VOLUME 42, NUMBER 6 PHYSICAL REVIEW LETTERS 5 FEBRUARY 1979

Metallic Xenon at Static PressuresDavid A. Nelson, Jr., and Arthur L. Ruoff

Department of Materials Science and Engineering, Cornell University, Ithaca, New York 14853(Received 27 September 1978)

Using a diamond indentor, diamond anvil technique along with nonshorting interdigitatedelectrodes produced on the anvil by lithographic processes, we have shown that the electri-cal resistance of a xenon sample at 32°K drops from 1013 n (or greater) to about 104 n at 0.33Mbar. Further studies using a second- method reveal that the resistivity has dropped to below10-1 n em and possibly much lower.

The present paper demonstrates the productionof a conducting state in xenon which is producedby the application of high pressure on a solidsample of xenon at 32"K. The experimental tech-niques are described first. Then there is a briefdiscussion of why xenon is expected to becomemetallic at high pressures.

When a spherical diamond tip of radius R ispressed against a flat diamond, a contact pres-sure is established. The pressure distributioncan be accurately calculated by the Hertz contacttheory / from a knowledge of the tip radius R,the applied force F, Young's modulus E, andPoisson's ratio 11.2•3 The fact that diamond isnear ly isotropic elastically, and .hence can berepresented by an isotropic elastic solid, hasbeen described elsewhere," If a is the radius ofthe contact circle and r is a variable radius, thenthe pressure distribution is given by

P=Po(1_a2/r2)1/2, (1)

wherePo= (%)1I37T-l[E/(1_112)]2I3R -2/3F1I3. (2)

We use E = 1141 GPa and II = 0.07.3 For diamondat 50 GPa, the pressure computed from Hertzcontact theory agrees with the directly measuredvalue obtained by the use of Newton's-ring tech-ntques.v" Ruoff and Wanagel have used this in-dentor-anvil technique to obtain pressures of 1.4Mbar,"

Measurements of insulator-to-metal transi-tions can be made using the interdigitated-elec-trode technique developed by Ruoff and Chan,"A schematic drawing of this electrode system isshown in Fig. 1. The actual electrodes involve

75 or more fingers. - They are produced by photo-lithography although electrodes with smallerfinger widths and smaller spacing can be pro-duced by electron-beam lithography. The valueof d in the present experiments is 3 J.lm. Theelectrodes used in these experiments are nickel,deposited by sputtering; they are 350 A thick.Electrical leads are attached to the anvil base.Then the sample is deposited on the anvil. Final-ly, the indentor is pressed against the sample-electrode-anvil assembly resulting in contactover the region shownby the dashed circle inFig.!. When the pressure near the center reach-es a sufficiently high value, the sample under-goes an insulator-to-metal transition and theelectrode circuit is closed. The metallic regionis represented by a solid circle in Fig. 1 for twodifferent cases of indentor location. The centerpressure will be different for these two caseswhen the transition is observed; by making thefinger widths and spacings sufficiently small,the pressure at which the transition is observedwill approach the center pressure. The tech-nique used with ZnS led to a transition pressure"of 14.0± 0.5 GPa; this transition is observed at15.0± 0.5 GPa on the ruby scale,"

In the present experiment the anvil (with its in-terdigitated electrodes) is placed in a vacuumchamber. Following evacuation, the anvil, whichrests on a plate through which helium can flow,is cooled to 32"K. The temperature is measuredwith a platinum resistance thermometer. Xenonis then introduced into the chamber and condens-es on the anvil. The thickness of the xenon ismeasured by a quartz thickness monitor, thequartz crystal being located adjacent to the dia-

© 1979 The American Physical Society 383

s ;

VOLUME 42, NUMBER 6 PHYSICAL REVIEW LETTERS 5 FEBRUARY 1979

Electrode 2

Electrode I

Cose A !il'-.fH--Cose B

t%I~M-cM-- ContactRegion

FIG. 1. Schematic of interdigitated electrodes on dia-mond. Actual electrodes have 75.or more fingers. Athin sample is present on top of these electrodes.Dashed circle shows the perimeter of the contact circlewhen the indentor is applied with a specific force. Theblack center circle shows the sample material whichhas become conducting.

mond anvil on the cold plate. Another quartzcrystal located on the plate but within a perIlla-nently evacuated chamber is used as part of thequartz thickness monitor. The xenon samplethickness used herein ranged from 800 to 1200A in different samples.

The diamond indentor is attached to a rod. Aflexible aluminum foil is connected between acold plate and the rod. A thermocouple is at-tached to the rod just above the indentor. Thecold indentor is then pressed against the sampleand the force is then measured by a calibratedload cell. The force measurement is expectedto be accurate to 1%0

When the sample thickness, t, is sufficientlysmall the pressure distribution will be essentiallythat for diamond-diamond contact as computedfrom Hertz contact theory. This will be the casewhere t« o. Here 0 is the relative displacementof two points along the axis of revolution, onepoint located in the indentor far from the contactsurface, and the other in the anvil far from thecontact surface. From Hertz contact theory

and

a 1- v2

R =11 ~Po.

Experiments by Gupta and Ruoff"using Newton's-

384

ttr---,---,----,---,----r---,10

o Loodingx Unloading

o 0 0 ()(09

8

••oc: 7E.."..••a:: 6

S?coo

x

5

4

3

20~--1~0--~2~0~-7~~~407-~50~--760·Pressure (G Po )

FIG. 2. Insulator-to-conductor transition in xenonat 32°K using the interdigitated electrodes. Transitionmay be first order or may involve continuous decreasein the band gap. The final resistance is the lead resis-tance; the sample resistance is substantially less.

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ring techniques to measure area show that Eq.(1) gives nearly the correct pressure even whent =0. For our experiments on xenon, at 33 GPa,t .:s 0/5.6. Tip radii of 39 and 100 J.Lm were used,with most of the experiments involving the latter.

Resistance measurements made with a Keithley160B multimeter are shown in Fig. 2 (the upperresistance is the limit of the device); the resis-tance drops by a factor of 104 to 105• [In a fewexperiments a Keithley 610BRelectrometer cap-able of measuring a resistance of 1013 n (1014

ideally) was used; then the total resistance dropobserved was by a factor of 109'] These experi-ments were repeated seven times always with anew xenon sample and led to essentially the sameresults. The resistance drop occurs at about33 GPa.

The following two types of control experimentswere performed. In one, H20 was used (at 78°K)in place of xenon; ice remains an insulator to72 GPa, the highest pressure used. The secondtype of experiment involves bringing the indentordowndirectly on the electrodes with no samplepresent"; no resistance drop was observed bythe multimeter at the highest pressure. Also atthe highest pressure used (45 GPa) subsequent

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VOLUME 42, NUMBER 6 PHYSICAL REVIEW LETTERS 5 FEBRUARY 1979

examination of the electrodes in the scanningelectron microscope revealed the area of con-tact. Similar scanning electron microscope stud-ies following experiments on xenon did not revealthe region of contact, thus clearly establishingthat the indentor did not punch through the xenon.This is not surprising since the ratio of the con-tact radius to the sample thickness at 33 GPa isabout 50; in experiments on ungasketed sodiumchloride, a ratio of 5-10 provides sufficient fric-tion to contain the sample at pressures of 30 GPaat room temperature," The shear strength ofxenon at 32°K (TIT m =0.2) is about 25 MPa as ob-tained from Fig. 3 of Towle.9 The shear strengthof heavily deformed sodium chloride is 100 MPaat room temperature.l?

In order to follow the resistance drop to lowerresistances a second procedure was used. Inthis case a solid metal coating was placed onboth the indentor and the anvil and leads were at-tached to both. The experiment was then carriedout as before. This method had been used earlierto study sultur ," The resistance behavior wassimilar to that obtained with the interdigitatedelectrodes, but because of the lower lead resis-tance, smaller final resistances could be ob-tained. Since the relation between resistanceand resistivity had been analyzed for this geom-etry /2 the final resistivity could be calculated.Curves similar to those shown in Fig. 2 were ob-tained although they extended to lower resistance.Altogether the transition was observed in eighteendifferent experiments with seven using the inter-digitated-electrode method and eleven using thecoated-piston method. We found that p < 10-1 Qem at the highest pressure. The technique wouldhave to be modified-for example, by using afour-lead measurement-to obtain accurately thefinal value of resistivity.

It is not surprising that xenon should becomemetallic. Both iodine (Group VIIB) and sulfur(Group VIE) become metallic by a band-overlapprocess. Iodine has been studied experimental-ly13and theoretically'? and the band gap reducesto zero at about 15-17 GPa. Sulfur exhibits asimilar behavior. In this case the band gap re-duces to zero at about 30 GPa.11.12.15One studysuggests 470 kbar ," From a study of the pres-sures at which iodine and sulfur and other insu-lating elements become metallic, it was expectedthat xenon would become metallic at 30-50 GP a.ROSSl7has studied the variation of the band gapof xenon with pressure using the Wigner-Seitzmodel. He predicted band-gap closure at 11.7

cm'i/mole. From pressure-volume relations byRoss and Alder, 18a transition pressure (band gapoverlap) of 70 GPa was predicted. The presentresult showing that band-gap overlap occurs inxenon at 33 GPa is more or less consistent withthese predictions considering the potential forerror in the P-V relations. It should be pointedout that the results of the present experiment donot distinguish between a continuous closing ofthe band gap which is complete at 33 GPa or afirst-order transition at 33 GPa. If the band gapdecreases linearly with pressure, the negativeof the slope of 10glJl vs P is given byl2

{3= AE 0 I4. 6kTP * , (5)

where AEo is the zero-pressure band gap, P" isthe pressure at which band-gap closing is com-plete, and T is the absolute temperature. For alarge-gap material such as xenon (AEo = 9.3 eV)19and for studies at low temperature (T = 32°K), themagnitude of the slope is very large; a drop inresistance by a factor of 105occurs over a pres-sure range of only 0.2 GPa. Hence it is experi-mentally impossible to distinguish between a con-tinuous band-closing mechanism and a first-ordertransition in the present experiments. [For com-parison, Eq. (5) predicts that in iodine a factorof 105 change in resistance at room temperatureoccurs over a pressure range of 8 GPa.]

Although the present experimental arrangementdid not allow for studies of possible superconduc-tive or magnetic behavior of metallic xenon, suchstudies would be of interest. Additional studiesalso requiring further development should obtainthe actual value of the final resistivity. Finally,it would be of interest to know the crystal struc-ture of the conducting phase. The most excitingexperiments on this conducting form of xenon lieahead. The present results lead us to infer thatradon will become metallic at 15 GPA, bromineat 30 GPA, and krypton at 60 GPa.

This work was supported by the National Aero-nautics and Space Administration. We would alsolike to acknowledge use of the facilities of the.Cornell Materials Science Center and of the Na-tional Research and Resource Facility for Sub-micrometer structures at Cornell, both of whichare supported by the National Science Foundation.Finally, we want to thank Professor Jeffrey Freyfor use of his equipment and for his help and en-couragement.

'a. Hertz, J. Reine Angew. Math. 92, 156 (1881).28. P. Timoshenko and J. N. Goodi-;:, Theory of

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Elasticity (McGraw-Hill, New York, 1970).3A. L. Ruoff, in Proceedings of the Sixth AIRAPT

(Association Internationale for Research and Technolo-gy) International High Pressure Conference, Boulder,Colorado, July 1977, edited by K. D. Timmerhaus andM. S. Barber (Plenum, New York, to be published),Paper No. D-4-A.

4A. L. Ruoff, Cornell University Materials ScienceCenter Report No. 2855, 1977 (unpublished).

5A. L. Ruoff and K. S. Chan, in Proceedings of theSixth AffiAPT International High Pressure Conference,Boulder, Colorado, July 1977, edited by K. D. Timmer-haus and M. S. Barber (Plenum, New York, to be pub-lished).

6G. J. Piermarini and S. Block, Rev. Sci. Instrum.46, 973 (1975).7M. C. Gupta and A. L. Ruoff, J. Appl, Phys. (to bepublished) .

&W.A. Bassett, private communication.9L. C. Towle, J. Appl. Phys. 36, 2693 (1965).

laD. A. Nelson, Jr., Master's thesis, Cornell Univer-sity, Ithaca, N. Y., 1976 (unpublished).

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11A. L. Ruoff and M. C. Gupta, in Proceedings of theSixth AIRAPT International High Pressure Conference,Boulder, Colorado, July 1977, edited by K. D. Timmer-haus and M. S. Barber (Plenum, Press, New York, tobe published).

12A.L. Ruoff, J. Appl. Phys., to be published.13A.S. Balchan and H. G. Drickamer, J. Chem. Phys.

34, 1948 (1961).14A. K. McMahan, B. L. Hord, and M. Ross, Phys.Rev. B 15, 726 (1977);

15p. Panda and A. L. Ruoff, J. Appl. Phys., to be pub-lished.

16K.J. Dunn and F. Bundy, in Proceedings of the SixthAIRAPT International High Pressure Conference,Boulder, Colorado, July 1977, edited by K. D. Timmer-haus and M. S. Barber (Plenum, New York, to be pub-lished).

11M.Ross, Phys. Rev. 171, 777 (1968),18M.Ross and B. J. Alder, J. Chem. Phys. 47, 4129

(1967). -19Rare Gas Solids, edited by M. L. Klein and J. A.

Venables (Academic, New York, 1976), Vol. I, p. 518.