Читать книгу Encyclopedia of Glass Science, Technology, History, and Culture - Группа авторов - Страница 289

When f < 0, a TD network cannot exist. The excess strain energy can, however, be accommodated in a variety of ways that increase the value of f toward f = 0. One possibility is that the network crystallizes, thereby reducing the number of independent constraints by converting some into dependent ones. A second possibility is that new structural units form by breaking weaker constraints. When constraints are broken within structural units, the polyhedra become distorted. The existence of an extended TD network of distorted AB_V polyhedral units (where the BAB angular constraint is broken at the A site but the AB length constraint remains intact) is demonstrated by the example of glass formation in the CaO–Al₂O₃ binary system. Since neither component is a network former, glass formation in this binary system is poor. If the presence of CaO stabilizes four‐coordinated aluminum ions, Al^IV, with two AlO₄ tetrahedra sharing an oxygen vertex (as in silica), then the composition having 50% CaO should be a good glass former. However, experimental results show that glasses in this system form only in a small composition range at about 65% CaO [18]. It is possible to rationalize this observation with the constraint theory. Recently, Jahn and Madden [19] have reported from MD simulations that at 2350 K aluminum is present in Al₂O₃ melt in several different coordination states; about 54% Al^IV, 41% Al^V, 4% Al^VI, and 1% Al^III. Further, it was observed that some of the oxygens are present as O^III, oxygen coordinated by three aluminums (also known as oxygen triclusters), and the remaining as normal bridging oxygens, O^II. One can use this structural information and PCT to rationalize why the 65% CaO composition forms best glasses in this system. First, it can be assumed that the structures of Ca‐aluminate and alumina melts are similar except for the incorporation into the network of O from CaO. Next, one can simplify the structural information by neglecting the concentrations of Al^VI and Al^III. Let z be the fraction of Al^IV and (1 − z) that of Al^V. Then, for the composition x CaO·(1 − x)Al₂O₃, one shows with PCT that the degrees of freedom, f, is given by

(8)

When f = 0, Eq. (8) gives the following expression for the isostatic composition x* [x(f = 0)] in terms of z:

(9)

For z = 0.54, Eq. (9) gives x* = 0.65, the same value as for the best glass‐forming composition [18].