Evolution of the elastic properties of glassy amber in 110 million years measured by inelastic X-ray scattering

25-03-2019

Glasses are metastable systems continuously evolving towards microscopic configurations of lower energy. The correlation of glass stability with structural and dynamic disorder was revealed by studying the vibrational properties of geological hyperaged amber with two inelastic X-ray scattering techniques.

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Glasses are characterised by their lack of long-range microscopic order and a structure continuously evolving to reach lower energy microscopic configurations. As a consequence, their physical properties are not uniquely defined and depend on their thermal history.

The correlations between the topology of the configurational energy landscape and the physical properties of the glass are crucial for understanding its metastability. Among these, the vibrational properties are particularly relevant, being responsible for universal thermodynamic anomalies with respect to crystalline solids. Moreover, the vibrational density of state (VDOS) g(E) of glasses exhibits a characteristic excess with respect to the Debye prediction for crystals g(E)∝E2, named Boson peak.

Since spontaneous stabilisation, or aging, would require unpractically long observation time, the conventional way of obtaining glasses of different degrees of stability (height in the energy landscape) is by cooling the liquid below the melting point at different quenching rates. The slower the rate, the lower the energy position of the basins in which the system gets trapped. The stability range covered by tuning the cooling rate is however limited, upwards, by thermal conductivity and annealing technology, downwards, by the occurrence of crystallisation.

Recently, glasses with high thermodynamic stability have been prepared by physical vapor deposition (PVD) and their study unveils a correlation between stability and vibrational dynamics [1,2]. However, the investigation of the VDOS of PVD glasses is extremely challenging for X-ray based techniques due to their limited thickness.

In this work, the vibrational properties were measured experimentally in the THz regime, including the Boson peak of the VDOS, as a function of stability by exploiting a glass that has experienced an extremely prolonged natural aging: a geological amber from El Soplao (Spain) dated back to 110 million years ago.

Specifically, the elastic properties of hyperaged amber were compared with that of its rejuvenated counterpart obtained by annealing a pristine sample into the supercooled liquid phase and cooling it down at the standard rate of 1 K/min to erase its thermal history.

The extreme stability of amber can be traced back in the endothermic peak in the specific heat at the glass-transition measured by differential scanning calorimetry (DSC) (see Figure 1a).  The different degree of stability, or age, is quantified by a 9% smaller fictive temperature Tf for pristine amber.

Specific heat of pristine and rejuvenated amber measured by DSC

Figure 1. (a) Specific heat of pristine and rejuvenated amber measured by DSC; (b) Normalised scattered intensity IQ and difference among raw data (red line) after scaling of 0.75% (blue line) and of 2% (green line) of the Q-axis of pristine amber; (c) Reduced VDOS and in the inset, corresponding fit with FET; (d) Phonon energy E dispersion, apparent velocity ν=E(Q)/Q and mode attenuation of pristine and rejuvenated ambers.

The structure was investigated by wide-angle X-ray diffraction (see Figure 1b) at the inelastic X-ray scattering beamline ID28. The scattering intensity (proportional to the static structure factor) shows similar structures in the two samples: a main peak at ≈ 10 nm−1 and two smaller, broader peaks at ≈ 28 nm−1 and ≈ 52 nm−1. The observed 2% densification of pristine amber corresponds to a shrinking of the main diffraction peak, which does not scale linearly with density (0.75% is the optimal q-axis scaling) as expected for homogenous densification.

The reduced VDOS g(E)/E2 was measured by performing an inelastic X-ray scattering experiment with nuclear resonance analysis (see Figure 1c) at the nuclear resonance beamline ID18. Remarkably, we observe that the Boson peak appears to be less intense (26% vertical scaling), blue-shifted and broader (11% horizontal scaling) in the pristine amber.

The collective excitations in the THz regime that contribute to the VDOS were examined by measuring the phonon dispersion and mode attenuation by means of momentum Q-resolved inelastic X-ray scattering (see Figure 1d) at the beamline ID28.

The hypersonic attenuation exhibits a similar quadratic power law dependence on acoustic energy for the two samples, with slightly reduced values for pristine amber.  The comparison of the acoustic phonon dispersions E(Q) reveals a mode stiffening for the pristine amber and the appearance of positive dispersion which is an excess in the apparent velocity ν=E(Q)/Q with respect to the low frequency limit measured by Brillouin light scattering (arrows in Figure 1d), indicating a longer relaxation time for the probed modes.

All these results can be rationalised by the fluctuation elasticity theory (FET) that describes the glass disorder in terms of microscopic random spatial fluctuations of the transverse elastic constant (shear modulus) with a certain degree of spatial correlation. The best fit for the Boson peak is reported in the inset of Figure 1c. Importantly, the FET quantitatively relates the vibrational properties to the width and correlation length of the elastic constant distribution, ruling out any density dependence.

The VDOS redistribution together with the lower hypersonic damping and positive dispersion of pristine amber in the framework of FET indicate that the elastic constants distribution of pristine amber is sharper and the correlation length longer compared to the rejuvenated sample, as summarised in Figure 2.

Sketch of the inherent structures explored with pristine (red dot) and rejuvenated (black dot) ambers on the potential energy landscape

Figure 2. Sketch of the inherent structures explored with pristine (red dot) and rejuvenated (black dot) ambers on the potential energy landscape and the observed correlation to the structural and elastic properties of the glass.

In conclusion, the experimental characterisation of the structural and elastic properties of a glass amber in different stability states revealed that its physical aging is achieved through a reduction of the disorder of the elastic matrix of the glass.

 

Principal publication and authors
Tracking the connection between disorder and energy landscape in glasses using geologically hyperaged amber, E.A.A. Pogna (a), A.I. Chumakov (b), C. Ferrante (c), M.A. Ramos (d), T. Scopigno (c), J. Phys. Chem. Lett. 10, 427-432 (2019); doi: 10.1021/acs.jpclett.9b00003.
(a) Laboratorio NEST, CNR-INFM and Scuola Normale Superiore, Pisa, and Dipartimento di Fisica, Politecnico di Milano (Italy)
(b) ESRF and National Research Centre “Kurchatov Institute”, Moscow (Russia)
(c) Dipartimento di Fisica, Universitá di Roma, La Sapienza, Rome, and Center for Life Nano Science@Sapienza, Istituto Italiano di Tecnologia, Rome (Italy)
(d) Laboratorio de Bajas Temperaturas, Departamento de Física de la Materia Condensada (IFIMAC) and Instituto Nicolás Cabrera, Universidad Autónoma de Madrid (Spain)

 

References
[1] E.A.A. Pogna, C. Rodríguez-Tinoco, M. Krisch, J. Rodríguez-Viejo and T. Scopigno, Sci.Rep. 3, 2518 (2013).
[2] E.A.A. Pogna, C. Rodríguez-Tinoco, G. Cerullo, C. Ferrante, J. Rodríguez-Viejo and T. Scopigno, PNAS 112, 2331–2336 (2015).