# Cold-and Hot-Densification of a Depolymerized Glass: A Multiscale Vibrational Investigation of PbSiO3

Rafaella Bartz Pena, T. Deschamps, Sylvie Le Floch, Alice Berthelot, Elodie

Romeo, T.R. Cunha, O. Peitl, A.D. Rodrigues, C. Martinet, P.S. Pizani

► To cite this version:

Rafaella Bartz Pena, T. Deschamps, Sylvie Le Floch, Alice Berthelot, Elodie Romeo, et al. Cold-and Hot-Densification of a Depolymerized Glass: A Multiscale Vibrational Investigation of PbSiO3. Journal of Non-Crystalline Solids, 2024, 646, pp.123246. 10.1016/j.jnoncrysol.2024.123246. hal-04746471

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# Cold- and Hot-Densification of a Depolymerized Glass: A Multiscale Vibrational Investigation of PbSiO₃

R.B. Pena<sup>a,b</sup>; T. Deschamps<sup>c</sup>; S. Le Floch<sup>c</sup>; A. Berthelot<sup>c</sup>; E. Romeo<sup>c</sup>; T.R. Cunha<sup>a,b</sup>; O. Peitl<sup>a</sup>; A.D. Rodrigues<sup>b</sup>; C. Martinet<sup>c</sup>; P.S. Pizani<sup>a,b</sup>

<sup>a</sup> Department of Materials Engineering, Center for Research, Technology and Education in Vitreous Materials, Federal University of São Carlos, 13565-905, São Carlos, SP, Brazil.

<sup>b</sup> Federal University of São Carlos, Physics Department, 13565-905 São Carlos, SP, Brazil.

<sup>c</sup> Institut Lumière Matière (ILM), UMR5306 Université Lyon 1 - CNRS, Université de Lyon 69622 Villeurbanne, France.

**Abstract:** In this study, we investigated the effect of different compression routes on the lead metasilicate (PbSiO₃) composition. Glass samples were compressed in a Belt press up to 5 GPa at room temperature (cold compression) and high temperatures (hot compression) up to 673 K, both at comparable experimental conditions concerning pressure and temperature gradients and times. The set of densified glasses was analyzed *ex-situ* by Brillouin, Raman and infrared spectroscopies, providing a multiscale structural probe. The dataset revealed a progressive decrease in the refractive index-weighted longitudinal sound velocities for the cold-compression and a minimum at about 450 K for hot-compression. Raman and infrared analyses indicate increasing depolymerization of the silicate network as an effect of densification, which is more pronounced at higher temperatures. Moreover, distinct mechanical properties are discussed regarding the inherent structural modifications resulting from the compression treatments.

**Keywords:** High-Pressure; Elastic Anomaly; Mechanical Properties; Lead Metasilicate Glass.
# 1. Introduction

How do sound velocities change as a function of the material density? By investigating a plethora of rocks with different compositions under pressure, Birch [1] reported that sound velocities correlate positively with mass density, although not as single-valued functions. In the realm of engineering and material science, these sound velocities demonstrate a strong correlation with mechanical properties, which holds significant relevance for the increasing advancement and application of vitreous materials [2, 3]. In isotropic materials, the longitudinal (L) and shear (T) moduli are such that:

$$L = \rho v_L^2 \qquad (1)$$

$$T = \rho v_T^2 \qquad (2)$$

Where $\rho$ is the density and $v_L$ and $v_T$ are the longitudinal and transversal sound velocities, respectively. Remarkably, from these linearly independent relationships as expressed in Eq.(1) and Eq.(2), the remaining elastic moduli can be derived [4, 5], as displayed in Table 1. As an extension of the ‘Birch law’, these fundamental parameters – namely $\rho$, $v_L$ and $v_T$ – generally increase upon pressure-induced densification. In other words, materials that follow the Birch law might display, when densified, increasing sound velocities relative to their uncompressed values. To the best of our knowledge, exceptions to the aforementioned law at room conditions were recognized in cold- and hot-densified vitreous silica [6], and lately they have been evidenced in cold-densified lead metasilicate (PbSiO$_3$, henceforward ‘PS’) glass [7].

<table><caption>Table 1: Relationships between elastic moduli as a function of $\rho$, $v_L$ and $v_T$ in isotopically homogeneous matter.</caption><thead><tr><th>Young modulus (E)</th><th>Bulk modulus (K)</th><th>Poisson's Ratio (v)</th></tr></thead><tbody><tr><td>$E = \rho \left( \frac{3v_L^2 - 4v_T^2}{\left(\frac{v_L}{v_T}\right)^2 - 1} \right)$</td><td>$K = \rho \left( v_L^2 - \frac{4}{3} v_T^2 \right)$</td><td>$v = \frac{v_L^2 - 2v_T^2}{2(v_L^2 - v_T^2)}$</td></tr></tbody></table>

Regarding some definitions, densification refers not only to cases where glass density increases through an appropriate treatment, but more generally, to those situations where the retrieved glass structure undergoes permanent modification, such as after a compression-decompression cycle in the plastic regime. Furthermore, processing achieved under high-pressure at room temperature conditions is usually denoted as ‘cold-densification’, whereas that carried out under high pressure
and high temperatures is referred to as ‘hot-densification’. For a given glass composition, different processing conditions such as pressure, temperature, treatment duration, loading, and unloading rates may give rise to densified glasses with distinct structures and properties. Such treatments are reported to induce changes in the glass structure, encompassing cation-oxygen bond lengths and angles, coordination numbers, network polymerization, ring statistics, and higher range ordering scale [8, 9].

The study of the treated glasses by vibrational spectroscopies relies on indirectly observing the related modifications in their dynamic character of vibration. Brillouin spectroscopy probes the acoustic vibrational modes, whereas Raman and infrared spectroscopies access the optical vibrational modes [10]. In glasses, the acoustic modes tend to be propagating plane waves with a large wavelength compared to the atomic distancing, whereas the optical modes are usually characterized by spatially localized vibrations [11]. In turn, the combination of these vibrational probes can provide valuable structural information at the different spatial ordering scales within the glass, along with mechanical property insights.

Regarding the exemptions to the Birch law, vitreous silica presents a completely polymerized structure composed of $SiO_2$ tetrahedra interconnected by the corner, while the addition of 50 mol.% PbO leads to a depolymerized silicate structure. While the effect of cold- and hot-compression in vitreous silica was probed by vibrational and X-ray diffraction methods [12, 13], studies contrasting the outcomes of these distinct compression treatments in silicate glasses are quite scarce in the literature. Noteworthy, investigations addressing the hot-densification of lead silicate glasses comprised exclusively the work of Yoshimoto *et al.* [14]. These authors reported enhanced mechanical properties of the hot-densified glass compared to the uncompressed glasses of varying lead content, thereby providing a good description of the densification across the PbO-$SiO_2$ system constrained to a specific P,T treatment. The change in Young's modulus and hardness for the PS composition showed the lowest enhancement.

Recently, we have studied the effect of cold densification on the structure of PS glass [7, 15]. Raman spectroscopy measurements of a set of glass submitted to different maximum pressures indicated permanent structural modification above 4 GPa as the silicate network depolymerized [15]. The notably low elastic limit was confirmed by Brillouin spectroscopy, which indicated an anomalous decrease of $n \cdot v_L$ values as a function of the maximum pressure, where n is the refractive index and $v_L$ is the longitudinal sound velocity [7]. Ellipsometry measurements performed on a
macroscopic specimen cold-densified at 5 GPa confirmed the increase of *n*, whereas $v_L$ slowdown.
Despite the similar depolymerization trend observed after the hot-densification of the PS glass to
6 GPa and ~500 K, an increase in $v_L$ is inferred from the elastic moduli increase [14].

At first glance, as hot- and cold-compression treatments seem to affect the elastic properties of
the treated PS glasses in opposite directions, our objective is to thoroughly examine the outcome
of these different densification routes. In this work, a set of PS glass samples were compressed at
comparable rates and times in a Belt press. The effect of compression up to 5 GPa and different
maximum temperatures was investigated by Brillouin, Raman, and infrared spectroscopies,
unveiling details on the resulting structural and elastic modifications arising from the different
compression treatments.

## 2. Experimental Methods

### 2.1 *Sample preparation and densification*

Lead metasilicate ($PbSiO_3$, PS) glass specimens are from the same batch as the macroscopic
sample in Ref. [7], presenting an accurate lead-to-silicon ratio, then prepared by the standard melt-
quench method and annealed close to the uncompressed glass transition, $T_g* \approx 687$ K.

Figure 1 illustrates a cross-section schematic of the Belt press [16], identifying its main
components. Due to the geometric requirements, samples were cut into cylinders displaying 5.7 ±
0.1 *mm* height and 3.95 ± 0.05 *mm* diameter, which were densified up to 5 GPa, settled at the
apparatus pressure limit, either at room temperature or higher temperatures. In each run, the PS
sample was enclosed either in a boron nitride or gold crucible, according to the target compression
temperature. The assembly was inserted into a graphite tube heater and subsequently placed within
a pressure-transmitting pyrophyllite gasket, which allowed quasi-hydrostatic conditions. The
temperature was raised by supplying electric current to the graphite tube, heating the system by
the Joule effect. The compression treatment, including P,T ramp increment and holding time,
followed a protocol analogous to those used in Refs. [12, 17]. For each sample, the pressure was
increased (5 bar/min) up to 5 GPa, and then heated to the labeled temperature (Tmax = 300, 473,
573, or 673 K), such that the glass was held on the extreme P,T condition for 10 minutes, cooled
down to room temperature at constant pressure, and then smoothly decompressed (1 bar/min) to
room pressure. Vibrational spectra were acquired at room conditions after their respective P,T treatments.

<figure><img src="image_1.png" /><figcaption>Figure 1: Cross section schematic of an assembly used for Belt experiments; 1. Tungsten carbide anvil, 2. Polytetrafluoroethylene O-ring, 3. Pyrophyllite gasket, 4. Steel plug, 5. Pyrophyllite spacer, 6. and 10. Sample capsule (boron nitride crucible or gold crucible insulated from the graphite heater by a boron nitride capsule, 7. Graphite heater, 8. Pyrophyllite pressure medium, 9. Sample, 11 « Belt » chamber made in tungsten carbide.</figcaption></figure>

Density estimation was conducted using the flotation method based on Archimedes' principle in distilled water. For the sake of reproducibility, the measurements were performed multiple times on a hydrostatic balance, Mettler Toledo EL104. The cold-compressed glass sample is the same as the macroscopic sample presented in Ref. [4]. Despite evident changes in the optical properties, no appreciable density change was perceived in relation to the pristine glass, $\rho = 5.85 \text{ g.cm}^{-3}$, within a $0.02 \text{ g.cm}^{-3}$ error bar. For the sample compressed under 5 GPa and 473 K, a 2.7 % densification rate was observed. This densification rate agrees well with the value reported by Yoshimoto *et al.* [16] under comparable conditions, i.e., 2.6% densification for a PS glass sample compressed at 6 GPa and 500 K. When subjected to higher compression temperatures, the hot-compressed samples were enclosed in a gold crucible to avoid any chemical contamination. As a result of the retrieval process, the final samples were fragmented, thereby precluding an accurate density determination.
## 2.2 Analytical Vibrational Techniques

In both inelastic vibrational probes, Brillouin and Raman spectroscopies, the 532 nm laser wavelength was used as an excitation source, and the light was collected in back-scattering geometry by a 50x long working-distance objective. Brillouin scattering measurements were recorded using a Sandercock Fabry Perot tandem interferometer, whereas Raman measurements were taken using a LabRAM HR micro-Raman spectrometer from Horiba Jobin Yvon.

The Brillouin frequencies reported here are the average of the Stokes and anti-Stokes absolute values in GHz, corresponding to frequencies smaller than $1 \text{ cm}^{-1}$ [10]. Raman spectra were recorded in both parallel (VV) and perpendicular (HV) polarizations in between the excitation and scattered beams. Each Raman spectrum was acquired using the 1800 slits/mm grating, between $2 \text{ and } 1200 \text{ cm}^{-1}$. In their turn, Fourier transform infrared spectra were acquired in diffuse reflectance mode in a Spectrum 3 PerkinElmer spectrometer between $540 \text{ and } 1200 \text{ cm}^{-1}$. Parallelly polarized Raman spectra are displayed normalized by the highest intensity, which occurred at the Boson peak and allows for the observation of the evolution of Pb-O vibrations. In contrast, for the perpendicularly polarized Raman spectra and infrared spectra, normalization was performed with respect to the area of the high-wavenumber region.

## 3. Results

Glass submitted up to 5 GPa and 300 K underwent cold compression, whereas samples treated at 5 GPa and maximum temperatures ($T_{max}$) at 300, 473, 573, and 673 K comprised hot compression in the sub-$T_g$* region, where no visual or spectral indications of crystallization were observed. Given the propensity for crystal nucleation upon glass compression and shear stress [18], the absence of crystallization at such high temperatures suggests the normal behavior of an increase in $T_g$ with pressure processing [19, 20]. Therefore, we take it for granted to be investigating the effect of compression on the glass state [21]. Given their unstable thermodynamic condition, glasses not only entail resulting structures and properties dictated by the initial and final states, but also rely on temperature and pressure pathways [22], which were here systematically altered under comparable conditions. We further contrast the resulting hot-densification modifications to the cold-densification ($T_{max}=300 \text{ K}$) under different maximum pressures ($P_{max}$) obtained in a diamond anvil cell, for which detailed Brillouin and Raman analyses were conducted elsewhere [7, 15].
3.1. Brillouin Spectroscopy

Figure 2 illustrates the longitudinal Brillouin shift, $v_L$ (that is proportional to $n \cdot v_L$) for PS glass densified through different P,T treatments. As derived from in-situ experiments on the same glass system [23], the modulus of the sound velocities and their pressure derivatives are higher for longitudinal components than transversal ones, which justifies our ex-situ investigation ultimately addressing the most sensitive component. Regarding $v_L$ evolution, cold compression results in its continuous decrease, whereas hot compression displays a non-monotonic behavior as a function of the maximum temperature of compression, which decreases presenting a minimum at about 450 K, and then increases relative to the uncompressed value for temperatures above ~500 K. An analogous trend in $v_L$ was reported in hot-densified vitreous silica performed at a fixed compression temperature and varying maximum pressures [6].

<figure><img src="image_2.png" /><figcaption>Figure 2: Longitudinal Brillouin line shift ($v_L$) for PS glass densified through compression under different P,T conditions: blue squares varying the maximum pressure with fixed temperature (Tmax = 300K) and red circles with distinct temperatures with the same maximum pressure (Pmax = 5GPa). The horizontal line marks the uncompressed value. Data for the cold-densified glass obtained at different maximum pressures were retrieved from Pena et al., 2022 [7].</figcaption></figure>
## 3.2. Raman Spectroscopy

Vibrational assignments for the glasses in the PbO-SiO₂ system have been performed in the literature by observing spectral changes while systematically increasing the PbO content in vitreous silica, or by comparing the glass spectra with those of well-known lead-containing crystalline compounds. Parallelly polarized Raman spectra of PS glass exhibit in the low-wavenumber region: an intense feature often referred to as the Boson peak (BP) at 45 cm⁻¹, and two peaks centered at 95 and 135 cm⁻¹, attributed to the Pb-O vibrational modes [24-28]. In the spectral region between 460 and 550 cm⁻¹, the observed plateau is assigned to the mixed stretching-bending motion of the Si-O-Si bonding [29]. In the high-wavenumber region, the asymmetric envelope is due to the symmetric Si-O stretching of the silicon tetrahedra with different polymerization degrees, so-called Qⁿ entities. These last depict the degree of polymerization of the silicate network, with n varying from 0 to 4 and indicating the number of bridging oxygens per tetrahedron, where the more polymerized units tend to present the higher vibrational wavenumber [30, 31].

Figure 3 displays the parallelly and perpendicularly polarized Raman spectra as a function of the maximum compression temperatures. The Pb-O vibrational modes are almost entirely suppressed in the perpendicular geometry, and the high-wavenumber region presents expressive changes on the profile due to the decrease in the intensity related to the more polymerized tetrahedra in the high-wavenumber side of the band. This is in agreement with previous observations reported in the literature [24, 26]. With increasing maximum compression temperatures, we observe in the parallel polarization an increase in the intensity of the 95 cm⁻¹ peak, accompanied by a decrease in the 135 cm⁻¹ peak intensity. In the same spectral region, the perpendicular polarization evidences a decrease in the BP intensity with Tmax.
<figure><img src="image_3.png" /><figcaption>Figure 3: (a) Parallely (VV) and (b) perpendicularly (HV) polarized Raman spectra for PS glass densified through distinct temperatures with the same maximum pressure (Pmax = 5GPa). The insets highlight the respective modifications perceived in the low- and high-wavenumber regions.</figcaption></figure>

The evolution of the high-wavenumber region can be quantified by following the changes in the barycenter, presented in Figure 4. This geometrical mean parameter pictures the simultaneous effect of the peak shift and lineshape modifications, which redshifts for the ensemble of densified PS glass, either obtained after cold or hot compression. In the perpendicularly polarized Raman spectra, this one-parameter was saturated as the glass was densified. On the other hand, in parallell-polarized spectra, the barycenter of the high-wavenumber region decreases linearly with the maximum compression temperatures and through an exponential decay with the maximum pressures, as acknowledged by the authors therein [15]. Notably, despite being compressed under the same nominal conditions of 5 GPa and 300 K, the sample processed in the Belt press exhibits a higher shift of the barycenter compared to the sample compressed in the diamond anvil cell and reported in Ref. [15]. This behavior could be attributed to the non-uniform hydrostaticity of the former, since shear stress anticipates the pressure effects leading to an elastic limit at lower pressures [32].
<figure><img src="image_4.png" /></figure>

Figure 4: Barycenter of the high-wavenumber band in the parallell-polarized Raman spectra for PS glass densified through different P,T treatments: blue squares varying the maximum pressure with fixed temperature (T<sub>max</sub> = 300K) and red circles with distinct temperatures with the same maximum pressure (P<sub>max</sub> = 5GPa). Data for the cold-densified glass obtained at different maximum pressures were retrieved from Pena et al., 2021 [15].

### 3.3. Infrared Spectroscopy

In the spectral infrared region between 540 and 1200 cm⁻¹, the probed vibrations are due to the internal and external modes of the SiO₂ tetrahedra [33]. As regards the pressure effect on the infrared spectra (Figure 5), changes are noticeable in the asymmetric Si-O stretching region which comprises vibrational modes due to the non-bridging oxygens with distinct polymerization degree (Qⁿ entities), along with the Si–O stretching mode involving bridging oxygen [33]. In the ensemble of compressed glasses, a decrease in the 1090 cm⁻¹ modes occurred simultaneously with an increase in the intensity of the 890 cm⁻¹ and 970 cm⁻¹ modes relative to the uncompressed glass positions, indicating an overall redshift of the high-wavenumber region for which neither the barycenter nor the maximum converges in depicting the spectral evolution by a parametrization (not shown). Yoshimoto *et al.* [14] reported for their PS glass hot-densified at 6 GPa and 500 K, a displacement of -10 cm⁻¹ of the peak maximum compared to the pristine glass there explained as a silicon network depolymerization.
<figure><img src="image_5.png" /><figcaption>Figure 5: Infrared spectra for PS glass densified through with distinct temperatures with the same maximum pressure (P<sub>max</sub> = 5GPa).</figcaption></figure>

### 3. Discussion

Combining Brillouin, Raman, and infrared spectroscopies, we access the effect of the glass densification at a range of structural dimensions by the multiple vibrational techniques: (i) Brillouin spectroscopy depicts the glass as a continuum and hence depicts the *long-range scale*. In the low-wavenumber region of the Raman spectra, (ii) the BP probes a collection of domains with different sizes, such as a mosaic associated with *intermediate-range scales* within the glass structure [34, 35]. In the same spectral region, (iii) the Raman peaks at 95 cm⁻¹ and 135 cm⁻¹ correspond to the Pb-O vibrations. (iv) The high-wavenumber region probed complementarily by Raman and infrared spectroscopies shows the Si-O vibrations. Such that (iii) and (iv) characterize the pressure-induced modifications on the glass *short-range scales*. By probing the evolution of the Brillouin frequencies, we observe that the glass samples densified at 5 GPa and 300 K or 473 K display the anomalous $n \cdot v_L$ behavior, which is less prominent than that obtained after cold compression at 20 GPa [7]. Noteworthy, it indicates that despite the intrinsic structural distinctions, the elastic modulus anomaly manifests for densified glass obtained under specific P,T treatments, either after cold or hot compression analogous to vitreous silica [6]. The comprehensive determination of the elastic moduli, such as the Young modulus and Poisson's ratio (Table 1) for
the cold- and hot-densified PS glass would require the additional estimation of $v_T$, for which
attempting Brillouin measurements at the oblique configuration was unfeasible due to geometric
constraints related to the perfect face parallelism [10]. Macroscopically, this anomaly that
manifests observably on the longitudinal modulus may emerge if the following two conditions
occur simultaneously, as discussed in Ref.[7]: (i) the longitudinal sound velocity decreases after a
compression-decompression cycle; and (ii) density increases marginally. An attempt at a
microscopic description of the structural modifications in the PS glass is presented as follows.

Among the various models proposed to explain the excess of vibration modes at the
terahertz frequency range in glasses corresponding to the BP [36-41], the elastic heterogeneity
model proposed by Duval *et al.* [36, 37] states that glasses display non-continuous structures,
configuring a collection of non-crystalline nanometric domains with distinct elastic constants. The
vibrational modes of these cohesive domains separated by softer interdomain zones gives rise to
the BP [42]. From this approach, the observed decrease in the BP intensity as a function of the
maximum compression temperature (Fig.3) can be attributed to the softening of the cohesive
domains, lowering the elastic contrasts, and therefore homogenizing the network elasticity [43,
44]. At a fixed pressure, higher compression temperatures may minimize the internal stress due to
the reorganization and relaxation of the glass structure, which seems to hold for vitreous silica and
depolymerized glasses such as the PS composition. This structural homogenization could provide
higher stability of the densified state against temperature, as observed in vitreous silica [45, 46].
In this line, Onodera *et al.* [47] reported a partial relaxation of their cold-densified silica glass kept
at room conditions for a couple of years, while their hot-densified glass was stable. The metastable
state of cold-densified vitreous silica was also verified by Polian *et al.* [48], with faster timescales
than in hydrostatic conditions, but under uniaxial compression (where shear strain takes place
[49]). Despite the significantly lower Tg temperatures of the PS composition compared to vitreous
silica, we did not observe by vibrational probes the same trend as that of Ref. [47] in our densified
glasses maintained at room conditions for a comparable time frame.

In cold-densified PS glass submitted to different maximum pressures, densification was
reported to induce changes in the short-range ordering manifested by a silicon network
depolymerization and in the local environment around the lead cations [7, 15]. In the former, a
conversion of less polymerized into more polymerized tetrahedra was extrapolated to slightly
increase the NBO proportion in densified PS glass [15]. In the latter, the pressure effect on the
short-range ordering around the lead cations was suggested to comprise from the deformation of the tetragonal pyramids to the formation of highly coordinated PbO$_n$ polyhedra [7]. Given the high sensibility of Raman spectroscopy to the vibration of Pb-O bonds, we do not discard the formation of highly coordinated PbO$_n$ polyhedra as a possible structural modification upon densification, probably more expressive at higher compression temperatures. For the sake of comparison, in the stable crystalline polymorph, the monoclinic alamosite, Pb arranges with oxygen in triangular and two non-equivalent square pyramidal coordination, for which Raman modes present the highest intensity around 110 cm$^{-1}$ at room temperature [50]. These findings imply that the glass permanently densified at higher compression temperatures (Figure 3.a) may exhibit a lead environmental condition more closely aligned with the alamosite crystal than the pristine glass. Such a higher degree of similarity could facilitate the crystallization of PS after treatments under simultaneous extreme conditions of pressure and temperature [51], not necessarily as a straight process towards the most stable crystalline polymorph [52].

Considering the conventional two coordination cations neighboring in silicates, oxygen can be classified into three categories depending on its bonding to silicon in the network [53]: (i) Bridging oxygen (BO) is the oxygen connecting two silicon cations, playing a role in the cross-linking of the network. (ii) Non-bridging oxygen (NBO) is the oxygen bonding a silicon cation to a metallic cation acting as a network modifier, hence configuring a network terminator. (iii) Oxygen that is not bonded to the silicon atoms but to the metallic cation is referred to as free oxygen (O$^{2-}$). Depolymerization occurs by the conversion of BO into NBO with the participation of O$^{2-}$ due to the rupture of Si-O bonds, caused by chemical stoichiometry alterations or extreme pressure and/or temperature conditions, such that:

$$BO + O^{2-} \leftrightarrow 2NBO \quad (3)$$

For the ensemble of densified PS glass, Raman and infrared spectroscopies consistently demonstrate a redshift of the Si-O stretching modes. Considering the decrease in barycenter (Figure 4) and its correlation to the NBO increase, as derived in Ref. [15] for the PS cold-densified glass, the aforementioned depolymerization is more pronounced at higher compression temperatures when comparable maximum pressures are applied. Following Eq. (3), such an occurrence implies higher free oxygen consumption and availability. Indeed, ‘free oxygens’ have been directly observed in lead silicates [54], and their abundance is expected to increase at higher temperatures under constant pressure. By combining in-situ Raman and molecular dynamics,
Sampaio *et al.* [31] reported that the silicate network connectivity decreased with increasing temperature. Interestingly, densification and thermal treatment of glass at ambient pressure led to the same trend regarding the depolymerization, with the latter being more pronounced as the temperatures were higher than Tg [55].

Following our results for the lead metasilicate composition, some studies conducted on compressed silicate systems found a positive correlation between depolymerization and a decrease in sound velocity or mechanical properties. At room conditions, the degree of depolymerization of the silicate structure was demonstrated to affect the *in-situ* evolution of $v_L$ and $v_T$ under pressure [56, 57]. Cold-densified soda-lime silicates compressed in a multi-anvil apparatus up to 21 GPa showed a minimum in the Brillouin shift and changes in the $Q^n$ band [58], potentially being another exception to the Birch law. In lithium disilicate glass, cold-compression under maximum pressures above 7.7 GPa is reported to induce modifications in the radial distribution function and the $Q^n$ distribution [59, 60]. For the isochemical glass-ceramic, hardness and elastic moduli were found to decrease upon cold compression and notably increase after hot compression treatment [61]. In this sense, hot-densified soda magnesia silicate glass submitted to 2 GPa at Tg* exhibits modifications in the $Q^n$ distribution, resulting in a narrow decrease in the NBO proportion concomitant with an increase in the $O^{2-}$ proportion, whereas $v_L$ and $v_T$ increase [62]. These last authors further reported an increase in the elastic moduli accompanied by a decrease in the correlation length of the elastic heterogeneity. Indeed, the increase in elastic moduli induced by hot-densification was verified across different glass compositions compressed at 1 GPa and their respective Tg* [63]. On the other hand, the effect of densification on Poisson's ratio is reported to be non-trivial, due to the competing effects of modifier-oxygen bonding distance and increase in coordination [64].

Understanding the different elastic behaviors arising from the P,T treatments ultimately reflects how the changes in the glass structure at the short- and intermediate-range orders affect the long-range order. In vitreous silica, the microscopic reasoning for the elastic anomaly of the densified glass is primarily explained by the intermediate order, which involves the reorganization of 6-membered silicate rings [4]. In contrast, the elastic modulus anomaly in the PS glass seems to be strongly influenced by the short-range order and the interplay of the lead coordination and silicate polymerization degree, as mechanisms analogous to those for vitreous silica are ruled out in this depolymerized glass composition [7]. Despite the anomalous vibrational behavior on the
continuous scale, intermediate scale lengths that approach the BP wavenumbers seem to follow
the same trend observed on densified glass compositions, either with a low- or high-degree of
polymerization. In the case of lead metasilicates, the densification seems to induce
depolymerization, whereas lead coordination remains a topic of ongoing interest in the literature,
even regarding pristine glasses with different PbO content [65, 66]. In this sense, complementary
investigations applying NMR and X-ray probes [67] may provide quantitative information and
elucidate coordination modifications driven by these different treatments not directly accessed by
vibrational spectroscopies. Remarkably, the full comprehension of the mechanical properties and
their correlation with the glass structure is both promising and complex, and its extension to
densified samples is challenged by the reduced sample sizes involved. Even so, the multiscale
characterization of treated glasses – where the composition is held constant, while distinct extreme
conditions of pressure and temperature are at play – can provide deep insights into the
interconnection between structure and property, which is imperative for further understanding and
designing the future generation of glass materials.

Conclusion

In this work, lead metasilicate (PbSiO3) glass samples were subjected to cold and hot
compression and ex-situ investigated by Brillouin, Raman, and infrared spectroscopies. Guided
by the vibrational probes, this study described the effect of different compression treatments on
the multiscale vibrational modifications of a depolymerized glass structure. Specific compression
conditions result in the elastic modulus anomaly, where the refractive index-weighted velocities
(or simply the longitudinal Brillouin shift) decrease upon densification, whereas hot-compression
under the most extreme conditions drives the conventional increase in the sound velocities and
hence the elastic modulus. Despite its toxicity and general effort to eliminate lead-bearing glasses
from applications, such a composition still holds a promising fundamental role as a ‘glass model’,
for which a detailed study of the resulting pressure-induced structures may shed further light on
the intricate correlation between glass structure and mechanical properties.

Acknowledgments

We are extremely thankful to José Rodrigues da Silva (LaMaV, UFSCar) and Philippe Veber
(ILM, UCB Lyon 1) for their invaluable aid in producing and conforming the samples. The authors
are grateful to the São Paulo Research Foundation (FAPESP) for funding this research through the CEPID project no. 2013/07793-6, the Brazilian grant no. 2017/11868-2 (RBP), 2019/12383-8 (TRC), 2021/13974-0 (ADR), and the Brazil-France cooperation grant no. 2019/11446-6 (RBP), the CNPQ grant 2021-0/303020 (PSP). We are also thankful to CNRS-UCB Lyon 1 for their financial support. The high-pressure experiment conducted in a Belt press apparatus was performed at the Lyon Platform of Experiments under Extreme Conditions (ILMTech-PLECE). Brillouin and Raman experiments were carried out at the Vibrational Spectroscopies Platform at the University Lyon 1- France (ILMTech-CECOMO). Infrared experiments were performed at LaMaV, at the Universidade Federal de Sao Carlos - Brazil. The content of this paper was partially presented at the ICG-2022 Conference in Berlin: "Cold- and Hot-Densified Lead Metasilicate Glass: A Multiscale Vibrational Investigation".

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