Two-Level Systems and Boson Peak Remain Stable in 110-Million-Year-Old Amber Glass

The two most prominent and ubiquitous features of glasses at low temperatures, namely the presence of tunneling two-level systems and the so-called boson peak in the reduced vibrational density of states, are shown to persist essentially unchanged in highly stabilized glasses, contrary to what was usually envisaged. Specifically, we have measured the specific heat of 110 million-year-old amber samples from El Soplao (Spain), both at very low temperatures and around the glass transition $T_g$. In particular, the amount of two-level systems, assessed at the lowest temperatures, was surprisingly found to be exactly the same for the pristine hyperaged amber as for the, subsequently, partially and fully rejuvenated samples.

Figure 1

Schematic potential energy landscape (PEL) for supercooled liquids and glasses, including the hypothetical absolute minimum for a crystal state. An ideal glass would be obtained after an infinitely long aging at the Kauzmann temperature $T_{\mathit{K}}$. The likely level for the studied hyperaging process is indicated by $T_{\text{age}}$, $t_{\text{age}}$. The successive states obtained with the gradual isothermal annealings (rejuvenation) at some $T_{\text{ann}}$, $t_{\text{ann}}$ applied to the pristine sample of amber, are illustrated with the path described by the circles and the arrows. The locations labeled 1–6 in this PEL serve to identify the different samples throughout the Letter.

Figure 2

(a) Specific heat of amber from El Soplao at different states, measured by TM-DSC with heating rates of $1\mathrm{K}/\min$ and modulating amplitude $\pm 0.5\mathrm{K}/\min$ every 80 s. Only the first upscan (see the Supplemental Material [17]) for each sample is presented. The devitrification temperature of the pristine sample is located at $T_g^{*}=438\text{K}$, and then decreases with decreasing stability (rejuvenation). The aging signal is clearly seen as a huge endothermic peak at the glass transition, which is maximal in the case of the pristine sample 1. Rejuvenation of amber was done stepwise (Table 1) by performing different isothermal treatments to the pristine sample near the glass transition. (b) Corresponding enthalpy curves from the specific-heat ones in (a), running from lower to upper solid curves when going from sample 1 to sample 5 in the same order as in the legend. The fictive temperature $T_{\mathit{f}}$ for each sample (indicated by the arrows, going from left to right following the same order as in the legend) is obtained as the intersection of the extrapolated liquid curve ($+$) and the glass curve extrapolated from temperatures well below its $T_g^{*}$ (see the Supplemental Material [17]).

Figure 3

(a) Comparison of specific-heat data for three Spanish amber samples (pristine, partially rejuvenated, and fully rejuvenated) at very low temperatures, 0.05–2 K. The upper dashed line shows the best quasilinear fit to the experimental data below 0.4 K given by $C_p\propto T^{1.27}$, hence faster than the simple linear dependence indicated by the lower dashed line. (b) $C_p/T^3$ plot of the same data in (a), displayed in a wider temperature range. The height of the boson peak is observed to further increase with rejuvenation, though the values of both the minimum and the maximum of $C_p/T^3$ remain constant: $T_{\min }=1.2\pm 0.1\mathrm{K}$ and $T_{\max }=3.4\pm 0.1\mathrm{K}$, respectively. The corresponding Debye levels determined from the sound velocity and density data (Table 2) are indicated by solid lines and exhibit the same trend as the boson-peak height (both sets follow the same order as the symbols in the legend).