Connection between Boson peak and elastic properties in silicate glasses

Low- versus Mid-frequency Raman Spectroscopy for in Situ Analysis of Crystallization in Slurries

Slurry studies are useful for exhaustive polymorph and solid-state stability screening of drug compounds. Raman spectroscopy is convenient for monitoring crystallization in such slurries, as the measurements can be performed in situ even in aqueous environments. While the mid-frequency region (400–4000 cm^–1) is dominated by intramolecular vibrations and has traditionally been used for such studies, the low-frequency spectral region (<200 cm^–1) probes solid-state related lattice vibrations and is potentially more valuable for understanding subtle and/or complex crystallization behavior. The aim of the study was to investigate low-frequency Raman spectroscopy for in situ monitoring of crystallization of an amorphous pharmaceutical in slurries for the first time and directly compare the results with those simultaneously obtained with mid-frequency Raman spectroscopy. Amorphous indomethacin (IND) slurries were prepared at pH 1.2 and continuously monitored in situ at 5 and 25 °C with both low- and mid-frequency Raman spectroscopy. At 25 °C, both spectral regions profiled amorphous IND in slurries as converting directly from the amorphous form toward the α crystalline form. In contrast, at 5 °C, principal component analysis revealed a divergence in the detected conversion profiles: the mid-frequency Raman suggested a direct conversion to the α crystalline form, but the low-frequency region showed additional transition points. These were attributed to the appearance of minor amounts of the ε-form. The additional solid-state sensitivity of the low-frequency region was attributed to the better signal-to-noise ratio and more consistent spectra in this region. Finally, the low-frequency Raman spectrum of the ε-form of IND is reported for the first time.

Vibrational disorder and densification-induced homogenization of local elasticity in silicate glasses

We report the effect of structural compaction on the statistics of elastic disorder in a silicate glass, using heterogeneous elasticity theory with the coherent potential approximation (HET-CPA) and a log-normal distribution of the spatial fluctuations of the shear modulus. The object of our study, a soda lime magnesia silicate glass, is compacted by hot-compression up to 2 GPa (corresponding to a permanent densification of ~ 5%). Using THz vibrational spectroscopic data and bulk mechanical properties as inputs, HET-CPA evaluates the degree of disorder in terms of the length-scale of elastic fluctuations and the non-affine part of the shear modulus. Permanent densification decreases the extent of non-affine elasticity, resulting in a more homogeneous distribution of strain energy, while also decreasing the correlation length of elastic heterogeneity. Complementary 29Si magic angle spinning NMR spectroscopic data provide a short-range rationale for the effect of compression on glass structure in terms of a narrowing of the Si-O-Si bond-angle and the Si-Si distance.

Low-frequency vibrational modes of stable glasses

Unusual features of the vibrational density of states D(ω) of glasses allow one to rationalize their peculiar low-temperature properties. Simulational studies of D(ω) have been restricted to studying poorly annealed glasses that may not be relevant to experiments. Here we report on D(ω) of zero-temperature glasses with kinetic stabilities ranging from poorly annealed to ultrastable glasses. For all preparations, the low-frequency part of D(ω) splits between extended and quasi-localized modes. Extended modes exhibit a boson peak crossing over to Debye behavior (Dex(ω) ~ ω2) at low-frequency, with a strong correlation between the two regimes. Quasi-localized modes obey Dloc(ω) ~ ω4, irrespective of the stability. The prefactor of this quartic law decreases with increasing stability, and the corresponding modes become more localized and sparser. Our work is the first numerical observation of quasi-localized modes in a regime relevant to experiments, and it establishes a direct connection between glasses' stability and their soft vibrational modes.

Damping of vibrational excitations in glasses at terahertz frequency: The case of 3-methylpentane

We report a compared analysis of inelastic X ray scattering (IXS) and of low frequency Raman data of glassy 3-methylpentane. The IXS spectra have been analysed allowing for the existence of two distinct excitations at each scattering wavevector obtaining a consistent interpretation of the spectra. In particular, this procedure allows us to interpret the linewidth of the modes in terms of a simple model which relates them to the width of the first sharp diffraction peak in the static structure factor. In this model, the width of the modes arises from the blurring of the dispersion curves which increases approaching the boundary of the first pseudo-Brillouin zone. The position of the boson peak contribution to the density of vibrational states derived from the Raman scattering measurements is in agreement with the interpretation of the two excitations in terms of a longitudinal mode and a transverse mode, the latter being a result of the mixed character of the transverse modes away from the center of the pseudo-Brillouin zone.

Anharmonic damping of terahertz acoustic waves in a network glass and its effect on the density of vibrational states

We report the observation, by means of high-resolution inelastic x-ray scattering, of an unusually large temperature dependence of the sound attenuation of a network glass at terahertz frequency, an unprecedentedly observed phenomenon. The anharmonicity can be ascribed to the interaction between the propagating acoustic wave and the bath of thermal vibrations. At low temperatures the sound attenuation follows a Rayleigh-Gans scattering law. As the temperature is increased the anharmonic process sets in, resulting in an almost quadratic frequency dependence of the damping in the entire frequency range. We show that the temperature variation of the sound damping accounts quantitatively for the temperature dependence of the density of vibrational states.

High-frequency vibrational density of states of a disordered solid

We investigate the high-frequency behavior of the density of vibrational states in three-dimensional elasticity theory with spatially fluctuating elastic moduli. At frequencies well above the mobility edge, instanton solutions yield an exponentially decaying density of states. The instanton solutions describe excitations, which become localized due to the disorder-induced fluctuations, which lower the sound velocity in a finite region compared to its average value. The exponentially decaying density of states (known in electronic systems as the Lifshitz tail) is governed by the statistics of a fluctuating-elasticity landscape, capable of trapping the vibrational excitations.

Low-temperature thermal properties of a hyperaged geological glass

We have measured the specific heat of amber from the Dominican Republic, an ancient geological glass about 20 million years old, in the low-temperature range 0.6 K ≤ T ≤ 26 K, in order to assess the effects of its natural stabilization (hyperageing) process on the low-temperature glassy properties, i.e. boson peak and two-level systems. We have also conducted modulated differential scanning calorimetry experiments to characterize the thermodynamic state of our samples. We found that calorimetric curves exhibit a huge ageing signal ΔH ≈ 5 J g(-1) in the first upscan at the glass transition Tg = 389 K, that completely disappears after heating up (rejuvenating) the sample to T = 395 K for 3 h. To independently evaluate the phonon contribution to the specific heat, Brillouin spectroscopy was performed in the temperature range 80 K ≤ T ≤ 300 K. An expected increase in the Debye level was observed after rejuvenating the Dominican amber. However, no significant change was observed in the low-temperature specific heat of glassy amber after erasing its thermal history: both its boson peak (i.e., the maximum in the Cp/T(3) representation) and the density of tunnelling two-level systems (i.e., the Cp ∼ T contribution at the lowest temperatures) remained essentially the same. Also, a consistent analysis using the soft-potential model of our Cp data and earlier thermal-conductivity data found in the literature further supports our main conclusion, namely, that these glassy 'anomalous' properties at low temperatures remain essentially invariant after strong relaxational processes such as hyperageing.

Acoustic excitations in glassy sorbitol and their relation with the fragility and the boson peak

We report a detailed analysis of the dynamic structure factor of glassy sorbitol by using inelastic X-ray scattering and previously measured light scattering data [B. Ruta, G. Monaco, F. Scarponi, and D. Fioretto, Philos. Mag. 88, 3939 (2008)]. The thus obtained knowledge on the density-density fluctuations at both the mesoscopic and macroscopic length scale has been used to address two debated topics concerning the vibrational properties of glasses. The relation between the acoustic modes and the universal boson peak (BP) appearing in the vibrational density of states of glasses has been investigated, also in relation with some recent theoretical models. Moreover, the connection between the elastic properties of glasses and the slowing down of the structural relaxation process in supercooled liquids has been scrutinized. For what concerns the first issue, it is here shown that the wave vector dependence of the acoustic excitations can be used, in sorbitol, to quantitatively reproduce the shape of the boson peak, supporting the relation between BP and acoustic modes. For what concerns the second issue, a proper study of elasticity over a wide spatial range is shown to be fundamental in order to investigate the relation between elastic properties and the slowing down of the dynamics in the corresponding supercooled liquid phase.

Equivalence of the boson peak in glasses to the transverse acoustic van Hove singularity in crystals

We compare the atomic dynamics of the glass to that of the relevant crystal. In the spectra of inelastic scattering, the boson peak of the glass appears higher than the transverse acoustic (TA) singularity of the crystal. However, the density of states shows that they have the same number of states. Increasing pressure causes the transformation of the boson peak of the glass towards the TA singularity of the crystal. Once corrected for the difference in the elastic medium, the boson peak matches the TA singularity in energy and height. This suggests the identical nature of the two features.

Acoustic dissipation and density of states in liquid, supercooled, and glassy glycerol

Combined Brillouin spectra collected at visible, ultraviolet, and x-ray frequencies are used to reconstruct the imaginary part of the acoustic compliance J'' over a wide frequency range between 0.5 GHz and 5 THz. For liquid, supercooled, and glassy glycerol, J'' is found to be linearly dependent on the tagged-particle susceptibility measured by incoherent neutron scattering up to ≃1  THz, giving evidence of a clear relation between acoustic power dissipation and density of states. A simple but general formalism is presented to quantitatively explain this relation, thus clarifying the connection between the quasielastic component observed in neutron scattering experiments and the fast relaxation dynamics probed by Brillouin scattering.

Scaling the temperature-dependent boson peak of vitreous silica with the high-frequency bulk modulus derived from Brillouin scattering data

The position and strength of the boson peak in silica glass vary considerably with temperature T. Such variations cannot be explained solely with changes in the Debye energy. New Brillouin-scattering measurements are presented which allow determining the T dependence of unrelaxed acoustic velocities. Using a velocity based on the bulk modulus, scaling exponents are found which agree with the soft-potential model. The unrelaxed bulk modulus thus appears to be a good measure for the structural evolution of silica with T and to set the energy scale for the soft potentials.