Pii: S0038-1098(99)00248-3

Raman scattering and temperature-modulated differential scanning calorimetry measurements on SixSe12x glasses show that onset of rigidity occurs over a wide compositional window 0:20 , x , 0:27 across which glass transitions are found to be thermally reversing in character. There is a ten-fold reduction in the non-reversing heat flow at the transition within the window in relation to that outside the window. The large compositional width associated with the onset of rigidity in this chalcogenide glass is in sharp contrast to the solitary transition predicted by mean-field constraint counting and by existing numerical simulations in random networks. q 1999 Elsevier Science Ltd. All rights reserved. Keywords: A. Disordered systems; A. Semiconductors; D. Heat capacity; D. Phase transitions; D. Phonons Network connectivity plays a central role in determining the physical behavior of solids. In crystalline solids, the effect is strikingly illustrated if one compares the physical properties of group IV (Si,Ge) with those of group VI (S,Se) elements. Even though the strength [1] of a single S–S bond (51.9 kcal/mol) exceeds that of a single Si–Si bond (42.2 kcal/mol) by nearly 20%, the higher connectivity (or coordination number, r) of crystalline (c)-Si …r ˆ 4†; tetrahedral network in relation to that of rhombic-S …r ˆ 2†, monomeric S8 ring structure completely dominates the mechanical, elastic and thermal properties as reflected in the hardness, Young’s modulus, and melting points of the two elemental solids. In covalent solids, these ideas on network connectivity were formalized using meanfield constraint counting algorithms [2,3]. These have served to distinguish [4] rigid from floppy networks quantitatively in terms of the excess or deficit of the average number of Lagrangian constraints per atom, nc with respect to nd, the number of degrees of freedom per atom (nd ˆ 3 here). Constraints come from bond-bending and bond-stretching forces, and nc is found to scale with r as follows: