R. E. Duff- Shock-Wave Studies in Condensed Media

8/3/2019 R. E. Duff- Shock-Wave Studies in Condensed Media

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,' ,-,'SHOCK-WAVE STUDIES IN CONDENSED MEDIAR. E. Duff, W. H. Gust, E. B. Royce, M. Ross, A. C. 2\litchcll

R. N. Keeler , and W. G HooverLawrence Radiation Laboratory, University of C;:Jlifol'nLa

Livermore, CaliforniaIN'rRODl]CTION

This paper is an experiment. We ilave tried to lump togethl'r' sCVt ' I ' ; l lpieces or research into a single paper i II the hope that we could convC'y Su ! l l l 'idea of the work underway ~ l t our Llbor;:ltory. Obviously, the disclIssion ()reach topic will be sketchy, but we hope it will aler t those interested in somepart icular subject to watch for the detailed account of each investigatioll wheni t is published in due course.

EQUATION -OF-STATE MEASUREMENTS ON RARE-EARTH IvlETA LS j \NDTHEIR IMPLICA TIONSOver the years shock-wave Hugoniot measurelnents have been nwde 1'01' avery large number of substances, but the rare earths and yttrium and scandi umhad escaped close scrutiny. This is surprising in view of the known peculiadt iesof these elements. We decided to investigate nine ra re ear ths chosen to spanthe lanthanide ser ies , plus yttrium and scandium which have s imilar physicalpropert ies.The elements chosen and their atomic numbers a re shown in the followingr table. An S behind the atomic number means that this e l e m ~ n t was ~ 1 l s o l't)centlyI investigated by AI' tshuler et (1),

(")l candium 21 Samariunl S) ,)Yttrium 39 Europium (' "Lanthanum 57 S Gadolinium G-lCerium 58 S Dyspr'osium G(j S

Praseodymium 59 Ytterbium 70Neodymium 60Shock and f ree-sur face velocity measurements were made on 6.4- and3.2-mm-thick samples by well-known optical flash-gap techniques. Theexperimentally determined shock and part icle velocities for several of th eelements are summarized in Fig. 1. The results from the Soviet group whichcan be compared with our measurements: a re also included in Fig. 1. I t is

dea r that the tw o investigations are in substantial agreement, but somedifferences do exist. Note that the initial shock compressibi l i ty for theserare-earth elements is high (low intercept and slope in the U , - U > gruph).IFur thermore , the U - U l ines are not straight. T h e r e f o r e , S t h e s ( ~ Ill;lterialsS p".-,-----"'Work performed under the auspices of the U. S. Atomic Energy COllunissior1..


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are character is t ically different from the majority of other elements that havebeen investigated.A careful look was taken at the systematics of atomic compressibil i tyas revealed by shock-wave measurements (2) with special attention paid to the

rare earths. The changes in atomic radii as a function of pressure at 00 Kshow that s-electron bonded metals (the alkali and alkali earth elements) arerelatively more compressible than the d-electron bonded metals. All of therare earths except europium and ytterbiu.q1 are normally d-bonded. The abovecorrelat ion suggests that they should be r ~ l a t i v e l y incompressible, contrary toobservation. I t is, therefore, concluded that the 5d electron in these rareear ths is promoted to the unfilled 4f level at quite low pressures . Thispromotion would mean that rare earths would then become s-bonded. Theobserved compression of these elements agrees well with the compression ortheir s-orbitals . This is determined by scaling the Z dependence of the I'adiusof the orbital for s-electron' metals and rare earths as determined fromHartree-Fock calculations.

The conclusion is strengthened by tw o additional observations. At highpressure , all of the rare earths have essential ly the same density. The largedensity difference between the normally d-bonded rare earths and the s-bondedra re earths europium and ytterbium is completely eliminated. In addition,yttr ium and scandium, the elements above lanthanum in the periodic table, ared-bonded and have no f-levels energetically available to accept the d-electrons.They are incompressible as expected.

This reasoning may explain the high initial compressibi l i ty of the ra re -earth metals, but it does not explain the decrease in compressibi l i ty at highpressure . This is thought to be caused by the closed 4p xenon shell which isobservable in this case because the rare earths are d-bonded at zero pressureand are, therefore, relatively dense. The combination of abnormally highipitial density and high ini t ia l compressibility leads to atomic volumes sufficiently small at readily a t t a i n a b l , ~ shock IJressures for the closed inner shellof electrons to influence the interatomic forces. We have observed a sim,ilaritiffening of the Hugoniot for yttrium; Bakanov and Dudoladov (3) have seen theeffect for calcium and strontium. This stiffening appears to occur when thec;losed-shell atomic cores f irs t start to overlap. Therefore, the decrease incompressibi l i ty may ar ise from repulsion of closed electron shells though itoccurs at a smaller core overlap than thctt characterizing the stiffening in thera re earths. -

The Soviet group has proposed that these breaks in the Hugoniots of therare earths and of calcium and strontium are the result of a promotion of anelectron to a d-level in a second-order phase transit ion. This seems unlikely,since any significant population of a d-level at these large compressions appeaIisto be energetically unfavorable, as one can est imate from the cohesive energycurves for typical d-electron bonded metals.

ELECTRONIC BAND STRUCTURE CALCULATIONS AND EQUA TIONS OFSTATEA s part of the overall program in the study of equations of state at highpressures , the inert gases, argon and :tenon, have been shock-compressed to
http:///reader/full/ytterbiu.q1http:///reader/full/ytterbiu.q1


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two and three t imes their normal liquid density (4). These experiments weret theoretically analyzed, using the Monte Carlo method, and a repulsive intermolecular potential for argon was determined and shown to be in good agreementwith results obtained from molecular beam methods (5), I f one applies the law

of corresponding states to the Hugoniots and scales the argon measurementsto the xenon measurements, it is found that below 200 kbar the two sets of dataare in very good agreement. However, above this pressure the xenon pointslie significantly below those of argon in the P-V plane. These results areshown in Fig, 2, where solid curve A is the averaged argon experimentalresults scaled up to xenon, and the dashed extension is an extrapolation of thetheoretical curve which fits the entire Hugoniot. The disagreement betweenthe tw o Hugoniots at high pressure is probably related to differences inelectronic excitation in the tw o cases, Because of the high temperaturesgenerated and the fact that the first excited state of xenon (8.4 e V) is significantly lower than argon (11.5 eV), xenon will undergo considerably moreelectronic excitation than a ~ g o n , and its Hugoniot will be softer. In order toplace these qualititative ideas on a more quantitative basis, energy bandcalculations have been made for both materials as a function of compression.

The energy band calculations show that at the highest xenon pressures th eenergy gap between the valence and conduction band has narrowed about 2 volts,and the 5d-like conduction bands now lie below the 6s, as is the case in compressed cesium. Using the results of these band calculations, a theoreticalHugoniot curve, B in Fig. 2, has been obtained which is in agreement with thexenon experimental curve. At the highest point on the xenon Hugoniot th etemperature is near 2 eV, and the energy gap is about 6 eV. Therefore,electrons from one atom in five are promoted into the conduction band. Underthese conditions xenon becomes metal-like, even though a large band gap stillexists,ELECTRICAL CONDUCTIVITY STUDIES

Measurements of electrical conductivity of shock-compressed substanceshave been made in many laboratories, including our own (6-9), Unfortunately,the scatter of the data is rather larger than one would like to see. This led usto investigate the problems of making conductivity measurements and todetermine their solutions. I t has also led to some excellent data on theconductivity of shock-compressed liquid carbon tetrachloride between 70 and160 kbar and of liquid xenonat150 kbar.Several experimental factors m ust be taken into consideration in

measuring conductivity in shocked media between parallel plane electrodes.The field lines surrounding the conductivity electrode will not, in general, beone-dimensional. To account for this, a fringing field correction must beapplied. The sample and electrode dimepsions must be such that the effect oflateral rarefactfons behind the shock front is minimized. The conductivityelectrode must be a close shock-impedance match to the sample to minimizethe reflected shock and rarefaction waves. The shock-wave motion should benormal to the surface of the conductivity electrode if ' the effects of the residualreflected shocks and rarefactions on the conductivity measurements are to beEasily calculated. Allowance must be made for the attenuation of the initial.shock wave and the decreasing pressure behind the shock front. The error 111


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determining conductivity as a function of pressure depends on the pressuremeasurement as well as the conductivity measurement , and these error::; mustbe included in the data analysis. There will be a capacitance effect caused bythe movement of the shock front relative to the electrode face. This will generate a voltage which begins when the shock wave enters the sample and increasesas the shock front approaches the conductivity electrode. Shock tilt relativeto th e electrode face and this capacitance effect will reduce the r ise time of theconductivity signal and perhaps reduce the accuracy of the measurement .Circuit response is l imited by the presence of stray-shunt capacitance. Al lthese factors must be considered i f accurate conductivity measurements arcto be made.

. The ['act that p r ( ~ c i : - 3 e conductivity IllCLlSnrementH can lw l11adl' is i l lusi l 'atl 'dby Fig. ;{ which showH a plot o[ expe r'irncntal data ror' carbol l t ( ~ t n t ( ' I l L ( ) r i d t ' shocked between 70 and lGO kbar. The data cover seven onlers uf magllitude'in conductivity, and the equation-of-state measurements contribute tIl l ' Illajoruncertainty to the data, I t most certainly is necessary to corrcct th e t)leaHUrements for wave attenuation and electr ic fringing fields i f precise (10%) data arcto be obtained.The shock-impedance matching p r o ~ l e m turned out to be particularlyimportant, as is i l lustrated in Fig. 4 which shows experimental records takenwith anvils of different shock impedance. The calcium is an excellentmatch, while magnesium, aluminum and copper produce progessively highershock impedances. In each case the slow r ise of the signal is caused by th ecapacitance change as the shock front approaches the electrode. The signal riseat la ter t ime in the metal anvil experiments is caused by increased conductivitybehind the shock reflected from the anvil ' itself. I t is clear ly difficult toest imate the conductivity of singly shocked CCl from the aluminum record,4and i t becomes more so if even higher impedance electrodes l ike copper are

used. In fact, if the lower flat part of tne Cu anvil t race were read as thesingly shocked state, an e r ro r of tw o o:r;ders of magnitude in conductivitywould be made. We suggest that a significant part of the scat ter in previouslypublished data may have ar isen from insufficient attention to these details.These experimental techniques have been applied to l iquid xenon becauseequation-of-state measurements (4) and the calculations mentioned above suggcEitthat electronic excitation makes a significant contribution to its energy above .shock pressures of 300 kbar. At 150 kbar, the measured conductivity is0.1/ n cm. Experiments are c o n t i n u i n g ~ The experimental techniques appropriate for CCl and liquid xenon are4not appropriate for metals. We have begun conductivity measurements of

metallic foils by looking at shock-induced resis tance changes by methodss imilar to those suggested by Fuller and Price (9). Figure 5 shows experimental records for copper and iron. The copper record is as expected, shoWin g increased resis t ivity upon shock ar r iva l 0,3 Msec after the s tar t of th erecord. The iron t race shows much more structure. The high-voltage spikeis not an instrumental artifact. I t is a manifestation of the shock-induceddemagnetization of iron that occurs above the 130-kbar transition. Beforethe shock ar r ives , a relat ively large magnetic field within the wire is inducedQY the resis tance-measuring current. The shock demagnetizes the wire, and


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the original magnetic field can no longer be supported by the current in thewire. Therefore, eddy cur rents are induced which dissipate the magneticenergy. The currents generate a voltage spike which superficially indicatesthat iron has a negative resis tance. The decay of the voltage pulse isgoverned by the conductivity of the wire. The conductivity deduced from thet ransient signal is in good agreement with the value indicated on the samerecord af ter the decay of the transient. This observation provides dramaticproof of the non-magnetic nature of f; -iron. The step change in voltage oeforethe spike is caused by the arr iva l of an elastic wave in A1203 J,.tsec in whichthe sample was buried. I t appears that demagnetization is occurring at a~ l o w rate at a pressure of 80 kbar.

OPTICAL TECHNIQUES, Modern nonlinear optical techniques have been successfully applied inshock-wave experiments. Stimulated Brillouin scattering has been carriedout in shock-compressed fluids, with the experimental configuration shown inF'ig. 6 (10). The three- laser system provided a spectrally pure, 20-nseepulse, t imed to ar r ive behind the shock front just before the shock wavereached the lens. This experiment provided a value of the velocity of f'{)undin acetone, shock-compressed to 35 k b a r ~ 31% compression, and 910oK. Thevelocity of sound was calculated from the i modified Brillouin formula,

2vO { , .6.v I =C - n2v + (n2 - n 1) Us - n 2 Up} ' s

Here .6. v I is the downward shift in freqtiehcy of the back-scat tered light asdetermined from the Fabry-Perot in terferometer , n2 the refract ive indexin the shocked medium, and n1 is the refractive index in the unshocked medium.Us and Up are the shock and particle velocity, and Vs is the velocity of sound.The measured value of sound velocity obtained agreed with the theoreticalvelocity within experimental accuracy (about 5%).Having shown the feasibility of carrying out such experiments, we arep'resently developing a simpler , more rel iable la se r osci l lator to producesingle-mode pulses 20-40 nsec in duration, t imed to bet ter than 0.1 J,.tsec.This system should make possible measurement of the velocity of sound athypersonic frequencies, determination of t ranspor t properties in shockedt ransparent materials , and direct Doppler measurements of part icle velocity.Other laser techniques will undoubtedly provide valuable tools for th e

measurement of free surface velocity. The paper by Barke r at this meeting .provides an excellent i l lustration. Workers in another par t of our Laboratory (11)have developed a somewhat s imilar system which uses a short, low-finesseFabry-Perot interferometer as the frequency demodulation detector of Dopplerlshifted l aser radiation. In this system, velocity is indicated by a change in .t ransmission coefficient of the in terferometer . The interferometer fillingt ime is smal l compared to 1 nsec, and the system can be designed to rnc:a:.wresurface velocities in any velocity range. This tobl will be useful in s t u d j ( ~ s firphase t ransi t ions and elastic-plastic phenomena.

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PHASE TRANSITION STUDIESShock-induced phase t ransit ions have been observed in many laboratorieswith many different techniques. We have undertaken a modest effort to redetermine several observed transition pressures so as to provide more reliablevalues for the calibration of static high -pressure scales, and to provide moredefinitive tests of the equivalence of static an d dynamic compression wherereally firm static data exist.A redetermination of the pressure of the lowest bismuth transition, usingquartz gage techniques, has demonstrated (12) excellent agreement betweenstatic and dynamic determinations i f the elastic precursor present in the dynamiccase is properly taken into account. Internally reflecting prisms (13) have beenused to determine the phase transition in tin. In this case we have shown thatthe elastic wave contribution is very small. Our value of 94 kbar is in excellentagreement with the currently accepted static value of 92 kbar, but the temperature of the shocked sample should be determined before such comparisons aremade. The calculations of McQ ueen suggest that t in shocked to 94 kbar has atemperature of approximately 190C. The work of Kennedy (14) and Barnett (15)suggests that the white ti n - tin II t ransit ion pressure is 75 kbar at 190C. This25% disagreement between the static and dynamic determinations of phase

t ransit ion pressure in tin is a source of concern.I t has been proposed that post-experimental, metallographic observationof whether or not a phase transition had o.ccurred in a Fe-Ni-Cr alloy couldprovide a rough measure of the pressure to which a system was subjected.The transition pressure for several alloy compositions has been measured bypin techniques (16), but it seemed desirable to verify the measurements by theinclined mirror method.Figure 7 summarizes the results. Qualitatively, the agreement betweenthe two sets of experiments is good except for the 18 -8 stainless steel and the30% C r alloy. We find the transition pressure for the stainless steel to be morethan a factor of two higher than the value previously reported. I t appears that

a relatively large elastic wave may have been mistaken for the transition wavein the ear l ier work.SHOCK WAVE STRUCTURE

The detailed structure of a shock wave has received considerable attentionover the years. The Navier-Stokes equations, the Mott-Smith bimodal distribuHon function, and more fundamental kinetic theory approaches have beenexploited to produce a good understanding of shock structure in gases. Thesituation is much less satisfactory in dense fluids and solids where analysesbased on the binary-collision Boltzmann equation cannot be t rusted. However,it is not unreasonable to assume that the shoc}\. transition in an ideal solid woulqbe quite thin. I f this were so, the t ransit ion could probably be investigated bythe numerical techniques of molecular dynamics. Such an investigation isunderway.

In a molecular dynamics calculation the coordinates and velocitier-; of al imited number of particles are specified, along with boundary conditions whichhopefully minimir,e the small-system distortions. The particles arc then


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-7advanced under constraints imposed by the assumed force laws between them.The calculation is continued until stat is t ical fluctuations have been averagedout. In the shock-wave problem, the propagation direction is singled out forspecial t reatment . Periodic boundaries normal to the propagation directionsimulate an infinite medium. Along the direction of shock propagation, acoordinate system centered on the shock wave is used. Part ic les enter at thelow-density, low-temperature side at the shock velocity. They leave at theother side, the hot side, at a velocity equal to the shock speed minus theparticle speed. The whole system needs only to be long enough for theconversion from initial to final states to take place well away from the boundaries where new particles are fed in and old ones discarded.

To obtain a precisely fixed shock front, one must correlate the propertiesof the incoming stream of particles with those of the outgoing s t ream. To dothis, i t would in principle be necessary f i rst to compute the equation of state,and then to solve the conservation equations to match the input and outputs t reams. In practice, an approximate match resulting in shock-front driftcan be used; the drift can then be halted by adjusting the output stream velocity.

The molecular -dynamic technique just outlined has been applied to thetwo-fold compression of a face-centered cubic crystal composed of particlesinteracting with a potential which varies as the inverse twelfth-power of thedistance between each pair of part icles. The lattice is initially at OI{. Pre -l iminary resul ts show that the shock transition, in te rms of distance separatingthe low-velocity and high-velocity streams, is only about three lattice parametersthick. The t ransi t ion app ears to be stable, and independent of the total length .of the system. The state behind the shock appears to be a hot, disorganizedfluid. Still to be studied is the dependence of shock structure on the directionof propagation through the crystal and on the interparticle force laws. I t isexpected that these studies will lead f i rst to an accurate molecular picture ofshock structure under a variety of conditions, and then to a unifying theoreticalt reatment valid for high-density systems.

REFERENCES(1) L. V. AI'tshuler, A. A. Bakanova, and 1. P. Dudoladov, Zh. Eksper. Theor.Fiz. , Pisma v Redakt. 3, 483 (1966) [Eng. Tr. JEPT Letters 3 ,315 (1966)].(2) E. B. Royce, Stability of the Electronic Configuration and Compressibili ty of Electron Orbitals in Metals as Determined from Shock Wave Data, Lawrence Radiation Laboratory Report UCRL-50102, November 21 , 1966. (3) A. A. Bakanov and 1. P. Dudoladov, Zhur. Expt. i . Theor. Fiz Pisma 5, 322

(1967) [Eng. Tr. JETP L et te rs 5, 265 (1967)] .(4) R. N. Keeler , M. van Th,iel and B. J. Alder, Physica 31, 1437 (1965).(5) M. Ross and B. J. Alder, Chem. Phys. 46, 4203 (196n.(6) B. J. Alder and R. H. Christ ian, Discussions Faraday Soc. 44 (1956).(7) L. V. Al'tshuler, L. V. KuleshovqL and M. N. Pavolovskii, JETP 39 , 16 (1960) [Eng. Tr. Soviet Phys. JETP.!1 , 10 (1961)] . (8) S. D. Hamann and M. Linton, Trans. Faraday Soc. 62 , 1 (1966).(9) P. J. A. Fuller and J. H. Price, Nature 193, 262 (1962).


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(10) R. N. Keeler , G. II. Bloom ;:md A. C. Mitchell , f'>hys. Hev. Lettvn; 17852 (1966).(11) T. ss , private communicat ion.(12) D. B. arson, J. Appl. Phys. 38, 1 1 (1967).(13) G. and P. W. Wright, FoUrth osium on Detonation, 11. S.Government Printing Office, (1965), p.(14) G. C. Kennedy and R. C. Newton, Solids Under Pressure , W. Paul and

D. M. Warschauer , Eds. (McGraw-Hil l Book Co. Inc., New York, 1(63) p. 163.(15) J . D. Barnett , R. B. Bennion and H. T. Hall , Science 141, 1041 (186:H.(16) C. M. Fowler , F. S. Minshall and E. G. Zukas, Response of Metals toHigh-Velocity Deformation (Interscience, New York, 1961) p. 175.

1 4 ~ - - - - - - - - - - ~ - - - - - - - - - - r - - - - - - - - - ~

500

400

j.>t 300I

200

100

0 L - - - 1 L 8 - - - - - - - 2 L O - - - - - - - 2 L 2 - - - - - - ~ - - - - - - ~ 2 6 V - cc/mol

Fig. 2. Exper imenta l m e a s u r e ~ e n t s andtheoret ical calculations of Hugol1lots forargon and xenon. The law of correspondingsta tes was used to scale the argon resul tsup to xenon. Curve A is the .scaled a r g ~ ) l 1 exper imenta l curve extended by theore t ica lcalculations. Curve 13 is based on the xenonband calculations. Calculated Ilugoqiot o.t empera tures on the two curvcS arc pU,OOO h ,_12,0000K, .16,0000K, and + Ul,OOOoK.

13

12

--DATA FROM REF. 13 CB={C]2 Cs2r/22 ~ - - - - - - - - - - ~ - - - - - - - - - - ~ - - - - - - - - ~ Q 1.0 2.0 3.0

U PARTICLE VELOCITY - km/secp

Fig. 1. Shock velocity - part icle velocityHugoniot data for five rare-ear th metals .Dashed l ines are fits to data from Ref. 1.


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Pressure - 260 kbar Pressure - fi rst wave 80 kbarsecond wave 175 kbar

-- -2. __ WITHOUT SHOCK WAVE ATTEN-"UATION CORRECTION BE-,pHIND THE SHOCK FRONT

_......::...-WITH SHOCK WAVE A7!TEN- 7UATION CORRECTION /BEH IND- THE SHOCKFRONT

7l/'/'/I11-!-O

It'Ii-FoIhI!HY.NG p tA " ox,l O - 7 ~ __ ____ ____ __ ____ __

UJ 80 100 140 lUJ 180PRESSURE (kbar)

Fig. 3. Electrical c : : m ~ u c t i v i t y of shockcompressed CCl4 .

Copper

(a)

(b)

(c )

(d)Fig. 4. The effect of shock wavereflection from a metal anvil onelectrical conductivity records.a. Calcium. b. Magnesium, c. Aluminum, d. Copper. The fi rst threerecords have a sweep duration of2 /./,sec; th e last has a duration of10/./,sec.

Iron

Fig. 5. Conductivity records for copper and iron. Total sweep duration of bothrecords is 1/./,sec.


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R. E. Duff- Shock-Wave Studies in Condensed Media