Onset of rigidity inSe1−xGexglasses: Ultrasonic elastic moduli

The onset of rigidity in ${\mathrm{Se}}_{1\mathrm{-}\mathrm{x}}$ ${\mathrm{Ge}}_{\mathrm{x}}$ glasses is probed by room-temperature longitudinal and transverse elastic moduli determined by ultrasonic measurements. The longitudinal modulus displays linear behavior with increasing x up to x=0.3, corresponding to an average coordination number 〈r〉=2.6. The transverse modulus displays linear behavior with a slight upturn at 〈r〉=2.4, saturating beyond 2.5. The onset of rigidity percolation at 〈r〉=2.4, predicted on the basis of random-network models, is not seen. Other experiments indicate a rigidity threshold near 2.7. The present results are consistent with a departure from random-network models in the form of medium-range structural order.