VOLUME 78, NUMBER 23 PHYSICAL REVIEW LETTERS 9JUNE 1997 Direct Evidence for Stiffness Threshold in Chalcogenide Glasses Xingwei Feng, W. J. Bresser, and P. Boolchand Department of Electrical and Computer Engineering and Computer Science, University of Cincinnati, Cincinnati, Ohio 45221-0030 (Received 10 February 1997) Raman scattering in Ge x X 12x glasses, X  S or Se, reveals that the frequency of A 1 modes of corner- sharing GeX 12  4 tetrahedra displays a discontinuous jump between x  0.225 and x  0.230, which coincides with a minimum in the nonreversing heat flow at the glass transition T g established from modulated differential scanning calorimetry. These results constitute direct evidence for a stiffness threshold at a mean coordination r  c  2.461, which is well described by mean-field constraint counting procedures. [S0031-9007(97)03283-3] PACS numbers: 61.43.Fs, 63.50. + x, 78.30.Ly A covalently bonded random network progressively stiffens as its connectivity or mean coordination number r  increases. Networks consisting of chains (every atom having two nearest neighbors, r  2), as in elemental S or Se, are mechanically floppy because the number of nearest-neighbor bonding constraints [1] per atom 2 are less than 3, the degrees of freedom per atom. The reverse is the case for networks composed of tetrahedral units r  4, such as those of elemental Si or Ge, which are thus intrinsically rigid. In random networks, enumeration of mean-field atomic constraints due to bond stretching and bond bending forces as a function of mean coordination r  reveals [1,2] that the number of zero- frequency (floppy) modes per atom extrapolates linearly to zero when r  increases to 2.40. Thus at a critical mean coordination r  c  2.40, the number of constraints per atom n c  equals [1] the degrees of freedom per atom n d , and mean-field theory predicts [2] the onset of rigidity. In the macroscopically rigid region r  . r  c , numerical simulations [3] in random networks show that elastic constants C display a power-law behavior with r , i.e., C  r  2 2.4 p with p  1.40. These simple and elegant ideas on mean-field atomic constraints in random networks have attracted particular attention in glass science. Experiments on chalcogenide glasses not only display evidence of a threshold behav- ior in the electronic [4], thermal [5], vibrational [6,7], and structural [8,9] properties when r  approaches 2.40 with one exception [10], but the glass forming tendency itself appears to be optimized [1,11] when the network becomes mechanically critical, i.e., n c  n d . In spite of these developments, understanding of the physical na- ture of the stiffness transition, in network glasses, has re- mained largely qualitative. In this Letter we report Raman scattering and temperature modulated differential scanning calorimetry measurements (MDSC) in binary Ge x S 12x and Ge x Se 12x glasses which provide direct evidence for the stiffness threshold near r  c  2.461 in both glass sys- tems with the local elasticity displaying the anticipated power-law behavior in the rigid regime. The shift of the stiffness transition to a value slightly larger than the mean- field value of 2.40 may be generic for IV-VI glasses, and is shown to be associated with floppiness of chalcogen chain segments in which the bond-bending constraint at chalco- gen sites is intrinsically broken. The binary Ge x X 12x glass systems, with X  S or Se form homogeneous bulk glasses over wide compositions 0 , x , 0.43 and have been the subject of previous Ra- man [12–14] and Mössbauer [8] spectroscopic investiga- tions from which details of glass molecular structure have evolved. These glass systems are attractive also because stoichiometric chemical compounds occur at compositions x  0, 13, 12 far removed from the anticipated stiff- ness threshold x  15. We have synthesized about 40 glass compositions starting from 99.9999% elemental Ge, Se, and S, sealed in evacuated ,5 3 10 27 Torr silica ampoules in the desired molar ratio. Melts were homoge- nized at 1000 ± C for at least 48 hours and then equili- brated at about 50 ± C above the liquidus for an additional 24 hours before quenching in water. As a check on glass compositions, we measured glass transition temperatures T g x using a TA Instrument Model 2920 MDSC and the results (Fig. 1) show T g ’s to increase monotonically with x. Micro-Raman measurements performed in a FIG. 1. T g of Ge x S 12x glasses (top) from DSC measurements taken at a 20 Kmin scan rate, and of Ge x Se 12x glasses (bottom) from MDSC measurements at a scan rate of 3 Kmin and a modulation of 61K100 sec. 4422 0031-9007 97 78(23) 4422(4)$10.00 © 1997 The American Physical Society