The central role of broken bond-bending constraints in promoting glass formation in the oxides

Telluria (TeO sub 2) and silica (SiO sub 2) consist of networks in which the cations (Te, Si) are fourfold-coordinated and the anion (O) is twofold-coordinated. Trigonal bipyramid Te(O sub 1/2) sub 4 units (1) with a lone pair in the equatorial plane and tetrahedral Si(O sub 1/2) sub 4 units form the building blocks of respective crystalline (and glassy) networks (Fig. 1, A and C). In both cases bridging oxygen sites serve as linkages beween building blocks. Remarkably, although silica is the archetypal glass former (2), telluria, which has the same average coordination number, is the antithesis (3) of silica. However, alkali-oxide alloying in telluria produces nonbridging oxygen (NBO) and pronouncedly increases the glass-forming tendency (GFT) until, at x ==0.20, (Na sub 2O) sub x(TeO sub 2) sub 1-x melts display (3) a GFT that parallels that of silica.

In this report we show that there is a common physical origin for this behavior in both silica and telluria that follows directly from Phillips constraint theory (4). Both SiO sub 2 melt and alkali tellurate melt near x = 0.20 are optimally constrained because the bond-angle constraint associated with bridging oxygen in the former, and with NBO in the latter, is broken. These considerations promote formation of strain-free polymerized networks and enhance the GFT at the stiffness, or rigidity percolation, threshold (4,5). These basic ideas provide a sound basis for understanding the microscopic origin of the unusual glass-forming tendency in silica, which has not been without controversies (2). Furthermore, these ideas also furnish a basis for understanding the generic role of alkali modifier atoms in enhancing the GFT in a variety of oxides. In this work we use an atomic-scale probe of rigidity, sup 125-Te Lamb-Mossbauer factors, to establish the rigidity percolation threshold in the tellurate glasses.

Fifteen years ago, Phillips (4) asserted that a network constrained by bondstretching (alpha) and bond-bending (Beta) constraints sits at a mechanically critical point when the constraints per atom (n sub c) equal the dimensionality or degrees of freedom (n sub d) of the space in which it is embedded:

(Equation 1 omitted.)

These ideas were cast in the language of percolation theory by Thorpe (5), who showed that when atoms bond with a coordination number greater than...