface craze initiation in PMMA when the polymer is subjected to biaxial tension. The segmental mobility of the polymer will increase due to dilative stresses, thus provoking cavitation and the orientation of molecular segments along the maximum stress direction. 

For a prescribed magnitude of c, the magnitude of s is thus proportional to , the difference in the components mobilities, to N, their resistance to motion, and to the geometrical factor. For most values of A, Li is negligible and s becomes proportional to 1/A the larger A, the less steep the concentration gradients that tend to drive motion, and hence the smaller the stress fluctuations that are produced. But when A is of the order of 4L , the two parts of the denominator are equal, and if A diminishes below this value, the factor as a whole does not increase so strongly. 

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