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Elastic-plastic and phase transition of zinc oxide single crystal under shockcompression
Xun Liu,1 Tsutomu Mashimo,1,a) Wei Li,1 Xianming Zhou,2 and Toshimori Sekine31Institute of Pulsed Power Science, Kumamoto University, Kurokami, Kumamoto 860-8555, Japan2The Peac Institute of Multiscale Sciences, Chengdu 610207, China3Department of Earth and Planetary Systems Science, Hiroshima University, Higashi, Hiroshima 739-8526,Japan
(Received 16 December 2014; accepted 24 February 2015; published online 6 March 2015)
The Hugoniot data for zinc oxide (ZnO) single crystals were measured up to 80GPa along both theh11!20i (a-axis) and h0001i (c-axis) directions using a velocity interferometer system for anyreflector and inclined-mirror method combined with a powder gun and two-stage light gas gun. TheHugoniot-elastic limits of ZnO were determined to be 10.5 and 11.5GPa along the a- and c-axes,respectively. The wurtzite (B4) to rocksalt (B1) phase transition pressures along the a- and c-axesare 12.3 and 14.4GPa, respectively. Shock velocity (Us) versus particle velocity (Up) relation ofthe final phase is given by the following relationship: Us (km/s)! 2.76" 1.51Up (km/s). Based onthe Debye-Gr"uneisen model and Birch-Murnaghan equation of state (EOS), we discuss the EOS ofthe B1 phase ZnO. The bulk modulus (K0) and its pressure derivative (K0
0) are estimated to beK0! 174GPa and K0
0 ! 3.9, respectively.VC 2015 AIP Publishing LLC.[http://dx.doi.org/10.1063/1.4914131]
I. INTRODUCTION
Zinc oxide (ZnO) has been widely studied during thepast few decades because of its photoelectric and catalysischaracteristics.1–3 At ambient conditions, ZnO crystallizes inthe B4 structure with a space group P63mc, in which both Znand O ions are tetrahedrally coordinated, surrounded by fourions of opposite charge. Under static compression, ZnOtransforms to the B1 (space group Fm!3m) structure at7.5–10GPa.4–10 The B1 structure is cubic, with Zn and Oions are in mutual octahedral coordination. B1 phase ZnOhas attracted attention because of its wide indirect band-gap,which makes it favorable for p-type doping, while it is diffi-cult to achieve in the B4 structure.1,11 B1 phase ZnO isunstable at ambient conditions, but it has been reported thatnanoscale ZnO is recovered successfully as the B1 phasefrom high-pressure and high-temperature conditions, becausethe high surface energy of nanoparticles hinders the reversetransformation.11 X-ray diffraction experiments indicate thatB1 phase ZnO can be stable up to at least 202 GPa at 300K.The high stability of B1 phase ZnO also makes it a potentialpressure calibrant in static compression experiments.12
Some shock recovery experiments have been carried outon ZnO previously, aiming to modify the structure or intro-duce defects to change its photoelectronic properties.13–15
One problem in these studies is, because of the lack ofHugoniot data for ZnO, the pressure and temperature condi-tions in the experiments cannot be well constrained. Thus,the measurement of the Hugoniot data of ZnO is indispensa-ble. Furthermore, the pressure-density relationship forcondensed matter can be measured directly by shock
compression without pressure calibration. Hugoniot datafor ZnO will help to promote its application as a pressurescale.
In this study, we measured the Hugoniot data for ZnOsingle crystals from #10 to 80GPa using a VISAR (velocityinterferometer system for any reflector) and inclined-mirrormethod combined with a powder gun or two-stage light gasgun. The Hugoniot elastic limit (HEL) and phase transition(PT) pressure are determined. The equation of state (EOS) ofthe B1 phase ZnO is discussed. To check if ZnO behavesanisotropically under shock compression, experimentswere performed along both the h11!20i (a-axis) and h0001i(c-axis) directions.
II. EXPERIMENTAL PROCEDURE
The samples were single crystals with a purity betterthan 99.99% and a density of 5.6676 0.002 g/cm3, as meas-ured by the Archimedes’ method. Samples were 12$ 15-mmrectangles with thicknesses of #2–3mm; both surfaces ofthe sample were polished with 800-grit sandpaper. Somebasic properties of the samples are listed in Table I.
Shock experiments were performed on the powder gun21
and two-stage light gas gun22 at the Institute of Pulsed PowerScience, Kumamoto University. In the VISAR experiments,LiF single crystals with diameters of 9mm and thicknesses of4mm, oriented in the h100i direction, were used as the win-dows. The windows were first polished to an optical finish onboth sides, and then 500-nm gold films were vacuum vapordeposited on the backing surfaces. The ZnO sample and LiFwindow were held together by a #1–2 -lm-thick epoxy layer.Copper or tungsten was used as flyer and driver plate. Theflyer velocities were measured by the electromagnetic methodwith an uncertainty of 0.1%–0.2%. The Hugoniot relation ofLiF is Us (km/s)! 5.15" 1.35Up (km/s), with an initial
a)Author to whom correspondence should be addressed. Electronic mail:[email protected]
0021-8979/2015/117(9)/095901/7/$30.00 VC 2015 AIP Publishing LLC117, 095901-1
JOURNAL OF APPLIED PHYSICS 117, 095901 (2015)
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density of 2.638 g/cm3.23 The refractive index correction ofLiF window is from Ref. 24. The interfacial particle veloc-ities were measured by a Valyn VISAR system.25 The config-uration for the VISAR experiments is shown in Fig. 1.The time resolution of the VISAR is 1 ns, and the error of theparticle velocity measured by VISAR is <1%. In theinclined-mirror method, the measurements were conductedusing a rotating-mirror type streak camera with a maximumwriting rate faster than 10mm/ls and a pulsed-dye laser.Using a 2 and 4lm-width slits, the basic time resolutions arehigher than 1 and 2 ns, in the use of the powder gun and two-stage light gas gun, respectively.26 We carefully access thearrival times of shock wave at the free surfaces of driver plateand specimen, the tilt of the flyers and curvature of the shockfronts were considered. The minimum measurement error inshock velocity is estimated to be 0.25%–0.4%, by consider-ing the measurement error of specimen thickness (<0.05%),the rise time of shock front of plastic-wave (<1 ns), time
resolution of the camera, the measurement error of propaga-tion time of shock wave on the printed photographic paper,etc. When the quality of streak photograph is poor, the errorincreases. The minimum error of particle velocity determinedby the impedance-matching method is estimated to be0.28%–0.5%, by summing the errors of density, shock veloc-ity, and impact velocity. The total errors of pressure and den-sity are estimated to be 0.38%–0.68%. When the shot numberincreases, the error statistically decreases.
III. RESULTS
The measured interfacial particle velocity profiles areshown in Fig. 2, two shots at low pressures (a-1 and c-1) andanother two shots at relative higher pressures (a-2 and c-2).For the two low pressure shots, we can see clearly the kinksdue to the elastic-plastic transition (ET) and PT. Above thePT point, another kink is seen. This kink, to our considera-tion, should be a consequence of interaction between therelease wave (from the sample-window interface) and theoncoming phase transition wave,27 as shown by the solidlines in the wave analysis of Fig. 3. For shock along thea-axis, in addition to the kinks due to ET and PT, an initialpeak (indicated by a red arrow in Fig. 2) is also seen. Thisdouble-wave precursors phenomenon (also seen in the higherpressure shot for shock along a-axis) may have a relationshipwith the plastic deformation mechanism of ZnO, which wewill discuss in Sec. IV. For the two higher pressure shots, inboth cases, a small kink is seen above the HEL (indicated bycircles in Fig. 2). If these kinks are caused by PTs, the corre-sponding plastic-wave velocities should be roughly equal tothe plastic-wave velocities in the low pressure cases. Thecalculated plastic-wave velocities are 4.45 km/s along a-axisand 4.51 km/s along c-axis, much higher than the plastic-wave velocities in the low pressure cases, which are3.61 km/s along a-axis and 3.85 km/s along c-axis. So thesekinks are not due to PTs, but due to wave interactionsbetween the elastic- and plastic-waves, as shown by the
TABLE I. Ultrasonic data and thermodynamic parameters for ZnO at ambi-ent conditions.
Properties Quantities
Density q0a 5.667 g/cm3
Longitudinal sound velocity clb 5.79 km/s (a-axis)
5.88 km/s (c-axis)
Transverse sound velocity ctb 2.70 km/s (a-axis)
2.62 km/s (c-axis)
Buck sound velocity Cbc 4.88 km/s
Bulk modulus K0c 128.4 GPa
Shear modulus Gc 42.7 GPa
Specific heat Cpd 0.118 cal/(gK)
Debye temperature he 418.8K
Gr"uneisen parameter cd 0.55 (B4 phase)
Gr"uneisen parameter cf 0.93 (B1 phase)
aAs measured by the Archimedes’ method.bFrom Ref. 16.cCalculated from the elastic constants in Ref. 16.dFrom Ref. 17.eFrom Ref. 18.fWe assume the thermal Gr"uneisen parameter equal to the longitudinal
acoustic mode Gr"uneisen parameter.19,20
FIG. 1. Experimental configuration of the VISAR method.FIG. 2. Interfacial particle velocities measured by VISAR. ET: elastic-plastic transition; PT: phase transition; ER: elastic-plastic release.
095901-2 Liu et al. J. Appl. Phys. 117, 095901 (2015)
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dashed line in Fig. 3. This phenomenon is not visible in thelow pressure shots. Possible reason is at low shock pressure,the impedance difference before and behind the plastic-wavefront is small, thus the wave reflection is weak.
In analyzing the VISAR results, we determined theshock velocities using the time intervals between the elastic,plastic, and phase transition waves. The elastic-wavevelocities were determined as the first wave arrival by theinclined-mirror method. The particle velocities were calcu-lated using the impedance-match method.28 For the two lowpressure shots, to reduce the effect of wave interactions, thevelocities of the final PT waves were calculated using amethod similar to that found in Ref. 29. The shock velocitiesare calculated as
Us2
Us1! 1% n c1=Us1& '
1" n; (1)
where
n !Us1c2 t3 % t2& '
h t2 % t1& 'Upi1 c1 " c2& ': (2)
In the above equations, Us1 and Us2 are the velocities of theplastic-wave and final PT wave, respectively. t1, t2, and t3 arethe arrival times of each wave; as illustrated in Fig. 3. h is theinitial sample thickness. Upi1 is the interfacial particle veloc-ity at the HEL. c1 and c2 are the velocities of the reverbera-tion waves, whose values can be approximated asc1!Us1%Up2 and c2!Us1"Upi2, where Up2 and Upi2 arethe particle velocity of ZnO and the interfacial particlevelocity at the PT point, respectively.30 Calculation using Eq.(1) results in a higher shock velocity (about 8%) than thatperformed ignoring the wave interactions. The plastic-wavevelocities for the two high pressure shots were calculatedwith a similar procedure to reduce the wave interactions. TheHELs along the a- and c-axes determined by VISAR areabout 9.9 and 11.5GPa, respectively. The PT pressures are12.3GPa along the a-axis and 14.4GPa along the c-axis.
For the two low pressure shots in Fig. 2, on the arrivalof the release-wave, the measured particle velocity first dropssharply, holds steady for a short duration (#200 ns,especially for shock along the c-axis), and then graduallydecreases. This characteristic is in accord with an idealelastic-plastic release (ER) model.31 In this model, the initialloading state is on the upper yield surface, and the state after
elastic release is located on the lower yield surface. Theirdifference in the strain-stress space is 4Y/3, where Y is theyield strength at the shock state. Following the method inRefs. 32 and 33, the yield strengths were estimated to be3.2GPa along the a-axis and 3.4GPa along the c-axis, withshock stresses of 18.8 and 21.8GPa, respectively. As a com-parison, based on Hooke’s law and the von-Mises yieldingcriterion,34 the shear strengths at the HELs (Y0) are calcu-lated to be 4.9 and 5.8GPa along the a- and c-axes, respec-tively. The shear strengths at the final shock states aresmaller than that at the HELs. Such a decrease has also beenseen in other ceramics.32,33 For the two high pressure shotsin Fig. 2, the ER characteristic is not seen, which may sug-gest the decrease of shear strength at higher shock pressure.
Typical inclined-mirror experimental photography (shockalong the a-axis) is shown in Fig.4. The elastic shock wavearrives at the front surface of the diver plate and specimen at t0and t1, respectively. The kink at t2 is due to the elastic-plastictransition. The double-wave precursors phenomenon observedby VISAR were not detected by the inclined-mirror method;one possible reason is that the inclined-mirror method is notsensitive to the rise shape of shock front.
The Hugoniot data of ZnO measured by VISAR andinclined-mirror method are summarized in Tables II and III,respectively, and plotted together in Fig. 5. Because of theexistence of the mixed-phase region, the Hugoniot data can-not be fitted by a straight line. For Up> 1.0 km/s, where thephase transition has been completed, we have Us (km/s)! 2.76" 1.51Up (km/s). Fig. 6 shows the Hugoniot-compression curve of ZnO up to about 80GPa. The errorbars are small, they are not shown in Figs. 5 and 6.
IV. DISCUSSION
Anomalous double-wave precursors were observed forshock along the a-axis. Our previous study on MgO withshock along the h110i direction also found such a character-istic; the possible reason is inversion of the slip system dur-ing plastic deformation.35 ZnO has a hexagonal structure, inwhich the possible slip systems include the basal slip system
FIG. 3. X-t diagram illustrating wave interaction in the VISAR experiments.
FIG. 4. Typical inclined-mirror photograph. Flyer and driver are both tung-sten, and the impact speed was 2.203 km/s.
095901-3 Liu et al. J. Appl. Phys. 117, 095901 (2015)
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{0001}h11!20i, the prismatic slip system {1!100}h11!20i, thepyramidal slip system {1!101}h11!20i, and the second-orderpyramidal slip system {1!102}h11!20i.36,37 We calculated theresolved shear stress (RSS) ratio s/rx for each slip systemaccording to the method given in Ref. 38; the results areshown in Table IV. For symmetry-equivalent planes, onlythe largest resolved shear stress ratio is shown. The possible
twinning system {10!12}h!1011i was also considered.39 Forshock along the c-axis, shock wave compression produces noresolved shear stresses on all the possible slip systems, indi-cating the inelastic deformation is caused by twinning. Forshock along the a-axis, shock wave compression producescomparable resolved shear stresses on prismatic, pyramidal,
TABLE II. Hugoniot data for ZnO determined by VISAR. up, Us, and P are particle velocity, shock velocity, and Hugoniot pressure, respectively.
Axis Thickness (mm) Flyer/driver Flyer speed (km/s) Shock state up (km/s) Us (km/s) P (GPa)
a 1.8166 0.001 Cu/Cu 1.2516 0.002 Elastic wave (0.2266 0.002 5.865a6 0.023 7.56 0.1)b
0.3076 0.003 5.1746 0.040 9.96 0.1
Plastic wave 0.4286 0.004 3.6126 0.050 12.36 0.1
Phase-transition wave 0.7216 0.004 2.9406 0.043 16.86 0.2
a 2.8296 0.001 W/W 1.5036 0.003 Elastic wave (0.2256 0.002 5.865a6 0.023 7.56 0.1)b
0.3076 0.003 5.3726 0.040 10.06 0.1
Plastic wave 1.0586 0.010 4.1686 0.060 27.36 0.3
c 1.9356 0.001 Cu/Cu 1.3986 0.003 Elastic wave 0.3316 0.003 6.105a6 0.024 11.56 0.1
Plastic wave 0.4696 0.005 3.8496 0.040 14.46 0.1
Phase-transition wave 0.7906 0.006 3.1966 0.038 19.86 0.2
c 1.9136 0.001 W/W 1.5026 0.003 Elastic wave 0.3336 0.003 6.105a6 0.024 11.56 0.1
Plastic wave 1.0506 0.010 4.2536 0.050 28.46 0.3
aDetermined by the inclined-mirror method.bThe first wave measured by VISAR for shock along a axis.
TABLE III. Hugoniot data for ZnO measured by the inclined-mirror method. up, Us, and P are particle velocity, shock velocity, and Hugoniot pressure, respec-tively. Subscripts 1 and 2 denote the elastic wave and plastic wave, respectively.
Axis Thickness (mm) Flyer/driver Flyer speed (km/s) up1 (km/s) Us1 (km/s) P1 (GPa) up2 (km/s) Us2 (km/s) P2 (GPa)
a 2.2786 0.001 Cu/Cu 1.5776 0.003 0.3256 0.002 5.8216 0.023 10.76 0.1 0.9766 0.006 4.2096 0.017 25.96 0.3
c 2.2836 0.001 W/W 1.3526 0.003 0.3336 0.002 6.1056 0.024 11.56 0.1 1.0226 0.006 4.3856 0.018 28.36 0.3
a 2.2696 0.001 W/W 1.5336 0.003 0.3436 0.002 5.8716 0.023 11.46 0.1 1.1616 0.007 4.5356 0.018 32.16 0.3
a 2.2746 0.001 W/W 2.2036 0.004 0.3176 0.002 5.8586 0.023 10.56 0.1 1.6506 0.010 5.2586 0.021 50.06 0.5
a 2.2786 0.001 W/W 2.5316 0.005 0.3166 0.002 5.8676 0.023 10.56 0.1 1.8856 0.011 5.5846 0.022 60.06 0.6
a 2.7356 0.001 W/W 2.9996 0.006 2.2086 0.022 6.0946 0.060 76.36 1.5
FIG. 5. Shock velocity versus particle velocity Hugoniot results for ZnO.HEL: Hugoniot-elastic limit; PT: phase transition. Solid lines are the linearfit to the Hugoniot data.
FIG. 6. Hugoniot compression curve for ZnO (solid line), together with thecalculated 300-K isotherm (short dashed line) and static compression datafrom Ref. 5 (solid triangles). The dashed-dotted line is a B-M fitting to the iso-therm between 70 and 100GPa. The dotted line is a B-M fitting to the highpressure phase data with a strength correction at the same pressure range.
095901-4 Liu et al. J. Appl. Phys. 117, 095901 (2015)
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and second-order pyramidal planes. Although the largestresolved shear stress appears on the twinning planes, twin-ning cannot be activated by negative stress.40 Therefore, slipshould govern the inelastic deformation process for shockalong the a-axis. However, the critical resolved shear stresseson the above slip planes are unknown; we thus cannot deter-mine which slip system is dominant. According to the exper-imental nanoindentation results, the pyramidal slip systemmay play the primary role.41 The double-wave precursors arepossibly caused by the different slip systems activated at dif-ferent stress levels, as we discussed for MgO.35
The PT pressure for shocks along the a- and c-axes weredetermined to be 12.3 and 14.4GPa, respectively, higher thanthe corresponding PT pressure under static compression(7.5–10GPa). The thermal pressure at the PT point is esti-mated to be #0.1GPa, which cannot account for such a largedifference. Two factors may response for this difference arethe strain rate effect and the shear strength effect. The strainrate in our study is #106/s, while the strain rate under staticcompression is #10%4–10%2/s. It has been reported that undera very high strain rate of #109/s, iron has a PT pressure of25GPa, nearly twice the value measured at low strain rates.42
But a quantitatively description of the relationship betweenPT pressure and strain rate is still lacking. Mashimo found formany materials, the PT pressures under shock compression(normal shock compression, #106/s strain rate) and static
compression are consistent with each other. These materialsincluding some metals such as Bi, Fe, and many compoundssuch as KCl, Si, Ge, ZnS, AlN, and GaAs. Exceptions areseen in some hard materials (with big HELs), such as BN,SiO2, and Si3N4, which have higher PT pressures underdynamic compression than under static compression.43 Theshock induced a%x PT in Ti and a% e PT in Fe are found tooccur on subnanosec time scales,44 much shorter than theloading time under normal shock compression. So we con-cluded that at a moderate strain rate, shear strength is the mainfactor, we only consider the shear strength effect in this study.
The hydrostatic PT pressure can be calculated as45,46
Pht ! Pt % 2Yt=3; (3)
where Pt is the PT pressure and Yt is the shear strength at thePT point. For many materials, the shear strength changeswith shock stress.28,47 In this study, the PT pressures areonly several GPs higher than the HELs, we can assume theshear strength does not change much within this pressurerange, which means Yt( Y0.
45 Then, the hydrostatic PT pres-sure along the a- and c-axes are estimated to be 9.0 and10.5GPa, respectively. This result is in agreement with thestatic compression results.
Fig. 6 shows the pressure-density relationship for ZnO,together with the 300-K isotherm calculated from theHugoniot data based on the Debye-Gr"uneisen model.48 Wefitted the isotherm to a third-order Birch-Murnaghan (B-M)equation between 70 and 100 GPa. The resulting bulk modu-lus (K0) and its pressure derivative (K0
0) of B1 phase ZnOare K0! 174GPa and K0
0 ! 3.9, respectively. The initial den-sity of the high pressure phase was fixed at 6.921 g/cm3 dur-ing fitting.4 The solid triangles in Fig. 6 are the staticcompression data from Ref. 5, which is somewhat steeperthan our fitting curve; in that study, there is a larger reportedbulk modulus, K0! 202.5GPa. As a comparison, the EOSresults from different studies are summarized in Table V.
TABLE IV. Resolved shear stress ratio s/rx for selected slip and twinningsystems in ZnO single crystals.
Slip/twinning system
Shock along
a-axis
Shock along
c-axis
Basal {0001}h11!20i 0.000 0.000
Prismatic {1!100}h11!20i 0.182 0.000
Pyramidal {1!101}h11!20i 0.162 0.000
Second-order pyramidal {1!102}h11!20i 0.177 0.000
Twinning {10!12}h!1011i %0.219 0.157
TABLE V. EOS parameters for B1 phase ZnO from different studies.
Reference PT (GPa) K0 (GPa) K00 Method
Experiments
This study 12.3 (along a-axis) 174 3.9 Shock wave, without strength correction
14.4 (along c-axis)
9.0 (along a-axis) 164 4.1 Shock wave, with strength correction
10.5 (along c-axis)
Ref. 4 10.0 Static (XRD, no medium)
Ref. 5 9.1 202.5 3.54 Static (XRD, silicone oil)
Ref. 6 10 194 4.8 Static (XRD, 4:1 methanol: ethanol)
Ref. 7 9.9 191 3.54 (fixed) Static (XRD, 16:3:1 methanol: ethanol: water)
Ref. 8 7.5 Static (ultrasonic, lead)
Ref. 9 9 204 4 (fixed) Static (XRD, silicone oil)
218 4 (fixed) Static (EXAFS, silicone oil)
Ref. 12 178 4(fixed) Static (XRD, helium)
194 4(fixed) Static (XRD, silicone oil)
Calculations
Ref. 10 7.6 DFT-LDA
Ref. 6 170 3.37 uCHF-PI
176 5.39 DFT-GGA
229 4.24 DFT-LDA
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These results vary greatly, with bulk modulus K0 varyingfrom 170 to 229GPa and its first pressure derivative K0
0
varying from 3.4 to 5.4.4–10 This experimental difference iscaused by the non-hydrostatic conditions under static com-pression, as discussed in Ref. 12. Our result is in agreementwith a study that used helium as the pressure medium, wherethe best hydrostatic conditions can be reached.12,49
We also consider the shear strength effect on the B1phase EOS. Here, we assume the high pressure phase has aconstant shear strength as determined from the VISARrelease wave profile. This shear strength (Y) is at moderatehigh pressure and is smaller than the shear strength at theHEL (Y0). The hydrostatic compression curve of the B1phase ZnO was deduced by subtracting 2/3Y from the calcu-lated 300-K isotherm. After this correction, once more fittingto the third-order B-M equation between 70 and 100 GPa,and the resulting bulk modulus and its pressure derivativeare K0! 164GPa and K0
0 ! 4.1. This bulk modulus is obvi-ously smaller than all the experiment and calculation resultslisted in Table V. The shear strength of ceramics is verycomplex. Yielding of solids can be classified as elastoplasticbehavior, in which considerable shear strength is preservedabove the HEL, or elastoisotropic behavior, in which shearstrength is catastrophically lost. Real materials often exhibita response that lies in between these two extremes. Thecause of this different behavior, however, is still not clear;possible factors are material properties such as chemicalcomposition, crystal state, thermal conductivity, microstruc-ture, porosity, and PT.50 The shear strength also changeswith shock stress. Ahrens et al. pointed out that if a materialundergoes a shock-induced PT in which the crystalline lat-tice undergoes completely rearrangement. It is unlikely thatan appreciable strength effect will be present in the highpressure phase material.46 We analyzed the EOS of B1 phaseZnO without or with strength correction. The former onegives reasonable result while the latter one not. So weinferred that the high pressure phase should have a smallshear strength, and a strength correction maybe not necessaryin discussing the EOS. The release wave profiles in Fig. 2 donot show ER characteristic for the two higher pressure shots,also suggest the decrease of shear strength at high shockpressure.
V. CONCLUSIONS
The Hugoniot data for ZnO were measured up to 80GPaalong both the a- and c-directions using VISAR and theinclined-mirror method combined with a powder gun or two-stage light gas gun. The HELs along the a- and c-axes are10.5 and 11.5GPa, respectively. Our analysis based on RSScalculation indicates that the plastic deformation for shockalong the a-axis is governed by slip systems, while the plas-tic deformation for shock along the c-axis is dominated bythe twinning system. The PT pressure after strength correc-tion along the a- and c-axes are 9.0 and 10.5GPa, respec-tively; which is consistent with the static compressionresults. Shock velocity (Us) versus particle velocity (up) rela-tionship for B1 phase ZnO is given by Us (km/s)! 2.76" 1.51Up (km/s) (Up> 1.0 km/s). Based on the
Debye-Gr"uneisen model and B-M equation, we discuss theEOS of the B1 phase ZnO. The bulk modulus (K0) and itspressure derivative (K0
0) are estimated to be K0! 174GPa,K0
0 ! 3.9.
ACKNOWLEDGMENTS
We are grateful for the financial support provided by theGrant-in-Aid from the Japanese Ministry of Education,Culture, Sports, Science and Technology. This work waspartly supported by X-ray Free Electron Laser PriorityStrategy Program (MEXT: Ministry of Education, Culture,Sports, Science and Technology-Japan).
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