Dec 10, 1990 - compressed and heated to the electron volt range between the impactor ..... Liu, L. G., On the (3/, â¢, 1) triple point of iron and the Earth's core,.
JOURNAL
OF GEOPHYSICAL
RESEARCH,
VOL. 95, NO. B13, PAGES 21,749-21,752, DECEMBER
10, 1990
Issues Concerning Shock Temperature Measurements of Iron
and Other
W. J. NELLIS
Metals
AND C. S. Yoo
H-division, Physics Department, Lawrence Livermore National Laboratory, Livermore, California Determining the melting temperature of iron at the Earth' s inner and outer boundary near 3 Mbar is an important problem in geophysics.A knowledge of the pressure, volume, temperature, and internal energy of solid and molten iron at megabarpressuresand several thousand degreesprovides a critical constraint for modeling the Earth' s core. An optical method measuringthe thermal radiation from the thin metal film deposited on an optically transparent window material is described. Issues which need to be addressedto obtain accurate thermodynamic shock temperatures of metals from the thermal radiation measured are discussed. These issues include characteristics of metal films, thermal conduction occurring at the metal/window interface, optical and thermal properties of metal and window material, and characteristics of the radiation measured.
INTRODUCTION
Measurement of the shock temperature of metals is an important unsolved problem of high-pressurephysics. Shock temperature data are needed to verify thermal equation of state calculations and to detect melting and polymorphic phase transitions at high pressuresand temperatures. Shock temperatures of metals have important implications for both deep-Earth geophysics and condensed matter physics. For example, measuring the pressure dependenceof the melting curve of Fe at pressures above 1.3 Mbar and 3000 K would provide a critical constraint for modeling the energy balance and chemical composition of the Earth's core. For this reason the melting of Fe has been of considerablegeophysical interest theoretically [Birch, 1952; Anderson, 1986] and
experimentally[Svendsenet al., 1987;Brown and McQueen, 1980, 1986; Liu, 1975; Boehler, 1986]. The method for measuring shock temperatures exceeding
a few thousand degrees Kelvin is time-resolved optical pyrometry. That is, the spectral radiance emitted from shocked
materials
is measured
as a function
of time
at
several discrete wavelengths. This method has been used successfully to measure the temperature of transparent matedhals under shock compressionsup to the megabarrange [Kormer et al., 1965; Radousky et al., 1985]. More recently, optical multichannel analyzers have been used to measure time-integrated (--•50 ns) spectral intensities with 1024channel systems [Radousky and Mitchell, 1989; Holmes et al., 1986]. In both types of measurements,spectral radiance is fitted to a grey body spectrum to derive an emission temperature and a wavelength independent emissivity. Complications are introduced in the case of nontransparent matedhalssuch as metals. The optical depth of a metal is so small, -10 nm, that a shock wave traverses this depth in less than 1 ps. Thus to observe the shock state directly, a spectralemissionmeasurementrequires subpicosecondtime resolution which is not available. For this reason an optical window is placed againstthe surfaceof a metal specimento tamp the shock-inducedfree surface expansion. In this case the optical emission is measured from the metal-window Copyfight 1990 by the American Geophysical Union. Paper number 90JB01690. 0148-0227/90/90JB-01690505.00
interface. This method has the advantage that the shocked metal specimen radiates for a time of several hundred nanoseconds, sufficiently long for spectral measurements. On the other hand, this interfacial configuration introduces several issues which
must be addressed
in order
to derive
validly a thermodynamic temperature from an emission spectrum and to relate the temperature to the pressure and density. The purpose of this paper is to discuss the issues connected with shock temperature measurements of metals. IDEAL
SHOCK TEMPERATURE
MEASUREMENT
In this section the configuration of a shock temperature measurement is described. These considerations place requirements on the experiments and indicate that additional supportingphysical data are required for the data analysis. In principle the ideal configuration would be to impact a window with an impactor of the metal whose temperature is to be measured. Direct impact restricts the metal to be on its Hugoniot, and the radiation emitted from the metal through the window would be used to determine shock temperature, provided that thermal conduction at the interface and optical properties of the shocked window could be taken into account. Unfortunately, this geometry has been inherently unsuitablefor such measurementsbecauseof the bright flash at impact, caused by "snowplowed" residual gas in the
evacuated(--•10-2 torr) target chamberand by surface roughness effects. This trapped residual gas is strongly compressed and heated to the electron volt range between the impactor and the window. Its cooling time is comparable to or larger than the experimental lifetime. Thus it has not been possible to observe reliably thermal emission from a metal specimen which shocks a window directly. A schematicof the experimental setup used for measuring optical emissionfrom a shocked metal, such as Fe, is shown in Figure 1 [Svendsenet al., 1987]. The impactor is accelerated to several kilometers per second, typically by a twostagelight-gas gun. On impact with the driver plate a strong planar shock wave is produced which then travels through the assembly.The Fe driver plate, typically --•1 mm thick, is used to isolate the Fe film, typically a few micrometers thick, from thermal effects of the hot compressed gas trapped between the impactor and the driver plate. An Fe film is
depositedon a flat window, suchas A1203 or LiF, to obtain 21,749
21,750
NELLIS AND YOO: SHOCKTEMPERATUREMEASUREMENTSOF IRON Metal
Film
t=0
IT I
SF
TI
I
t: 10ns•x•l Emission
I
Metal ]•T Shocked Unshocked sample j X,x• window ,window Ts•pJ ............ •//-•J TO-••//.•'•' Us
Detector
Radiation
Ipl(k , t•me)
0
Fig. 1. Typical experimental setup for measuring the shock temperature of metals [after Svensen et al., 1987]. The shock front in the window is moved with velocity us. The thickness of the sample film is exaggeratedfor clarity.
1
1;0
x(p.m)
Fig. 3. One-dimensionaltemperature distribution acrossthe interface between the reshocked sample and the optical window material at the instance of impact, t = 0, and 10 ns after the impact. Ta, Tsw, Ti, and To represent the temperaturesof the reshocked sample, the shocked window, the interface, and the initial ambient condition, respectively. SF indicates the shock front at t = 10 ns.
intimate gapless contact. The window is used to tamp the metal, as discussedin the previous section. If the window is not flat to less than the optical depth of the metal, observed radiation
is emitted
from
a mixture
of shocked metal
and
window material. If gaps exist between the Fe film and the window, the undesirable additional heating caused by reshock of the film against the window will affect the optical
dissimilar
materials
in thermal
contact
with different
initial
temperatures and constant thermal transport properties [Carslaw and Jaeger, 1959]. The interfacial temperature Tt
radiation from the interface [Urtiew and Grover, 1974].
is constant
Interfacial mixing and reshock effectsmust be eliminated so that the observed radiation corresponds simply to the expected thermal history described below. The material history is illustrated in Figure 2, which shows in Figure 2a that the metal releasesfrom its Hugoniot to a released state determined by the shock impedance of the window. The temperature of the metal specimenfirst cools thermodynamically and instantly from the Hugoniot temperature TH to the release temperature Ta. A theoretical equation of state is used to calculate the release state, a source of systematic error in the data analysis. Additional coolingfrom Ta to the interfacial temperatureT• occursby thermal diffusion of heat from the metal into the window, as
problem, as pointed out by Grover and Urtiew [1974]:
discussed below.
The temperature profile across the interface is shown schematicallyin Figure 3 at a time 10 ns after shock arrival at the interface; 10 ns is the typical time resolution of the optical detection system. Typical temperatures are T• • 4000 K and Tsw • 1500 K, where Tsw is the shock temperature of the window. The temperature profile was estimated from the solution of the heat flow equation for two
/
(a) P-Up (b) P-TH
/ Samp ie
J / 0
/
/i•
'i •
•'isentrøpe
........ i..... I[, :•,•
'•lmpactor
uH
uR ui
• The•ai
0
T•
in time within
+
the solution
to this initial-value
+
where
a = (KR/Ksw)(DR/Dsw) -1/2
TH
(lb)
and K• and Da are the thermal conductivity and thermal diffusivity of the metal in the release state, respectively, and Ksw and Dsw are the correspondingthermal propertiesof the window in the shock state. Figure 3 illustratesthat in the time resolution of the detection system the shock wave incidentfrom the metal specimentraversesa ---100-/xm-thick layer of shockedwindow, and a layer lessthan 1/xm thick of shocked window at the interface is substantially further heated by thermal diffusion from the metal. The assumptionsgenerally used to interpret optical emission data from such experiments are as follows. (1) The film is initially of ideal crystalline density. However, if the film has porosity, the shock temperature is higher than for ideal crystalline density. (2) The window remains perfectly transparent, neither absorbing nor emitting significantradiation. (3) The interface is perfectly flat without gaps so that equation (1) applies and Tt is constant. (4) The thermal transport properties of the metal and the window at the relevant conditions and Tsw are known accurately; the temperature dependenceof thermal transport propertiescan be neglected. (5) The interfacial temperature T• is determined simply from fitting the measuredspectralintensitiesto a grey body spectrum:
Ipl(A,T, e)= (eC1/A 5)(eCYAT-1)-1 TR
(la)
(2)
whereIp/(A,T, e) is the Plankfunction;A is thewavelength
of thermal radiation; T (= Tt) is the effective emission Fig. 2. (a) P-upand(b) P-T diagrams of theexperiment shown temperature; e is the effective emissivity, generally a conin Figure 1. The same material is used for the sampleand the driver stant within the scatter of measuredintensities;and C• and plate. The release state R is at the intersection between the release isentrope of the sample and the Hugoniot of the window. The temperaturemeasuredis Ti, the interfacial temperature.
C2aretheconstants of 1.11x 10-16W m-2 sr-1 and0.0144
m K, respectively.
NELLIS AND YOO: SHOCKTEMPERATUREMEASUREMENTSOF IRON ISSUES
the
The main issues in the data analysis arise in the following areas: (1) materials of the target, an area which essentially addresses the nature or the shock-heated radiating source; (2) the thermal transport coefficients of the metal and the window at relevant shock pressures and temperatures and the shock temperature of the window, which are used to derive TR from Ti; (3) validity of the solutionto the heat flow equation which is used to derive TR from Ti, in view of a large initial temperature discontinuity and temperature dependent thermal transport coefficients;(4) optical properties of shocked window materials: absorption and emission of both the relatively thick shocked layer and the thin interfacial layer which is also heated substantially by thermal conduction; (5) the theoretical equation of state used to relate the pressure and density of the impact Hugoniot state to the releasetemperature T•; and (6) experimentalimprovements which are directed at measuring a major portion of I (A), rather than just a few discrete A values, and faster time resolution. Materials
High-quality well-inspected targets are crucial to the validity of shock temperature measurements of metals. Careful target fabrication and characterization should be a basis for valid derivation of shock temperature from the recorded emission spectra. Metal films should be deposited on the window
surfaces which are flat to a few nanometers
over the
viewing area of the experiment. This requirement stems from the small optical depth of metals and the need to avoid appreciable mixing of metal and window material in the radiating layer. Films should be a few micrometers thick, sufficient to eliminate pinholes and possible effects of nonequilibrium heating from the film-driver plate interface. The surface of the driver plate in contact with the film could be diamond-turned machined to reduce surface roughness to well below 1/•m, if high-quality films cannot be made sufficiently thick. The interface should be inspected with a resolution of a few nanometers by transmission electron microscopy (TEM) lattice imaging. With the window alone, the surface roughness could be characterized. With the film on the window, gaps at the interface could be diagnosed. The bulk density of the film must be measured accurately because the initial density enters directly into the Hugoniot equations for pressure, density, and internal energy. Thus the initial film density has a strong effect on shock temperature via the internal energy. Metal
foil
should
not
be used
because
of its surface
roughness and the gap between the foil and the window.
Thermal Transport Coefficientsand Shock Temperatures of Windows The thermal conductivity and diffusivity of the metal and the window enter directly into (lb). Since these parameters are of intrinsic importancein deriving T• from Ti, accurate measurements of thermal transport coefficients should be made at relevant shock pressures and temperatures. Such data are not now available at megabar pressures and a few thousand degrees Kelvin. Use of calculated values introduces systematicuncertainties to T• which are difficult to estimate
and must be eliminated.
Shock temperatures of windows should be calculated with
most
accurate
theoretical
21,751 models.
Such
calculations
should be tested near the threshold shock pressure for measurable spatially homogeneous thermal emission from shocked
window
materials.
Solution to the Heat Flow Equation
The time interval during which an emission spectrum is analyzed should be minimized to minimize the influence of the optical properties of the shocked window. The important time
interval
film/window
is about
interface.
10 ns after
shock
At shock arrival
arrival
at
this interface
the
is the
site of a large temperaturediscontinuity,T• - Tsw, approximately equal to a few thousand degrees Kelvin. The heat flow equation must be solved with temperature dependent transport coefficients obtained by physically meaningful scaling on temperature and density to investigate the sensitivity of the solution to the large thermal gradients at the interface. The purpose is to test the validity of (1). Such a solution must be developed, especially once measured transport coefficients become available.
Optical Properties of Windows
Optical properties of window materials (sapphire, LiF, quartz, etc.) at megabar shock pressures have not been investigated to any meaningful extent. Yet, both optical opacity and nonthermal radiative processes in the window can introduce systematic errors into the temperature determined by emission spectra. The photon energy of shocked materials at megabar pressures can reach a few electron volts. These energetic photons can excite electrons from the valence
band
window
material
shock front
to
the
conduction
between
band
the film-window
and in unshocked
material
both
in
interface ahead
shocked and the
of the shock
front. Electronic excitation is largest in the shocked window where shock-induced defects can induce impurity states in the band gap; the band gap decreases somewhat because of compression,and the material is shock-heated.The resulting electron screening of thermal photons would result in a lower estimation of the radiative brightness (i.e., emission temperature) than the actual one. This electron screening effect has been observed in many alkali halides [Kormer et al., 1965] and is stronger in materials with a small band gap energy. Shocked materials can also emit nonthermal radiation. Such luminescence from shocked materials have previously been observed in LiF [Kormer, 1968], alkali halides [Harris, 1965; Ivanov et al., 1965; Linde et al., 1966], and quartz [Graham, 1962; Brooks, 1965]. This luminescence increases the radiative intensity and could result in a higher apparent shock temperature than the actual one. It is essential to measure as a function of shock pressure and temperature spectral absorption coefficients and emission spectra of window materials, both shocked and shocked and then heated, as in the interfacial window layer in Figure 3. This information would be used to obtain the net spectral intensity radiated by the metal specimen. It is possible that the interfacial window layer could dominate optical opacity, even though it is thinner than the simply shocked layer. The shock pressureat which heterogeneousnonthermal radiation effectively blends into homogeneous thermal emission shouldbe determined for window materials. If specimensare
21,752
NELLIS AND YOO: SHOCK TEMPERATURE MEASUREMENTS OF IRON
preheated, the optical properties should be measured for these resulting shock temperaturesas well.
All these issues introduce systematic uncertainties into the derivedthermodynamicshocktemperatures. These issuesfor accurate shock temperatures need to be Equation of State addressedby qualifying standardwindows, in a way analoThe experiment of Figure 1 yields the Hugoniot pressure, gous to the way in which equation of state standards were density, and internal energy (PH, PH, En) by measurement developed for shock wave equation of state experiments. of impactor velocity and use of the Rankine-Hugoniot equa- Until this is done, shock temperature measurements of tions. By taking into account thermal transport by (1), the metals will be subject to question. release temperature Ta is obtained from the interfacial Acknowledgments. This work was performed under the austemperature Ti. A Mie-Gr•ineisen equationof stateis usedto picesof the U.S. Department of Energy by the Lawrence Livermore associateTa with a Hugoniot pressure, density, and temper- National Laboratory under contract W-7405-ENG-48. We wish to thank N. C. Holmes for helpful discussions. ature (P•, p•, T•): REFERENCES
TH=T•exp - , • dV
(3)
where y is the Grfineisen parameter and V is the specific volume. This calculation effectively assumesthat the material remains in the same phase on release, because the effective y used containsno explicit informationaboutphase transitions. The value of yis usually obtainedfrom Hugoniot data for porous specimens. Since shock temperatures are often measured to determine phase transitions, use of the Mie-Grfineisen equation of state introduces systematic uncertainty into the data analysis by neglectingheats of transformation.
It would be useful to estimate the systematicuncertainty in Tu introduced by the calculation. One way is to compare results calculated
with the Mie-Gr•neisen
model with those
using a theoretical equation of state which includes the appropriate thermodynamicsof expected phase transitions, such as melting and polymorphic phase transitions. Experimental Methods
Because of concerns about the optical properties of the shockedwindow and emissivity,completespectralmeasurements of the optical emissionare needed, for example, using a 1024-channel gated linear diode array for recording. In addition, it is known that many shockedmaterialsare grey body radiators. The effective emissivity e and T are usually determinedby fitting the measuredradiative intensity to (2). Therefore it is important to minimize the correlation between parameters. Obtainingfull emissionspectra, or simply increasing the number of channels of detectors used, will provide a more critical constraint for these parameters. Faster time resolution
is also needed to time resolve and
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