CP620, Shock Compression of Condensed Matter - 2001
edited by M. D. Furnish, N. N. Thadhani, and Y. Horie
© 2002 American Institute of Physics 0-7354-0068-7/02/$ 19.00
SPATIAL EVOLUTION OF THREE-WAVE STRUCTURE IN
SHOCKED POTASSIUM CHLORIDE.
E. Zaretsky
Dept of Mechanical Engineering, Ben Gurion University, P.O.Box 653, Beer-Sheva 84105, Israel
Abstract The response of [100]-oriented KC1 single crystals having thickness ranged from 0,05 to 5
mm was studied in series of planar impact experiments with impact pressure higher than pressure of
KC1 transformation from Bl to B2 structure. Special attention was paid to providing the similar
velocities of aluminum impactor in all shots, VISAR velocity records were obtained from free
sample surface or from sample-PMMA window interface. The recorded velocity profiles have threewave structure containing elastic El, low-pressure phase Phi and high-pressure phase Ph2 waves.
The waves amplitudes were found decaying with the propagation time and corresponding relaxation
times were found equal to 118, 64 and 136 nsec, respectively. The closeness of the relaxation times
of Phi and Ph2 waves to the relaxation time of El wave allows us to assume that dislocation motion
is responsible of the growth of nuclei of the transforming phase.
transition in KC1 using attenuation of the Phi wave
with the propagation distance. He found, however,
that in the transmission experiments, where
aluminum disk impacts the KC1 sample backed by
the quartz gage, the steady Phi amplitude was
established so fast that any decay measurements
were impossible. Due to this fact the transition
kinetics was studied on the base of the front impact
experiments where the KC1 crystal glued on the
projectile front surface impacts the quartz gauge.
The stress records obtained by Hayes in the
transmission experiments and published recently [5]
give clear evidence of the existence of the threewave structure in KC1 single crystal shocked above
the transition pressure.
Accounting in that the gauges used in [2]-[5] do
not allow detecting the amplitudes of El, Phi and
Ph2 waves with the same accuracy we decided to
study the three-wave structure produced by the
impacts of equal strength in KC1 samples of
different thickness using the VISAR diagnostics.
INTRODUCTION
Barker and Hollenbach [1] performed VISAR
study of shock-induced a —»£ phase transition in
iron. All free surface velocity profiles recorded in
[1] after impacts above the transition pressure
reflected the three-wave structure of the shock
propagating through the transforming material: the
elastic precursor wave El, the second Phi wave of
low-pressure phase and the third Ph2 wave of the
high-pressure phase of iron. A similar three-wave
structures was observed in shock compressed
potassium chloride (KC1) by Al'tshuler et al. [2] and
Rosenberg [3] although the sensitivity of magnetic
[2] and manganine [3] gages was insufficient for
resolving weak elastic precursor in KCL Hayes [4]
studied the Bl to B2 transition in KC1 using the
quartz gages having both the sensitivity and
temporal resolution better then the gages used in [2]
and [3], and sufficient for resolving the three-wave
structure. He tried to study kinetics of the phase
217
series. Since the El wave in these experiments was
produced by a stress pulse of finite amplitude the
value of CEI should be slightly higher than the value
of the longitudinal sound velocity C/ obtained from
ultrasonic measurement. In the experiments of the
third type (KPS experiments) the samples were
made of 1-mm KC1 crystals backed (1 micron of
Loctite420) by 5-rnm sapphire window of 20-mm
diameter. The front surface of the KC1 crystal was
separated from 3,09-mm disk (buffer) of aluminum
alloy 6Q61-T6 by 0,145-mm spacers. In this series
the VISAR beam was focused on the back surface
of the aluminum buffer. Recording the apparent
buffer velocity allows measuring the time interval
between the buffer-KCl impact and the arrival of
the KC1 elastic wave at the KCl-sapphire interface:
Small recompression wave produced by the
reflection of the elastic wave from the interface is
accompanied by instant change of the KC1
refractive index and results in the appearance of a
small velocity ramp on the recorded velocity profile
[5], The parameters of the shots of all the series are
collected in Tab.L The VISAR records obtained in
KP series are shown in Fig. la together with the
record of KPME shot (KPC and KPME samples are
of the close thickness). The records after shots of
KPM series are shown in Fig. Ib.
The position of the bottom of the El wave on the
time axis was chosen for all shots of KP and KPM
series on the base of the sample thickness and the
velocity of the El wave propagation equal to CEI =
4630m/sec. The latter value was determined by
extrapolating the velocities of El wave, obtained in
EXPERIMENTS AND RESULTS
KC1 samples obtained from the Graseby-Specac
Ltd., UK were [100]-oriented single crystal disks of
about 1, 2 and 5-mm thickness and 25,4-mm
diameter. Three types of planar impact experiments
were performed with use of 25-mm pneumatic gun
accelerating hollow aluminum sabot with disk
impactors made of aluminum alloy 6061-T6. In the
experiments of the first type (KP experiments) the
free surface velocity of KC1 samples was monitored
by VISAR. In order to provide the surface
reflectivity the 7-u, aluminum foil was glued
(Loctite420 glue, 2 cP viscosity) to the free surface
of the samples. In the experiments of the second
type (KPM experiments) the KC1 samples of the
thickness ranged from 0.05 to 1.3 mm were studied.
In order to prevent bending and non-parallelism of
the thin samples the as-received 1-mm crystals
equipped, as in the previous case, with the foil
reflector were glued on the 5-mm PMMA window.
The crystal side of the sandwich was grinded down
to the wishful thickness and polished. In the KPM
experiments the velocity of the KC1-PMMA
interface was monitored by VISAR. Special efforts
were done in order to obtain the same impact
velocities in the shots of KP and KPM series. The
charged pins were used for the control of the impact
velocity and impactor-sample misalignment (tilt).
The tilt did not exceed 0.4 mrad in all shots. The
experiments of the third type were performed in
order to determine accurate value CEi of the velocity
of the El wave in the experiments of KP and KPM
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FIGURE L VISAR records after shots KP (A, B, C) and KPME (a) and after shots KPM series (b). The numbers are explained in the text.
0 .4
218
TABLE 1. Parameters of the experiments
Shot
KPA
KPB
KPC
KPMA
KPMB
KPMC
KPMD
KPME
KPSA
KPSB
Impactor, mm
5.06
5.06
5.07
5.06
5.06
5.06
5.07
5.06
5.06
5.06
Buffer, mm
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3.10
3.10
Sample, mm
5.047
2.135
1.323
0.581
0303
0.148
0.050
1.285
1.166
1.265
Window,ram
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3.80 (PMMA)
4,88 (PMMA)
4,88 (PMMA)
4,88 (PMMA)
4.88 (PMMA)
4.98 (sapphire)
5.00 (sapphire)
Imp, veL, m/sec
546
546
543
544
542
546
543
546
221
350
conservation laws
KPS shots, toward the impact velocity of about 550
m/sec (impact velocity of KP and KPM series). Al
the records of Fig. 1 contain features related to the
three-wave structure of the shock propagating in the
transforming KCI and marked by roman numerals.
Points 1 and 2 correspond to the arrival of El and
Phi waves, respectively, at the interface or free
surface. The points 3 and 4 are related to the Ph2
wave. It will be shown that the signal amplitude at
point 4 allows determining the amplitude of Ph2
wave. All three waves decay with the propagation
distance but the rate and the cause of the decaying
is different for different waves. The decay of the
elastic precursor wave El is mainly due to the stress
relaxation, while the decay of the Phi and Ph2
waves reflects the process of the development of
two-wave structure triggered by shock-compression
of KCI to some point on the extension of its lowpressure Hugoniot [4]. Extrapolating the amplitudes
of the signals at points 2 and 4 to the zero sample
thickness allows us to conclude that the very initial
stage of the transformation cannot be detected by
YISAR: even for 50-fi sample the separation
between Phi and Ph2 waves is clear. The initial
transformation rate that can be detected from decay
of the Phi wave amplitude [1] should be attributed
to the later stage of the transformation. This
coincides with the conclusion of [4]: the
transformation rate at the first stage, the fast one, is
higher than 500 sec"1, while the second stage is
essentially slower. In order to estimate the rate of
the decay of the waves the values of the interface or
free surface velocity should be converted into
stress. Using PMMA Hugoniot data of [7] and
applying to El and Phi the mass and momentum
ic w
(1)
first the stress at the top of El and, then, at the stress
at the top of Phi may be obtained. Here Ac% and
Auw are the changes of the stress and the particle
velocity carried by the corresponding wave W
having Lagrangian velocity Cw. Using for El
velocity Q/ = 4630 m/sec yields CPhi = 3440 m/sec
for Phi wave. In order to evaluate stress behind the
Ph2 wave the a - u and jc- t diagrams should be
analyzed. Such diagrams for the case of KPC and
KPME shots are shown in Fig, 2, For simplicity the
thickness of KCI samples is shown equal for both
the shots. Assuming that the velocities of loading
and unloading waves in low-pressure phase of KCI
are close, the velocity of Ph2 wave may be found
from x-t diagram of Fig. 2a. (and other shots, as
well). It is equal to Cpfj2 = 1790 m/sec. Accounting
in that KCI compression at the point 2' of <7-«
diagram is found equal to V/V® = 0.914, the slope of
the line P2 may be found. The intersection of P2
with aa! line yields the steady amplitude of the Ph2
wave equal to 2.25 GPa. Small additional increase
of the surface velocity (from 439 to 449 m/sec for
KPMF, and from 778 to 801 m/sec for KPC shot) is
due to the wave reverberation 3 - 4 between the KCI
surface and interface discontinuity, Fig. 2. The
a-u diagram allows one to convert the small
changes of the apparent interface velocity into the
small changes of the stress amplitudes of Phi and
Ph2 waves.
219
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FIGURE 2. x— t (a) and <j — « (b) diagrams of shots KPC and KPME. The wave velocities are given in km/sec near the corresponding
trajectories. Phi wave velocity (bold line in (a)) is 3,44 km/sec. Numerals, as in Fig, 1. Dotted line (a) corresponds to the interface between
transformed and untransformed material [1],
1,3
0.2
0
Assuming for all the three waves a simple linear
kinetics with single relaxation time t
ACT
dt
GPa. The instant drop of the stress from this value
to 2,33 GPa seems should be attributed to the very
fast, sub nanosecond, impact generation of large
amount of the nuclei of the new phase while the
following wave processes are related to the nuclei
growth and coalescence. Accounting in that the
relaxation time values, Eq. (4), found for the three
waves are close, it is possible to assume that the
mechanism of this growth is dislocation-based.
(2)
yields for the stress aw at the top of the wave W
aw -aw™ = (cF W /Q-~<j w / 00 )exp(~f/T).
(3)
Here am is the initial stress at the impact interface,
and <jWoo is the steady wave W stress amplitude. The
least square treatment of the stress data gives for the
three waves
CT HEL - 0,094 = 0.255 exp[-r/(2.0.118)]
aph{ - 2.085 = 0.107 exp[-f/(2-0.064)],
- 2.250 = 0.084exp[-r/(2-0.136)]
REFERENCES
L Barker, L. M., and Hollenbach, R. E., JAppLPhys., 45,
4872, (1974).
2. ATtshuler, L. V., Pavlovskii, M, N., and Drakin, V. P.,
Sov, Phys. JETF, 25, N2, 260, (1967).
3. Rosenberg, Z., JAppLPhys,, 53, 1474, (1982),
4. Hayes, D. B,, JAppLPhys., 45, 1208, 1974
5. Ding, J. L., and Hayes, D. B., in Shock Compression
of Condensed Matter-1999, edited by M.D.Furnish, et aL,
AIP Conference Proceedings 505, Melwille, N-Y, 2000,
p. 633
6. Wackerle, J., Stacy, H. L., and Dallman, J. C, in High
Speed Photography, Videography and Photonics V, Proc.
SPIE Vol. 832,San-Diego, 1987, p.72
7. Barker, L. M., and Hollenbach, R. E., JAppLPhys., 41,
4208,(1970)
(4)
where the stress units are GPa and the time units are
jisec. Equations (4) yield stress values at the impact
interface equal to OOP/,/ = 2.192 GPa and <j0p/i2 =
2,334 GPa, It is difficult to believe that immediately
after the impact two phases may coexist under
different stress. The initial interface stress has to be,
at least, 2.334 GPa, Thus, the relaxation time
T = 64 nsec found for the wave Phi seems to be
underestimated. Recall that the 543-546-m/sec
impact of aluminum impactor brings low-pressure
KC1 phase into the state with stress of about 2,75
220