# Thermal relaxation of silica phases densified under electron irradiation

Mahinour Mobasher, Matthieu Lancry, Jiafeng Lu, Daniel R. Neuville, Ludovic Bellot-Gurlet, Nadège Ollier

► To cite this version:

Mahinour Mobasher, Matthieu Lancry, Jiafeng Lu, Daniel R. Neuville, Ludovic Bellot-Gurlet, et al. Thermal relaxation of silica phases densified under electron irradiation. Journal of Non-Crystalline Solids, 2022, 597, pp.121917. 10.1016/j.jnoncrysol.2022.121917. hal-03784265

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# Thermal relaxation of silica phases densified under electron irradiation

M. Mobasher<fnref n="1" />, M. Lancry<fnref n="2" />, J. Lu<fnref n="2" />, D. Neuville<fnref n="3" />, L. Bellot Gurlet<fnref n="4" /> and N. Ollier<fnref n="1" />

## Abstract

The thermal relaxation of the silica metamict phase obtained after electron irradiation of 11 GGy Suprasil SiO₂ glass was characterized using Raman spectroscopy and compared to silica densified under high Pressure and high temperature irradiated at 10⁷ Gy. In parallel, we studied the densification relaxation kinetic by step isochronal annealing treatments. Starting from the metamict phase, local density indicators, D₁ and D₂ bands decreased quasi-monotonously under thermal treatment together with the glass density. However, for 10⁷ Gy samples, we evidenced an anomalous sharp increase of D₁ and D₂ bands between 800 °C and 1000 °C, which could be interpreted as a transition from low-density amorphous (LDA) to a high-density amorphous configurational state (HDA). Interestingly after an annealing at 1000°C, the overall Raman signature indicates that the “relaxed metamict phase” exhibits a higher configurational disorder than pristine silica whereas 10⁷ Gy samples simply relaxed towards pristine silica suggesting a low density amorphous megabasin with several minima.

**Keywords:** silica glass, high pressure, high temperature, densification, electron irradiation, metamict phase, thermal relaxation.

## 1. Introduction

SiO₂ oxide is omnipresent in nature, it is the main constituent of the earth mantle minerals. Silica-based glasses provide the backbone of many of nowadays rapidly expanding photonics applications, which cover diverse fields such as optical communications, electronics, sensor technologies, medicine, and materials processing. All these applications request ultra-high precisions and repeatability in the optical and thermo-mechanical properties of silica glass, which is very sensitive even to small structural modifications and the presence of point defects.

<footnote n="1">¹Laboratoire des Solides Irradiés, École polytechnique-CEA-CNRS, 91128 Palaiseau Cedex,
France</footnote>

<footnote n="2">²Institut de Chimie Moléculaire et des Matériaux d'Orsay, Université Paris-Saclay, Rue du doyen Georges Poitou, 91405 Orsay cedex – France</footnote>

<footnote n="3">³CNRS-IPGP, Géomatériaux, 1 rue Jussieu, 75005 Paris, France</footnote>

<footnote n="4">⁴MONARIS "de la Molécule aux Nano-objets : Réactivité, Interactions et Spectroscopies"
UMR 8233SU/CNRS, Sorbonne Université, 4 Place Jussieu 75252 Paris Cedex 05, France</footnote>
Despite the fact that it is a simple 4-fold coordinated glass and thus often used as a model glass system, amorphous silica presents anomalies that are still unresolved (e.g. the anomalous negative pressure derivatives of elastic moduli at low pressure or its anomalous density increase with increasing fictive temperature)¹. Another open question concerning silica is its potential polyamorphism², ³, ⁴ e.g. the fact that two or more energetically distinct amorphous states coexisting in different proportion according to pressure and temperature. Different amorphous states with distinct short- and/or intermediate-range orders can be produced by thermo-mechanical path engineering and one of the challenging questions to be addressed is the nature of the phase transformation between LDA (low density amorphous state) and HDA (high density amorphous, corresponding to the 2.6 g/cm³ phase obtained at 25 GPa). The coexistence of LDA and HDA states in silica coupled to the presence of floppy modes is one assumption that was advanced to explain the non-monotonic variation of sound velocity (or compressibility) when the pressure increases⁵. Because of a large free volume, permanent densification in silica can reach 21 % by applying high hydrostatic pressure (typ. 25 GPa at room temperature) whereas under irradiation (neutrons, electrons, ions, ...), a maximum densification of 3-4 % can be achieved⁶,⁷. Electron irradiation can alter not only SiO₂ glass density and structure but also its optical and mechanical properties⁸. As expected, the effects are quite different in silica and silicate glasses (with alkaline ions), which also depend on the irradiation dose and on the energy of electrons. One common feature in silica is the creation of point defects⁹ (like E', NBOHC or some unknown defects leading to green light emission in compacted silica¹⁰) that is usually accompanied by some modifications of the structure itself, especially for high-energy electron when dose is larger than 1 GGy⁸. In silicate glasses, at low energy electron (keV range) the formation of channels was observed by SEM due to the migration of alkaline ions¹¹ as well as oxygen bubbles or phase separation by TEM⁸, ¹². It is assumed that the observed compaction of silica glass is due to the accumulation of point defects that causes reorganization and re-bonding of the network⁷,⁸. Following this view, some Raman spectroscopic signature confirmed this, after high-energy electron irradiation (2.5 MeV) like an increase D₂ band area as a function of deposited dose associated to shift of the 440 cm⁻¹ band indicating a decrease of the Si-O-Si average angle¹³. This was also observed by Gavenda et al.¹⁴ for lower electron energy (50 keV).

We have recently studied the relaxation of densified amorphous silica glasses under electron irradiation¹⁵,¹⁶. It was found that the pre-densified silica glasses exhibit a relaxation of their macroscopic density with increasing the integrated dose of electron irradiation¹⁶. We have also shown that independently of its initial configuration disorder and density (ranging between 2.21 and 2.6 g/cm³), under a subsequent irradiation dose of 11 GGy, all silica samples relax towards a unique structure with a similar Raman signature and associated to a 2.26 g/cm³ density¹⁵, similar to the metamict phase obtained from quartz amorphization⁶. Structural information on the metamict phase is not so rich in literature. However, some information was obtained via electron diffraction patterns in ref. ¹⁷. The authors compare these patterns for α-quartz experiencing a progressive amorphization in a 100-kV electron beam and the metamict phases are determined to be topologically disordered and lack long-range translational order due to the absence of sharp electron spots ¹⁷. Furthermore, the distinct Si-O and O-O distinct interatomic distances were
evaluated, concluding that the SiO₄ tetrahedral structural unit remains intact. This was based on the radial density function derived from energy-filtered electron diffraction patterns of vitreous silica and metamict α-quartz, amorphized with 100-keV electrons and almost 1 MeV neutrons. In addition, the structure of metamict phase formed from several silica polymorphs precursors are different by the use of energy-filtered electron diffraction and no unique state is reached, the method of amorphization is also an important contributing factor¹⁷. Elsewhere, Hasegawa et al.¹⁸actually deduced that the positron lifetime measured in a metamict phase obtained after high dose neutron irradiation of quartz at 8.3x10¹⁸ n/cm² is the same as those for amorphous silica after being irradiated at the same dose¹⁸. Positronium atoms are found to form in micro voids in the metamict phase with an average radius of 0.3 nm¹⁸.

In the present study, we aim to use the thermal relaxation of the metamict phase to know better about its properties, including LDA, HDA and transitions between them. The thermal relaxation of densified silica samples by high pressure (HP) was recently investigated by Cornet, Guerette and Arndt ¹⁹⁻²¹ without any type of irradiation involved. Their samples were densified by two different methods: A) high pressure and high temperature (HP-HT also called hot compression) and B) densification of high pressure at room temperature (cold compression). They found out that samples densified under high temperature were more homogenous and stable, as they required longer duration to relax¹⁹,²⁰. On the other hand, samples densified at room temperature under high pressure relaxed faster and at lower temperatures¹⁹,²⁰. Furthermore, the relaxation occurred through a transitory state, which surprisingly revealed an increase in the D₂ band width¹⁹.

So, the main focus of this study is comparing high pressure and high temperature densified silica samples along different densification pathways followed by electron irradiation at 10⁷ Gy and 11 GGy (corresponding to the metamict phase). After a quick survey of the literature showing that all kinds of irradiations and whatever the initial silica density, high doses all converge towards the same density related to the metamict phase, we investigated the thermal relaxation of densification in these samples. In this view, we measured both the macroscopic density and the vibrational structure by means of Raman spectroscopy during step isochronal annealing experiments.

## 2. Experimental details

**Densification and irradiation pathways:** The high purity synthetic fused silica materials manufactured by flame hydrolysis of SiCl₄ were the starting materials for this study. Heraeus Suprasil F300HQ silica rod samples (<1 ppm of OH, <2500 ppm Cl) were densified at high Pressure-high Temperature conditions (HP-HT) under different pressure and temperature values as 5 GPa_1000 °C, 5 GPa_350 °C and 4 GPa_450 °C. The samples were densified using a belt press at the ILM Laboratoire in the PLECE Platform at Lyon1 University²². The samples' diameter is around 3.5 mm and the thickness ranges between 400 µm and 1 mm. After densification, the samples were irradiated at two doses: 10⁷ Gy and 11.10⁹ Gy (11 GGy) to obtain six samples in total. In this view we used high-energy electron irradiation of 2.5 MeV, which was carried out using SIRIUS facility (LSI/CEA/Ecole Polytechnique). The current used during irradiation was not exceeding 25 µA and the temperature was set not going higher than 60 °C
due to the presence of a water-cooling sample holder. There is an additional sample of pristine
silica that was irradiated at 11 GGy without previous densification labeled "Silica 11.10<sup>9</sup> Gy
"taken for comparison as well as a pristine silica sample without any treatment labeled "Pristine
Silica".

**Thermal relaxation:** After irradiation, all samples were step isochronal annealed at temperatures ranging between 25 °C and 1000 °C. The 11 GGy samples were annealed for δt=1 hour at a given temperature while the 10<sup>7</sup> Gy samples were annealed for δt=30 minutes at a given temperature. The annealing was done in an air furnace in Institut de Physique du Globe de Paris IPGP (10<sup>7</sup> Gy) and in MONARIS lab (11 GGy).

**Raman Spectroscopy conditions:** The Raman spectra were all obtained at room temperature. For the 11 GGy irradiated samples, Raman spectroscopy was performed using a HR Infinity (458 nm) in MONARIS Lab (Paris 6). For 10<sup>7</sup>Gy samples, Raman spectroscopy was performed using a HR Evolution from Horiba (488 nm) in Institut de Physique du Globe de Paris (IPGP). All the Raman spectra were submitted to the same analytical treatment using Origin software. First, we apply a baseline correction in order to adjust the intensity around 1750 cm<sup>-1</sup> at zero. Second, the intensity of all spectra was normalized to 1 according to the main band intensity, namely the R-band peaking around 440 cm<sup>-1</sup>. The intensity of Raman bands such as D<sub>1</sub> and D<sub>2</sub> were then estimated by reading the maximum at peaks. The typical error on D peaks normalized intensity is estimated to be ± 0.01. Concerning the full width at half maximum (FWHM) of R-band at 440cm<sup>-1</sup> for the 11 GGy samples, an additional baseline correction was done for all the temperatures explaining the lower values than for the 10<sup>7</sup> Gy irradiated samples. However, only the variation is of interest, we are not discussing absolute values.

**Density measurement:** Density measurements were held in Institut de Physique du Globe de Paris. Density was measured using the sink-float method based on the Archimedean technique following the equation of state of toluene liquid (density(T) = 0.8845 - 0.9159 × 10<sup>-3</sup> × T + 0.368 × 10<sup>-6</sup> × T<sup>2</sup>, T in °C)<sup>23</sup>. The samples were weighed in air and immersed in toluene, which was the immersion liquid used. In addition, the temperature of the toluene was also recorded. The density was measured first for each sample directly after densification and after irradiation at room temperature around 25 °C. Then, the density of each sample was recorded at room temperature successively after each isochronal annealing step like the acquisition of the Raman spectra.

**3. Results**

3.1 Survey of the literature related to the densification kinetics for various kinds of irradiations

Quartz metamict phase was first discovered by Primak ⁶ in 1958 after a high dose of neutron
irradiation of 1.8 x10²⁰ neutrons/cm². He noticed that the density of quartz and silica reach same
value of 2.26 g/cm³ after irradiation at this dose with a close amorphous system structure
(evidenced by Raman spectroscopy later in <sup>24</sup>). As seen in figure 1 gathering data from literature<sup>6,7,14-16,25-30</sup> the density of silica or its crystalline polymorph evolves always to 2.26 g/cm<sup>3</sup> after irradiating with neutrons, lasers, ions or electrons. The doses are expressed in eV/cm<sup>3</sup> for comparison and evidenced different efficiencies regarding to the type of irradiation. The slower kinetics is related to laser irradiations<sup>27-29</sup> whereas the faster one is for high-energy ions<sup>7</sup>,<sup>25</sup>

<figure><img src="image_2.png" /><figcaption>**Figure 1:** Density of silica (full symbols) or quartz (empty symbols) against irradiation dose expressed in eV/cm³ for different types of irradiations (UV laser, IR femtosecond laser, ions, electrons, neutrons)</figcaption></figure>

The densification assisted by irradiations (typ. 3-4 %<sup>6,7</sup>), usually based on point defect accumulation and glass restructuration, leads to a much lower densification rate efficiency compared to high pressure that can reach 21 %<sup>31</sup>. Moreover, the mechanisms leading to this densification are quite different for the various kinds of irradiations. As for neutrons and heavy ions, it is by knock-on with atomic displacement and for electrons, it is mainly by bond breaking accumulation <sup>6, 7</sup> induced by the point defects creation. For femtosecond laser, the mechanism is more complex with a key role of defects but also a temperature assisted relaxation<sup>32,33</sup> and even the development of strong dynamic stress at high energy <sup>34</sup>.
## 3.2 Study of the thermal relaxation through the density evolution

Figure 2 exhibits the density of all investigated samples according to the step isochronal annealing temperature. All measurements were done at room temperature. There are two sets of samples: full symbols are for samples irradiated at 11 GGy thus starting from the metamict density. In contrast empty symbols are for HP-HT samples irradiated at 10⁷ Gy resulting in an initial density higher than 2.26 g/cm³ prior thermal relaxation.

As it can be seen in figure 2, after being stable until almost 600°C, the density for all samples -no matter the irradiation dose and the densification pathway- is monotonously decreasing with temperature. The decrease continues until 1000 °C for which all samples are reaching a density of 2.20 g/cm³ that is equal to the one of pristine silica. Going one step further, we have performed a fitting of *Density*(*δt*, *T*) for all samples using a single component model. In ref ³⁵, the authors find that if the erasure kinetics is Arrhenius type with distributed activation energy, and if this distribution is according to a sigmoidal derivative (a quite common attribute in irradiated silica) we can use the following expression:

$$Density(\delta t, T) = 2,2 + \alpha \left( \frac{1}{1 + \exp(-2\ln(3)T_0/\Delta_T^{\delta t}) (3)^{\Delta_T^{\delta t}}} \right) \quad Eq. (1)$$

Here $T_0$ is the inflection point of the falling curve (step isochronal annealing), $\Delta_T^{\delta t}$ is a T deviation of which corresponds to the fall of *Density*(*δt*, *T*) around $T_0$ and *δt* being the isochronal annealing time (typ. 30min). Fitting results are given in the discussion section.

<figure><img src="image_3.png" /></figure>
**Figure 2:** Silica density evolution versus step isochronal annealing temperature. Empty symbols are for 10⁷ Gy samples whereas full symbols are for 11 GGy samples. Fitting against a sigmoidal function is shown.

### 3.3 Study of the thermal relaxation through Raman spectroscopy

Figure 3 displays one example of the evolution of the normalized Raman spectra along step isochronal annealing for the 5GPa_350°C SiO₂ sample irradiated at 10⁷ Gy. We can notice obvious modifications concerning the D₁ and D₂ band intensities as well as FWHM of the R-band (peaking around 440 cm⁻¹). These modifications are exposed and analyzed in the following section and compared to pristine silica prior any annealing (green full line in figure 3) for the sake of comparison.

<figure><img src="image_4.png" /><figcaption>**Figure 3:** Raman spectra evolution during 30min step isochronal annealing for HP-HT silica (5GPa_350°C) irradiated at 10⁷ Gy. Measurements are done at room T.</figcaption></figure>

D₂ band peaking at 606 cm⁻¹ relates to the breathing mode of the oxygen atoms in the 3-membered rings of silica³⁶⁻³⁸. We plotted the evolution of the D₂ normalized intensity according to the annealing temperature in figure 4. The D₂ band intensity is normalized by the following equation: $D_{2norm}(δt, T) = D_2(δt, T)/D_2(0,20°C)$. Figures 4A and 4B are corresponding to the silica samples irradiated at 10⁷ Gy and 11 GGy respectively. Obviously, there is a key difference in the trends followed by the $D_{2norm}(δt, T)$ with annealing temperature according to the pre-
irradiation dose: a non-monotonous decrease for 10⁷ Gy samples and a quasi-monotonous one for 11 GGy samples.

In the following, we consider that the measured D₂ amplitude is composed by additive/subtractive local contributions. In addition, they all present different erasure kinetics based on their thermal stabilities. Here we assume that the erasure kinetic of each “i” component follows a sigmoidal evolution:

$$D_{2norm}(\delta t, T) = a_i \left( \frac{1}{1 + \exp(-2\ln(3)T_i / \Delta_{T_i}^{\delta t}) (3)^{\frac{2T}{\Delta_{T_i}^{\delta t}}}} \right) \quad \text{Eq. (2)}$$

In this equation³⁹ “aᵢ” represents the relative contribution to D₂norm(δt, T), “Tᵢ” is the temperature where the curve falls for the “i” component”, and ΔTᵢδt (in K) regulates the slope of decay. Following this view, we have performed a decomposition of the normalized D₂ band evolution, D₂norm(δt, T), for all three samples (4 GPa_450 °C, 5 GPa_350 °C, 5 GPa_1000 °C) using a two-component model as shown in figure 4A. In contrast the 11 GGy irradiated samples in figure 4B follow a less pronounced non-monotonous evolution but were also fitted with a two-component model revealing that the erasure kinetics are quite similar for all these samples.

In figure 4A, we observe the D₂ intensity increase around 800-900°C. For the 5 GPa_1000 °C sample particularly, the D₂ intensity is stable until 700 °C, followed by an anomalous sharp increase to reach a steady state at 1000 °C. In addition, we can see that the higher the temperature during the hot compression, the higher “T₀” i.e. the temperature where the curve fall. On the other hand, figure 4B shows a slight non-monotonous behavior for the normalized D₂ intensity evolution: a slight increase below 500°C then monotonously decreasing from 500 °C until 1000 °C.

<figure><img src="image_5.png" /></figure>

<figure><img src="image_6.png" /></figure>
**Figure 4:** D₂ band normalized evolution against step isochronal annealing temperature for samples irradiated at 10⁷ Gy (A) and 11 GGy (B). Insets are showing some examples of D₁ normalized evolutions. Measurements are done at room T in SiO₂.

Another interesting feature that was investigated is the D₁ band peaking at 495 cm⁻¹ as shown in figure 3 and that relates to the breathing mode of the oxygen atoms in the 4-membered rings of silica³⁶⁻³⁸. As seen in the insets of figure 4, its trend is similar to D₂ band evolution as there is an anomalous change in D₁ intensity between the 800 °C -1000 °C range for the 10⁷ Gy irradiated samples. In contrast a monotonous decrease in the D₁ intensity is noticed for the samples irradiated at 11 GGy from 700 °C till 1000 °C, this is again similar to D₂ band.

For going one step further we have extracted the full width at half maximum (FWHM) of the Raman main band centered around 440 cm⁻¹ (R-band) as shown in figure 3. This broad band centred at ~ 440 cm⁻¹ corresponds to the symmetrical Si–O–Si stretching vibration mode. It is widely accepted that this band can be ascribed to the predominant motions of oxygen atoms, involved in Si–O–Si bonds in five-, six or higher membered rings⁴⁰⁻⁴². This band is then usually correlated to the glass disorder and its FWHM is usually attributed to the “dispersion” of the Si–O–Si angle. FWHM of the R-band as a function of the step isochronal annealing temperature is displayed in figures 5A and 5B for 10⁷ Gy and 11GGy irradiated samples respectively. As it can be seen in figure 5A, the 5GPa_1000°C sample irradiated at 10⁷ Gy exhibits a stable FWHM of the R-band until 700°C and then rapidly increases for higher temperatures. This contrasts with the two other samples irradiated at the same dose as their FWHM early increase at 250°C thus revealing a quite “unstable” densification. As for the 11 GGy samples, there all exhibit a quasi-monotonous increase of FWHM values with increasing temperatures. One additional concern here is to compare the final “steady” state at 1000 °C for all the samples with the Raman signature of pristine silica that is indicated as green horizontal dashed line in figure 5. As seen for 10⁷ Gy samples (figure 5A), all of them reach a value of FWHM very close to that of pristine silica after the heat treatment at 1000°C. However surprisingly, the FWHM for samples irradiated at 11 GGy (figure 5B) becomes much higher than that of pristine silica indicating a larger distribution of the Si–O–Si angles.

<figure><img src="image_7.png" /></figure>
**Figure 5:** Full width at half maximum (FWHM) of the R-band evolution against step isochronal annealing temperature for samples irradiated at $10^7$ Gy (A) and 11 GGy (B). Measurements are done at room T in $SiO_2$.

Thus, despite having a similar final density value of 2.20 g/cm$^3$ like pristine silica (as seen in figure 2), the vibrational signature of the 11 GGy (metamict like phase) samples annealed at 1000 °C, i.e. the relaxed metamict phase, is clearly different than that of pristine silica. This feature is not an isolated one, this result is supported by other Raman indicators, which are plotted with respect to density to see the effect directly. One of them is the $D_2$ band intensity whose evolution according to density is reported in figure 6 where the temperature increase is indicated by the color gradient arrow. As it can be seen for the 11 GGy samples, the intensity of $D_2$ band after a 1000°C annealing is much lower than that of pristine silica whereas they all reach a density of 2.20 g/cm$^3$. In addition, we evidenced a wide variety of the $D_2$ intensity values for a same density around 2.24-2.26 g/cm$^3$ (see rectangular zone together with the solid curve) that might be related to an amorphous-amorphous transition from the metamict phase to the “relaxed metamict phase”.

<figure><img src="image_8.png" /><figcaption>**Figure 6:** Evolution of $D_2$ band intensity of 11 GGy $SiO_2$ samples with respect to the density. Measurements are done at room T after each annealing step. Red dashed rectangle highlighting a kind of “amorphous-amorphous transition” with a solid blue curve as a guide for eye.</figcaption></figure>

After revealing that the “relaxed metamict phase” obtained after heat treatment at 1000°C own a different vibrational structure compared to pristine silica, further annealing were done at higher
temperatures on the HP-HT densified samples irradiated at 11 GGy. Following a treatment at 1100 °C, the Raman spectra are similar to those obtained after annealing at 1000 °C. It seems that the complete recovery from the metamict phase towards the pristine silica structure is not reached even at high temperature despite having a similar density of 2.20 g/cm³. This might indicate that the glass structure has been so much depolymerized through defects accumulation during irradiation so that the final state exhibits a higher configurational disorder as seen through the FWHM of the R-band that is much wider than pristine silica (figure 5B). Finally, for heat treatments performed at 1250 °C, the samples crystallize so the Raman data are quite difficult to exploit in a reliable manner.

## 4. Discussion

Different results were evidenced in this work. Firstly, concerning the relaxation of the density for samples irradiated at low dose (10⁷ Gy), we evidenced a stability up to 600°C especially for silica densified at high temperature (typ. at 1000°C) in agreement with the results of Guerette²⁰. As it can be highlighted from the fitting results shown in Table 1, examining the glasses irradiated at 10⁷ Gy, we notice that T₀ decreases (whereas Δₜ²t increases) significantly in correlation with the glass initial density e.g. 5GPa_1000°C being the most stable while 4GPa_450°C own the faster relaxation. Note that using the Variable Reaction Pathway (VAREPA) framework developed by Poumellec et al.³⁵, we can tentatively give a physical meaning to these parameters. T₀ is related to the center of activation energy distribution E₀ = kₛT₀ln(k₀t) and Δₜ²t to the FWHM ΔE of the distribution that can be rewritten as ΔE= kₛΔₜ²tln(k₀t). Following this view and assuming that the relaxation constant rate k₀ (expressed in s⁻¹) is quite similar for these 3 samples, this indicates that the distribution of activation energy at the root of the densification process is much wider (higher ΔE) and centered at lower activation energy E₀ for low density samples (4GPa_450°C) whereas it is much narrower (less distributed) and centered at higher activation energy for 5GPa_1000°C. However, a more in-depth discussion would need to determine these numerical values that requires knowing the k₀ and thus performing additional accelerated ageing experiments for different times and temperatures.

<table><caption>Density vs Temperature fitting (See Equation 1 & Figure 2)</caption><thead><tr><td>Sample</td><td>a</td><td>T₀</td><td>ΔT</td></tr></thead><tbody><tr><td>5GPa_1000 10<sup>7</sup>Gy, d<sub>init</sub>= 2.6448 g/cm<sup>3</sup></td><td>0.44 ± 0.01</td><td>883 ± 11</td><td>104 ± 27</td></tr><tr><td>5GPa_350 10<sup>7</sup>Gy, d<sub>init</sub>= 2.34407 g/cm<sup>3</sup></td><td>0.14 ± 0.01</td><td>790 ± 23</td><td>203 ± 45</td></tr><tr><td>4GPa_450 10<sup>7</sup>Gy, d<sub>init</sub>= 2.32255 g/cm<sup>3</sup></td><td>0.13 ± 0.01</td><td>630 ± 17</td><td>283 ± 41</td></tr><tr><td>4GPa_450 11x10<sup>9</sup>Gy, d<sub>init</sub>= 2.24975 g/cm<sup>3</sup></td><td>0.055 ± 0.01</td><td>824 ± 20</td><td>163 ± 37</td></tr></tbody></table>
<table><caption>Table 1: The different fitting parameters used in Equation 1 to represent the thermal relaxation of samples densified in various conditions.</caption><tr><td>Silica 11x10<sup>9</sup>Gy,<br>d<sub>init</sub>= 2.25222 g/cm<sup>3</sup></td><td>0.049 ± 0.01</td><td>812 ± 17</td><td>172 ± 39</td></tr></table>

In contrast, for samples exhibiting different thermo-mechanical history but extensively irradiated at 11 GGy (so they all reached the “metamict like phase” before thermal relaxation), they exhibit quite similar thermal relaxation kinetics for both the density and D₂ band decay (see figure 4B). More precisely they have nearly the same T₀ and ΔT values (see table 1) thus indicating a quite similar activation energy distribution or “energy landscape” that is attributed to the fact they all “start” from a quite similar state i.e. the “metamict like phase”. Note here that the densification process related to the metamict phase (e.g. 4GPa_450°C 11.10⁹ Gy) exhibits a higher thermal stability (higher E₀ and lower ΔE) than that of (4GPa_450°C 10⁷ Gy) sample indicating that high dose irradiation seems to have populated a numbers of high-energy configurational states with a narrower distribution (a lower width ΔE of the distribution function).

Now let’s exploit the vibrational data deduced from Raman spectroscopy. Starting from densified samples under HP-HT and only “slightly” irradiated at 10⁷ Gy, we noticed a monotonous decrease of the density but an anomalous evolution of the local density indicators namely D₁ and D₂ bands. In particular, the related thermal relaxation kinetics appear to be strongly impacted by the temperature used during the prior hot compression treatment i.e.:

- Comparing both samples densified at 5GPa, the higher the temperature during hot compression, the higher the amplitude of the anomalous behavior of D₂ (and D₁, see insets in figure 4) bands. This can be quantitatively reflected through the fitting results of the D₂ band using a two-component model (see fitting curves in solid lines in Figure 4A). To some extent, this reveals a higher quantity (or rather proportion) of high-density configurational states that are generated under thermal treatment in (5GPa_1000°C 10⁷ Gy) SiO₂ sample.

- Additionally, the formation of these high-density local indicators looks “easier” (need a smaller thermal energy) in samples compressed at 350 °C or 450°C, which corresponds to a lower T₀ value of the 1st component of the fit (i.e. the anomalous increase). Note that this correlates with the evolution of the FWHM of the R-band, which starts its monotonous increase at the same time.

- Finally, it appears clearly that (5GPa_1000°C 10⁷ Gy) SiO₂ sample exhibits a higher thermal stability: no decay of its overall vibrational signature until 750-800°C whereas others start to relax above 400°C. This agrees well both with results reported in the literature¹⁹,²⁰ and with the density evolution reported here indicating that the densification is based on an activity energy distribution that is quite narrow and centered at high energies.

One major result here concerns the significant deviation to the monotonous relaxation with temperature of D₁ and D₂ band intensity observed for highly dense silica (slightly irradiated) in contrast to the “metamict like” samples (irradiated at 11 GGy). Such a transitory anomalous
evolution was already observed during the thermal relaxation of densified silica ¹⁹, ²⁰, ⁴² without
any irradiation involved. As a matter of fact, the relaxation occurred through a “high local
density” transitory state, which appears through an increase in the D₂ band in ref ¹⁹. Same
authors in ⁴³ evidenced the same transitory state characterized by a large structural disorder
during dense silica thermal relaxation by SAXS and WAXS. They tentatively associated this
result to the existence of two “megabasins” in the energy landscape with an “amorphous-
amorphous transition” between high-density configurational states (HDA) and low-density states
(LDA). In the present paper, we suggest that the glass firstly densified at 5 GPa_1000°C and
then irradiated at 10⁷ Gy own a thermal relaxation that is quite similar to Cornet studies
¹⁹,⁴³.Concerning silica samples with a lower density (5GPa_350°C and 4GPa_450°C), they also
show a transitory state but less intense and less sharp (so likely more distributed), indicating the
proportion of HDA and LDA states are rather different. Examining the Si-O-Si angle dispersion
revealed by the FWHM of the R-band, it displays a sharp transition as well in the 800-1000°C
with an abrupt increase in the most densified glass inferring the existence of this transitory
structural disorder. Note here that the final state reached after thermal relaxation is similar to
pristine silica in terms of macroscopic density and vibrational signature.

Starting from metamict phase (11 GGy samples) we have a much smaller increase of local
density indicators (namely D₁ and D₂ bands) before the monotonous relaxation observed above
400°C. This suggests that the relaxation of metamict phase own a much less pronounced
transitory step (through HDA) and mostly evolves towards LDA states. In particular, by
analyzing the relaxation kinetic of metamict phase as a function of density (figure 5B), we notice
a large dispersion of the R-band wavenumber (thus related Si-O-Si average angle) as well as a
very sharp transition (factor 7-8) of 3-membered rings in the 2.24-2.26 g/cm³ density range. Such
a sharp peculiarity in the fast relaxation versus the density around 2.26 g/cm³ was also depicted
by Surovtsev et al⁴⁴. These authors report this phenomenon to a particular inhomogeneous
structure of silica metamict phase reminding that its density is really close to tridymite
polymorph. This result could reflect an amorphous-amorphous transition between “metamict like
phase” towards a more disordered phase than pristine silica (mostly related to LDA states) that
could imply other megabasins. Indeed, surprisingly the “relaxed metamict phase” owns a
different vibrational signature from pristine silica. This is characterized by a larger Si-O-Si angle
dispersion and a lower number of small membered rings whereas both samples exhibit a similar
glass density around 2.20 g/cm³. A more detailed analysis of the structure of this “relaxed
metamict state” will be necessary. But this result might suggest that the LDA megabasin is
probably constituted like the HDA depicted by Guerette¹⁸ with a multiplicity of minima?

**5. Conclusion**
___

To sum up, we investigated the distinct metamict phase obtained after electron irradiation of 11 GGy in Suprasil SiO₂ glass along thermal relaxation kinetics using Raman spectroscopy and density measurements. The thermal relaxation of these samples was compared to HP-HT samples irradiated at a much lower dose (10⁷ Gy). Starting from the “metamict like phase”, a slight non-monotonous evolution in the D₁ and D₂ bands intensities can be observed as well as a monotonous decay for the density and an increase of R-band bandwidth. This contrast with 10⁷
Gy HP-HT SiO₂ where a strong anomalous evolution of local density indicators was evidenced namely a transient increase in the 800-1000°C range in agreement with previous results of literature on HP-HT glass. This might suggest an amorphous-amorphous phase transition between low-density amorphous (LDA) configurational states and high-density amorphous (HDA) states. Furthermore, Raman vibrational signature of the “relaxed metamict phase” obtained after annealing at 1100°C evidenced a more inhomogeneous structure than pristine silica itself despite having the same density of 2.20 g/cm³. This suggests the existence of a LDA megabasin similar to HDA with several minima.

## Acknowledgments

The authors acknowledge support from the EMIR&A French network (FR CNRS 3618) on the platform SIRIUS. We would like to thank also Sylvie Le Floch for the HP-HT samples (ILM). This research was partly funded by Agence Nationale pour la Recherche, FLAG-IR project ANR-18-CE08-0004-01, CNRS Défi "Instrumentation aux Limites", UltraBragg project and LABEX Charmmmat for the Master2 grant.

## Data Availability

Data are available upon reasonable request.

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