The challenge

Glass is a solid in which atoms are arranged in a disordered manner. Many materials form amorphous solids when a liquid is rapidly cooled below its freezing temperature. A common example is silica (silicon dioxide), which forms a transparent glass when its high-temperature melt is quenched. By contrast, the most stable form at low temperatures is crystalline quartz, where atoms are arranged on a regular lattice, reflected in the macroscopic symmetry of the crystal. 

This structural disorder has important consequences for macroscopic behaviour. Glasses typically have a lower mass density than their crystalline counterparts, as disordered packing fills space less efficiently. Some regions are therefore locally less dense, which allows limited atomic motion. Single atoms or small groups of atoms may occasionally switch between nearly equivalent configurations, even though the material remains macroscopically rigid. This residual motion persists even at very low temperatures and leads to thermal properties that differ from those of crystalline solids.

Ultrastable glasses represent the most stable amorphous states. They approach the kinetic and thermodynamic stability of crystals while remaining disordered. In terms of the potential energy landscape, they occupy deeper energy minima, closer to the crystalline ground state (Figure 1). Previous measurements, including heat capacity, suggested that residual atomic motion is strongly reduced in these materials, raising the possibility of an “ideal glass” without defects. Whether this suppression also affects low-frequency atomic vibrations has remained unclear.
 

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Fig. 1: Artistic view of the potential energy landscape of a glass. An ordinary glass presents multiple nearly equivalent configurations, allowing residual atomic motion such as thermally activated transitions or quantum tunneling between them (TLS: two level systems). Atomic vibrations (red arrows) are measured at different degrees of stability. More stable glasses correspond to deeper energy minima.

The experiment

Vapour-deposited glasses were used as a model system, prepared by depositing molecules layer by layer onto a substrate held at a controlled temperature. The stability of the glass was tuned by adjusting the substrate temperature. The organic molecule TPD, commonly used in organic light-emitting diodes, was used as the model system.

Using nuclear resonant analysis of inelastic X-ray scattering at the recently developed hard X-ray spectrograph at beamline ID14, scattered radiation was resolved with an energy precision of approximately one part per billion (ΔE ≈ 0.1 meV). This enabled the first measurement of vibrational dynamics at extremely low frequencies (~70 GHz) in glasses with different degrees of stability.

A reduction in low-frequency vibrations with increasing stability was expected, consistent with the suppression of residual motion observed in thermal measurements and predicted by numerical simulations. These simulations suggested that increased stability suppresses quasi-localised vibrational modes associated with structurally soft regions of the glass network.

Instead, the measurements show that increasing glass stability has little effect on harmonic low-frequency vibrations (Figure 2). This indicates that quasi-localised modes contribute only weakly in this regime. Low-frequency vibrations are therefore similar across glasses of different stability and are primarily dominated by sound waves attenuated by structural disorder. In this respect, both ordinary and ultrastable glasses resemble the corresponding crystal, although sound propagates more efficiently in the ordered structure.

Fig. 2: Density of vibrational states, g(ν), normalised to the Debye density of states, g_D(ν), as a function of the frequency, ν, normalised to the Debye frequency ν_D. The ordinary glass (red circles) shows a higher density of low-frequency modes than the ultrastable glass (blue diamonds). However, the harmonic components of the spectra (dotted red line and dashed blue line) are similar in both cases.

The impact

These results challenge current theoretical expectations regarding the role of quasi-localised modes in the low-frequency dynamics of glasses. They indicate that, even in highly stable amorphous states, low-frequency vibrations are governed primarily by extended, wave-like excitations rather than by localised modes.

This behaviour suggests a closer connection between glasses and crystals than previously assumed, with disorder mainly affecting the propagation and attenuation of sound waves. The dominant attenuation mechanism is analogous to the scattering responsible for the blue colour of the sky, where shorter wavelengths are more strongly scattered.

It remains to be established whether these findings are general to all glass systems or specific to the organic molecular system studied here.