Shock wave profiles in vitreous GeO2 (6.56 Mg/m^3) under planar loading were measured using stress gauges to 14 GPa. New and previous data yield Hugoniot: D=0.974 (km/s)+1.711 u for shocks of 6 to 40 GPa. We show that the phase change from 4- to 6-fold coordination of Ge+4 with O–2 in vitreous GeO2 occurs from 4 to 15 GPa. Hugoniots of vitreous GeO2 and SiO2 are found to approximately coincide if the pressure in SiO2 is scaled by the ratio of SiO2 to GeO2 initial density

Ahrens, Thomas J.

Brar, N. S.

Liu, C.

English

Caltech Authors - Main

CP505, Shock Compression of Condensed Matter - I999 
edited by M. D. Furnish, L. C. Chhabildas, and R. S. Hixson 
0 2000 American Institute of Physics l-56396-923-8/00/$17 .OO 
VITREOUS GeOz RESPONSE TO SHOCK LOADING 
C. Liul, Thomas J. Ahrensl and N. S. Brar1y2 
1 Seismological Laboratory, California Institute of Technology, Pasadena, CA 91125. 
2 University of Dayton Research Institute, Dayton, OH 45469-0182. 
Abstract. Shock wave profiles in vitreous GeOa (6.56 Mg/m3) under planar loading were 
measured using stress gauges to 14 GPa. New and previous data yield Hugoniot: D = 0.974 
(km/s) + 1.711 u for shocks of 6 to 40 GPa. We show that the phase change from 4- to 6-fold 
coordination of Gef4 with Oe2 in vitreous GeO2 occurs from 4 to 15 GPa. Hugoniots of vitreous 
Ge02 and SiO2 are found to approximately coincide if the pressure in SiO2 is scaled by the ratio 
of SiO2 to GeO2 initial density. 
INTRODUCTION 
It has been long recognized that phase transi- 
tions in germanates occur at lower pressures than 
similar phase transitions in silicates. Jackson and 
Ahrens (1) reported Hugoniot data for Ge02 for 
the high-pressure range, up to 160 GPa, and sug- 
gested that both vitreous and rutile phases trans- 
form to a common phase under high pressure, 
which is about 5 percent denser than the rutile- 
type structure. Chen et al. (2) speculated that 
vitreous GeO2 undergoes an irreversible phase 
change when shock pressure exceeds 8 GPa. How- 
ever, it was still unclear what pressure range is re- 
quired for the phase change to occur under shock 
loading and if the response of GeO2 to shock load- 
ing is similar to that of SiO2. In order to inves- 
tigate the GeO2 phase transition pressure range 
and the similarity between GeO2 and SiO2 re- 
sponses to shock loading, we conducted a series 
of planar impact experiments on vitreous GeO2 
with the Caltech 40 mm powder gun. 
Foam 
Al. or OFHC Cu 
Figure 1: Target assembly for measuring shock 
profiles in Ge02. 
to power four stress gauges (Mn4-50-EK, Dy- 
nasen, Inc.) among three GeO2 slices in each ex- 
periment. The voltage change upon shock loading 
is converted to gauge resistance change (4). Stress 
wave profiles are deducted using the calibration 
relations (3). A cylindrical disc (100 mm diam- 
eter and 150 mm height) of bubble-free vitreous 
GeO2 was cut into 40x40 mm cubic samples with 
the thickness ranging from 1.7 to 10 mm. The 
density is measured to be 3.655 Mg/m3. 
EXPERIMENTAL METHOD 
Embedded piezoresistance manganin stress 
ewes (3) were employed to monitor stress wave The samples used in the experiments were first 
polished to within 0.005 mm of uniform thickness. 
Then, stress gauges mounted on mylar film (0.013 
profiles under planar impact. Two two-channel 
power supplies (CK-2, Dynasen, Inc.) were used 
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Shot 1024 
20 - 
15 - 
Shot 
---- 
.----= 
---- 
0.2 0.7 1.2 
Time (ps) 
1.7 2.2 
Figure 2: Stress wave profiles in vitreous GeO2 for 
planar loading. 
mm thickness) were sandwiched between samples. 
Epoxy was used to force air out of the contact 
surfaces between the gauges or samples and mylar 
film. After the epoxy cured (typically 24 hours), 
the whole sample assembly was encapsulated in 
epoxy as shown in Figure 1. 
EXPERIMENTAL RESULTS 
Table 1 lists experimental parameters of the im- 
pactor and samples. Recorded stress wave profiles 
in vitreous Ge02 (Figure 2) show that two stress 
gauges at the same interface gave nearly identical 
stress wave fronts, and showed only small differ- 
ences in the peak stress behind the wave front. 
These differences are believed to be typical of the 
response from stress gauges (3). The wave profiles 
have a three wave structure: an elastic precursor 
with relatively long rise time, a ramp wave and 
then a normal shock wave when the peak stress is 
> 6 GPa. 
The precursor rise-times are long, z 100 and 
150 ns at 1.8 and 4.2 mm from the impact surface 
(Figure 3), respectively. In order to verify that 
the long rise times are not the response of the 
measurement system, Figure 3 provides a com- 
parison among the wave profiles that are aligned 
with respect to each arrival time. If the long rise 
time arose from the measurement system, it would 
not simply depend on wave propagation distance. 
However, Figure 3 clearly demonstrates that the 
precursor rise time increases with propagation dis- 
tance. As a result, we infer that the longitudinal 
6 I I 
Shot 1028 Gauge-l (1.84) 
Gauge-3 (4;20), / ’ / 
I I 1 
0.1 0.2 0.3 
Time (ps) 
Figure 3: Vitreous GeO2 elastic wave front rise time 
versus propagation distance. Number in brackets is dis- 
tance (mm) between gauge and impact surface. 
modulus of vitreous Ge02 decreases with increas- 
ing stress during precursor wave loading and the 
precursor is an elastic ramp wave. Therefore, the 
whole elastic precursor can not be treated as a sin- 
gle wave with a constant wave velocity. Because 
the deformation rate associated with ramp wave 
loading is lower than that during shock loading, 
the ramp wave loading can be approximated as 
an isentropic process. In addition, the precursor 
stress does not decay with propagation distance 
(Figure 3), therefore, the phase velocity at con- 
stant particle velocity and stress is constant (5). 
The methods of (5) are used to determine the pre- 
cursor parameters. Calculated results are shown 
in Figures 4 and 5. The peak stress of the ini- 
tial ramp, its wave and maximum particle velocity 
are: 4 GPa, 3.5 km/s and 333 m/s, respectively. 
The above method also provides parameters of 
the ramp wave between 4 and 6 GPa. Results are 
shown in Figures 4 and 5. 
Because the release wave from the rear im- 
pactor surface has not overtaken the shock front 
(in all experiments), the peak stress is assumed to 
be constant at two-stress gauge locations. There- 
fore, we averaged the peak stress from two gauges. 
A least square fit was obtained based on present 
data and previous data of (1). The Hugoniot re- 
lation for vitreous Ge02 (3.655 Mg/m3) in the 
pressure range of 6 to 40 GPa is 
D = 0.974 + 1.711u, for u > 0.6 km/s, (1) 
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Volume (m3/Mg) (SQ) 
, Normal shock wave ----------------) I 
Jackson and Ahrens (1979) 
D = 0.974 + 1.711~ 
Rutile Ge@ 
A Jackson and Ahrens, 1979 This work 
Particle velocity (km/s) 
Figure 4: Shock wave velocity versus particle velocity 
for vitreous GeO2. 
where D and u are shock and particle velocity. 
Volume (m3/Mg) (GeO2) 
RESULTS OF ANALYSIS 
Figure 5: Pressure versus volume for vitreous GeO2 
and SiO2. The P-V plot for SiO2 is aligned to the GeO2 
plot so that initial volume and volume for completion of 
phase change to rutile phase coincides. Vertical axis of 
pressure for SiO2 (right) is scaled by the ratio of initial 
SiO2 to GeO2 density. 
Vitreous GeOa response 
Based on the present data (Figure 5), the re- 
sponse of vitreous Ge02 under planar shock load- 
ing is divided into three stress ranges: O-4, 4-6, 
and 6 GPa and higher. 
When the peak stress is below 4 GPa, the 
present data show that the compressibility of vit- 
reous GeOa increases with increasing stress. This When peak impact stress is > 6 GPa, a normal 
shock wave forms. Shock wave formation reveals 
that the compressibility of vitreous GeOz starts 
to decrease with stress increasing from 6 GPa. 
When shock stress is greater than N 15 GPa, vit- 
reous GeOa compression data closely match that 
of rutile phase GeOa (1) (Figure 5). Therefore, we 
conclude that the phase transition to rutile phase 
in vitreous GeOa starts at N 4 GPa and is com- 
pleted in the pressure range of 14 to 16 GPa. It 
is also inferred that the 4- to 6-fold GeOz transi- 
tion occurs between 5.6 and 13 GPa under static 
loading (6). 
is also observed u nder hydrostatic loading (6). In 
results from densificati .on general, a ramp wave 
processes like those which occur upon irreversible 
compression of lattice vacancies and upon coordi- 
nation increases that accompany large shear de- 
formations. 
When the peak stress is between 4 and 6 GPa, 
the compressibility increases dramatically under 
both planar impact and hydrostatic loading (Fig- 
ure 5). Smith et al. (6) found that the deforma- 
tion is not reversible when pressure is higher than 
4 GPa under hydrostatic loading. He suggested 
that a new phase (six-fold) starts to nucleate at 4 
GPa. Grady (7) suggested that the large change 
of compressibility in brittle materials results from 
fracture incubation and nucleation, and melting 
along microfaults under shock loading when pres- 
sure is higher than material elastic limit. Because 
phase transition, melting and fracture processes 
result in compressibility increasing, it is possible 
that all the processes may occur in this pressure 
range. 
GeOz-Si02 similarities 
Because vitreous GeOz has a similar structure 
to fused SiOz, it is interesting to investigate their 
pressure-volume (P-V) relation similarities. De- 
formation or phase transition processes in mate- 
rials are generally completed at the shock front 
because the energy needed for the processes is 
only available from stress or particle velocity gra- 
dient at the shock front. We use the density ratio 
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at zero-pressure of SiOz (glass) to Ge02 (glass) 
to scale the pressures in SiOz. Figure 5 shows 
the comparison between fused SiO2 and vitreous 
GeOz P-V relations. When the shock pressure 
is between 10 to 30 GPa, the pressure in fused 
sio2 ((8) and (2)) &PP ears to be slightly higher 
than the pressure in GeO2. Grady (7) indicated 
that a possible misinterpretation of the SiO2 data 
has occurred. The shock wave velocity in the 10 
- 30 GPa pressure range was measured and re- 
ported as having a nearly constant shock velocity. 
(8). However, the stress wave profile measure- 
ments (7) suggest that a single wave is not stable 
in this pressure range in SiO2. The shock wave ve- 
locity appears to be slightly lower than that given 
by Marsh (8). In spite of this problem, Figure 5 
demonstrates a reasonable similarity of P-V re- 
lations of fused SiO2 and vitreous GeO2. This 
similarity demonstrates that the response of vit- 
reous GeO2 at lower shock pressure can be used to 
analyze the response of fused SiO2 under higher 
pressure, especially in the phase transition regime. 
CONCLUSIONS 
Based on the present data and discussion, the 
features of a stress wave in vitreous GeO2 to 
planar shock loading include an elastic precursor, 
with a peak amplitude of 4 GPa, and a peak 
particle velocity of 333 m/s, a ramp wave with an 
amplitude N 2 GPa and then a normal shock wave 
form when the peak shock stress is higher than 
6 GPa. The Hugoniot relation of vitreous GeO2 
is D = 0.917 + 1.711u, for u > 0.6 km/s. 
When shock stress is higher than N 15 GPa, 
vitreous GeO2 compression data appears to 
approach those of rutile GeO2 ((1)). There- 
fore, the phase change from 4- to 6-fold 
GeO2 starts at about N 4 GPa and is completed 
at N 15 GPa. A similarity between the pressure- 
volume relations for fused SiO2 and GeO2 
appears when the ratio of SiO2 to Ge02 density 
is used to scale shock stress in SiO2. This 
similarity provides the basis for using GeO2 as 
an analogous material to SiO2. 
ACKNOWLEDGMENTS 
This work was supported by Army Research Of- 
fice and NASA. Contribution number 8663, Divi- 
sion of Geological and Planetary Sciences, Califor- 
nia Institute of Technology, Pasadena, CA 91125. 
References 
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PI 
PI 
PI 
PI 
PI 
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Jackson, I. and T. J. Ahrens, Physics of the Earth 
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Chen, G. Q., T. J. Ahrens, W. Yang and J. K. 
Knowles, J. Mech. Phys. Solids 47, 763-783, (1999). 
Rosenberg, Z., D. Yaziv and Y. Partom, J. Appl. 
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Marsh, S. P., LASL Shock Hugoniot Data, published 
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Table 1: Experimental parameters for shock loading, Ge02 glass. 
Shot # Impactor Impactor Impactor Hl H2 H3 
material thickness (mm) velocity (km/s) (mm> (mm> (mm> _ 
1024 OFHP Cu 5.997&0.001 1.547~tO.006 1.857~tO.0041 1.745~l~O.0034 10.378 
1026 2024 Al 4.02sfO.001 2.062kO.013 2.454~tO.0021 2.23850.0019 5.883 
1027 2024 Al 6.015&0.005 2.310&0.001 2.202ztO.0038 2.588zkO.0021 6.192 
1028 2024 Al 6.02LtO.0043 1.304*0.001 1.836~tO.004 2.36OztO.005 5.298 
Hr , Hz and H3 are thicknesses of three slices in each experiment. 
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Vitreous GeO2 response to shock loading

Brittle material response under impact loading, PhD Thesis,

LASL Shock Hugoniot Data, published by

http://authors.library.caltech.edu/5914/1/LIUaipcp00b.pdf

Vitreous GeO2 response to shock loading

Abstract

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