The Central Role of Broken Bond-Bending Constraints in Promoting Glass Formation in the Oxides

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Abstract
A glass network of N atoms with n1 of the atoms with a coordination number of 1, and m2 of the atoms with a coordination number of 2 about which the bond-angle constraint is broken, will in general display a stiffness threshold (rigidity percolation threshold) when the average coordination increases to a critical value (r)c = 2.4 – 0.4 (n1 – m2)/N. Silica and sodium tellurate glasses provide model examples for which this general relation predicts the observed rigidity percolation threshold; this relation predicts the percolation threshold only if one includes broken bond-bending constraints due to bridging oxygen in the former network and nonbridging oxygen in the latter network. The rigidity percolation threshold in (Na2O)x,(TeO2)1–x glasses observed to occur near x ≃ 0.18 in tellurium-125 Lamb-Mössbauer factor measurments.