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JOURNAL OF GEOPHYSICAL RESEARCH, VOL. 95, NO. B13, PAGES 21,767-21,776, DECEMBER 10, 1990 ShockTemperatureMeasurementsin Metals' New Resultsfor an Fe Alloy JAYD. BASS x, THOMASJ. AHRENS 2, JOHNR. ABELSONSAND TAN HUA 2,4 The temperatureof a Fe-Cr-Ni alloy (304 stainlesssteel) has been measuredduring shock compressionusing a high-speedradiometric technique. Experiments were performed on highquality thick films deposited on sapphire and LiF windows. The samples had no observable porosity or defectsand closelymeet the ideal criteria for shocktemperature measurements.Data obtained with both A1203 and LiF windows axeinternally consistent,indicating that they remain transparent to high pressuresand axe thus suitable windowsfor shocktemperature measurements. Our data yield stainless steel melting temperatures ranging from 45704-310K at 138 GPa to 57104-340 K at 215 GPa, and additionally provide bounds on the initial Hugoniot temperatures of the samplebetween56004-340K at 234 GPa (near the solidus)and 65804-440K at 283 (in the liquid field). Takentogether,thesedata definea smoothcurvefor melting of the alloy up to 271 GPa and 5860 K, which should representa point on the liquidus. Melting along the Hugoniot beginsat approximately 234 GPa and 5600 K, as comparedwith 242 GPa and 6400 K for pure Fe. At the pressure of the inner core-outer core boundary, the melting point of 304 stainless steel is lower than that of pure Fe by m1450 K, as compared with only 110 K at I atm. These results demonstrate that upon alloying with Ni and Cr the melting point depressionof Fe and thus material likely to comprise the inner core increaseswith increasing pressure. •NTRODUCTION Grover,1977;LyzengaandAhrens,1979],the experimentis Studiesof the meltinõrelationsin metMlicsystemsat hiõh difficult in both execution and interpretation. Specifically, pressureshave direct imphcationsfor the thermal structure the ideal shock temperature experiment on metals places and composition of the Earth's coreand lowermantle. Becausethe primary constituentof the liquid outer core is believedto be an iron alloy, the high-pressuremelting behavior of Fe-bearingcompoundsare of singularimportance for understandingthe nature of the innermostportions of stringentrequirements on the sampleassembly used. Only the Earth. In particular, the temperature of the inner core- sure at the inner core-outer core boundary. These results recently has there been a sustained effort to measure the temperatureof shockedopaquesolids. Basset al. [1987] carried out a series of temperature measurementson iron at Huõoniot pressuresup to 300 GPa, closeto the pres- outer coreboundary,at a pressureof 329 GPa [Dziewonski were found to be in close agreementwith static compresand Anderson,1981],is controlledby the meltingpoint of sion measurementsof melting temperaturesin Fe at lower the iron alloy at this pressure.With the developmentof new pressuresby Williams et al. [1987] and with theoretical temperatures calculated by McQueenet al. [1970]. techniquesin the areasof shockwave research,the pressure I-Iugoniot However, these results yielded higher melting temperatures rangeoverwhichmeltingphenomenahavebeenstudiedhas greatly expanded,thus offeringthe potentialfor construct- than thoseobtained by the theoretical calculationsof Brown ing improvedmodelsof the Earth's interior. Shockwavemethodshavelong playeda particularlyim- and McQueen[1986],and the diamondanvilexperiments of Boehler[1986]and Boehleret al. [thisissue].In this report portant role in studiesof core materials due to the extreme we review the basis of shock temperature measurements on temperatures andpressures that are accessible, therebyal- metals and recent developmentsin the analysisof suchdata, lowingpropertiesto be measuredunder conditionssimilar and we presentnew data on shocktemperaturesmeasured to thosein the core itself. The temperature achievedunder shockconditionsis not, however,a readily measuredvariable, andthis hasbeena seriouslimitation to the application of shockwaveresults. Although the possibilityof measuring shocktemperaturesin opaquematerialssuchas metalshas on an Fe-Cr-Ni alloy. The experiments were performed on samplesof extremelyhigh quality, therebyeliminatingsome of the uncertainties that were present in the previous data on Fe. Our results constrain the melting curve of the alloy over a pressurerangeof about 138-271 GPa and are consisof Fe due to alloying beenrecognized for sometime [Urtiew, 1974; Urtiew and tent with a meltingpoint depression with Ni and Cr. These new results support our previous conclusionson the melting curve of Fe at core pressures. 1 Depaxtment of Geology, University of Illinois,Urbana. 2 Seismological Laboratory, California InstituteofTechnology, Pasadena. 3 Coordinated Sciences Laboratory, Universityof Illinois,Ur- EXPERIMENTAL METHODS Shock TemperatureMeasurements Althoughthe opticalpyrometrictechniqueusedin our 4 Permanently at BeijingInstituteofTechnology, Beijing,Peo- shocktemperature measurementshas been presentedpreviples Republic of China. ously[LyzengaandAhrens,1979;Basset al., 1987;Boslough and Ahrens,1989], a brief descriptionof the experimentis Copyright 1990 by the American Geophysical Union. givenasbackgroundfor the followingdiscussion. The tembanao Paper number 90JB02163. 0148-0227] 90/90JB-02163505.00 perature T of a sampleshockedto high pressureP is obtained by measuringthe intensity of thermal radiation emit21,767 21,768 BASS ET AL.: SHOCK TEMPERATURES ON AN IRON ALLOY ted by the sample at several discrete wavelengthsA. The temperature and emissivity ½of the sample are obtained by fitting the observedspectral data to a Planck greybody diation function L(A)= ½ClX-5[exp(C2/AT)1]-1 (1) whereL(A) are the spectralradiancesand C1 and C2 are constantswith valuesof 1.191 x 10-16 and 1.439 x 10-2 respectively. The challangeand complicationsof performing such an experiment on a metal arise from the simple fact that metals are opaque, and it is possibleto collect radiation emitted only from the surface of a sample and not from the interior. Becausethe shockpressurereleasesto i arm at a free surface and is accompaniedby an adiabatic decreasein T, it is necessaryto maintain the sample at high P and T by means of a transparent anvil in contact with the sample surface. The anvil material alsoservesas a window through which the thermal radiationmust be transmitted(Figure 1). In contrast,a transparentsampleservesasits ownanvil the data reduction. We discuss these effects in more detail below. In the designand preparation of sample assemblies,the objectiveis to avoid any sourcesof spuriousthermal radiation which would contaminatethe observedsignal. The mostobviousimperfectionsare sampleporosityand spaces, or gaps,betweenthe sampleand anvil. At a givenHugoniot pressurean initially poroussampleattains highertemperatures than a sample of ideal crystal density. Samplematerial adjacent to a gap is multiply shockedand alsoreaches anomalouslyhigh temperatures. In addition, it is desirable for the samplesto be as thick as possible.Irregularitiesat the driver-sampleinterfacecanlead to a high temperaturein thisregion(shownschematically at thebottomof Figure1), and this thermal "spike"canpossiblyconductto the sampleanvil interface during a measurement. Interactions at this interfacehavebeenanalyzedby approximatingirregularities in the surfacesas thin porouslayerswhichreachvery high shocktemperatures[Urtiew and Grover,1974].Reasonable and window. An overriding considerationin the choice of as this approximation may appear, it should be noted that the validity of this model has not been demonstrated,and anvil/window material is, therefore,that it remain trans- it is unclear(as notedby Urtiewand Grover[1974])how parent, or nearly so, up to the pressuresof interest. For work in the megabar pressurerange and above, sapphire a given state of surfaceroughnessmight be quantitatively equatedwith a specificdegreeof porosity.In any event, the (single-crystal A120:•)and LiF are the onlyknownsuitable problemof surfaceroughness is minimized,if not eliminated, window materials. by usingvapor depositedfilms, as opposedto mechanically It is generally not possibleto find an anvil with properties that match the shockimpedence and thermal characteristics of the sample. Therefore, upon arrival of a shock wave at the sample-anvil interface the pressurewill either partially releaseto a lower value or be reshockedup to higher P. In polished samples placed in contact with the anvil. Electron micrographs of vapor-deposited Fe films showed the roughnessto be of the order of the microscoperesolution (• 0.02/•m) [Ahrenset al., 1990a],approximately2 orders of magnitude smaller than the casesexaminedby Urtiew and Grover[1974].Althoughroughness of the film surface Projectile Metal Thin Metal Driver Film should therefore have a minimal Transparent effect on the observed tem- peratures, we have made a considerableeffort to obtain thick films in order to thermally isolate the sample-anvilinterface from any driver-sample effects. ••J "i• Mask Samples I i i ,, T Fig. 1. Sample assembly for optical shock temperature measurements. The sample consists of a metal film deposited on a transparent substrate which servesas both an anvil and a transparent window through which thermal radiation is emitted. Rapid compression of gassesand surface irregularities at the interface between the sample • and the driver produce very high temperatures in this region. The bottom portion of the figure illustrates Stainlesssteel films were depositedon sapphireand LiF substratesusingplanar magnettonsputteringin an argor. atmosphere.The compositionof the sputteredsampleswas determined by electron probe microanalysisto be nearly identical to the 304 stainlesssteel usedin the equation of state measurements of McQueenet al. [1970],with Cr and Ni asthe primaryelementsalloyingwith Fe (Table1). Using a standard micrometer, the thicknessesof severalfilms were measuredand found to be in the range 12-14 J:2/•m. It is noteworthy that thesefilms were approximatelyan order of magnitude thicker than someof the Fe films usedby Basset al. [1987],therebyreducingpossiblecontamination of the thermal signal by heat from the driver-anvil interface. Adhesionof the films to the anvil substrateswas excellent; no gaps could be seen at the anvil-sampleinterface by vi- sual observationwith and without an optical microscope, and there were no interferencefringes upon illumination of the interface with monochromaticradiation. Moreover, the the thermal distributionacrossthroughthe assembly[after Bass surfaceof the films had a mirror-likeappearanceand no obef al., 1987]. servableroughness.The state of the film material was that of a finepolycrystallineaggregatewith no obviousintergranaddition, there is an exchangeof heat betweenthe sample ular spaces. and anvil due to the different Hugoniot temperatures atBecauseporositycan greatly affectthe Hugoniottemperrained in each of these materials. The magnitudesof these atures, it is important to accurately characterize the deneffects are in fact substantial and must be accounted for in sity of films used in shock temperature experiments. The BASS ET AL.: SHOCK TEMPERATUllES ON AN IttON ALLOY TABLE 1. Chemical Composition of Samples Stainless Steel [McQueeneta/., 1970] Fe, wt % 69.3 68.0 Cr Ni Mn Si c 19.4 9.1 -0.7 -- 19.0 10.0 2.0 1.0 0.08 Total 98.5 100.08 Density, g/cm 3 into the sample upon arrival of the initial shock wave at the sample-anvilinterface. Pressurescorrespondingto both the initial Hugoniot state and partially releasedstate of the sample are listed in Table 2. Type 304 Stainless Film 7.829:0.08 21,769 The raw data from our experimentsconsistof voltage as a function of time, with the voltage proportional to the intensity of thermal radiation. The source of the radiation is the surface of the partially released sample which is in thermal contact with a relatively cool anvil. As discussed below, models of Fourier heat transport suggesta tempera- 7.896 ture for thisinterfacewhichis time independent[ Groverand Urtiew,1974; Tan andAhrens,1990]. However,we observed an increasein voltage at later times of all shot records,even if the initial part of the shot record appearedfiat (Figure Archemedian density of our films was measured using a 2). A time dependence of the thermal signalin sapphire temperature-monitored toluene bath. The room tempera- windowswas similarlyobservedby Urtiew [1974],and Mctureinitialdensity obtained was7.82-4-0.08Mg/m3 forthe Queenand Issak [this issue]. This could indicate that the stainless steel films. This value is in agreement with the actual thermal interactions near the sample-window interface are more complex than indicated by theoretical models should be noted that a primary source of error in the den- thus far proposed, and that the temperature at this intersity measurementsis surface tension of the hanger used to face will change with time even for perfect sample assemsupport the sample, an effect which tends to systematically blies. Alternatively, the rise in voltage could conceivablybe underestimatethe sample density. Calibration runs using due to radiation from the layer of shocked window matesapphire and quartz chips of approximately the same mass rial whichthickenswith time [Svendsen et al., 1989].Yet a valueof7.896Mg/ms reported byMcQueen et al. [1970].It as the foilsyieldedresultswhichwereon averageabout 0.5% third possibility is that heat from the driver-sample interface is diffusing to the sample-windowinterface on the time ments indicate that the film samplesare essentiallyof ideal scale of the experiment, despite the thickness of the films. bulk crystal density. Due to the difficulties of interpreting later portions of the shot records, we use the early part of the record, immediatly Shock Wave Measurements after the initial rise time, for the purpose of obtaining shock All of the shock temperature measurements were per- temperatures. These data should represent an interface temformedusinga two-stagelight-gasgun [JeanlozandAhrens, perature viewed through unshockedwindow material, before 1977]. Tantalum flyer platesmountedin Lexan projectiles heat has diffusedfar from the interfaces. Although complete were accelerated to velocities of between 5.884 and 6.048 analysesof the time evolution of the thermal signal will be (-4-0.002)km/s and impactedFe driver plates on the tar- an important area of investigation in future shock temperget assemblies. The pressurein the sample was calculated ature studies, we limit ourselvesfor the present to a more by the impedence-matching method [Rice et al., 1958],us- straightforwardinterpretation of the initial observableintering the equation of state parameters given by Mitchell and face radiation. lower than the true densities. The results of our measure- Nellis [1981], Brown and McQueen[1986], Carter [1973], Marsh [1980],and McQueenet al. [1970]for Ta, Fe, LiF, A1203, and 304 stainlesssteel, respectively. Thermal radiation emitted by the sample was focusedonto four photodiodes in front of which were interference filters centerd at wavelengthsof 450, 600, 750, and 900 nm. A mask was used so that only light from the central area of the samplereached the pyrometer, and light from the edgesof the sample was blocked. Prior to each experiment the pyrometer was calibrated usinga tungstenfilament quartz halogenlamp which serves as a spectral irradiance standard and which is itself It should be noted that none of the stainless steel records showed an initial spike or sharp peak in radiant intensity. Such a feature would indicate a high transient temperature from either a poor interfacewith gapsbetweenthe sample and window or a "flash"from compressionof gassesand surface irregularities at the driver-sampleinterface. It is possible, however, that evidence of a thermal transient could have been obscured in some of our shots due to relatively long rise times (• 100 ns). The rise time was sometimes lengthened(as for shot 218 shownin Figure 2), by tilt of the projectile which resulted in non-planar impact onto the target. This tilt was clearly evident on X radiographsof the The spectral data were recordedby either high-speedTextronix oscilloscopes (shots214 and 215) or Hewlett-Packard projectile in flight and was correlated with the observedrise Model 54111D digital oscilloscopes.In addition, a LeCroy time from oscillographtraces of the light intensity. NontheModel 7600A digital recording system was used as a back- less, even for shots with much shorter rise times of ~ 20 the response time of the detection up system. Further details of the temperature measuring ns or less(approximately calibrated relative to a National Bureau of Standards systemare givenby Boslough andAhrens[1989]. source. system),therewasnoindicationof a thermalspike.We thus conclude that our sampleswere sufficiently thick so that the P•ESULTS initial observed radiation was uncontaminated by processes Three experiments were conducted using sample assem- at the driver-sample interface. blies of steel deposited on sapphire, and one was performed It has sometimes been suggestedthat any time depenusingLiF as the window/anvil material. Becausethe shock dence of the voltage is a sign of the window materials beimpedencesof A1203 and LiF are lower than that of staincoming opaque. In this event, however, the temperature lesssteel, a rarefaction, or releasewave was propagatedback should approach that of the window material at the release 21,770 BAss ET AL ß SHOCK TEMPEI•ATUI•ES ON AN IRON ALLOY TABLE 2. Shot Summary: 304 Stainless Steel Shot Anvil Velocity PH km/s GPa PR GPa TI , K observed TM , K TH , K • observed 218 A1203 5.480 234 181 45384- 40 51304-240 56004-340 0.394-.02 219 LiF 5.884 260 138 42434-110 45704-310 56304-410 0.174-.02 214 215 A1203 A1203 6.048 6.218 271 283 204 215 47394-130 53424-140 51604-330 57104-340 58604-430 65804-440 0.484-.06 0.384-.04 TI is the observedtemperature of the interfacebetweenthe stainlesssteel foil and the anvilwindow substrate;TM is the melting temperature of stainlesssteel at pressurePR inferred from the analysisof Tan and Ahrens,[1990];TH is the infmwedHugoniottemperatureof stainlesssteel usingthe analysisof Groverand Urtiew [1974],whichignoresmelting in the sampleand/or anvil. pressure.Theoretical Hugoniot temperatures,calculatedus- or less(onestandarddeviation),for all shots.In the data ing the procedureof Ahrens[1987],indicatethat the win- reduction,the weightingfactor for eachpyrometerchannel dow is at a much lower temperature than the metal sample included uncertainties in cahbration as well as those related and, therefore, that the voltage should decreasewith time, to the reading of shot records. Little differencein the results not increase as is observed. In several other investigations was obtained by using an unweightedfitting procedure. of the optical properties of potential window materials, it Our interpretation of the radiance data necessarilyashas similarly been concludedthat single-crystalA1203 and sumesthat there is no wavelengthdependenceto the emisLiF remain transparent to high Hugoniot pressures;these sivity of the sample. Although this assumptioncouldhave a include a reanalysisof Urtiew's [1974]temperaturemeas- significanteffecton the resultanttemperatures,it is common urementson Mg [Ahrenset al., 1990a;McQueenand Issak, to all measurementsof temperaturesby optical pyromerry, this issue],experimentson Fe [Basset al., 1987; Svendsen regardlessof whether the measurementsare made under dyet al., 1989],and measurements by McQueenandIsaak[this namic or static conditionsin a diamond cell. The only alissue]usinga varietyof samplemateriMs. ternative at presentis to assumea wavelengthdependent Spectral radiancesat four wavelengthswere fit by a wei- emissivity identicalto, for example,that of tungsten(oneof ghtedleast-squares methodto equation(1) in orderto ob- thefewmateriMsfor whichc(T) hasbeenmeasured).There tain the effectiveemissivity and temperature of the interface is no clear basisfor preferringone of theseassumptionsover (Table 2). The quahty of the fits was generallyexcellent the other. Furthermore, we assumethat the metallic sam(Figure 3), with uncertainties in temperaturebeing140 K ple is radiating homogeneouslyand that no "hot spots" or Shot -½218' 304 Stainless Steel on AI203 900 nm PH= 234 GPa, 84.6 T[ = 4538 K mV Shock arrives 65 ns at sample-anvil interface Shock arrives a t anvil freesurface Fig. 2. Digital oscilloscope record of a shocktemperatureexperiment(shot 218). The sampleis a 304 stainless steel film on a window/anvil material of A1203. The horizontal arrow on the record indicatesthe voltage which was used in the data reduction to obtain shock temperatures. BASS ET AL ' SHOCK TEMPERATURES ON AN IRON ALLOY 10.5 21,771 lds a lowerbound on the releasevolumeand releasetemper- - ature. ,--, The questionof heat exchangeby the windowand sample wasfirst investigatedby Groverand Urtiew[1974]. These 9.5 authorsconcludedthat the interfacetemperature TI should be time independentand is givenby E = Ta+ ( (1-9 - Ts a)) c:) o 7.5 (3) where subscript a refers to the transparent anvil material. ,_ a in equation(3) is definedas -• 6.5 = 304STAINLESS STEEL onLIF Tx=4243K 5.5 œ=0.17 4.5 I 400 I 500 • i • 600 i 700 • i 800 • I • 900 Wavelength (nrn) Fig. 3. The optical data measured for a shock temperature experiment using a stainlesssteel film on a LiF window. The solid curve is a weighted least squares fit to the data using a Planck greybody function. (•;nPnCn) 1]2 (4) where n is the thermal conductivity, p is the density, and C is the specific heat. A point of concern in the evaluation of shock temperature results is the error in TH introduced by uncertainties in thermal properties, particularly n. However, it is important to bear in mind that these thermal properties are used to obtain a temperature correction, which is much smaller than the observed temperatures. As an example, consider the effect of errors in • on the inferred TH of Fe, using the data for shot 189 of Basset al. [1987]at PH = 202 GPa and TI = 4010K. Using the data and method given by Tan "shearbands"(localizedregionsof hightemperatures) ex- andAhrens[1990]to calculatethe necessary thermalprop- ist in the sample. This assumptionis justified on the basis of lower-pressureshock wave studies which show that shear band deformation characteristically yields high tem- erties, we obtain a value of a = 4.4. Allowing a to vary by a factor of 2 changesthe calculatedTH by -t-250K. This peratures and low emissivities that are at least one order of magnitude lower than those obtained so far in shock tem- is a rather extreme variation in a which is chosen to over- peratureexperiments on metals[SchmittandAhrens,1984]. estimate likely errors in this parameter. Moreover, related data are available to constrain the thermal properties. The electrical conductivity a of Fe under shock compressionhas It will be important to test this assumptionin the future by high-speedframing photographyof the radiating sample. related to • by the Wiedemann-Franz relation n = LaT, been measured[Keeler,1971; Matassov,1977], and this is whereL is the Lorenznumber[Ashcroftand Metrain, 1976]. A Debye-Grfineisenmodel, which is in good agreementwith DISCUSSION As originally conceived, optical radiometric measurements on shockedopaquematerials could be usedas a means of obtaining Hugoniot temperaturesTH. Anticipating the results of the following discussion,it is also possibleunder certain conditionsto infer the melting temperaturesTM of a availabledata on alkalaihalidesandminerals[Roufosse and Jeanloz,1983],canbe usedto estimatethe pressuredependenceof n for windowmaterials[Basset al., 1987]. The heat capacity of anvil materials can be approximated by the high temperature DuLong-Petit value, whereaspossible electronic contributions to C for Fe and its simple alloys has metal overa rangeof releasepressures PR [Tan andAhrens, beeninvestigatedtheoreticallyby Bonesset al. [1986]. It 1990]. We showbelowthat valuesof TM and TH from our is unlikely that our calculations of thermal properties would stainlesssteel data are internally consistentand are inferred to constrain the melting temperatures of 304 stainlesssteel at pressuresbetween approximately 138 and 271 GPa. Although the metallic samplein a shocktemperature experiment is, by virtue of its contact with an anvil, in a partially releasedand cooled state during a measurement,the effects of pressurerelease and thermal conduction near the interface can be accountedfor. The isentropic release temperatures, TR, are related to Hugoniot temperatures by Tn= Tnezp- V dv (2) be cooperatively biased in such a way as to yield an error in TH that is decidedly nonrandom. The use of equations(2)-(4) has been appliedto a majority of shock temperature measurementsmade by optical radiomerry[Urtiew and Grover,1977;Lyzengaand Ahrens, 1979; Bass et al., 1987; McQueenand Issak, this issue]. However, it has usually been assumedthat the sample does not undergo any phase transitions, in particular melting, upon partial releaseof pressure.When the initial Hugoniot state is in the vicinity of the melting curve, releasemelting can have a significanteffecton the interpretation of observed interfacetemperatures[Tan andAhrens,1990].A schematic illustration of the releasemelting processis shownin Figure where VH and VR are the Hugoniot and releasedvolumes, 4, where a material releasessufficiently far from an initial respectively,and 3' is the Grfineisen parameter. VR is ob- Hugoniot state that the releaseisentropeintersectsthe melttained via an approximation to the Riemann integral for- ing curve(point 2). Thereafter,the releasepath followsthe mula [LyzengaandAhrens,1978].This approximation yie- melting curve with the production of an increasingamount 21,772 BASS ET AL' SHOCK TEMPERATURES Release Melting and / ON AN IRON ALLOY leasepath would leave the melting curveand enter the melt field. Alternatively, at very high Hugoniot pressureswhere the shockedsamplemay be completelymolten, the melting curve will not affect the releasepath. However, the sample will not be able to cool below the melting curveby thermal contact with the anvil until the heat of fusion is overcome, so the temperature is again buffered at about TM. A complete discussion of variouspossiblereleaseand coolingpaths Shock Temperatures Release ,. •ite Iht?nU• •. /' / P. / is givenby Tan andAhrens[1990]. Just as the cold windowcan causefreezingof the sample, the hot sample can induce melting of the window materiM. In this case,a melt front will propagateinto the window, a solidification front will propagateintothe sample(Figure5), and the energeticsof both transitionswill affect the observed interface temperature. This case has been treated in detail by Tan andAhrens[1990]andis referredto in theirpaperas model III. Calculationsof the melting curvesand Hugoniot statesfor anvils and samplesindicate that this model apphes to the present experiments on stainlesssteel and most of the previous work on Fe samples. The importanceof the analysisof Tan andAhrens[1990] I is that it allows the observedinterface temperature to be related to the melting temperature at the releasepressure. For model III of these authors, the interface temperature is time independent and given by = Tw + Pressure Fig. 4. A schematic diagram illustrating the T-P path followed by a sample that melts upon partial release of pressure. The sam- ple is initially shockedto state 1 at pressurePH on the Hugoniot and releasesto pressurePR when the shockarrives at the sampleanvil interface. The release isentrope intersects the melting curve at point 2 and followsit to PR (point 3). The ratio of melt to solid increasesbetween points 2 and 3. Without partial melting the final release state would be point A. Contact with a cold anvil causes the temperature to drop from point 3 to 4 and is accomparfled by freezing of melted sample. The temperature decrease without freezingof melt is much greater (points A to B) due to - Tw) TI= Tat+ c•32erferf It (TM--Tw) A - erf/• (6) whereTw and TM are melting temperaturesof the window and sample, respectively,and a32 is defined as in equation (4), but with respectto the solidmetalandliquidanvil(see Figure 5). The rate parameters• and/t are relatedto the positionX of the melting front in the window and freezing front in the metal: the latent heat of fusion. The final state of the sample is thus buffered by the melting curve. of melt and a decreasein temperature which is determined by the thermodynamic properties of the phases. In Figure 4 the final release state is at point 3 on the melting curve, indicating that the sample did not completely melt upon release. For comparison,without any melting the sample would have released to point A. Consider further that if the partially released sample is then placed in contact with a relatively cold anvil, the temperature does not decreaseuntil freezing of the melt is complete, due to the latent heat of fusion. The temperature decreasedue to heat conduction a32 erf A c•32erf A - erf/• Xw: 2,•(n2t) 1/2 (7a) XM = 2/•(nat) 1/•' (7b) where subscripts 2 and 3 refer to molten window and solid metal(Figure5). The methodof solvingfor A andtt is given by Tan and Ahrens[1990].An observedinterfacetemperature Tt is used to obtain TM by TM = Tw + (Tl• - Tw) Stainless erf/•) 1•32erf A (8) Steel Data The above analysis has been applied to the data obtained (points 3 and 4, Figure 4) is thereforemuchsmallerthan it would be in the absenceof a melting transition(points on our four stainless steel experiments. These four data A and B, Figure 4). The centralpoint to be madeis that represent all of our experimental results at this stage: we the final state of the sample is either on the melting curve or very close to it. That is, the melting curve essentially buffers the state of the sample, and the interface temperatures observed in our shock experiments should be close to the melting temperature of the sample at the releasepressure. have not selectively culled the data or rejected any points. Thermal properties are calculated using the methods given by Tan and Ahrens[1990],and we alsoadopt their values for the materiM properties of the anvils. The Debye temperature of stainless steel under room conditions, which is needed to scale thermal properties, is taken from McQueen Figure 4 illustrates only one of several possiblerelease et al. [1970],whereasthe averageof the liquidusandsolidus paths involving melting. For example, if release melting temperatures (1699K) [Lewis,1977]is usedfor the melting were completed at a higher pressurethan P•t then the re- temperature of 304 stainless. A constant value of P'r = 15 is BASS ET AL' SHOCK TEMPERATURES ON AN IRON ALLOY Sample-window that the simpleranalysisof Groverand Urtiew[1974],which ignoresmeltingeffects,may actuallybe a reasonableapproximation of TH. To investigatethis possibility,we have calculated theoreticalinterfacetemperaturesby both methods, In[efface • 21,773 AI203 I• using Fe and stainlesssteel sampleson AlaO3 and LiF win- 0 5 TM I 0 0 dows as examples. The simulationsshow that for a given PH, the interface temperatureswhich ignore melting, Ti, can be either greater or less than the actual interface temperature TI, dependingon the propertiesof the sampleand T^ the amount of releasemelting that occurs. If T/ < TI, then using the Grover-Urtiew analysisfor the higher observedinterface temperature will overestimateTH, while if T/ > TI the oppositeholds true. The magnitudeof the errorsis ap- TW I.•...-SolId:fication "-- Front • 3 '- I Liquid E 1 I 4 I 2 Solid Liquid 3 I Solid 2I i XM 1 0 Xw 1 2 3 Distance from Interface, Fig. 5. Temperature as a function of position in the target for model III of Tan and Ahrens [1990]. The sampleis originallya partial or complete melt which freezes due to contact with the anvil. The anvil is likewise melted due to contact with the hot sample. Note that the interface temperature TI is closeto the melting point of the sampleTM. TR is the initial releasetemperature in the sample, and TA is the Hugoniot temperature of proximately 200K or less for conditions similar to those of previousexperimentson Fe [Basset al., 1987;Ahrenset al., 1990b],and the presentexperiments.Applyingtheseresults to our stainlesssteel data, Hugoniot temperatures calculated from equations(2)-(4) for the three lowest-pressure shots(214, 218, 219) shouldplacelowerboundson the true Hugoniottemperatures; for the highest-pressure shot(215), the calculated Hugoniot temperature is an upper bound. Thus far it has been implicitly assumedthat an equilibthe anvil. The thermal profile is calculated for an Fe sample and rium state is achievedupon both shockreleaseand conducsapphire anvil 0.1/•s after arrival of the shockat the sample-anvil tive cooling of the sample. There is no absolute assurance (x=o) 1990]. that this conditionis met, and it is possiblethat superheated solidsor supercooledmelts persistoutsideof their stability fields. In such a situation, equilibrium phase boundaries assumed, similarto that for Fe [BrownandMcQueen,1986]. would have lesseffect on releaseand coolingpaths than inAll other thermodynamic properties are taken as equal to dicatedby the calculationsof Tan and Ahrens[1990],and thoseusedin the earlierworkon Fe [Tan andAhrens,1990]. the analysisof Groverand Urtiew[1974]couldbe moreapWe thus obtain the melting temperature TM of stainless propriate for obtaining Hugoniot temperatures. steel at the release pressuresdefined by the shock impedence of the anvil materiMs. The inferred TM values are listed in Table 2 and are plotted in Figure 6. These values 9000304STAINLESS define a melting curve with a positive Clapyron slope. For the present, we ignore the difference between the liquidus 8000 and solidus,which at one atmosphereis ~100 K and beyond the resolutionof our experiments.It is significantthat the datum obtained using a LiF window is entirely consistent ,,,(, 7000 T/ with the trend for shotsusing A12Os windows. BecauseLiF and A12Os attain very different temperatures at high shock - 6000_ pressures [Svendsen et al., 1989],the internalconsistency of these data strongly suggeststhat we are observingthe temperature of the sample surface and that the windows are remaining transparent. If this were not true, the LiF window wouldyield a substantiallyhigher temperature than the Al•Oa window. It should be emphasized that the analysis of Tan and Ahrens[1990]relatesthe interfacetemperatureonlyto melting at the releasepressure,TM. These authors concluded that it is possibleto extract the Hugoniot temperature only at low shock pressures, where release melting does not occur, or at the highest pressureswhere a metal is completely melted and heat conduction to the anvil is not sufficient to inducesolidification.In suchcases,equations(2)-(4) are appropriate and TH can be extracted. However, it is apparent from Figure 4 that the two effectsof releasemelting partly offset each other: Relative to simple releaseand heat conduction, in the absenceof melting or freezing, the tem- peraturedrop dueto releasemeltingis greater(becausemelt is produced),whereasthe temperaturedrop due to contact with the window is smaller (becauseof the latent heat of fusion). The compensating nature of theseeffectssuggests STEEL -.- .__.•.•. f ,,,3øøø I LLI 4OOO II • _ 2000 k• x• O Interface T * Melting T 1000 • 0 I , • J , , m 0 oHugonio T , J ! , , , , , , , , , I , , , , I I I I I I lOO PRESSURE 2oo 3oo (GPa) Fig. 6. Data from this study on 304 stainlesssteel. From the raw interfacetemperatures(circles),pointsonthcmeltingcurveof the metal (stars) are obtainedusingthe analysisof Tan and Ahrens [1990]. Arrowsare calculatedusingthe analysisof Groverand Urtiew[1974],whichignoresmeltingeffects,andprovidebounds on the HugoniottemperaturesTH. The arrowspoint in the direction of TH. SolidsymbolsrepresentshotsusingA1203 windows; open symbols indicate use of a LiF window. Theoretical values of TH [McQueenet al., 1970]are givenby the solidcurve;the dashedHugoniotis inferredbasedupon the presentstudy. 21,774 BASS ET AL.: SHOCK TEMPERATURES ON AN IRON ALLOY Taken together, the data plotted in Figure 6 define an internally consistent trend for the melting curve of stainlesssteel. The fact that the inferred Hugoniot temperatures appear to extend the trend of the release melting temperatures indicates that the lower-pressureHugoniot data are on the melting curve. Moreover, the datum at 234 GPa and 5600 K is in excellent agreement with the calculated Hugo- 9000 Williams/ et a1.{1987) 8000 ß 7000 niot by McQueenet al. [1970],suggesting that the Hugoniot • 6000 intersectsthe melting curve near this pressure.The highestpressure datum at 283 GPa and 6580 K falls above the melting curve, axtdis likely a point on the liquid Hugoniot. The onset of melting along the Hugoniot at approximately 234 GPa and 5600 K is comparable with the values of 243 GPa and ,-,5000K obtained for Fe on the basis of sound speed I!1 • 000 4000 measurements [Brown and McQueen,1986]. However,the // 2000 I pressurerange over which the Hugoniot and melting curve coincideappears to be much greater for stainlesssteel than 1 for Fe (usingthe data of Basset al. [1987]and Williamset al. [1987]). Presumably,melting alongthe Hugoniotinitiatesat a solidustemperature(234 GPa and 5600K in this case),whereasthe Hugoniotentersthe totally moltenregion at a liquidustemperature(•271 GPa and 5860K). A comparison of the stainless steel data with previous experimental studies on the melting of Fe is shownin Figure 7. The hatchured area for Fe melting is bounded on etal.{1970) i!1 3000 (x//• e• Boehler CMB 0 ,,,,,, 0 ,,, I ,, 100 ,,,, ICf• ,, • I_j,, 200 ,,, ,,, I,,, 300 ,, PRESSURE (GPa] Fig. 7. A comparisonof the resets from this study with previo• meas•ements on Fe. Hat•e• area for Fe me]ting is •e•e• by the resets of • •( •1. [1987], •11• •( •1. [1987],• J•re• e( •. [1990b]. The melting c•e labeled "Boe•er" is .ok or [986] ,, ,½. the lowersideby the curveof Williamset al. [1987],which r.o is basedon shocktemperaturemeasurements [Basset al., 1987], and static measurements in a laser-heateddiamond anvil cell. The upper bound is based on a reanalysis of the shock temperature data alone, taking into account re- laserheatedfoilsin a diamondcell. A detailedcomparison leasemelting[Ahrenset al., 1990b].The differences between of the availablestatic compression workis beyondthe scope these curves stem largely from the choice of data used in of this paper (see Williamset al. [1990],and Boehleret for eachanalysis.Williamset al. [1987]obtaineda curvecon- al. [thisissue]),but it is fair to state that the reasons sistent with the shock wave data that yielded the lowest the discrepancies amongthe data are currentlyunresolved. Hugoniottemperatures[Basset al., 1987],andwhichis also For the presentwe simplypoint out the internalconsistency consistent with the static compression data of Williams et between the shock and static compressiondata of Williams al. Five of the 13 shockwave data of Bass et al. [1987] et al. [1987]and that the meltingdata of Boehler[1986] were used. The rational for rejecting data was that any and Boehleret al. [thisissue]seemto requirethe existance imperfections in the samples would likely result in an overestimation of the Hugoniot temperature and that the lowest temperature data should best approximate the true Hugo- niot temperatures.In contrast,Ahrenset al. [1990]used an energybalanceconsiderationto decideif a portion of the of a new, as yet unidentified phase in order to reconcile their phasediagramfor Fe with Hugoniotsoundvelocity measurements [BrownandMcQueen,1986]. Comparedwith the Fe Hugoniot temperaturesof Bass et al. [1987],the stainlesssteeldata indicatelowershocktem- thermal radiation in the shocktemperature experimentswas peraturesat all pressures.This behavioris expectedon the spurrious. These authors used eight of the data from Bass basisof the higher bulk modulusof stainlesssteel, and is et al. [1987].If the analysisof Ahrenset al. is limitedto the supportedby theoreticalcalculationsof shocktemperatures five lowertemperaturedata usedby Williamset al. [1987] [McQueenet al., 1970].Moreover,the Fe meltingcurveof to the meltingcurveof and Basset al. [1987],then the resultantmeltingcurveis at Williamset al. [1987]is subparallel steel,whichis not surprisinggiventhe highFe conlower temperatures and is in significanty better agreement stainless with the Williams et al. curve. In the following discussion tent of the steeland similarityin the propertiesof Fe, Cr, we usethe meltingcurveof Williamset al. [1987]as a ba- and Ni. If we considermelting temperatures,the resultsof sis for comparison with our new data because we feel that Williamset al. [1987],indicatethat the meltingpointof Fe our original criterion for assessingthe shock data is more stringent. The melting curve of Williams et al. represents a higher degree of internal consistencybetween the shock wave and static compressiondata. In addition, their Hugoniot temperaturesfor liquid Fe are in better agreementwith thosecalculatedby Anderson [1990]. The meltingcurvesof Williamset al. [1987]and Ahrens et al. [1987]are in poor agreementwith that determined for Fe to ~ 114 GPa by Boehler[1986]and Boehleret al. [thisissue].The latter meltingcurveis baseduponoptical pyrometric measurements on resistively heated wires and at thepressure of theinnercore-outer coreboundary(ICB) is 7600+500K. By comparison,stainlesssteel with •20% Cr and •10% Ni melts at a temperaturelowerby approximately 1450 K (Figure 7), whichis substantiallygreater than the difference of ~ 100 K between the 1-arm melt- ing points. Thus these studies indicate that the addition of Ni and/or Cr to Fe yieldsa meltingpoint depression of Fe whichincreases dramaticallywith increasing pressure. In contrast, a comparison of the stainless steel data from the presentworkwith the Femeltingcurveof Boehleret al. [this issue]wouldindicatethat the meltingcurvesof thesemate- BASS ET AL.: SHOCK TEMPERATURES ON AN IRON ALLOY rials cross at pressuresof ~ 20-40 GPa, and that at higher pressuresthe stainlesssteel melting temperature is greater than that of Fe. Although neither of these possibilitiescan be ruled out with certainty, it would be an interesting surprise if the melting point of Fe were elevated at high P by 21,775 parameter, and elasticity for shocked iron between 77 GPa and 400 GPa, J. Geophys.Res., 91, 7485-7494, 1986. Carter, W.J., Hugoniot equation of state of somealkaJJhalides, High Temp. High Pressures,5, 313-318, 1973. Dziewonski, A.M., and D.L. Anderson, Preliminary reference Earth model, Phys. Earth Planet. Inter., 25, 297-356, 1981. the addition of Ni and/or Cr. Not only wouldthis behavior Grover, R., and P.A. Urtiew, Thermal relaxation at interfaces followingshockcompression,J. Appl. Phys., •5, 146-152, 1974. Hansen, M., and K. Anderko, Constitution of Binary A !!oys,1305 pp., McGraw-Hill, New York, 1958. Fe-Ni-S-O system up to 15GPa showsevidencefor a melt- Jeanloz, R., and T.J. Ahrens, Pyroxenes and oilvines: structural ing point depression,relative to the Ni-free system, at all implications of shock-wave data for high-pressurephases, in High-PressureResearch: Applications to Geophysics,edited by pressuresinvestigated. M.H. Manghnani ahd S. Akimoto, pp. 439-461, Academic, San Cosmochemicaland meteoritic evidencesuggeststhat the Diego, Calif., 1977. core containsapproximately5 wt % Ni [Ringwood,1977; Keeler, R.N., Electrical conductivity of condensedmedia at high Brett, 1976],whereasCr is thoughtto be far lessabundant. pressures,in Physics of High Energy Density, Proc. Int. Sch. Although our results, as well as those of previous studies Phys. Enrico Fermi XLVIII, edited by P. Caldirola and H. (e.g., Urakawaet al. [1987]),imply that the meltingpoint Knoepfel, pp. 106-125, Academic, San Diego, Calif., 1971. of Fe is significantly depressedat core pressuresby al]oying Lewis, J.R., Physical properties of stainless steels, in Ifandbook of Stainless Steels, edited by D. Peckher and I.M. Bernstein, with Ni and Cr, it is unfortunately not possible with our pp. 19-1--19-36, McGraw-Hill, New York, 1977. data on stain]esssteel to decouplethe effects of Ni and Cr. Lyzenga, G.A., and T.J. Ahrens, The relation between the shockClearly, further work is required to quantify the melting induced free-surface velocity and the postshock specific volume relations for Fe alloys. Therefore, the value of 76004-500 of solids, J. Appl. Phys., •9 201-204, 1978. K for the melting point of Fe at the inner core-outer core Lyzenga, G.A., and T.J. Ahrens, Multiwavelength optical pyrometer for shockcompressionexperiments, Rev. Sci. Instrum., 50, be in marked contrast to the one atmosphere melting point depression,but the data of Urakawaet al. [1987]on the boundary[Williams et al., 1987]remainsa reasonable upper bound on the temperature at that depth. Acknowledgments. We thank Q. Williams R. Jeanloz, R.G. McQueen, D. Isaak, R. Boehler, and A. Chopelas for preprints of their work. E. Gelle, M. Long, and K. Gallagher provided critical assistancein conducting these experiments. We appreciate the comments of two anonymous reviewers on an earlier version of this work. We thank the Max Planck Institut 1421-1424, 1979. Marsh, S.P. (Ed.), LASL ShockHugoniotData, pp. 260-263, Uni- fiir Chemie for assistancewith the preparation of this manuscript. This research was supported by NSF grants to the University of minois and the California Institute of Technology.Contribution 4895, California Institute of Technology. REFERENCES Ahrens, T.J., Shock wave techniquesfor geophysicsand planetary physics, Methods Exp. 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Ahrens, The melting curve of iron to 250 gigapascals:A constraint on the temperature at Earth's center, Science, 236, 181-182, 1987. Williams, Q., E. Knittle, and R. Jeanloz, The high-pressuremelting curve of iron: A technical discussion,J. Geophys.Res., in press, 1990. 21,776 BASS ET AL.: SHOCK TEMPERATURES J.R. Abelson, Coordinated SciencesLaboratory, University of Illinois, Urbana, IL 61801 T.J. Ahrens, SeismologicalLaboratory, California Institute of Technology,Pasadena, CA 91125. J.D. Bass, Department of Geology, University of Illinois, 1301 W. Green St., Urbana, IL 61801 ON AN IRON ALLOY T. Hua, Beijing Institute of Technology,P.O. 327, Beijing, Peoples Republic of China. (ReceivedJuly 23, 1990; revised September 28, 1990; acceptedOctober14, 1990.)