19 May 1972, Volume 176, Number 4036

The Pressure VariableMaterials Resear4

Experiments at high pressure reveal trends in cry.structure, superconductivity, and magnetiL

D. B. McW

The variation of physical propertieswith pressure provides new insight intomaterials at 1 atmosphere, and the pres-sure variable adds a new dimension tothe synthesis of materials. Building onthe pioneering work of P. W. Bridgmanatnd sparked by the successful synthesisof diamonds in the laboratory, the fieldof research at high pressure has ex-panded at a rapid rate during the lastdecade. It is now possible to carry outa wide variety of sophisticated experi-ments at ever increasing ranges of pres-sure and temperature. In order to con-vey the flavor of this field, I will con-centrate in this article on the tip of theiceberg, namely, the elements of theperiodic table and will illustrate theeffect of pressure on only a few prop-erties. Clearly, many more fascinatingthings can occur in the vast number ofcompounds that can be made.

It has been found that the applica-tion of pressure tends to smooth outdifferences in crystal structure, density,and compressibility in the elements andthat, with increasing pressure, many in-sulators are transformed into metalswhich are often superconducting at lowtemperatures. At high pressure the sim-ple metals such as the alkali metalshave properties similar to those of typi-cal transition metals, and the onset ofmagnetic ordering in the 3d transitionmetals is very sensitive to pressure.

The author is a member of the technical staffat the Bell Telephone Laboratories, Mtirray Hill.New Jersey 07974.

19 MAY 1972

These are only a fewmore detailed informattopics of research at hibe found in other revii8). I will not discuss t]aspects of research at hcept to comment that vtechnology it is possipressures of several hi(I kilobar = 987 atltemperatures ranging frabout 1000K. In manysible to design small, inement, thus making lartinstallations Linnecessar

Trends in the Periodic

Many physical propements exhibit a markedincreasing atomic numb(the cohesive energy, demodulus are shown in Ifact that the least denmalso the most compressthe speculation that thdensity will be smoothsures of about 10 melnow appears that the pments become discontinipressible at high pressuperiodicity in compressiduced. This discontinucits implications are disci

In the absence of p1the properties plottedsmooth functions of pr

SOlE:NCES

available compression data can be rep-resented by a two-parameter equationif we assume a linear dependence ofthe bulk modulus B on pressure P:

in B=-(UP/O ln V)r-B.+B.' P (1)

ch where V is the volume, T is the tem-perature, and B(, and B,' are the bulkmodulus and its first pressure deriva-

stal tive in the limit of P -- 0 [see the curvefor tungsten in Fig. 2 (11) ] (12).

smi. The curve (Fig. 2) for cesium ismarkedly different from that for tung-sten. Between the phase transitions at

han 42.5 and 120 kilobars the bulk modulusincreases dramatically (13). At a pres-sure of 120 kilobars the ratio of thebulk modulus of tungsten to that of

v samples, and cesium has been reduced from the valuetion on specific of 200 at 1 atmosphere to 3. This typegh pressure can of anomaly is not limited to cesium;Dew articles (1- almost all of the pretransition elementshe experimental and many of the d and f transition ele-igh pressure ex- ments near the beginning of each seriesvith the present also have abrupt increases in bulkible to achieve moduli. For example, in the 4d transi-undred kilobars tion series the anomalies occur at 330mospheres) at kilobars (strontium), 460 kilobarsom about 1 to (yttrium), 530 kilobars (zirconium),y cases it is pos- and 860 kilobars (niobium) (14).-xpensive equip- These anomalies oCCur in elements withge high-pressure partially filled d bands, and they mayy. reflect electronic transitions in which

electrons are transferred from sp bandsto d bands (14, 15).

Table This abrupt increase in bulk modulusmay be contrasted to the larger bulk

rties of the ele- moduli of the d transition metals com-periodicity with pared with those of the sp-bonded ele-er; for example, ments at I atmosphere (see Fig. 1). Innsity, and bulk both cases the larger bulk moduli coin-Fig. 1 (9). The cide with the higher densities, a resultse elements are which suggests that their origin maysible has led to lie in the interaction of the ion corese periodicity in with the bonding electrons.ed out at pres- The present theory of cohesion ingabars (10). It metals does not account for these largeIretransition ele- bulk moduli. In the simple metals theuously less com- kinetic energy of the conduction elec-ire and thus the trons is lower than that of the isolatedbility is also re- atoms because the electrons can moveDus change and throughout the metal. This freedom ofussed below. motion allows the electrons to take bet-hase transitions, ter advantage of the potential energyin Fig. 1 are of the ions and results in a lower energyessure, and the in the metal than in the isolated atoms,

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that is, a cohesive energy. This effectis balanced by the Pauli exclusion prin-ciple which says that electrons of iden-tical spin and momentum may notoccupy the same volume (16). The in-creased cohesion in the transitionmetals is attributed to the broadeningof the atomic d levels into a band asthe atoms are brought together. Theaverage energy of the total d band is

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the same as that of the atomic levels;however, for an unfilled d band theaverage energy is lower, and this leadsto additional cohesive energy. This sim-ple picture gives approximately theobserved energy and its parabolic vari-ation with the number of 4d or Sdelectrons (17). It does not include arepulsive term which can account forthe observed bulk moduli, however. If

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Fig. 1. Periodic table showing the occurrence of phase transitions (heavy borders) atroom temperature and pressures up to several hundred kilobars. The occurrence ofsuperconductivity at low temperatures is indicated by diagonal lines (1 atmosphere)or solid triangles (only at high pressure). The curves below the periodic table showthe periodic variation in (A) the cohesive energy (in kilocalories per gram atom),(B) density (in gram atoms per cubic centimeter), and (C) bulk modulus (in kilobars)with atomic number: (solid lines) potassium through krypton; (dotted lines) rubidiumthrough xenon; (dashed lines) cesium through radon. The vertical step in the curvesfor cesium through radon is the lanthanide contraction from lanthanum to lutetium.The crystal structurse are designated by numbers. The Structurbericht notation is usedfor structures 1 through 20, that is, 1 _= Al (face-centered cubic), 2 - A2 (body-centered cubic), 3 A3 (hexagonal close-packed), and so forth; 21, double hexagonalclose-packed; 22, samarium structure; 23, w phase related to body-centered cubic; 24,tetragonal; 25, cubic-intermediate high pressure phase; 26, tetragonal-intermediate highpressure phase; 27, tetragonal distortion of body-centered cubic; 28, simple cubic; 29,monoclinic related to A5; 30, similar but unknown structure; 31, simple rhombohedral;32, antiferromagnetic, orthorhombic distortion of body-centered cubic. The data arefrom (9, 18-23, 30).

752

the origin of this term is the interactionbetween the conduction electrons andthe ion cores, then it may be moreprofitable to study the simple metals athigh pressure. In this way the inter-action could be increased in a con-trolled manner.The band-broadening model for co-

hesion in the transition metals does notwork even at 1 atmosphere for the 3dseries. The elements in the series whichare magnetic have lower cohesion ener-gies than one would expect on the basisof a scaling with the 4d and Sd series.The very low value of cohesive energyfor manganese implies that it is muchmore atomic-like and that it does notgain the band energy which contributesto the cohesive energy of the solid.Perhaps under pressure manganese be-comes more band-like, and experimentsat very high pressures would be animportant way to study the delocaliza-tion of the 3d electrons.

Trends in Crystal Structure

Physical properties are often struc-ture-sensitive, and trends in structureas a function of pressure are a usefulguide for the synthesis of new materialswith a given structure or property. Overone-third of the elements have phasetransitions at room temperature andpressures of a few hundred kilobars.The available data are summarized inFig. 1. Evidence for the occurrence ofa transition is taken from x-ray dif-fraction studies (18), resistivity mea-surements (19), and the discontinuousappearance of superconductivity at lowtemperatures (20). In favorable casesthe high-pressure phase may be re-tained in a metastable state at 1 atmo-sphere (21). The elements with phasetransitions are indicated by the darkborders, and the structures are desig-nated by numbers with the highestpressure phase on the bottom. Thenumbers in parentheses indicate thatthe structure is not known unambigu-ously (22).

There is a clear trend for elementsin any given group of the periodic tableto adopt similar structures at high pres-sure. In the transition metals only amanganese is not isostructural with therest of its group, but it is anomalousin most of its properties, as indicatedabove (23). The data in Fig. 1 (whichadmittedly are incomplete and cover alimited pressure range) lead to thespeculation that, if enough pressure

SCIENCE, VOL. 176

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were applied to the elements in eachgroup of the periodic table, the ele-ments would become isostructural. Thisidea implies that it is possible to con-struct generalized phase diagrams foreach group as shown for the group Velements phosphorus, arsenic, anti-mony, and bismuth (Fig. 3) (24) andthe rare-earth metals (Fig. 4) (25).The diagram for the group V ele-

ments is speculative and probablywould not be valid for alloys madefrom other than adjacent elements be-cause of size differences. However,there is a clear trend both with increas-ing pressure and with atomic numberfrom a semiconductor to a semimetalwith a distorted simple cubic structureto a metallic, simple cubic phase. Thismetallic phase and the higher pressurephases all become superconducting atlow temperatures.A series of structures involving only

different stacking sequences of hexag-onal close-packed layers of atoms isfound in the rare-earth metals (26).Here there is a relation between thevolume at which a certain phase existsand the atomic number (or number of4f electrons).The theoretical analysis of phase

stability is very complicated because ofthe small energy changes involved inmost phase transitions (27). There areroughly two classes of transitions:those involving major changes in bond-ing character, as exemplified by thegroup V elements (Fig. 3), and thoseinvolving slight distortions from simplestructures or small changes in volume,as in the rare-earth metals (Fig. 4).Little real progress has been made inunderstanding the former class of tran-sitions, but perhaps some of the recentextensions of Pauling's concept of"ionicity" will lead to new insight intothis area (28). In the latter class oftransitions it may be possible 'to sepa-rate a structure-determining factor be-cause many of the contributions to thetotal energy of each phase are mainlyvolume-dependent. In one reasonablysuccessful model the structure-deter-mining factor is assumed to be the con-tribution to the total energy arisingfrom the electronic band structure(29). The energy spectrum of theelectron gas will be perturbed by thelattice. In many cases a distortion orchange in the stacking sequence ofsimple structures can lower the bandstructure energy, and in this way manyof the observed structures and phasetransitions have been rationalized (29).19 MAY 1972

A Dozen New Superconductors

The occurrence of numerous phasetransitions at high pressure has led tothe discovery of many new supercon-ductors. At the present time it is knownthat one-third of the elements that be-come superconducting are supercon-ducting only at high pressure. This in-formation is summarized in the upperpart of Fig. 1 where the diagonal linesindicate the superconducting elementsand the solid triangles designate thosethat are superconducting only at highpressure (30). In some cases it is pos-sible to quench the high pressure phases[for example, antimony (31)] and tostudy the superconducting properties atI atmosphere, but this possibility is morecommon in compounds than it is in theelements. The compounds containingelements from groups III and V, suchas InSb (32), were among the first tobe quenched, and recently reasonablyhigh transition temperatures (15 to17K) have been observed in somecarbides that were synthesized at highpressure and then quenched to ambientconditions (33). In the case of theelements it has been necessary to carryout experiments under the difficult con-ditions of simultaneous ultrahigh pres-sures and ultralow temperatures. These

Pressure (kbar)Fig. 2. A plot of bulk modulus versuspressure for tungsten and cesium showinga linear increase in tungsten and anoma-lous stiffening in cesium between phasetransitions at 42.5 and about 120 kilobars.Below and above these transitions cesiumhas a linear increase in bulk modulus withpressure. Circles and triangle are fromstatic compression measurements, andsquares and diamonds are from shock-wave experiments, as discussed in thetext and (11, 13).

studies have led to a much broader viewof superconductivity than one mighthave had a decade ago. Not only doessuperconductivity occur in some transi-tion elements and in a few elementslike tin and lead, but it has been foundat high pressure even in the alkali[cesium (34)] and alkaline-earth [bari-um (35)] eiements and in many of theelements on the right side of the peri-odic table [selenium (36) and tellurium(37), for example]. There appears tobe a general trend in which the super-conducting transition temperatures im-crease in successive high pressurephases; for example, the sequence inbismuth is 3.9, 7.10, and 8.3K (38).In essentially all cases the appearanceof superconductivity is accompanied bya change in crystal structure. This re-sult further emphasizes the sensitivityof many phenomena to structure. [Inthe case of yttrium there is no evidencefor a phase transition, but high pres-sure x-ray studies have not been made(34).] Studies at high pressure havenot yet led to a definitive answer to thequestion of how or whether supercon-ductivity is destroyed by pressure in agiven structure. In many materials thesuperconducting transition temperaturedecreases with pressure. Whether it ap-proaches zero exponentially or linearlyas a function of volume is difficult todecide experimentally. This investiga-tion would be an interesting test ofsome aspects of the theory of super-conductivity.

Onset of Magnetism in TransitionMetals

Although superconductivity is a verycommon phenomenon among the ele-ments, magnetism is limited to the 3dmetals chromium, manganese, iron, co-balt, and nickel and to the rare-earthmetals with partially filled 4f states. Inan effort to understand the origins ofmagnetism, the onset at chromium hasbeen studied extensively. The magneticproperties of chromium are very sensi-tive to the detailed shape of the Fermisurface which proves, in turn, to bevery pressure-sensitive.Chromium is probably the unique

example of itinerant antiferromagne-tism; that is, above a Neel temperatureTN of 312K there is no evidence forthe existence of localized magnetic mo-ments such as are found, for example,in the rare-earth metals. The Fermisurface is such that there are pockets

753

of electrons and holes of similar sizeand shape. It is believed that the at-tractive coulomb interaction betweenthe electrons and holes in the matchingpockets causes them to condense intoelectron-hole pairs with parallel spin(triplet excitons) at low temperatures.This condensation is a cooperative ef-fect which results in a spin density wavewhose periodicity may or may not becommensurate with the lattice (39).The fact that the electron-hole pairshave a lower energy at low tempera-tures results in the formation of atemperature-dependent energy gap inthe electronic spectrum. The density ofstates at the Fermi surface is reducedas the excitons condense. This causesthe electrical resistivity to increase be-low TN. By studying the electrical re-sistivity as a function of temperatureat different pressures, the dependence

of TN on pressure may be determinedas shown in Fig. 5 (19, 40). In addi-tion, by scaling the resistivity in theparamagnetic region of two curves atwidely different pressures, the magneticcontribution to the resistivity below TNmay be obtained. This contribution maybe interpreted in terms of the tempera-ture-dependent energy gap and thefraction of the Fermi surface that isdestroyed by the magnetic ordering(40). This is shown in the inset in Fig.5. The energy gap at T = 0K, ob-tained from fitting the data to the theo-retical curve (solid line in the inset),is close to that observed directly inoptical measurements (41).The Neel temperature of chromium

is much more strongly pressure-depen-dent than that of any of the other ele-ments which order magnetically, with(d ln TN)/(d ln V) = 26.5 for chro-

mium and 0 to 2 for other elements(4). Furthermore, the pressure depen-dence is not linear but follows the rela-tion

TN = TN(O) exp(-26.5AV/Vo)where TN(O) and V0 refer to quantitiesin the limit of P--0. This exponentialvariation is predicted by the theory forhigh temperatures (40). In the availa-ble pressure range (P < 80 kilobars)the antiferromagnetism in chromiumcannot be completely suppressed, but,by alloying chromium with smallamounts of vanadium or molybdenum,it is possible to lower the critical pres-sure into the experimentally observablerange. This result is shown in Fig. 6for three alloys for which the magneticcontribution to the resistivity in thelimit of T-*0K is plotted versus pres-sure (41, 42). Theoretically it has been

E0-W

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0 l I \II I 1] Fig. 3 (left). Tentative generalized phase diagram for theP As Sb Bi group V elements showing the trend with increasingpressure or atomic number from semiconductor to metal.

Squares and diamonds are from resistivity measurements of McWhan and Kolobyanina et al. (24), respectively; open and solidsymbols designate different phase transitions; triangles are the pressures at which discontinuous changes in the superconducting transi-tion temperature occur; circles are from x-ray measurements; the inverted triangle is from Bridgman's resistivity measurements [see(13)]. Fig. 4 (right). Tentative generalized phase diagram for the rare-earth metals showing the sequence of close-packedphases as a function of volume and of the number of 4f electrons or atomic number (25); (circles) face-centered cubic to doublehexagonal close-packed transition; (diamonds) samarium type to double hexagonal close-packed transition; (squares and triangles)hexagonal close-packed to samarium type transition in elements and alloys, respectively.

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SCIENCED VOL. 176754

shown that at low temperatures theband structure of the group VI ele-ments (chromium, molybdenum, andtungsten) leads to anomalies in the one-electron band susceptibility (43). Asa result of these so-called "Kohn cusp-type" anomalies, it has been predictedthat the Neel temperature as TN-Oshould be a linear function of (P -PC)where P, is the critical pressure for thesuppression of antiferromagnetism (41).In alloys there are depairing effects(that is, breaking up of electron-holepairs by impurities) which tend tosmear out the anomalies and to changethe pressure dependence. The availableresults on a series of alloys stronglysuggest that in pure chromium TN willgo to zero linearly in agreement withthe theory. The shape of the magneticresistivity curves shown in Fig. 6 ismuch more difficult to calculate. Alarge change in slope is expected be-tween the low- and high-temperatureregions because of the impurity depair-

1.0, . .

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0.60.7 0.8 0.9 1.0

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100 200

ing effects, but the detailed shape ofthe curve is not understood (42).

Pure chromium has a periodicity thatis incommensurate with the lattice, butthe addition of manganese to chromi-um results in a discontinuous jump toa commensurate structure. A similartransition as a function of an externalvariable such as pressure was predictedtheoretically on quite general grounds(44). Recent experiments show a sharpchange in the pressure dependence ofTN as a function of pressure in a seriesof chromium-manganese and chromi-um-ruthenium alloys, in agreement withthe theoretical prediction (42). Bymapping out the temperature-pressurephase diagram for these alloys, it hasbeen possible to determine experimen-tally the change in TN resulting fromthe depairing effects of the impurities.Thus significant contributions to theunderstanding of magnetism in chromi-um have been made by the use of thepressure variable.

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Semimetal-Semiconductor Transitions:The Group V Elements

The magnetism in chromium is de-pendent on a subtle matching of partsof the Fermi surface, and the magnet-ism is very pressure-sensitive. It is alsopossible to have electronic transitionsthat involve not cooperative effects butthe crossing or uncrossing of the con-duction and valence bands as a functionof pressure at temperatures above 0K.This type of semimetal-semiconductortransition seems to occur in the face-centered cubic, divalent metals calcium(19), strontium (45), and ytterbium(45, 46) and also in some of the groupV elements. In an effort to illustrate thevariety of phenomena that can occur, Iwill discuss the group V elements inmore detail.The crystal structures of arsenic,

antimony, and bismuth at 1 atmospheremay be viewed as a rhombohedral dis-tortion of a simple cubic structure in

20 40 60Pressure (kbar)

300

Temperature (OK) Fig. 5 (left). A plot of resistance R versus temperature forchromium at pressures of 26.5, 45.7, and 64.9 kilobars (from

top to bottom) showing the strong dependence of the Neel temperature on pressure (from 40). The inset shows the temperaturedependence of the magnetic contribution to the resistivity; points in the inset are the difference between the solid and scaled dashedcurves in the main figure (see text). The solid, theoretical curve in the inset is calculated as described in the text and (40). Fig. 6(right). Variation of the magnetic contribution to the resistivity with pressure at 4.2K for several chromium alloys showing the sup-pression of the itinerant antiferromagnetic state with pressure [from (42)]. Distinct symbols represent separate experiments.19 MAY 1972 755

which there are two atoms per unit cellat the positions (u,u,u). If -the rhom-bohedral angle, a, equals 600 and thepositional parameter, u, equals 1/4, thenthe structure is simple cubic. The param-eters for the group V elements are inthe range a = 540 to 570 and u = 0.23to 0.24 with the distortion from thesimple cubic structure decreasing as onegoes from arsenic to bismuth (47).Both a and u approach the cubic valueswith increasing pressure (48). This in-crease in a toward 600 with decreasingvolume, ( V0- V) / V0, is illustrated forantimony and arsenic in Fig. 7 (49).

Although the structural properties ofthe group V elements show a markedsimilarity with increasing pressure, theirelectrical properties vary quite differ-ently. The temperature coefficient ofelectrical resistivity of bismuth becomesnegative at high pressure (see Fig. 8),thus suggesting that bismuth has a con-tinuous transition from a semimetalwith a small overlap of the valence andconduction bands to a semiconductor(50, 51). Measurement of the pressuredependence of both the frequency ofthe de Haas-Shubnikov oscillations (52)and the residual resistivity (51) con-firms that the Fermi surface shrinksto zero at P = 25 kilobars.The Fermi surface of bismuth con-

sists of separated pockets of electronsand holes in momentum space, where-as that of arsenic consists of holes andpockets that are connected (53). If thepockets become disconnected, therebychanging the topology of the Fermi sur-face, then the resulting electronic transi-tion will cause anomalies in many ofthe physical properties (54). Frommeasurements of the pressure derivativeof the de Haas-van Alfen frequenciesand from band structure calculations, ithas been shown that this transition oc-curs in arsenic as a function of pressureat 1.8 kilobars and 1.1K (55). Theelastic properties of arsenic are muchmore anisotropic than those of anti-mony and bismuth as illustrated in Fig.7 (56). Initially the rhombohedral angleincreases rapidly and then approachesthe slope observed for antimony (57).It is possible that this result reflects theelectronic effects observed at low tem-peratures, and further work on arsenicmay lead to new insight into this typeof electronic transition.

In both bismuth and arsenic theFermi surface shrinks with increasingpressure, making them less metallic. Inantimony, however, which lies betweenarsenic and bismuth in the periodictable, the number of carriers increases

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Xi 54t f0.05 0.10 0.15 0.20

(VO v)/vOFig. 7. Variation of the rhombohedralangle of the unit cells of antimony andarsenic with volume, showing the ap-proach toward an undistorted simple cubiccell (a = 600). Triangles are from linearcompression measurements, and other sym-bols are from x-ray measurements (49).The initial slopes for antimony and arsenicare calculated from elastic constant andx-ray measurements, respectively (56). Thedotted curve for antimony is from Kolo-byanina et al. (18).

with increasing pressure, making itmore metallic (58). This is illustratedin Fig. 8 where the temperature depen-dence and magnitude of the resistivityof antimony are those corresponding tometallic behavior even at 45 and 60kilobars (59). Using band structurecalculations based on the pseudopo-

o-2

Bismuth

10~ 25 kbar

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-6 Antimony

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Temperature (K)

Fig. 8. Resistivity versus temperature atdifferent pressures for bismuth (51) andantimony (59) showing how bismuth be-comes less metallic and antimony becomesmore metallic with increasing pressure.Curves for bismuth are for 25 kilobarsand after releasing pressure.

tential method, one can fit the experi-mental Fermi surface data at 1 atmo-sphere, but one cannot at presentexplain the differences in the pressuredependence of the Fermi surfaces ofarsenic, antimony, and bismuth (60).

New Transition Metals?

A more fundamental change in bandstructure as a function of pressure isthought -to occur in some of the pre-transition elements and the light rare-earth metals. It appears that underpressure these elements become similarto d transition metals. The most com-plete data are available for cesium andcerium for whic;h it is believed that6s and 4f electrons, respectively, arepromoted to Sd states. Recent experi-ments on both metals suggest that asingle transition to d states does nottake place but that an intermediatephase exists.

Cesium is the most anomalous ofthe alkali metals with respect to theeffects of pressure. It has a maximumin its melting point as a function ofpressure and a subsequent minimumat the 42.5-kilobar transition (61). Ata pressure of 42.5 kilobars there areactually two closely spaced transitions.At the first there is no change in struc-ture, but there is a 12 percent changein volume and an increase of a factorof 2 in the electrical resistivity (62).When the pressure has increased by lessthan 1 kilobar, there is another transi-tion accompanied by a phase change toan unknown structure and a drop inthe resistivity to the value observed forthe first phase (62). Both the first andthird phases have an anomalously largeT2 term in the resistivity which peaksat the transition in each phase (63).There are further anomalies in the be-havior of cesium near 120 kilobars. Asshown above, the bulk modulus risesanomalously between 42.5 and 120kilobars. Superconductivity has beenobserved only above 120 kilobars (34).Finally, there is a large rise in resistivityat 120 kilobars. A similar rise in resis-tivity has been observed at higher pres-sures in the other alkali metals withavailable d states (for example, rubidi-um and potassium) (64). These resultssuggest that the conversion to a d tran-sition metal starts at 42.5 kilobars, butthat it is not complete until 120 kilo-bars.The transition from rare-earth metal

to d transition metal in cerium appearsto take place in stages. At a pressure

SCIENCE, VOL. 176

of I atmosphere cerium has one local-ized 4f electron, and it orders antiferro-magnetically at low temperatures. At 7kilobars there is a transition with nochange in structure and an 11 percentchange in volume (18). However, ce-rium becomes superconducting only at50 kilobars where there is another phaNetransition (65). The structure of thehigher pressure phase resembles thatfound in the group IV elements tita-nium, zirconium, and hafnium, whichis the structure cerium would have if ithad completely lost its 4f electron (18.22). The intermediate phase appears tobe a transitional one between localized4f states and Sd states, as it is neithermagnetically ordered nor superconduct-ing (66).

Summary

In this article I have touched on onlya few of the areas of research in whichthe pressure variable has led to new in-sight into materials at 1 atmosphere.Clearly in compounds other trends instructure and physical properties aresignificant, and many of them havebeen studied extensively. One examipleis in the transition from metal to in-sulator which occurs in several transi-tion metal oxides. The combination ofdoping experiments and experiments athigh pressure has shown that V.Oa0must be considered as part of a more(eneral phase diagram for metal-insula-tor transitions (67). It has been arguedthat the transition involves a funda-mental change from band states in themetal to localized states in the insulator(67) and that it is a "Mott" transition(68). As theoretical interest in thepressure variable increases, it is reason-able to look forward to the continuedgrowth of research at high pressure.

References and Notes

f. Electrical properties: H. G. Drickamci,G. K. Lewis, Jr., S. C. Fung, Science 163.885 (1969); H. G. Drickamer, ibid. 156, 1183(1967); ibidl. 142, 1429 (1963).

2. Semicondtictors: W. Paul and D. M.Warschauer, in Solids utnder Pressutre, W.Paul and D. M. WarschauLer, Eds. (McGraw-Hill, New York, 1963).

a. SUperconductivity: R. 1. Boughton, J. L.Olsen, C. Palmy, Progr. Low Temp. Ph/'s. 6,169 (1970): N. B. Brandt and N. I. Ginzburg,Sci. Aster. 224, 33 (April 1971); Usp. Fiz.Nauik 98, 95 (1969) [Sos'. Phys. Usp. 12, 344(1969)].

4. Magnetism: D. Bloch and A. S. Pavlovic,Ad/san. High Pressure Res. 3, 41 (1969); D.Bloch, High Temp. High Pressutre 1, 1 (1969).

5. Ferroelectricity: G. A. Samara, Adi'ani. HighPressure Rei. 3, 155 (1969).

6. Geophysics: F. R. Boyd, Science 145, 13(1964); R. C. Newton, Ads an. High Pre.ssureRes. 1, 195 (1966).

7. Chemistry: E. Whalley, AnIill. Rev'. Phy,s.Chein. 18, 205 (1967).

8. StrLicture: D. B. McWhan, Ed. "Proceedings19 MAY 1972

of the Sympositlill on X-ray Diffraction atHigh Pressure," Tranis. Amer. Crystallogr.Ass. 5, 1 (1969); M. D. BantLis, High Tenip.Higli Pressu(re 1, 483 (1969); W. Klement, Jr.,and A. Jayaraman, Progr. Solid State Chem.3, 289 (1966).

9. Data taken from K. A. Gschneidner, Jr.,Solid State Phys. 16, 275 (1964): L. Brewer.Scienice 161, 115 (1968).

10. L. V. Al'tshuler, Usp. Fiz. Nauik 85, 197(1965) [Sos'. Phys. Usp. 8, 52 (1965)].

11. Data f1 om (9) and from R. G. McQueen andS. P. Marsh. J. Appl. Phys. 31, 1253 (1960).

12. See, for example, 0. L. Anderson, J. Phys.Chein. Solids 27, 547 (1966). The linearcompressicn in a hexagonal crystal can beobtained by using the more drastic assump-tion of constant contributions to Eq. 1 fromthe different directions [D. B. McWhan, J.A ppl. Ph 's. 38, 347 (1967) and R. N.Thurston, J. Acoiist. Soc. Amner. 41, 1092(1967)]. Other empirical equations based onin expansion of the frce energy in powersof strain are equally useful in representingcompression data and for extrapolating topressures above the measured range. ForpressuLres in excess of a few kilobars an ex-pansion of the volume as a power series inpressure with only two or three terms isinadeqtiate.

3. The curve for cesium in Fig. 2 was ob-tained from a presstire-volume curve con-striscted from available static, bulk, and x-raycompression meastirements [M. S. Anderson,E. J. GtLitman, J. R. Packard, C. A. Swenson,J. P/hys. Cheuu. Solids 30, 1587 (1969) andH. T. fll, L. Merrill, J. D. Barnett, Science146, 1297 (1964)]. The 100-kilobar data ofBridgman were scaled to agree with therevised pressuLre and VolIme of the 42.5-kilobar transition [P. W. Bridgman, Proc.Assser. Acad. Arts Sci. 76, 55 (1948)]. Thebulk moduli wese then determined graph-ically. The higher pressure points were cal-CUlated from stLiccessive data points obtainedfrom shock-wave experiments [M. H. Rice,J. Phi's. Chem. Solids 26, 483 (1965)]. It isnot strictly correct to compare the adiabatic,dynamic data with the isothermal, static data,but the necessary cos-rections will not changethe qualitative ti-cnd shown in Fig. 2.

14. L. V. Al'tshuler and A. A. Bakanova, Usp.FiZ. Nassk 96, 193 (1968) [Sos. Phys. Usp.11, 678 (1969)].

15. R. Sternheimer, P/hys. Res. 78, 235 (1950);E. S. Alekseev and R. G. Arkhipov, Fiz.Ts'erd. Tela 4, 1077 (1962) [Sos'. Phys. SolidState 4, 795 (1962)].

16. R. E. Peeitls, Quantumn T/heory' of Solids(Oxford Univ. Press, London, 1955).

17. J. Friedcl, Trasis. Met. Soc. A,sser. Inst. Miti.ELtg. 230, 616 (1964); in P/l 'sics of Metals,J. Zimnan, Ed. (Cambridge Univ. Press, Lon-don, 1969). vol. 1; R. E. Watson and H.Ehrenteich, Committ7etits Solid State Phys. 3,116 (1970).

18. Ccsium: H. T. Hall ,et al. (13); magnesium:H. G. Drickamer, R. W. Lynch, R. L.Clendenen, E. A. Perez-Albuerne, Solid StateP/lirs. 19, 135 (1966); strontium: D. B.McWhan and A. Jayaraman, Appl. P/hy's.Lett. 3, 129 (1963); barium: J. D. Barnett,R. B. Bennion, H. T. Hall, Science 141, 534(1963); titaniumi and zirconium: J. C.Jamieson, ibid. 140, 72 (1963); chromium:NM. 0. Steinitz, L. H. Schwartz, J. A.Marcus, E. F;awcett, W. A. Reed, Phys. Re'.Le'tt. 23, 979 (1969); iron: T. Takahashi andW. A. Bassett, Scienice 145, 483 (1964); mer-cuiry: M. Atoji, J. E. Schirber, C. A. Swen-son, J. C/seiis. P/hYs. 31, 1628 (1969); gallium:L. F. Vereslclagin, S. S. Kabalkina, Z. V.Troitskaya, Dokl. Akad. Nauk SSSR 158,11561 (1964) [Sos. P/si's. Dokl. 9, 894 (1965)];C. E. Weir, G. J. Piermarini, S. Block, J.Chem. Phys. 54, 2768 (1971); thallium: G. J.Piermarini and C. E. Weir, J. Res. Nat. Bur.Stand. Ser. A 66, 325 (1962); silicon andgermanium: J. C. Jamieson, Scienice 139, 762(1963); J. S. Kasper and S. M. Richards,Acta Cr.stallogr. 17, 752 (1964); tin: J. D.Bas-nett, R. B. Bennion, H. T. Hall, Science141, 1041 (1963); lead: T. Takahashi, H. K.Mao, W. A. Bassett, ibid. 165, 1352 (1969);phosphorus: J. C. Jamieson, ibid. 139, 1291(1963); arsenic: M. J. Duggin, personal com-mtinication: antimony: T. N. Kolobyanina,S. S. Kabalkina, L. F. Vereshchagin, L. V.Fedina, Zl/. Eksp. Teor. Fiz. 55, 164 (1968);Sos. P/hsi. J. Exp. T/leor. Phys. 28, 88 (1969);T. R. R. McDonald, E. Gregory, G. S.Barberich, D. B. McWhan. T. H. Geballe.

Ci. W. Hull, Phls. Lett. 14, 16 (1965); D. B.McWhan, unpublished results; bismuth: R. M.Brugger, R. B. Bennion, T. G. Worlton,Phys. Lett. A 24, 714 (1967); J. S. Kasper,Tranis. Amner. Crystallogr. Ass. 5, 16 (1969);R. M. Brugger, R. B. Bennion, T. G.Worlton, W. R. Myers, ibid., p. 152; tellur-iuLm: J. C. Jamieson and D. B. McWhan,J. Chemii. Phys. 43, 1149 (1965); S. S.Kabalkina, L. F. Vereshchagin, B. M.Shuleniin, Zh. Eksp. Teor. FiZ. 45, 2073(1963); Sov. Phys. J. Exp. Theor. Phi's. 18,1422 (1964); lanthanum: D. B. McWhanand W. L. Bond, Re'. Sci. Itnstrissm. 35, 626(1964); ceriuLm: A. Lawson and T. Y. Tang,Phys. Rer. 76, 301 (1949); D. B. McWhan,Phys. Rev. B 1, 2826 (1970); E. Franceschiand G. L. Olcese, Phlys. Rev. Lett. 22, 1299(1969); lanthanum, praseodymium, neodym-ium: G. J. Piermarini and C. E. Weir,Scienc e 144, 69 (1964); T. R. R. McDonald,G. S. Barberich, E. Gregory, in 1964 Symn-pusi/um on High-Pressuire Techns.ology, E. C.Lloyd and A. A. Giardini, Eds. (AmericanSociety of Mechanical Engineers, New York,1965); samarium: see A. Jayaraman andR. C. Sherwood (26); gadolinitim: A. Jayara-nman and R. C. Sherwood, Phlvs. Res'. Lett.12, 22 (1964); terbium, dysprosium, holmium,erbium, thulium: D. B. McWhan and A. L.Stevens, Ph/is. RePi. 139, A682 (1965); ibid.154, 438 (1967); D. R. Stephens and Q.Johnson, J. Less Commoon Metals 17, 243(1969); see under magnesium, H. G. Drick-amer et al. (18); ytterbium: H. T. Hall, J. D.Barnett, L. Merrill, Scienice 139, 111 (1963).

19. Lithium, potassium, rtibiditim, calcium, cad-mium, zinc, selenitim, europium: H. G.Drickamcr, Solid State Phi's. 17, 1 (1965):chromium: P. W. Bridgman, Proc. Amler.Acad. Arts Sci. 68, 27 (1933); T. Mitsui andC. T. Tomizuka, Plh s. Rev. 137, A564 (1965).

21). Arsenic: see N. B. Brandt and N. I. Ginz-burg (U): scleniUm: sec .1. Wittig, Phys.Rei. Lett. 15, 159 (1965).

21. Phascs of titaniuLm, zirconitim, silicon, ger-mnanium, antimony, praseodymium, neo-dymiilll, samnaritLm, gadolinitim, and tcrbitimhaive been quenched from high pressures. Insome cascs (silicoti, gcrmanitLim, antimony)the retained phase does not always corre-spond to the equilibriuLm phase at the pres-sure and temperature fiom which the samplewas quenched.

22. For example, structure changes involvingdifTerent stacking arrangcments of hexagonalclose-packed laycrs (magnesium, zinc, cad-tlliLm, gadoliniuLm throtigh thullium). Similaranomalies in resistivity wes-e observed inmnagnesitim, zinc, and cadmium but only ininagnesitLim was there evidence fromr x-raydiffraction. There are conflicting reports on/inc and cadnmium [D. B. McWhan, J. Appl.P/ii's. 36, 664 (1965)]. BismuLth Ill and anti-mony Ill are isostrLucttLIal, but the structureis tinknown; a recent suLggested structureq S. S. Kabalkina, T. N. Kolobyanina, L. F.Vereshchagin, Zli. Eksp. Teor. Fiz. 58, 486(1970) [Soi. P/Ys. J. ELp. T/ieor. Phys. 31,259 (1970)]1 does not fit the data of R. M.Brtigger, R. B. Bennion, T. G. Worlton,W. R. Mlyeris [Tsanis. Amner. C'ri s, allogr.Ass. 5, 141 (1969)] or satisfy the deWolffreliability test [P. M. deWolff, ActaCrystallogr. 14, 579 (1961)]. Early reportsof a phase of tellurium with the arsenicstructure are apparently incorrect. The datafor cei-ium above 50 kilobars do not fit ahexagonal close-packed struLcture as well asexpected, but the earlier suggestion of yet an-other face-centered cubic phase is notconfirmed.

23. X-raly measurements ulp to pressuLres in excessof 100 kilobars showed no evidence for aphase transition in a inanganese.

24. Figtire 3 is based on the structural datagiven in Fig. 1 and transition pressures de-i-ived from resistivity (Bi1 rSb,), superconduc-tivity measurements g phosphoius: J. Wittigand B. T. Matthias, Scienice 160, 994 (1968);see also (3); for arsenic, see (3) and phasediagram studies of alloys of neighboring ele-mients at I atmospheIc [M. Hansen and K. P.Anderko, Cotnstitutionl of Binary Alloys (Mc-Graw-Hill, New York, ed. 2, 1958) and firstsupplement by R. P. Elliott of M. Hansen,Coisitit/itioti of Binary Alloys (McGraw-Hill,New York, cd. 2. 1965)11. The Bil-.rSb,data are from the work of McWhan andfrom T. N. Kolobyanina, S. S. Kabalkina, L.F. Vereshchagin, A. Yamichkov, M. F.Kachan, Z/i. Ek-sp. Teor. Fiz. 59, 1146 (1970)

757

[Sov. Phys. J. Exp. Theoret. Phys. 32, 624(1971)]. McWhan made measurements of re-sistivity versus pressure in a 0.5-inch (1.2-centimeter) Bridgman anvil geometry. Singlecrystal samples of bismuth and a bismuthalloy were measured simultaneously. X-raymeasurements on various samples up toBi0. Sbo06 confirmed that they are isostructuralabove the transition. The simple cubic phaseof antimony was not observed in McWhan'smeasurements, and so it is presumably stableonly over a narrow range of pressure.

25. Figure 4 was constructed from the data inFig. 1 and bulk compression data (D. B.McWhan, paper presented at the 6th RareEarth Research Conference, Gatlinburg, Tenn.,1967). Included are points for the pure ele-ments and for alloys of the heavy rare-earthelements with each other and with yttriumwhich is assumed to be similar to lutetium.

26. A. Jayaraman and R. C. Sherwood, Phys.Rev. 134, A691 (1964).

27. P. S. Rudman, J. Stringer, R. I. Jaffee, Eds.,Phase Stability in Metals and Alloys (Mc-Graw-Hill, New York, 1967).

28. J. C. Phillips, Science 169, 1035 (1970);and J. A. Van Vechten, Phys. Rev. B 2, 2147(1970).

29. See review by V. Heine and D. Weaire[Solid State Phys. 24, 249 (1970)].

30. Data obtained from (3, 31, 34-38).31. See under antimony, T. R. R. McDonald

et al. (18).32. H. E. Bommel, A. J. Darnell, W. F. Libby,

B. R. Tittmann, Science 139, 1301 (1963);S. Geller, D. B. McWhan, G. W. Hull, Jr.,ibid. 140, 62 (1963).

33. M. C. Krupka, A. L. Giorgi, N. H. Krikorian,E. G. Szklarz, J. Less Common Metals 19,113 (1969).

34. J. Wittig, Phys. Rev. Lett. 24, 812 (1970).35. - and B. T. Matthias, ibid. 22, 634

(1969).36. J. Wittig, ibid. 15, 159 (1965).37. B. T. Matthias and J. L. Olsen, Phys. Lett.

13, 202 (1964).38. J. Wittig, Z. Phys. 195, 228 (1966).39. W. M. Lomer, Proc. Phys. Soc. London 80,

489 (1962); A. W. Overhauser, Phys. Rev.128, 1437 (1962).

40. D. B. McWhan and T. M. Rice, Phys. Rev.Lett. 19, 846 (1967).

41. T. M. Rice, A. S. Barker, Jr., B. I. Halperin,D. B. McWhan, J. Appl. Phys. 40, 1337(1969).

42. T. M. Rice, A. Jayaraman, D. B. McWhan,J. Phys. Paris 32, C39 (1970).

43. T. M. Rice and B. I. Halperin, Phys. Rev.B 1, 509 (1970).

44. C. Herring, in Magnetism, G. T. Rado andH. Suhl, Eds. (Academic Press, New York,1966).

45. D. B. McWhan, T. M. Rice, P. H. Schmidt,Phys. Rev. 177, 1063 (1969), and referencestherein.

46. D. Jerome and M. Rieux, Solid State Com-mun. 7, 957 (1969).

47. R. W. G. Wyckoff, Crystal Structures (Inter-science, New York, ed. 2, 1963).

48. B. Morosin and J. E. Schirber, Phys. Lett. A30, 512 (1969).

49. The linear compression measurements arefrom P. W. Bridgman (Proc. Amer. Acad.Arts Sci. 77, 189 (1949)]. The x-ray measure-ments are from C. W. Huddle, unpublishedresults (inverted triangles) and McWhan, un-published results (other symbols).

50. P. C. Souers and G. Jura, Science 143, 467(1964); R. Jaggi, in Proceedings of the In-ternational Conference on the Physics ofSemiconductors, 7th, Paris, 1964, M. Hulin,Ed. (Academic Press, New York, 1965), vol.1, p. 413.

51. D. Balla and N. B. Brandt, Zh. Eksp. Teor.Fiz. 47, 1653 (1964) [Sov. Phys. J. Exp.Theor. Phys. 20, 1111 (1965)].

52. E. L. Itskevich and L. M. Fisher, Zh. Eksp.Teor. Fiz. 53, 98 (1967) [Sov. Phys. J. Exp.Theor. Phys. 26, 66 (1968)].

53. P. J. Lin and L. M. Falicov, Phys. Rev. 142,441 (1966).

54. I. M. Lifshitz, Zh. Eksp. Teor. Fiz. 38, 1569(1960) tSov. Phys. J. Exp. Theor. Phys. 11,1130 (1960)].

55. J. E. Schirber aind J. P. Van Dyke, Phys.Rev. Lett. 26, 246 (1971).

56. The initial slope for arsenic is from x-raymeasurements of B. Morosin and J. E.Schirber [Solid State Commun. 10, 249 (1972)],and that for antimony is from the elastic con-stants [S. Epstein and A. P. deBretteville,Phys. Rev. 138, A771 (1965)].

57. An even larger initial slope was calculatedfrom elastic constants [N. G. Pace, G. A.Saunders, Z. Stimengen, J. Phys. Chem. Solids31, 1467 (1970)] and linear compression mea-surements [see Bridgman (19)]. However, theformer is within the experimental error ofthe x-ray measurement and the latter was notreproducible from sample to sample.

58. N. B. Brandt, N. YaMinina, Yu. A. Pospelov,Zh. Eksp. Teor. Fiz. 55, 1656 (1968) [Sov.Phys. J. Exp. Theor. Phys. 28, 869 (1969)];J. E. Schirber and W. J. O'Sullivan, SolidState Commun. 7, 709 (1969).

59. Measurements were made as described in(45).

60. L. M. Falicov, in Physics of Solids at HighPressures, C. T. Tomizuka and R. M. Emrick,Eds. (Academic Press, New York, 1965).

61. A. Jayaraman, R. C. Newton, J. M. Mc-Donough, Phys. Rev. 159, 527 (1967).

62. See H. T. Hall et al. (13).63. D. B. McWhan and A. L. Stevens, Solid

State Commun. 7, 301 (1969).64. H. G. Drickamer, Rev. Sci. Instrum. 41, 1667

(1970); Solid State Phys. 17, 1 (1965).65. J. Wittig, Phys. Rev. Lett. 21, 1250 (1968).66. M. R. MacPherson, G. E. Everett, D. Wohlle-

ben, M. B. Maple, ibid. 26, 20 (1971).67. D. B. McWhan, T. M. Rice, J. P. Remeika,

ibid. 23, 1384 (1969); D. B. McWhan andJ. P. Remeika, Phys. Rev. B 2, 3734 (1970),and references therein.

68. N. F. Mott, Proc. Phys. Soc. London 62,416 (1949); Phil. Mag. 6, 287 (1961); J.Phys. Paris 32, Cl (1970).

69. I thank Dr. J. E. Schirber for helpful dis-cussions on the effect of pressure on arsenic.I thank my colleagues at Bell Laboratories,in particular T. M. Rice, W. F. Brinkman,M. Marezio, and A. Jayaraman for manystimulating discussions, and A. L. Stevensfor technical assistance.

Ever since the introduction of anti-biotics as a means of controlling infec-tious disease, bacterial strains haveemerged that are resistant to a varietyof chemotherapeutic agents. The exam-ination of the mechanism of resistancein resistant strains which have been iso-lated from nature or derived in thelaboratory has revealed a variety ofways in which microorganisms can

758

survive in the presence of antibiotics.According to the tenets of microbialgenetics, mutant strains should acquireresistance to only one antibiotic at atime, and organisms resistant to severaldrugs should arise in nature only by theaccumulation of successive mutations.It is therefore quite extraordinary thatthere has been a dramatic increase inthe frequency of occurrence of Entero-

bacteriaceae with multiple drug resis-tance in essentially all countries inwhich the problem has been examined.

In general, the multiple resistance ofthese microorganisms does not seem tohave arisen in a series of discrete steps;but rather, resistance to all of the drugsappears to have been acquired simul-taneously. Genetic analysis has revealedthat multiple drug resistance is speci-fied by an extrachromosomal element,which is referred to as a drug-resistancefactor or R factor. Over the past decade,R factors have been studied extensivelythroughout the world because of theirtheoretical and practical consequences.We will review a number of their prop-erties, particularly those that are relatedto the biochemical mechanism of mul-tiple drug resistance and to the waysin which the level of drug resistance ofhost bacteria may be varied by the rep-lication and the dissociation and re-association of the components of Rfactors.

The authors are affiliated with the Departmentof Biochemistry and the Laboratory of MolecularBiology at the University of Wisconsin, Madison53706.

SCIENCE, VOL. 176

Transmissible Multiple DrugResistance in Enterobacteriaceae

The structure, replication, and mode of action ofdrug-resistance episomes are discussed.

J. E. Davies and R. Rownd