Hugoniot states and optical response of soda lime glass shock compressed to 120 GPa

Understanding the dynamic response of silica-rich glasses is important because of their use as window materials in a wide variety of applications involving high-velocity impacts. Silicate glasses are also used as model systems for understanding the behavior of melts and liquids in planetary interiors and during planetary impact events.

Soda lime glass (SLG) is a widely used commercial silicate glass that contains variable amounts of sodium and calcium cations.¹ Pure SiO₂ glass (fused silica—FS) is a fully polymerized glass consisting of a 3D network of corner sharing oxygen anions with each oxygen bonded to two Si cations. The addition of network modifying cations such as Na and Ca results in a local charge imbalance. These cations modify the structure of the glass decreasing the connectivity by disrupting the Si–O–Si network and creating a more open structure.¹ Modeling the dynamic compression response of soda lime glass, in general, requires the knowledge of high-pressure equation of state (EOS) and the underlying atomic arrangements. In particular, soda lime glass (SLG) has attracted recent interest for the following reasons: (1) it can be used as a low-cost substitute transparent window under dynamic loading conditions,^2–5 and (2) it is a good representative of network-modified glasses that contain significant fractions of additive cations. A comparison between SLG and FS can give insights into how network modifying cations change the dynamic response of glasses.

The shock compression response of soda lime glass (SLG) has received considerable interest in the past.^1,6–16 However, most of these studies have focused on SLG shocked under 40 GPa where a variety of complex behaviors including ramp wave loading and material strength loss have been extensively examined.^1,10,13,17 In contrast, the dynamic compression of SLG above 40 GPa is poorly explored and not well understood. In one study,¹² radiation pyrometry was used in plate impact experiments to measure shock temperatures of SLG in the stress range from 54 to 109 GPa. Above 54 GPa, an additional volume compression was inferred when compared to lower stress experiments. It was suggested that the dense, high-pressure state of soda lime glass was likely liquid based on the temperature measurements. However, given the limitations of the time-resolved pyrometry measurements and the large uncertainty in the shock speed measurements due to the long rise time in the photomultiplier tube output in this work,¹² the high-stress response of SLG remains an open question.

There has also been recent interest in the dynamic compression of fused silica. In a recent x-ray diffraction study under plate impact loading,¹⁸ FS was observed to transform from the amorphous state to untextured, polycrystalline stishovite above 34 GPa. The transformation is accompanied by a large change in the compressibility from a compressible amorphous phase below 34 GPa to a fairly stiff crystalline phase at higher stresses. Longitudinal sound velocities were also recently measured in shock compressed FS to 72 GPa.¹⁹ Understanding whether more chemically complex silicate glasses can undergo similar transformation to crystalline phases under shock loading conditions remains an open question that needs further exploration.

In this work, we have examined the mechanical response of SLG shocked to peak stresses of 120 GPa by determining the Hugoniot response through well-characterized plate impact experiments; optical measurements, though limited, were also undertaken. We specifically address the following questions: (1) What is the shock response of SLG at peak stresses beyond 35 GPa? (2) What is the effect of network modifying cations on the shock response of silica glasses? (3) How does the dynamic high-pressure response of SLG differ from FS?, and (4) What are the optical properties of shock compressed SLG?

Soda lime glass (SLG), termed Starphire^®, was obtained from Pittsburgh Plate Glass (PPG); this particular SLG has also been used in previous^1,3,5,10,12 shock studies. The measured ambient density was 2.495 ± 0.003 g/cm³ and the longitudinal and shear sound speeds were 5.85 ± 0.02 mm/μs and 3.46 ± 0.03 mm/μs, respectively. The chemical composition (wt. %), as determined by EAG laboratories using x-ray fluorescence, was: 71.1% SiO₂, 14.6% Na₂O, 10.8% CaO, 3.18% MgO, 0.084% SO₃, 0.047% Al₂O₃, 0.036% Fe₂O₃, and other trace elements.

A schematic view of the experimental setup is shown in Fig. 1. Targets consisted of SLG bonded to a lithium fluoride (LiF) window. Samples were prepared by lapping and polishing one of the surfaces using progressively finer grits down to 0.5 μm grit size to obtain a mirror finish. This was used as the impact surface. The sample thicknesses are listed in Table I. The sample lateral dimensions were chosen to permit acquisition of a complete wave profile before the arrival of edge waves to ensure uniaxial strain conditions in the sample. Prior to bonding the target components, a thin aluminum mirror was vapor deposited onto the front surface of the SLG sample and at the center of the LiF window, which served as a reflector for the laser interferometry measurements (Fig. 1).

The SLG–LiF sample assemblies were impacted with oxygen-free high conductivity (OFHC) copper or aluminum alloy (Al-1050) impactors launched using a 2-stage gas gun. The measured projectile velocities have a typical precision of ∼0.15% (Table I). Upon impact, shock waves are propagated into both the SLG sample and the impactor. The forward propagating shock wave reaches the sample/window interface, resulting in a transmitted wave propagating through the LiF window, and a reshock wave reflected back into the sample. The reshock wave in the SLG sample reflects from the impactor/sample interface, resulting in a second jump at the sample/window interface. Additionally, the shock wave propagating in the impactor reflects from the impactor rear surface and propagates back through the impactor–SLG–LiF system as a release wave.

As shown in Fig. 1, particle velocity histories were measured at the SLG sample/window interface using laser interferometry (VISAR—velocity interferometer system for any reflector²⁰ or PDV—Photon Doppler velocimetry²¹). The VISAR uses a 532-nm wavelength laser, while PDV uses a 1550-nm wavelength laser. By using two VISAR interferometers with different velocity per fringe (VPF) sensitivities,²² the particle velocity histories at the sample/window interface were determined unambiguously.

To obtain precise shock velocity measurements and impact tilts, shock wave arrival times at the impact surface were obtained at three locations using PDV probes (Fig. 1—red arrows). These three measurements are used to determine the impact time at the impactor/sample interface location that was laterally coincident with the center probe (Fig. 1—red/green arrows). Using the sample thickness and timing fiducials, the shock wave velocities in the SLG samples were obtained precisely (this is referred to as the conventional method henceforth). The interferometry data, discussed below, were used to determine the in-material particle velocity, peak stress, and density.

Eight experiments were performed on SLG samples shocked to varying peak stresses. Figure 2 shows the wave profiles (corrected for the shock-induced change in the refractive index of LiF²³) obtained using the VISAR at the sample/window interface for all experiments. We note that the wave profiles obtained using the dual VISAR and the PDV center probe showed good overall consistency. The sample/window interface particle velocity, following the shock wave, for each experiment is listed in Table I. In all profiles shown in Fig. 2, the reference time (t = 0) corresponds to the time of impact. The time shown is normalized to sample thicknesses in order to better compare the measured profiles.

The single waves observed in our experiments are in marked contrast to the complex wave structures measured in the lower stress experiments.^1,10 Our data show that, at high stresses, a stable single shock wave propagates through the SLG. The particle velocity behind the shock remains constant until the arrival of the reflected wave from the impactor/sample interface discussed earlier; depending on whether the impactor is Al or Cu, the particle velocity decreases or increases as the material experiences a partial stress release or reshock. The arrival of the reflected wave is followed by the arrival of the release wave from the back of the impactor.

In addition to the transmitted wave profiles (Fig. 2) obtained at the sample/window interface, impact surface measurements were also obtained in these experiments. Figure 3 shows the uncorrected or apparent particle velocity profiles at the impactor/SLG interface, obtained using PDV measurements. Upon impact, we observe an initial jump in particle velocity to the peak state, followed by a second jump when the shock wave reaches the sample–window interface (Fig. 3—purple arrows). Using the time of arrival of this feature in the wave profile and the sample thickness, the shock velocity could be obtained directly from a single PDV probe (Table I). Within experimental uncertainty, the shock wave velocities obtained using the impact surface wave profiles showed good consistency with those measured using the conventional method. Because the PDV lasers were transmitted through the SLG sample onto the impact surface, loss of the interferometry signal is an indication that the SLG lost transparency. We were able to observe particle velocity measurement at the impact surface only for six experiments. At the two highest stresses, the SLG samples lost transparency.

A pair of experiments performed using similar experimental configurations and comparable projectile velocities (Expts. 3 and 4) produced very similar results, demonstrating good reproducibility in our transmitted wave profile measurements as well as at the impact surface (Figs. 2 and 3).

The in-material quantities in SLG were determined from the measured shock velocities $(Us)$ and particle velocities using the Rankine–Hugoniot jump conditions and impedance matching.²⁴ Because the particle velocities $(up)$ and longitudinal stresses $(σ)$ in the sample and the impactor must be continuous at the impactor/sample interface, we can determine the in-material states using the Rankine–Hugoniot (R-H) jump conditions for mass and momentum conservation. These are given by

where $ρ0$ is the initial density.

Over the stress range examined here, both Al-1050²⁵ and OFHC Cu²⁶ have been well characterized using a linear $US−up$ relationship $US=A+Bup$ with $A=5.35mm/μs$ and $B=1.32$ for Al; and $A=3.97mm/μs$ and $B=1.479$ for Cu.

For the SLG sample, the R-H jump condition can be written as:

where the superscripts denote SLG values. For the impactor with projectile velocity $(uproj)$⁠, we have the equation

Equations (3) and (4) were solved to obtain the in-material particle velocity $(up)$ in SLG. The in-material stress $(σ)$ and peak state density $(ρ)$ can then be calculated using the momentum [Eq. (2)] and mass [Eq. (1)] conservation equations, respectively. The calculated in-material quantities are listed in Table I.

Shock wave velocity–particle velocity and stress–volume (⁠$V≡1/ρ$⁠) compression $(V/V0)$ results from our work are plotted and compared with previous results^1,4,6,10,12 in Fig. 4. The red solid line in the $US–up$ plane denotes the linear relation obtained from a fit to our data; the red solid curve in the $σ–V/V0$ plane was obtained from the linear $US–up$ relation and the R-H jump conditions. The SLG Hugoniot from our work (applicable above 36 GPa) is well described by the following equation:

The fit parameters and the correlation/covariance matrix for the linear fit are given in Table II. Below the stress range of our experiments, we show the extrapolation from Eq. (5) as a broken line.

At lower stresses, between the elastic limit (∼4 GPa) and ∼34 GPa, the measured wave profiles in shock compresses SLG are quite complex,^1,10,13,17 and do not display the steady wave propagation rigorously required to use the R-H jump conditions to analyze the data. However, for completeness, we show in Fig. 4 the results that have been reported in the literature.

Two observations are noteworthy about the low stress (<35 GPa) SLG response. Above a particle velocity of 1 km/s, the results reported in some of the earlier work^1,10 are in reasonable agreement with the extrapolation of our linear fit in Eq. (5). We also note that the extrapolation of the linear fit to the ambient stress (⁠$up=0$⁠) results in a wave velocity considerably lower than the bulk sound speed (C_B) at ambient conditions. For brittle solids, because of the reduction in stress deviators beyond the elastic limit (or strength loss), this is not an uncommon feature.²⁷ The same is also evident in the stress–volume compression plot in Fig. 4.

Finally, we note that in our data we did not observe any discontinuities in the $US–up$ fit, suggesting the lack of a first-order phase change. In contrast, an earlier study¹² (green triangles in Fig. 4) had suggested that shock compressed SLG transforms to a denser, possibly liquid state, at higher compressions. This suggestion of additional density compression could arise from significant uncertainties in determining the shock velocities $(US)$ in the earlier work.¹² Precise measurements of the shock velocity are necessary for accurately determining the particle velocity, density, and peak stresses. Although the reasons for differences in the $US–up$ results are not known with certainty, Kobayashi et al.¹² used photomultipliers to measure the shock velocity that have large rise times. Because details describing the shock velocity determination from these photomultiplier outputs were not provided, it is difficult to determine the precision of the shock velocities in Ref. 12.

In addition to the mechanical response, knowledge of the optical response of glasses under dynamic compression is potentially important for the deployment of window materials in applications involving high-velocity impacts and for velocity interferometry in shock wave research. For use in velocity interferometry, the material must exhibit optical transparency and possess a well-characterized optical and mechanical response. To date, LiF is the most widely used optical window for laser interferometry in shock experiments ranging between ∼20 GPa and well over 100 GPa.²³ Below, we present an analysis of our optical measurements in shock compressed SLG.

Previous studies have examined the optical response and refractive index of shocked SLG^2–5 at the 532-nm wavelength up to 30 GPa; at this wavelength, the SLG retains transparency up to 24 GPa but is opaque by 30 GPa. In contrast, our results show that shocked SLG remains transparent at the PDV wavelength (1550 nm) up to 81 GPa. Specifically, SLG is completely transparent when shocked up to 55 GPa; for stresses between 55 and 81 GPa, the PDV signal was lost in tens of nanoseconds (Fig. 3) after impact, suggesting a time-dependent reduction in transparency. SLG loses all transparency upon impact, when shocked above 81 GPa. Below, we discuss the window correction and refractive index determination using approaches presented in earlier studies.^5,28

During shock wave propagation through an optical window, the material compresses and its refractive index changes^29–32 resulting in a change in its optical path length. In general, laser interferometry measurements monitor the optical path length changes from the window reflecting surface. The measured (or apparent) particle velocity is different from the actual particle velocity at the window reflecting surface due to an optical effect, which is discussed in detail in previous studies^29–32; and the window correction factor, $Δu$⁠, is defined as the difference between the measured (apparent) and the expected (actual) particle velocities after impact: $Δu=u′p−up$ where $u′p$ is the observed/apparent particle velocity and $up$ is the actual/expected particle velocity, which is calculated previously in Sec. IV A.

For our SLG experiments, the two sets of particle velocities, are listed in Tables I and III and plotted in Fig. 5. A fit to our results demonstrates a linear relationship between the two quantities, as given by $u′p=1.163up$⁠.

Previous work^30,33 has shown that when a steady planar shock wave propagates in the window material, the refractive index of the window in the shocked state can be expressed as

where $n0$ is the refractive index of the uncompressed window, and the other quantities are listed in Tables I and III. Using Eq. (6), the index of refraction in the compressed state was determined for each experiment and plotted against peak state density in Fig. 6; the stress scale on top in Fig. 6 was calculated using the Hugoniot determined in our work.

To use Eq. (6), we require the ambient refractive index of SLG at 1550 nm. Since there have been no previous studies to determine $n0$ (at $1550nm$⁠) in the particular SLG (Starphire) used in our work, we used the following approach. Using laser interferometry, we measured the ambient refractive index at 532 nm to be $n0=1.525$ and our value agreed well with a previously reported SLG value.³⁴ Therefore, the ambient refractive index of SLG at $1550nm$ $(n0=1.506)$⁠, reported in that study,³⁴ was used here. Because the actual particle velocity $up$ and apparant particle velocity $u′p$ have a linear relationship, Eq. (6) reduces to

where $K$ is the slope of the equation, treated as an unconstrained parameter. The refractive index data (Fig. 6) were fit using the linear equation [Eq. (7)] and the slope $K$ was determined to be 0.137. We note that the fit determined from this method showed good agreement with $no$ and provides additional confidence in the linear window correction observed in our work. Thus, the refractive index increases from 1.506 to 1.801 over the stress range from 37 to 81 GPa.

Silica (SiO₂), the most abundant oxide constituent of the Earth's crust, is one of the most extensively studied materials under dynamic compression due to its importance in geophysics and materials science. In general, pure SiO₂ exists in a crystalline form (e.g., quartz) and an amorphous form (e.g., fused silica).¹ In contrast to pure silica glass, commercial silica-rich glasses contain significant fractions of additional oxide components. Below, we have compared the results obtained from our work and previous work on shocked FS to examine the effect of adding network modifying cations on the shock response of silica-rich glasses.

Figure 7 compares shock wave velocity, $US$—particle velocity, $up$ and stress, $σ$—volume compression, $V/V0$ for shocked SLG and FS.¹⁹ Also shown in Fig. 7 are data from previous studies for SLG¹ and for FS.³⁵ The slope of the $US−up$ curve for SLG (71% SiO₂) is somewhat smaller than that observed for FS (100% SiO₂).¹⁹ However, the shock speed for a given particle velocity is significantly higher for SLG compared to FS. When shocked above 34 GPa, FS transforms from the amorphous phase to a dense crystalline stishovite phase¹⁸ and eventually melts when shocked to 72 GPa.¹⁹ As observed from the $σ–V/V0$ curve, FS is highly compressible at low stresses until it reaches a volume compression of ∼47%–49% (34 GPa), where it abruptly becomes much less compressible upon the transformation to stishovite. In contrast, SLG is observed to follow a smooth compression curve without any abrupt change in slope up to 120 GPa. More specifically, a comparison of the compression curves of SLG and FS in Fig. 7 suggests that (1) SLG and FS undergo similar amounts of compression up to ∼17 GPa, each reaching about ∼35% compression, (2) From 17 to 34 GPa, FS continues to be highly compressible eventually reaching ∼47%–49% compression, whereas SLG exhibits less compression over this range, reaching only ∼39%–40% compression, and (3) above 34 GPa, SLG continues to exhibit smooth compression, while FS transforms to stishovite and becomes highly incompressible. Thus, there is a reversal in the relative compressibility in the two materials. Hence, significantly different dynamic response is observed between shocked SLG and FS: SLG compresses uniformly to 120 GPa, whereas FS undergoes a two-stage compression consisting of a high-compressibility glass at low stresses and a low-compressibility crystalline solid at high stress.

A plausible explanation for the above indicated behavior is as follows: up to 17 GPa, both SLG and FS are able to compress by densification mechanisms such as bond bending and tetrahedral rotation.³⁶ At higher stresses, fused silica is able to more rapidly adopt higher coordination states of the glass, eventually approaching 6-fold coordination of silicon³⁷ and then transforming to stishovite at 34 GPa. The network modifying cations of SLG, on the other hand, serve to impede the formation of the higher coordination oxygen environments and so the material compresses much less than fused silica and is impeded from forming a crystalline structure. The higher coordination states of FS and its high-pressure phase allow it to achieve substantially higher degrees of compression than SLG.

To study the effect of network modifying cations in the shock compression response of silica-rich glasses, soda-lime glass (SLG) samples were shock compressed between 37 GPa and 120 GPa, and the results were compared with published results on pure silica glass [fused silica (FS)]. Transmitted wave profiles were measured at the SLG/window interface using laser interferometry—both VISAR (532 nm) and PDV (1550 nm)—while particle velocities at the impact surface of SLG sample were measured using PDV. Clean single shock wave profiles were measured in all our experiments. These profiles were analyzed using Hugoniot jump conditions and impedance matching to determine the in-material continuum variables to gain an understanding of the dynamic response of SLG. The main findings from this work are summarized below:

1. The SLG Hugoniot in the stress range examined can be well described by a linear relation given by $US=2.22(±0.09)+1.61(±0.03)upkm/s$⁠. Our results differ significantly from the reported results of an earlier study.¹² 

2. The Hugoniot for SLG is markedly different from that found in recent fused silica (FS) experiments.¹⁹ Shocked SLG was observed to be much less compressible compared to FS and likely does not transform to a crystalline phase or phases at these timescales. We observe a change in volume compression (⁠$V/V0$⁠) from 0.61 to 0.51 for SLG shocked from 37 to 120 GPa. At the highest stress examined, the density of SLG is nearly a factor of two larger than its ambient stress value, indicating that SLG can achieve highly dense amorphous states.

3. Over the stress range examined, SLG remained transparent for the PDV (1550 nm wavelength light) below 55 GPa peak stress, but retained transparency for only tens of nanoseconds after impact when shocked to stresses between 55 and 81 GPa. Above 81 GPa, SLG lost all transparency when shocked.

4. The apparent particle velocity $u′p$⁠, for SLG at 1550 nm was observed to be a linear function of the true particle velocity $up$ with a relationship given by $u′p=1.163up$⁠. A linear function between the refractive index $(n)$ at 1550 nm and the density $(ρ)$ was also determined given by the relationship, $n=1.163+0.137ρ$⁠.

The presence of network disrupting cations (Na⁺ and Ca²⁺) in SLG alters the network structure, resulting in an open structure compared to the fused silica structure (pure SiO₂). The addition of these network modifying cations affects the dynamic response of silica-based glasses significantly as seen from this work. The crystalline phase transformation observed for shocked FS is inhibited by these network modifying cations for SLG at these stresses. Whether SLG melts under shock compression could not be determined from the present experiments and will require other types of measurements such as broadband reflection and/or x-ray diffraction.

N. Arganbright, Y. Toyoda, and K. Zimmerman are thanked for their expert assistance with the plate impact experiments. Dr. J. M. Winey is thanked for many insightful discussions and suggestions regarding this work. This work was supported by the Department of Energy/NNSA (Cooperative Agreement No. DE-NA0003957) and by the Office of Naval Research (ONR) Grant (No. N00014-18-1-2267).

The data that support the findings of this study are available within the article.