Download Shock temperature measurements in metals

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.
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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.)