yanzhang ma et al- in situ x-ray diffraction studies of iron to earth-core conditions

8/3/2019 Yanzhang Ma et al- In situ X-ray diffraction studies of iron to Earth-core conditions

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Physics of the Earth and Planetary Interiors 143144 (2004) 455467

In situ X-ray diffraction studies of iron to Earth-core conditionYanzhang Maa,, Maddury Somayazulub, Guoyin Shenc, Ho-kwang Maob,

Jinfu Shub, Russell J. Hemleyba Department of Mechanical Engineering, Texas Tech University, Box 41021, Lubbock, TX 79409, USA

b Geophysical Laboratory, Carnegie Institution of Washington, 5251 Broad Branch Rd. NW, Washington, DC 20015, USAc Consortium for Advanced Radiation Sources, University of Chicago, Chicago, IL 60637, USA

Received 30 January 2003; received in revised form 29 May 2003; accepted 24 June 2003

Abstract

The high-pressure, high-temperature behavior of iron has been investigated to 161 GPa and 3000 K by in situ synchX-ray diffraction with double-side laser-heated diamond anvil cells. We found that only-, - and -Fe can be clearly veriedas the stable solid phase in thePT range studied. Only -Fe is observed from deep lower mantle (1500km) to outer coreconditions. Within thePT range examined, we did not observe a signicant change with pressure or temperature on tc / a ratio of -Fe. The melting curve of iron has been determined to 105 GPa. A Lindeman law t gives a melting poiiron at the inner core boundary of 5800 ( 200) K, which provides an upper bound on the temperature at that depth. We alsexamine numerous experimental factors that may complicate the analysis of highPT diffraction data, and discuss the effectsof sample stress on the X-ray diffraction results. 2004 Elsevier B.V. All rights reserved.Keywords: Iron; Phase diagram; High pressure; High temperature; X-ray diffraction

1. Introduction

The Earths core is mainly composed of iron and anadditional light element component. Thus the struc-tural properties and phase diagram of iron at coreconditions are critical for understanding this most

inaccessible region of our planet. From seismology,the inner core is known to be solid whereas the outercore is liquid. At the inner core boundary ICB, thisiron-rich material crystallizes and releases latent heatand gravitational energy that at least in part drives thedynamo (Anderson, 1990). The melting temperatureof iron at ultrahigh (i.e., megabar) pressures thus gives

Corresponding author. Tel.:+ 1-806-742-0971;fax: + 1-806-742-3540. E-mail address: [email protected] (Y. Ma).

a bound on the temperature regime of the core. In ad-dition, there is evidence for unusual elastic anisotropyof the inner core (e.g.,Song and Helmberger, 1993),a property that is controlled by the crystal structure of the material. Hence, investigation of the high-pressuremelting curve, phase relations, and lattice parameters

of the stable phases of iron at deep Earth conditionsis of fundamental geophysical importance.Iron has been reported to have at least six phases

based on X-ray diffraction at high pressure andtemperature, i.e., , body-centered-cubic (b.c.c.);,face-centered-cubic (f.c.c.);, b.c.c.; , hexagonalclosed-packed (h.c.p.); double-h.c.p. phase (d.h.c.p.);and an orthorhombic phase. The-, -, and -phasesat lower pressures are well established and broadlyaccepted. The -phase, rst observed at a high pres-sure and room temperature (Takahashi and Bassett,

0031-9201/$ see front matter 2004 Elsevier B.V. All rights reserved.doi:10.1016/j.pepi.2003.06.005


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456 Y. Ma et al. / Physics of the Earth and Planetary Interiors 143144 (2004) 455467

1964), has been proved a dominant phase in a widePT range approaching Earths core conditions. Otherhigh-pressure phases of iron have been observed at

temperatures near its high-pressure melting line. Aphase (called ) was proposed based on reportedtemperaturelaser power relations and highPT X-ray diffraction (Saxena et al., 1995; Dubrovinskyet al., 1998, 2000). Other experiments revealed adouble-hexagonal close-packed structure (d.h.c.p. or ) that was believed to be identical to the-phaseand identied as metastable (Yoo et al., 1995). Anorthorhombic phase was also reported at 30100 GPaand temperatures to 2370K (Andrault et al., 1997).These results, however, could not be reproduced inother experiments (e.g.,Shen et al., 1998), where itwas found that the -h.c.p. phase persists to the melt-ing points of iron over a range of pressures. This isconsistent with the proposal that the identied phaseswere either metastable (Yoo et al., 1995) or incor-rectly identied (Yoo et al., 1997; see alsoHemleyand Mao, 2001a). In view of the continuing discussionof these issues and the importance for understandingthe core (e.g.,Boehler, 2000), further claricationof the high-pressure solid phases of iron and theirstability elds, as well as discussion of the relevantexperimental details, is needed.

The high-pressure melting curve of iron is also con-troversial (seeHemley and Mao, 2001a). Although ithas been extensively investigated by many availableexperimental methods, including Joule heating (Maoet al., 1987; Boehler, 1986), laser heating with visualobservation (Williams et al., 1987; Boehler, 1993),laser heating with synchrotron X-ray diffraction (Shenet al., 1998), and shock compression (Brown andMcQueen, 1986; Yoo et al., 1993), most of the resultsare inconsistent with each other, particularly at higherpressures where direct measurements become dif-

cult. The differences in melting temperatures amongdifferent determinations can exceed 1000K whenpressures approach the megabar range. Thus, as inthe case of the solid-phase studies, it is necessary tocarefully re-examine earlier results and further inves-tigate the solidliquid equilibrium line to pressures of the Earths core.

The continued development of synchrotron radi-ation and diamond cell laser heating techniques hasresulted in an ideal method for the study of materialsunder the extremePT conditions of the Earths core

(Mao et al., 1997; Shen and Heinz, 1998; Hemleyet al., 2002). However, differences in techniques, dis-tinctions that are often subtle, can have major effects

on the experimental results. With the increasing num-bers of experimental studies, however, the evaluationof experimental factors becomes particularly impor-tant. For example, we nd that some earlier disputeson the behavior of iron at high pressures and temper-atures can be attributed to the experimental accuracyof specic methods and the degree to which key ex-perimental factors can be manipulated and controlled.This attention to experimental detail is crucial fortesting the broad range of increasingly accurate the-oretical predictions of the behavior of iron (and ironalloys) at Earths core conditions (e.g.,Alf et al.,1999, 2000; Steinle-Neumann et al., 2001).

In this paper, we present the results of experimentalstudies of the highPT phase diagram and structuralproperties of iron to 161GPa and 3000 K obtainedusing recent improvements in diamond cell laserheating/synchrotron X-ray diffraction techniques.Preliminary reports of some of this data have beenmentioned in earlier review articles (Shen and Heinz,1998; Hemley and Mao, 2001a). Here we presentadditional experimental details that are critically im-portant for assessing the accuracy of the results, aswell as new data and analyses of the highPT be-havior of iron to compare with recent theoreticalpredictions.

2. Experimental

2.1. Sample loading

We employed symmetric diamond anvil cells withat diamonds for lower pressures experiments and

beveled diamonds at higher pressures (over 60 GPa).Flat diamond culet sizes ranged from 300 to 400m,and the beveled diamond culets from 80 to 110m.Rhenium and stainless steel gaskets were used in theseexperiments; gaskets were pre-indented to 20m orless before drilling holes for the sample chambers.The diameter of the sample chambers were larger than120 m with at diamonds, and were the same sizes asthe diamond culet for beveled diamonds. NaCl, MgO,and Al2O3 served as pressure media and heating insu-lators in our experiments; these materials were pressed


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Y. Ma et al. / Physics of the Earth and Planetary Interiors 143144 (2004) 455467 457

to form transparent akes, and sandwiched the sam-ple on either side within the sample chamber. Experi-ments were carried out with all three pressure media to

verify their possible chemical reactions with the sam-ple. The sample was pure iron powder with grain sizessmaller than 1 m,compressed into a5 mthickand3040 m wide ake before loading. During sampleloading, the iron was located at the center, and carewastaken to avoid bridging the gasket by the sample, i.e.,no portion of the sample was in contact with the edgesof the gasket during the course of the experiment. Wealso removed all sample debris on the gasket within thediamond at surface before compression. In the runswith beveled diamonds, we loaded the samples suchthat no gasket remained on top of the diamond culetafter increasing the pressure (Fig. 1).After loading thesample, we evacuated and lled the cell with argon re-peatedly over a period of several hours, and then kept itin an oven at a temperature of 90 C in an environmentof owing Ar gas for 72 h to eliminate water and oxy-gen. In our experimentsbelow 60GPa,we also used Argas as a pressure medium, and 5m-sized ruby chipsas spacers to keep the sample from contacting the di-amond before lling with liquid argon. Other aspectsof these runs are similar to those described above. Theiron equation of state was used as a pressure scale(Mao et al., 1990).

Fig. 1. Cross-section of a sample loaded in a diamond anvil cellwith beveled diamonds. Note that the size of the gasket hole isthe same as that of the diamond culet.

2.2. Laser heating

We conducted our experiments both at GSECARS,

Sector 13 of the Advanced Photon Source (APS),Argonne National Laboratory, and beamline X17Bof the National Synchrotron Light Source (NSLS),Brookhaven National Laboratory. In the experiments,we used a double-sided laser heating system with adual imaging setup, which allows us to visually ob-serve the sample during the heating process (Fig. 2).We measured the temperature by the thermal radiationmethod in these systems. In the system at APS, twoNd:YLF single-mode lasers are combined together,with a total output of 105 W, which has been provensufcient to generate stable temperatures higher than3000 K. One laser was operated in TEM00 mode andthe other in the donut mode to create a homogeneousat top power distribution (with radial gradient lessthan 3%) at the laser spot center. A detailed descrip-tion of this system and an explanation of the experi-mental method has been published previously (Shenet al., 2001). At NSLS we used a multimode YAGlaser with output power in the order of 50 W.

2.3. Synchrotron X-ray diffraction

We carried out our in situ highPT X-ray diffractionmeasurements of iron using energy-dispersive syn-chrotron radiation methods. The experiments above60 GPa were carried out at the APS. With the insertionof the linear arrays of northsouth permanent magnetswith alternating polarity in a straight section, the APSprovides a brilliant beam with very low divergence(283 40 rad). This has yielded signicant improve-ments in the quality of in situ highPT diffractionmeasurements at megabar pressures and thousands of degrees Kelvin with diamond cells, where the sample

is thin and the gasket hole becomes much smaller thanoriginally drilled. The low divergence of the X-raybeam helps to eliminate the detectable scattering fromthe gasket and other contamination on it. We reducedthe size of the X-ray beam using two perpendicularslits with paired tungsten carbide cubes having sharpedges, and eliminated the tails of the beam with an-other pairs of slits made out of tungsten plates. Withthis conguration, we obtained X-ray beam sizes of less than 8 m 10 m at the sample position. NoX-ray focusing mirrors were used in experiments at


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Fig. 2. Schematic diagram of synchrotron X-ray diffraction system with double-sided laser heating apparatus.

APS. Several experiments below 60 GPa were carriedout at NSLS to verify the phase boundaries. In theseruns, we used a Kirkpatrick-Baez mirror to enhance

the beam intensity; the X-ray beam size at the sampleposition was 25m 30 m.With energy-dispersive synchrotron X-ray diffrac-

tion, a well-resolved diffraction pattern of a stronglyscattering sample such as iron can be collected withinseveral seconds. This allows real-time capture of thesignal that can reveal ongoing processes taking placein the sample at a given pressure and temperature. Asconventionally applied, however, it does not permitany signal to be collected away from the point of detection; hence, information away from the detect-

ing point is not available. This effect becomes morecritical at high temperatures where recrystallizationand crystal coarsening from an originally ne-grainedpowder sample can occur. To overcome such aneffect in phase identication experiments, we devel-oped a two-dimensional X-ray diffraction method fordouble-sided laser heating of diamond anvil cells (Maet al., 2001), where the diamond cell is mounted ona high-precision rotation stage and the sample centercoincides with its rotation center. We estimated theoff-center error caused by the alignment to be less

than 23 m. Thus, it is impossible for the samplecenter position to drift out of the at part of the heat-ing spot, which is about 25m in diameter and fully

covers the X-ray beam.We used the rotating diamond cell method (bothcontinuous and step-wise rotation) in our experiments.In the continuous-rotation method, we kept the sam-ple rotating at a preset speed during data collection;the diffracted signals detected within all covered an-gles are added to make one pattern producing a goodaverage spectrum. In the step-wise-rotation method,we rotated the sample by discrete steps and collectedthe signal at each rotation angle. This method is moreeffective for simultaneously detecting the existence of

new peaks without accumulating the high backgroundcharacteristic of the continuous-rotation method. Thepossible failure to detect any signal between twosteps can also be avoided by decreasing the step sizeto correspond to the systems spatial resolution in therotation angle, which is dened by the tip opening andcollimation system of the detector. The step-rotationmethod was used to identify the high-pressure phaseof iron to 161 GPa. We selected several rotation stepsto detect possible peaks at angles as low as 0.5 .We could not resolve any change in the diffraction


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pattern at steps below 5 . At steps higher than 5 , weobserved intensity changes between steps. Therefore,we chose 5 steps in most of our experiments.

The application of the cell-rotation methods is fa-cilitated by high-resolution CCD cameras in the laserheating system, where we use the X-ray-induced visi-ble uorescence from the pressure medium in the cellto locate the X-ray position, then move the sample onthe rotation center to this position and couple the lasersfrom both sides to it. Such an alignment allows theX-ray beam and the lasers from two sides of the sam-ple to be coincident within23 m. Another possi-ble effect of the cell rotation is that the laser couplingposition may drift during heating because of the dif-ferences in diamond thickness in different directions(i.e., within a machining error). This effect was provedminor in our experiments, and can be further elimi-nated by aligning the laser beam perpendicular to thediamond surfaces.

3. Results and Discussion

3.1. Artifacts and experimental errors

High-pressure/high-temperature phase identicationusing synchrotron X-ray and laser-heated diamondanvil cell techniques cell involves many advancedexperimental methods, and error analysis becomes amost important issue. Disputes about on the highPT phases of iron are commonly related to the estima-tion of certain experimental errors, which are hardto clarify. We feel it is highly valuable and bene-cial to evaluate some common errors involved in theexperiments that have long been ignored.

Fig. 3shows X-ray diffraction patterns acquired insome of the experiments carried out to deliberately

introduce systematic errors. Most of the diffractionpeaks appear to show a broad shoulder. These patternsare unstable during heating, and the shoulders can di-minish after some ne alignment. Such a phenomenonindicates that the shoulders, sometimes considered asdiffraction peaks, are directly related to the effects of heating under pressure. The pressure gradient causedby stress in the sample chamber of a diamondanvilcellduring compression has been studied since the earliestapplication of the device (e.g.,Sung et al., 1977). Atypical radial pressure gradient for NaCl, a soft pres-

Fig. 3. Examination of errors associated with X-ray diffraction pat-terns of iron. (a) Temperature-quenched sample heated to 1400Kat 82 GPa through 360 rotation; (b) in situ pattern at 85 GPa and1400K at different rotation angles with heating spot away form thediffracting position; (c) in situ pattern at 82 GPa and 1400K withone-sided heating. Arrows point to the shoulders in the patterns.

sure medium often used in laser heating, has been mea-sured to be5GPa/50 m at 3540 GPa (Meade andJeanloz, 1988), whereas iron itself and other pressuremedia can give much larger gradients. Recent experi-mental results show that the stress difference betweenthe axial and radial directions can cause as high asa 20% difference in thed -spacings of iron at 50GPa

(Mao et al., 1998). Even argon, the conventional pres-sure medium, has a 10% radialaxial pressure differ-ence at 60GPa (Mao et al., in preparation;Hemleyand Mao, 2001b). At ambient temperature, the effectof such a stress can only broaden the diffraction peaks,while at high temperature, the effects of stress can bemuch more complicated.

Another experimental issue of concern withlaser-heated diamond cell techniques is the tempera-ture gradient across the sample, which can be affectedby several factors, including the difference in power


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Fig. 4. Schematic diagram of the temperature-distribution effecton d -spacings. Left: temperature distribution of a heated spotalong the axial direction illustrating the temperature differencebetween the two sides:T h, highest temperature (A side);T l, lowesttemperature (B side);T c, stress relaxation critical point. Right:d -spacing changes with temperature.

input from the two sides, quality of sample loadingand processing, and alignment of the laser heatingsystem. The early one-sided heating experiment typ-ically produced large axial temperature gradient as aresult of the power drop-off from one side of the cellto the other. Even with the improved double-sidedlaser heating technique, this phenomenon may stillexist. From our visual observations, we can clearlyobserve the glowing heated spot (above 1200 K) fromone side, while the other side with an equal powerinput remains dark (below 1000K). The measuredtemperature difference between the two sides can beas high as 1000K.

Experimental results also show that even though thestress is released inside the heating spot at tempera-tures higher than 1200 K (unpublished data), pressuregradients still exist outside and on the border of theheating spot (see alsoShim et al., 2000). With the po-tential buildup of stress and the manner in which stresscan be released with increasing temperature, we rec-ognize that the assumed experimental condition mayalso cause the diffraction peaks to split. In our modelwe assume a laser-heated sample as shown inFig. 4,with side A at higher temperature,T h, and side B atlower temperature,T l. The temperature distribution

between A and B continuously decreases fromT h toT l.Our experimental data suggests the existence of aT c,the temperature at a critical point of stress relaxationat high pressure. WhenT l < T c < T h, a two-layersample is created: one layer with temperatures higherthanT c and another with a temperature lower thanT c.In the high-temperature layer, the stress is released,while in the low-temperature layer the stress still ex-ists. Because of this stress release, thed -spacings ac-cordingly adopt the same value in every direction, andthe diffracted peak could be shifted by as much as

20%. This effect has also been extensively discussedby Kavner and Duffy (2001). The X-ray beam passesthrough both layers, and the detector collects the scat-

tered signal from both the stressed and unstressed lay-ers. Hence we can almost certainly expect a splitting of the diffraction peaks. We demonstrated this effect byheating an iron sample from one side to 1400 K (ther-mal emission was recorded from one side whereas theother side remained dark). We clearly observed split-ting of the peaks (i.e., shoulders appeared on the iron(10 0) and (1 0 1) peaks), similar to patterns reportedin single-sided laser heating experiments (Fig. 3c).

Moreover, even for a well-controlled axial tem-perature distribution (i.e., well-aligned double-sidedlaser heating), the radial temperature distribution mayalso complicate the measurements. An ideal radialtemperature distribution has a attened peak with asharply decreasing half-Gaussian-shaped edge (Maoet al., 1997). The at top can range from as smallas several microns to several tens of microns. Thetemperature distribution within this spot is far fromhomogeneous, in the case of an X-ray measurement,the probe beam is comparable with, or even biggerthan, the heating spot. We must also take into accountother experimental factors, such as the mismatchof the laser heating and X-ray diffracted spots, andcell translation during and after heating, because of the typical symmetric thermal expansion of the celland its holder. To test these effects, we intentionallymismatched the X-ray beam with the laser heatingspot by 1020m at high pressures; all the clearlyresolved peaks produce a shoulder when the collect-ing time was long enough (i.e., producing diffractionpatterns similar to those depicted inFig. 3b and c).This phenomenon disappeared when the laser heatingspot, X-ray beam, and sample were well aligned.

Another important factor that can adversely af-

fect the experimental result is X-ray diffraction fromthe gasket. As can be inferred fromFig. 5, we cansee that the source X-ray distribution also has aGaussian-shaped space intensity distribution. Also,we need to further consider the method used to gen-erate a highly collimated X-ray beam. For example,scattering from the slits used to dene the X-ray beamsize and the wings (extra intensity away from thebeam center) generated from focusing mirrors canaffect the diffraction pattern. The signals diffractedby these unexpected sources are usually negligible.


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Fig. 5. Spatial distribution of the X-ray beam as shown by the sharp edge in a step scan. Left axis (solid square marks): detected cwith scan motor position; right axis (solid curve): differential of the intensity (counts) with motor position.

However, under the special circumstances associated

with laser-heated diamond anvil cell experiments,these effects must be carefully considered. In mostcases, the sample thickness is about one-third that of the gasket. We can reasonably expect that 10% of thepeak X-ray intensity can easily generate detectablediffraction from the gasket. When a strong scatterersuch as rhenium is adopted as a gasket material, theX-ray intensity required to generate a signal fromthe gasket can be low. The scatter due to the wingsof the X-ray beam previously mentioned can also beintense; their effect on the diffraction data should be

carefully checked.We have tested these effects in our experiments.We used a synchrotron X-ray source with a beamsize of 8 m 10 m obtained with two pairs of slits. The rhenium gasket hole was 80m in diame-ter, and a 30 m-sized iron sample was loaded in thecenter of the sample chamber. When the X-ray andlaser were well aligned at the center of the sample,we clearly obtain diffraction patterns that are charac-teristic of the pure h.c.p. phase of iron at high pres-sures and high temperatures. If the X-ray beam shifts

by 10 m (the magnitude of this shift can be easily

caused by the thermal expansion of parts of the cellor its mounts), the diffraction from the gasket appearsas shoulders on the iron peaks (Fig. 3a). Some of these shoulders have intensities comparable to thoseof the iron peaks. These rhenium peaks disappear af-ter the sample is re-centered with the X-ray beam.This phenomenon is reproducible; we conclude thatthe area affected by scattering from the gasket can be2030 m larger in each direction than the beam size.This result strongly suggests that experiments withgasket hole diameters less than the sum of the X-ray

beam size plus 2

30 m should be carefully checkedfor any scattering from the gasket. Further, the me-chanical mounting of the diamond cell can shift by10 m on heating. Frequent checking of the posi-tion of the sample relative to X-ray and laser beams(e.g., by X-ray transmission scans) is therefore re-quired to ensure accurate highPT measurements. Weconclude that a narrow, well-dened X-ray beam and ahomogeneous temperature distribution are critical forhighPT phase X-ray diffraction for obtaining qualitydata.


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Fig. 6. Temperature distribution compared with the X-ray beam size for the laser heating at 105GPa and 3500K on the samp

3.2. PT stability of -Fe

As discussed byShen et al. (2001), the laser heating

method adopted at GSECARS has a highly improvedtemperature distribution relative to previous systems.The temperature difference within the dimension of the X-ray beam and between the two sides of the sam-ple can be as low as 30K.Fig. 6shows a temperaturedistribution at 105 GPa and 3500K. The temperature

Fig. 7. X-ray diffraction image obtained with varying rotation angles and summed to give an integrated pattern.

gradient within the X-ray range is about 100Katthispressure, which can be considered as the maximumerror in our experiments. An X-ray diffraction image

of iron at 161GPa and 2410 K at rotation angles from0 to 90 at 5 steps with data collected for 30 s at eachstep is presented inFig. 7. The dark regions representcorresponding photon counts at certain energies androtation angles. The dark lines (mostly diffractionlines) are straight and smooth, indicating homogenous


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Fig. 8. X-ray diffraction pattern of iron at 161GPa and 2450 K. Inset shows intense peaks of iron on a smaller scale. FL denotes uorepeaks.

PT conditions in the sample and no coarse crystalformation.Fig. 8is an integrated diffraction pattern of iron at 161GPa and 2500K. From this pattern, we canclearly observe ve peaks from the h.c.p. phase, withrened parametersa = 2.238(1) , c = 3.594(4) ,c / a = 1.605(7), and V = 15.595(18) 3. At thisPT point, thec / a ratio is very close to that at lowerpressure (1.604) (Takahashi and Bassett, 1964). Theintense peaks, (10 0) and (10 1), have linewidths(FHWM) of 378 and 384 eV, respectively, which arealmost at the resolution limit of the detector (300 eV).

This pattern demonstrates the existence of only theh.c.p. phase of iron under thesePT conditions. Fur-thermore, from our experiments, we can only observethree solid phases in ourPT range, b.c.c. at lowerpressure, f.c.c. at higher temperature, and nally theh.c.p. phase. At pressures higher than 60 GPa (pres-sure at the - -liquid triple point), only two phases canbe identied, the solid -h.c.p. phase and the liquid.At this point there is no compelling experimental evi-dence for any other solid phase of iron stable between1500 km depth and the inner core boundary (ICB).

We clearly observed a change in the relative intensi-ties of the iron diffraction peaks in a limited tempera-ture interval (marked in the phase diagram (Fig. 9)). Atdifferent times, the intensity of the most intense (1 0 0)and (10 1) peaks vary, and the (00 2) peak will appearand disappear. The peak positions also drift systemat-ically under these conditions, indicating a small pres-sure change. No additional features (i.e., shoulders) orrelative intensity changes can be observed when thepatterns were collected after a sufciently long timehad elapsed for the system to reach equilibrium and

the X-ray and laser beams were well aligned at thecenter of the sample. We believe that this phenomenonis caused by the relaxation of the sample inside thecell at high pressures and temperatures.

We selected different pressure media (Ar, NaCl,Al2O3, and MgO) to examine possible reactions be-tween sample and medium. In runs with the above-described experimental congurations, we couldclearly identify the expected phases of the pressuremedium and the iron sample from the diffractionpattern. We did not observe other phases of iron.


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Fig. 9. Phase diagram of iron determined from this study. Open circles:-phase; open diamonds: -phase; lled circle: - -liquid triplepoint; lled square: melting point; lled diamonds: melting points from shock compression data; lled triangle: melting point froYooet al. (1995). Curve (a): melting curves calculated using the Lindeman law; curve (b): melting curve calculated using the KrautKenlaw. The shaded area shows thePT region where diffraction peaks change relative intensities (the cross marks the beginning temperatof these changes, and asterisk gives the ending point of such changes). Thermal pressure corrections are not accounted for thisdiagram. Williams et al., 1991;Anderson and Isaak (2000); Boehler (1990, 1993).

Discounting the peaks due to the pressure media, thediffraction patterns collected with different media areentirely consistent with each other. Thus, we foundno evidence for the pressure medium reacting withthe iron sample at the highPT conditions studied.

3.3. c/a ratio of -Fe

The c / a ratio of -Fe has signicant implicationsfor the Earths inner core. Recent rst-principles cal-culations predict that the axial ratio of -Fe increases

substantially with temperatures, reaching 1.7 at a tem-perature of 5700K (Steinle-Neumann et al., 2001).Fig. 10shows the measured temperature dependenceof c / a at 161 GPa, together with pressure dependenceat 300 K up to that pressure. No systematic variationin c / a with temperature can be observed. The valuesfor c / a fall between 1.596 and 1.608 (a range of 0.011), which is comparable to our experimental er-ror. Though the calculations were carried out at higherpressures, the theoretical results suggest that temper-ature dependence is larger at lower pressures (i.e., ap-

proaching those of the present study). Furthermore, thepressure effect onc / a also is equally weak, consistentwith previous experimental results, at pressures suf-ciently above the transition (Jephcoat et al., 1986;Mao et al., 1990). Additional highPT data are re-quired to directly address the question of thec / a ratioand the associated elastic anisotropy of iron at innercore conditions. Nevertheless, the current comparisonsuggests the need for improved theoretical treatmentof the elastic anisotropy of iron at high pressures andtemperatures.

3.4. Melting line

When the temperature was raised to 3510K at105 GPa, we observed the loss of all diffraction peaksfrom iron, while the diffraction from the diamondremained persisted during continuous rotation of di-amond anvil cell. This temperature reects the lowerbound on the melting point of iron (e.g.,Shen et al.,1998), and is about 700 K higher than that obtainedby Boehler (1993), and appears to be lower than the


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Fig. 10. Variation in thec / a ratio of -Fe with temperature, at 161GPa, (solid line) and comparison to theory (dashed lines;Steinle-Neumannet al., 2001). The inset shows the pressure dependence of c/a at 300K (solid line) and earlier results (dashed line;Mao et al., 1990).

results of shock wave experiments. We now considerthe application of various melting laws to the data.A simple linear extrapolation from the triple point at60GPa and 2750K (Shen et al., 1998) to higher pres-sure yields a melting temperature above 7200 K at

328 GPa (ICB), which of course neglects the expectedcurvature in the melting line.According to the KrautKennedy law (Kraut and

Kennedy, 1966),

T m = T m0 1 + CV

V 0, (1)

whereT m is the melting temperature at pressureP , T m0the melting temperature at ambient pressure,V / V 0the compression at pressureP , andC a constant. Usingthe equation of state determined byMao et al. (1990)

to calculate the volume compression, along with ourdata above the - -liquid triple point, we determinedthe constant coefcientsT m0 and C in Eq. (1)to be551 K and 21.2, respectively. The extrapolated meltingtemperature of iron at 330GPa is therefore 5220K.

Assuming that the uncertainty of our temperature mea-surement is 100 K, the error in melting temperatureat the ICB is 320 K. In this calculation, thermal pres-sure and thermal expansion effects are not included.

Finally, consider the application of the Linde-man melting law, which has been more widely used.This melting relation is conventionally written as(Anderson and Isaak, 2000)

dT mdP

= 2 T mK T

13 .


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The equation can be recast as

T m

T m0

=V

V 0

2/ 3exp 2 0

q1 V

V 0

q

,

where V / V 0 corresponds to volume compression athigh P and T , i.e., thermal pressure and thermal ex-pansion have been taken into account. Our use of thisformulation is close to that reported byAnderson andIsaak (2000), who used experimental data to xT mat low pressure (seeHemley and Mao, 2001a). As-sumingq = 1, and usingT m = 3510K at 105GPa,and 0 = 1.92, we obtainT m0 = 1608 K. Accordingto this formulation, the melting temperature of ironat ICB is 5830 K. Including uncertainties in the mea-sured temperatures, the calculated temperature rangesfrom 5600 and 6000 K. This is an upper bound on theactual temperature of the ICB because of the melt-ing point depression associated with the presence of other components; for further discussion and review,seeHemley and Mao (2001a).

3.5. Phase diagram

Fig. 9shows the phase diagram of iron accordingto our experimental result and calculation of the melt-ing line. As pointed out in Section 2.4, we observeonly the -, -, and -phases of iron within the highPT range studied. At lower pressures (< 60GPa),our experimental results are consistent with those of Shen et al. (1998); thus no adjustment in the lowerpressure phase boundaries, including the triple point,is required. The calculated melting curves from boththe KrautKennedy and Lindeman laws based on ourexperimental data are shown in the phase diagramwith the curve calculated from thermochemical databy Anderson and Isaak (2000)for comparison. The

-

-liquid triple point from our calculation using theLindeman law is 2835 K, which is also within the ex-perimental error range when compared with the resultof Shen et al. (1998). The calculated melting curvealso falls within the range determined byBrown andMcQueen (1986)based on shock wave experiments.This analysis also assumes that no new highPT phases exist; there is as yet no experimental evidencefor such phases, though this has been the subject of some discussion in the literature (seeHemley andMao, 2001a).

4. Conclusions

Resolution of the debates about the highPT phase

relations of iron based on static pressure experimentsrequires careful analyses of experimental details inthese challenging experiments. Our systematic testsindicate that there are many factors that can pro-duce misleading experimental results, and care isrequired to evaluate their reliability. We believe thatthe most crucial factor is the existence of signicantstress in samples arising from the high strength of iron at high pressures, which can produce consid-erable splitting of peaks in the measured diffractionpatterns. Direct investigation of the iron phase dia-gram to 161GPa and 3000K reveals that the -Feis the only solid phase of iron at pressures beyondthe - -liquid triple point. Direct measurements onthe - and -phases were consistent with the previ-ously determined triple point. Careful experimentalstudy reveals no evidence of other solid phases atthese conditions. At high temperatures but below themelting line, we observe a region where the diffrac-tion peak intensities change. We ascribe this to theexistence of a pressure-dependent temperature in-terval of stress release in the material. We extendedthe melting point measurement by X-ray diffractionto 105GPa, and estimated the upper bound on thetemperature at the inner core boundary to be between5600 and 6000 K. Finally, measurements of the tem-perature dependence of thec / a ratio at high pressureindicate the need to examine theoretical predictionsof the origin of the elastic anisotropy of the innercore.

Acknowledgements

We would like to thank the staff of GSECARS at theAdvanced Photon Source for their help with setting upthe apparatus, and J. Hu and Q. Guo at beamline X17Bof the National Synchrotron Light Source for usefuldiscussions and experimental assistance. Thanks arealso due to T.S. Duffy, G. Fiquet, and an anonymousreviewer for constructive comments. We are partic-ularly grateful to S. Gramsch for careful reading of the manuscript. We thank NSF, NASA, DOE-BES,DOE-NNSA, and the W.M. Keck Foundation, forsupport.


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