Behavior of soda-lime silicate glass under laser-driven shock compression up to 315 GPa

Silicate glasses are an integral part of the modern society with applications in electronics, housing, communication technologies, and terrestrial and space vehicles. They are of particular importance in military and space applications, where shuttle or aircraft windows can undergo high-energy ballistic impacts and encounter high-speed debris from micro-meteorites or broken satellite fragments or as the space shuttle reenters the Earth’s atmosphere.¹ These high-energy impacts are characterized by high pressures, temperatures, and strain rates. Silicate glasses are also used in high-power lasers as optical elements, in optical fibers, and as screens where they are often under thermal or mechanical stress. Under such dynamic loading conditions, pressure or strain-driven shock waves in solid materials can result in damage and deformation.^2,3 In order to assess and reduce the risk of damage that can cause structural failure, the behavior of glass under high pressure or strain rate conditions must be accurately studied using experimental and theoretical techniques. Understanding the behavior of various silicate glasses under dynamic compression would allow us to not only predict their behavior under high-energy impacts but will also allow us to establish a composition and network structure that can best sustain impacts without significant loss in transparency and strength.^2,3 Furthermore, silicate glasses at high pressures are used as model systems for understanding melts and liquids in planetary interiors.

Silicate glasses contain silica (SiO $2$⁠) as the main component with varied amounts of additional oxides. The structure of a typical silicate glass can be explained using the random network model where Si-oxygen polyhedra are connected through corner-sharing oxygen atoms to form a 3D network.^3,4 The oxygen polyhedra are usually trigonal planar or tetrahedral around the network forming cation. The network structure and, therefore, the behavior of the silicate glasses can be modified by changing the composition. The additional cations in the silicate glass can either act as a network former (B, Al, etc.) or a network modifier (Na, Ca, etc.). A network modifier breaks the network connectivity, creating a more open structure while a network former replaces Si and maintains the network connectivity to an extent. Understanding how the composition and network structure influences the dynamic response of silicate glasses is critical for tailoring and developing specific compositions based on required applications. Fused silica (FS), the simplest silicate glass consisting of only SiO $2$⁠, is typically used in space shuttles as it has a high thermal resistance and can withstand the extreme conditions during shuttle reentry. However, high purity fused silica is very expensive. Recent studies on fused silica observed the formation of crystalline stishovite upon shock compression.^1,5 While the dynamic response of fused silica has been studied extensively, the dynamic response of other silicate glasses, such as soda-lime glass (SLG), or borosilicate glass has not yet been systematically explored.

In this study, we report the dynamic behavior of SLG under laser-driven shock compression up to 315 GPa. The additional Na $+$ and Ca $2 +$ cations in the SLG break the Si–O–Si network connectivity leading to a more open structure with more non-bridging oxygen ions. Hugoniot measurements were performed using the long pulse optical laser at the Matter in Extreme Conditions (MEC) hutch at the Linac Coherent Light Source (LCLS). MgO and Lithium Fluoride (LiF) were used as the window material and as the standard for impedance matching. The velocity interferometer system for any reflector (VISAR) was used to measure the particle velocity at the Kapton (ablator)/SLG interface and the SLG/MgO(or LiF) window interface.^6–8 A U $s$–u $p$ relationship was obtained for the laser-driven shock studies and was compared to those from parallel plate impact studies. Comparison with previous studies on fused silica (FS) showed that in contrast with transformation to stishovite for pure FS, no amorphous to crystalline transformation is observed for SLG within the error bars up to 70 GPa.

$2×2$ mm $2$ double-side parallel-polished SLG of thickness 50  $μ$m and density 2.53 g/cm $3$ was obtained from Asphera Inc. The composition of SLG was measured using an Electron Probe Micro Analyzer (EPMA) to be $72.7%$ SiO $2$⁠, $12.9%$ Na $2$O, $10.2%$ CaO, $2.9%$ of MgO. The refractive index was measured to be 1.521 by observing the Becke line under an optical microscope with the sample immersed in oils of known refractive index. Two experimental target stacks were used for the measurement. For stack 1, as shown in Fig. 1(a), the SLG samples were glued to a 25  $μ$m thick Kapton B polyimide ablator using Hardman double bubble fast set epoxy glue. A 200 nm Al layer was deposited on the ablator, facing the laser drive, to prevent pre-shock from the tails of the laser pulse. A 100 nm Au layer was deposited in the Kapton/SLG interface on the SLG side as a reflecting surface for VISAR laser to measure the interface particle velocity following the shock wave entry. The glass samples were then glued to a LiF window of thickness 100–150  $μ$m, which was used as the standard with a known equation of state (EOS). A 100 nm Al layer was deposited at the SLG/LiF interface on one-half of LiF window, which also acted as a reflecting surface for the VISAR. The thickness of each SLG sample and LiF window was measured prior to the build. The thickness of the stack was measured after each gluing stage. A total glue thickness of 0–5  $μ$m was measured with the individual glue thickness at the Kapton/SLG side varying from 0 to 2  $μ$m and the glue thickness on the SLG/LiF varying from 0 to 3  $μ$m. This was measured for each stack and was included in the U $s$-u $p$ calculations. The error in thickness measurement was 0.5  $μ$m.

Figure 1(b) also shows a VISAR image captured during shock compression of SLG in the stack 1 geometry. The VISAR images for all the stack 1 data are shown in Sec. S1 in the supplementary material. The shock breakout into the interfaces is characterized by the motion in the VISAR fringes. There are two breakouts corresponding to the two reflecting surfaces. The first breakout (yellow dashed line) corresponds to the shock front entering the SLG through the Kapton/SLG interface and the second breakout (white dashed line)corresponds to the shock front exiting the SLG into the LiF window through the SLG/LiF interface. The difference between the breakout times can be used to estimate the transit time through the glass.

Stack 2, shown in Fig. 1(c), consists of SLG samples glued with the epoxy to a 25  $μ$m thick Kapton B polyimide ablator with a 200 nm Al layer facing the drive laser. The glass samples were then glued to an MgO window of thickness 500  $μ$m, which was used as the standard with a known EOS. A 100 nm Al layer was deposited at the SLG/MgO interface on the MgO window side, which acted as a reflecting surface for the VISAR laser to measure the interface particle velocity following the shock wave entry. The MgO window EOS was used to calculate the pressure inside the SLG sample through impedance matching. The total glue layer thickness for the stack 2 geometry was found to vary between 0 and 10  $μ$m. Figure 1(d) shows the interference image obtained from the 532 nm VISAR beam obtained upon laser-driven shock compression of SLG in target stack 2 geometry. A breakout, characterized by the motion in the VISAR interference fringes, is observed as the shock enters the MgO window from the SLG sample through the SLG/Al/MgO interface. The VISAR images for all the stack 2 data are shown in Sec. S2 in the supplementary material.

The 527 nm Nd:glass long pulse optical laser at the MEC end-station at LCLS was focused to a 300  $μ$m (stack 1) and 250  $μ$m (stack 2) spot size to drive the shock through the sample. Upon laser irradiation, the ablator produces a self-sustaining plasma that extends outward while simultaneously causing a compression wave to travel through the sample. In this study, we employed a 10 ns flat top pulse (FT 10 ns) for the drive laser. The samples were compressed to multiple pressure-temperature points in the Hugoniot space by changing the drive laser energy. The maximum drive laser energy employed was 60 J leading to a maximum intensity of $1.21× 10 13$ W/cm $2$ allowing the glass sample to reach pressures up to 315 GPa.

Figure 2 shows the apparent interface particle velocity evolution over time for different pressures inside the SLG sample. The peak particle velocity measured increases as a function of the drive laser energy for stack 1 and stack 2. The shock breakout into the SLG through the Kapton/Au/SLG interface in stack 1 is characterized by a sharp increase in the interface velocity measured from the VISAR. A steady shock is assumed for both stacks. The uncertainties in the particle velocity are obtained from the difference in the interface velocities immediately after the breakout in VISAR1 and VISAR2. The structure of the interface velocity curve could be potentially due to the structure of the flat top pulse or due to the arrival of edge release waves. For stack 2, the shock was seen to persist for about 5 ns in the samples. This was followed by release resulting in the observed decrease in the interface particle velocity.

The interface velocities were obtained from the magnitude of the fringe shift in the VISAR image using the Igor Pro 8 software and using LLNL’s AnalyzeVISAR code.^6–8 The peak interface particle velocity measured immediately after the shock breaks out, which corresponds to the peak position right after the sudden increase in the velocities in Fig. 2, was used in the analysis. This corresponds to interface velocity measured 300 ps after laser shock and includes detector response time, shock laser, and VISAR laser jitter.

For stack 1 geometry, the measured apparent interface particle velocity was corrected for the refractive index using the correction factor² to obtain the SLG particle velocity (u $p$⁠). To calculate the shock transit time through the SLG, the two breakout times corresponding to when the shock enters the Kapton/Au/SLG interface [dashed yellow line in Fig. 1(b)] and subsequently when shock enters the SLG/Al/LiF interface [dashed white line in Fig. 1(b)] were used. The shock velocity (SLG U $s$⁠) was then calculated from the transit time using the thickness of each SLG sample, which was carefully cataloged before the experiment.

The U $s$–u $p$ relationship for stack 2 is shown in Fig. 3 (red points). For stack 2, the shock velocity was determined in the following manner. The breakout times in the VISAR data were used to calculate the transit time through the SLG and Kapton. The time at which the shock breaks out into the SLG/Al/MgO interface was determined from the time of first fringe motion in both the VISAR1 and VISAR2. This was then corrected for the drive laser incident timing (t $0$⁠) using calibration files taken in the beginning of the day where a small amount of the drive laser light was allowed to directly pass through the VISAR legs and allowed to interfere. Therefore, the shock breakout time, i.e., the shock transit time through the Kapton, glue layers, and the SLG to the SLG/Al/MgO was determined. The shock velocities through Kapton for the incident laser energies were obtained from previous experiments performed at MEC^1,5 and were used to calculate the transit time through the Kapton layer. This Kapton transit time was subtracted from the shock breakout time to obtain the transit time through SLG. The shock velocity (U $s$⁠) for SLG was then calculated from the SLG transit time and the known sample thickness through which the shock transited. Note that the glue thicknesses were higher for stack 2 compared to stack 1. In order to account for the error due to glue thickness (0–10  $μ$m), an average glue layer of 5  $μ$m with a spread of 0–10  $μ$m was assumed for the calculations. The epoxy glue and the polyimide ablator were assumed to have similar shock speeds in determining the shock transit time through it. The U $s$–u $p$ relationship fit obtained from the stack 1 measurements were used as the Hugoniot for analysis of the stack 2 samples.

For stack 2 geometry, the SLG/Al/MgO interface particle velocity was measured after refractive index correction for the MgO window (⁠ $n=1.773±0.016$¹⁰) and corresponded to the reshocked state inside the SLG. To obtain the pressure–particle velocity (P–u $p$⁠) state in the SLG stack 2 samples, the SLG Hugoniot obtained from stack 1 measurements was impedance matched to the MgO Hugoniot obtained from the Los Alamos Shock Hugoniot databook by S.P. Marsh.¹¹ When the shock moves from SLG to MgO, a reshock wave is sent back into the SLG. The conservation equations dictate that the pressure and particle velocity are conserved across the contact interface between the MgO standard and the SLG sample. Therefore the pressure–particle velocity (P–u $p$⁠) state for the reshocked SLG and the shocked MgO must be the same.^9,12 Impedance matching was done by reflecting the SLG Hugoniot across the MgO Hugoniot (shocked state) at the measured interface particle velocity (reshocked state) in the pressure–particle velocity (P–u $p$⁠) space. The shocked state was then obtained from the point of intersection between the forward-facing SLG Hugoniot and the reflected SLG Hugoniot.^9,12 The density and the volume compression were obtained from Eqs. (2) and (3). The summary of all the shots including the drive laser average intensity, drive laser energy, U $s$⁠, u $p$⁠, and pressure (P) of samples in stack 2 geometry shock compressed by a 250  $μ$m spot size FT 10 ns pulse is presented in Table II.

Figures 3 and 4 show that U $s$–u $p$ is linear upto 315 GPa within the experimental error bars. Furthermore, the shocked SLG is seen to compress smoothly from 30 to 70 GPa without any sudden changes in the compressibility. Specifically, in comparison to FS, SLG is seen to be more compressible with increasing stress indicated by pressure vs volume dependence [Fig. 4(b)]. No noticeable discontinuity observed in the U $s$–u $p$ or the calculated pressure vs volume compressibility indicates toward lack of phase transition or polymorphic behavior in the SLG sample. This behavior is also consistent with the recent parallel plate impact studies done by Renganathan et al.² However, additional measurements, such as longitudinal modulus and sound velocity calculations, along with x-ray diffraction/pair distribution function analysis can further confirm the structural changes (i.e., continuous transition to a high density phase) under laser-driven shock compression.

The lack of sudden changes in the pressure vs volume compression $( ρ o ρ)$⁠, as well as the higher compressibility of shocked SLG in comparison with FS, indicates that the presence of Na $+$⁠, Ca $2 +$⁠, and Mg $2 +$ cations in SLG might impede the phase transformation to stishovite that is observed in fused silica. It is also possible that SLG undergoes a smaller change in volume during the transformation as observed by Renganathan et al.¹⁷ for a pressure range of 52–58 GPa, which shows solid to liquid transformation marked by an abrupt decrease in sound velocities and moduli. Our studies, thus, show that composition (i.e., the addition of Na $+$ Ca $2 +$⁠) can strongly influence the shock compression behavior of silicate glasses. While we focused on SLG in this study, studying the behavior of other silicate glasses, such as borosilicate, aluminum borosilicate, etc., which contain network former cations (B $3 +$⁠, Al $3 +$⁠), in the same pressure range would provide further information on how the additional oxides (both network formers and modifiers) influence phase transformations in the silicate glasses.

The dynamic response of soda-lime silicate glass was studied using laser-driven shock compression up to 315 GPa to investigate the effect of network modifying cations. The measured U $s$–u $p$ relationship was seen to agree well with the literature, indicating that shock behavior is similar in SLG for both laser-driven shock and gas gun studies. The lack of kinks or discontinuities in U $s$–u $p$ data within the error bars suggests there is no phase transition to stishovite up to 70 GPa, contrary to that observed for fused silica. These observations show that the presence of network modifiers impedes the phase transition to crystalline stishovite. This agrees well with the recent observations made in parallel plate impact measurements in the soda-lime glass indicating that despite different strain rates for gas gun and laser shock, the material behavior is similar. Detailed dynamic diffraction measurements are required to unequivocally identify the phases present during laser-driven shock compression.

The VISAR data for all the stack 1 and stack 2 SLG samples are shown in the supplementary material.

This work was supported by the Office of Naval Research (Grant No. N00014-19-1-2074). We also acknowledge the support by the U.S. DOE Office of Science, Fusion Energy Sciences under Contract No. DE-AC02-76SF00515: the LaserNetUS initiative at MEC, the Linac Coherent Light Source (LCLS), SLAC National Accelerator Laboratory. Use of the Linac Coherent Light Source (LCLS), SLAC National Accelerator Laboratory, is supported by the US Department of Energy, Office of Science, Office of Basic Energy Sciences under Contract No. DE-AC02-76SF00515. The MEC instrument is supported by the US Department of Energy, Office of Science, Office of Fusion Energy Sciences under contract DE-AC02-76SF00515. The VISAR analysis was done using LLNL’s AnalyzeVISAR code. This code was originally developed by Jon Eggert (JHE), which includes algorithms and methods from Peter Celliers (PMC) and Damien Hicks (DH) and contributions by multiple people in the LLNL group, including Stewart MC Williams, Marius Millot (MM), Dayne Fratanduono, Suzanne Ali, and others.

The authors have no conflicts to disclose.

Meera Madhavi: Data curation (equal); Formal analysis (equal); Investigation (equal); Methodology (equal); Writing – original draft (equal); Writing – review & editing (equal). Rahul Jangid: Investigation (supporting). Joyce Christiansen-Salameh: Investigation (supporting). Yu Hsing Cheng: Investigation (supporting). Pooja Rao: Investigation (supporting). Jianheng Li: Investigation (supporting). Surya Teja Botu: Investigation (supporting). Spencer Jeppson: Investigation (supporting). Jugal Mehta: Investigation (supporting). Scott Smith: Investigation (supporting). Jared T. Isobe: Investigation (supporting). Sovanndara Hok: Investigation (supporting). Rahul Saha: Investigation (supporting). Eric Cunningham: Investigation (supporting); Methodology (equal); Resources (equal). Philip Heimann: Investigation (supporting); Methodology (equal); Resources (equal). Dimitri Khaghani: Investigation (supporting); Methodology (equal); Resources (equal). Hae Ja Lee: Investigation (supporting); Methodology (equal); Resources (equal). D. K. Spaulding: Investigation (supporting); Methodology (equal); Supervision (supporting); Visualization (supporting). Danae N. Polsin: Investigation (supporting); Methodology (equal); Software (equal); Visualization (supporting). Arianna E. Gleason: Investigation (equal); Methodology (equal); Supervision (supporting); Visualization (supporting). Roopali Kukreja: Funding acquisition (equal); Investigation (equal); Methodology (equal); Supervision (equal); Visualization (equal); Writing – original draft (equal); Writing – review & editing (equal).

The data that support the findings of this study are available from the corresponding author upon reasonable request.