Читать книгу Encyclopedia of Glass Science, Technology, History, and Culture - Группа авторов - Страница 287

The isostaticity condition is satisfied in three dimensions for tetrahedral structural units (V = 4) with two units sharing every vertex (C = 2) as is the case for SiO₂, GeO₂, and BeF₂, which are known as excellent glass formers. The isostatic condition is also satisfied for two‐dimensional networks made of corner‐sharing triangles. This is often considered to be the reason why B₂O₃ is a strong glass former.

An interesting application of the isostatic boundary concept is identification of limiting isostatic composition for glass formation. Consider the example of nitridation of alkali‐silicate glasses. In silicon oxynitride glasses, nitrogen substitutes for oxygen forming two kinds of vertices: oxygen vertices with C = 2 and nitrogen vertices with C = 3. Adding nitrogen to silica (for which f is 0) makes f negative. This suggests that nitridation of silica will be difficult. However, addition of alkali creates non‐bridging oxygens (with C = 1). Thus, nitrogen can be added to alkali‐silicates while keeping f non‐negative. In fact one can calculate the maximum amount of nitrogen that can be incorporated into an alkali‐silicate glass as a function of the alkali content. Consider glass formation in an alkali silicon oxynitride system of the general composition x Na₂O·(1 − x)[SiO_(2−y) N_(2y/3)]. Note that 0 ≤ y ≤ 2 and 0 ≤ x ≤ 1. This system has three types of vertices: non‐bridging oxygens with C = 1, bridging oxygens with C = 2, and bridging nitrogens with C = 3. The isostatic condition gives the limiting solubility of nitrogen, y_max = 3x/(1 − x). For y > y_max, f becomes negative. Whereas systematic investigations of nitridation of alkali‐silicate glasses are not available, it is known that nitridation becomes easier upon increasing the alkali content [16].

Another example is provided by binary alkali‐tellurite systems. Pure TeO₂ with trigonal bipyramid structural units is over‐constrained and does not form glass. Glass formation improves upon addition of alkali oxide because of formation of non‐bridging oxygens, thereby increasing f and thus making it possible to form glasses when sufficient alkali oxide is added. Narayanan and Zwanziger [17] have rationalized in this way glass formation in alkali‐tellurite systems.