Pressure Raman effects and internal stress in network glasses

Raman scattering from binary ${\mathrm{Ge}}_x{\mathrm{Se}}_{1-x}$ glasses under hydrostatic pressure shows onset of a steady increase in the frequency of modes of corner-sharing $\mathrm{Ge}{\mathrm{Se}}_4$ tetrahedral units when the external pressure $P$ exceeds a threshold value $P_c$. The threshold pressure $P_c\left(x\right)$ decreases with $x$ in the $0.15<x<0.20$ range, nearly vanishes in the $0.20<x<0.25$ range, and then increases in the $0.25<x<1∕3$ range. These $P_c\left(x\right)$ trends closely track those in the nonreversing enthalpy, $\Delta H_{\mathit{nr}}\left(x\right)$, near glass transitions $\left(T_{g}s\right)$, and in particular, both $\Delta H_{\mathit{nr}}\left(x\right)$ and ${P_c}_{\left(x\right)}$ vanish in the reversibility window $(0.20<x<0.25)$. It is suggested that $P_c$ provides a measure of stress at the Raman-active units, and its vanishing in the reversibility window suggests that these units are part of an isostatically rigid backbone. Isostaticity also accounts for the nonaging behavior of glasses observed in the reversibility window.

Figure 1

(Color online) (a) Schematic of the three elastic phases observed in network glasses as a function of increasing connectivity. In select cases of truly random networks the intermediate phase collapses yielding a solitary elastic phase transition from a floppy to a stressed rigid. (b) Observed intermediate phases or reversibility windows in indicated binary and ternary glasses. In the two chalcohalide glasses ${\mathrm{Ge}}_{1∕4}{\left(\mathrm{S}\text{or}\mathrm{Se}\right)}_{3∕4-y}{\mathrm{I}}_y$, note that the intermediate phase almost totally collapses.

Figure 2

(Color online) $T$-modulated DSC scan of a ${\mathrm{Ge}}_{15}{\mathrm{Se}}_{85}$ glass showing a $T_g=129.7\left(1.0\right)°\mathrm{C}$, inferred from the inflexion point of the reversing heat flow signal. Note a sizable nonreversing heat flow $\Delta H_{\mathit{nr}}$ (shaded area) for this floppy-glass composition. The scan rate was $3°\mathrm{C}∕\min$ and the modulation rate was $1°\mathrm{C}∕100\mathrm{s}$.

Figure 3

Summary of MDSC results on $\mathrm{Ge}\mathrm{Se}$ glasses showing variations in (a) glass transition temperature $T_g\left(x\right)$ and (b) nonreversing enthalpy near $T_g$ $\Delta H_{\mathit{nr}}\left(x\right)$. DAC results on variations in Raman pressure thresholds $P_c\left(x\right)$ is plotted in (c). The ◻ gives the $P_c$ result on $\alpha -\mathrm{Ge}{\mathrm{Se}}_2$. Note $\Delta H_{\mathit{nr}}\left(x\right)$ and $P_c\left(x\right)$ both vanish in the IP.

Figure 4

Raman line shapes observed as a function of $P$ in (a) $\alpha \text{−}\mathrm{Ge}{\mathrm{Se}}_2$, (b) $\mathrm{Ge}{\mathrm{Se}}_2$ glass, and (c) ${\mathrm{Ge}}_{21}{\mathrm{Se}}_{79}$ glass. Note $P_c=0$ in ${\mathrm{Ge}}_{21}{\mathrm{Se}}_{79}$ glass, a composition in the intermediate phase, but not in $\mathrm{Ge}{\mathrm{Se}}_2$ glass (stressed rigid).

Figure 5

Variations in the frequency of CS tetrahedral units as a function of P for select ${\mathrm{Ge}}_x{\mathrm{Se}}_{1-x}$ glasses studied in the present work ●. The results show the existence of pressure thresholds $P_c$ in the stressed-rigid (25%, 30%, and 33.33%) and floppy (15%, 17%) glass compositions, but not in the IP (20%, 22%) ones. The At $x=15\%$, a two-line fit (as shown) not only yields a lower $\chi$-square than a one-line fit but also yields a slope $(d\nu ∕dP)$ that is nearly 65% larger and forms part of a general trend as $x$- or $\nu$- decreases as sketched in Fig. 6. The ▵ data points are taken from the work of Murase and Fukunaga (Ref. 21).

Figure 6

(a) Fractional blue shift of the Raman vibrational modes in $c\text{−}{\mathrm{As}}_2{\mathrm{S}}_3$ ●,[27] $\alpha \text{−}\mathrm{Ge}{\mathrm{Se}}_2$ ◻ and present ${\mathrm{Ge}}_x{\mathrm{Se}}_{1-x}$ glasses ▴ plotted as a function of mode frequency. The steady decline in the response with increasing frequency reflects the higher restoring force associated with the covalent interations in relation to the van der Waals ones. (b) Fractional blueshift of the CS mode frequency showing a steady decrease with glass Ge concentration $x$ reflecting the increased rigidity of the network with increasing connectivity.

Figure 7

Pressure-induced changes in the (a) CS/ES fraction (b) FWHM of CS mode and (c) FWHM of ES mode for a ${\mathrm{Ge}}_{25}{\mathrm{Se}}_{75}$ glass composition.

Figure 8

Schematic drawing of (a) CS and (b) ES units. The four-fold coordinated atom is Ge while the two-fold coordinated one is Se.

Figure 9

Pressure-induced changes in the (a) CS/ES fraction (b) FWHM of CS mode, and (c) FWHM of ES mode for a $\mathrm{Ge}{\mathrm{Se}}_2$ glass composition.

Figure 10

Pressure induced changes in CS mode frequency of ${\mathrm{Ge}}_x{\mathrm{S}}_{1-x}$ glasses at (a) $x=15\%$, (b) 23%, and (c) 33% showing that $P_c\sim 0$ in all three glass compositions. See text for details.