Solid State Communication, Vol. 24, pp. 753—757, 1977. Pergamon Press. Printed in Great Britain.

THE R4MAN SPECTRAOF THE SUPERIONIC CONDUCTORCu! IN ITS THREE

PHASES

GeraldBurns,F. H. DacolandM. W. Shafer

IBM ThomasJ. WatsonResearchCenter

P. 0. Box 218Yorktown Heights,New York 10598

RichardAlbenGeneralElectric ResearchandDevelopmentCenter

Schenectady,New York 12301

(Received 1 October 1977 by M. Cardona)

ABSTRACT: We reportRamanmeasurementsof thesuperionicconductorCu!in all threephases. We showthat themajorfeaturesof thespectra,particular-ly the highest temperaturea’-phase,can be accountedfor by simple latticedynamicscalculationsif the defectnature of the phaseis taken into account.Thus, while someof the more specializedideas that have beenproposedtoexplain thesetypesof spectraare undoubtedlyappropriate,themajor featuresactually can be explainedratherstraightforwardly.

The superionicconductorCuU’2’3 exists in three reversablechangesbetween the phasesare seen.phases.4The lowest temperaturephasehasthecubic Our principal conclusions are as follows: (1)thezincblendecrystal structure(spacegroup F~3m-Td2) largechangeswith temperatureobservedin thezinc-shown in Fig. 1. The I-ions areshown as solid black blendephasecan be understoodin termsof thex-raycircles (the 4a-sitesof this spacegroup), and the evidence4which shows that the Cu-ions move fromCu-ions as cross-hatchedcircles (4d-sites). The their ideal sites; (2)the hexagonalphaseindeed ap-open circles should be ignoredfor themoment. Dis- pearsto havethe wurtzite crystalstructuresince weorder increaseswith increasingtemperatureso that can calculatethe frequencyof theRaman active E

2Cu-ions are presumed to be randomly displaced mode and find it agreesvery well with the experi-slightly from the ideal 4d-sitesinto four very close ment; (3)in the a’-phasethe four Cu-ions are sui--neighboringsites

4 in a direction away from one of roundedtetrahedrally by I-ions and most probablythe four neighboringI-ions. At T

1=369°C,thereis a randomly occupy the eight sites shown in Fig. Iphasetransition to a hexagonallattice with a c/a (open and cross-hatchedcircles). (4)Finally, weratio close to the ideal value, (8/3)1/2. It has been calculate the Raman responseusing simple latticesuggested,

4on the basis of the crystal chemistry of dynamicsbut taking thedefectnatureof thea’-phasesimilar compounds,that this structure is a wurtzite into account. The calculationaccountsfor the majorphase(P6

3mc-C6~4).Above T

2=407°C,the material spectralfeatures. Thus, while somemore specializedis what hasbeen called the a’-phase. The experi- ideas~

3are undoubtedly required to explain somemental evidence suggests4 that this is a face- featuresof thespectralresponseabove 10 cm1, thecentered-cubicstructure (Fm3m-0h5) with several major featuresarestraight-forward.proposedpositions for the Cu-ions, as will be dis-cussedlater. The 1-ion positionsarethesameas for We were only able to makethe measurementsatthe zincblendephase. high temperaturesby cooling the Cu! in a quartz

tube with squarecross section,keeping it above T2,

In this paper, we report the temperaturedepend- and measuringin situ. By lowering the temperatureent Raman scatteringfrom all threephasesof Cul. to betweenT1 andT2, we couldmeasurein thehex-The spectrumof eachphase is distinct and abrupt agonal phase. The elastic laserscatteringincreased

753

754 RAMAN SPECTRA OF Cul Vol. 24, No. 11

‘Red = WIRam/(I+fl) (1)

where n is the Bose-Einstein factor[exp(t,~,/kT)—1]—’ andthe other symbols havetheirusualmeaning. For kT>>he, ‘Red ~°~R~m’ Thus,‘Red is much smaller at low frequenciesthan ‘Ram’

The useof ‘Red is a preferredwayof presentingfirstorder Raman spectra of glasses5and amorphoussemiconductors6-8since it involves only density ofstates and frequency dependentmatrix elements.Another useful aspectof ‘Red is that for a single

___________ dampedharmonicoscillator, with harmonicfrequen-

~ x hedralcoordination,a largeandpredictable’°changecy u.,~anddamping~ ‘Red alwayspeaksat inde-pendentof y/w.~.9This is very helpful in the caseofCu! which hasseveralphasetransitions. For exam-ple, if Cu~ions were to go from tetrahedralto octra-in ~ would beexpected.

Figure 1 The structure if the zincblende and a—phase of Cul. The small solid circles,at the face—centered—sites,are I—ions. ‘Red for the low temperature,zincblendephaseisThe cross—hatchedcircles are Cu—ions shownfor two temperatures.The results in the oth-in a perfect zincblende structure at er phasesarevery much lesstemperaturedependent(3/4, 1/4, 1/4), (1/4, 3/4, 1/4), (1/4, and are only shown at one temperature. Raman1/4, 3/4) and (3/4, 3/4, 3/4). If theCu—ions are randomly distributed over measurementson Cul at room temperatureand be-the cross—hatchedand open circles, one low havebeen reportedpreviously” and our resultshas the proposed a—phase. agree. The intensity of the longitudinal optic (LO)

modedecreasesrapidly with increasingtemperature,considerablyin going through a phasetransition and andat room temperatureit is a weakshoulder,atmany attemptswere required. Thus, theexperimen- 140 cm—’, on the main transverseoptic (TO) re-tal resultswe report areon unorientedcrystals. How- sponsewhich peaksat 126 cm’. At 100°C,as canever, dueto the consistencyof the experimentalre- be seenin Fig. 2, the LO mode is essentiallyunob-suits from onecrystal to anotherandfrom onephase servable,but an “extra” responsebegins to build upto another, the resultsappearto be very isotropic, as between70 and 100 cm~and a much weakerre-we havealso found in Ag!. We concludethat the sponse at a 45 cm—’. This extra responsegrowsresultsare equivalent to powder Ramanspectraand rapidly in the zincblendephaseup to T, as shown,in the theoreticalcalculationsthe light polarizations yet the peak in the reducedRaman spectraremainsaretakenin skew directionsto roughly mimic a pow- at 125 cm~’indicating that in this phase, theder spectrum. Cu+~ionremainstetrahedrallybound to four 1-ions.

___________________________________________ Disorder increasesrapidly, however, which allowsCul - featuresin the density of states12to becomeRaman

3.0 -

active. A calculation similar to that for Ag!’3 showsthat defects in the zincblendelattice of the type ob-

— — Wur. (391°C) - servedby x-rays4causea polarizedRamanresponse~ 2.0

Zb. (367°C) very similar in spectralresponseto the density ofZb. (100°C) state. The calculation also shows that any special

1.0- features, such as the difference in forces resulting

from the Cu-ion being closer to three of the four- I-ions which tetrahedrally surroundingit, will also50 00 ISO 200 250 300

appearas strongspectralfeatures. It should be not-ENERGY SHIFT (cm~) ed that there are no strong spectralfeaturesat fre-

]~igure2 The experimental Raman results for Cul quencieswell above125 cm1 that might arisefromin the various phasesas noted, two phonon overtone or combination bands. This

suggeststhat thespectraareprimary defectinduced,Figure 2 shows the reducedRamandata in the first order Raman. By assuminga distribution of

threephasesof Cul. If ‘Ram is the experimentally defects, we can calculate’3 from simple harmonicobservedStokes part of the Ramandata, then the lattice dynamicsthe main featuresof the observedreducedRamandata is: spectrain this phase.

Vol. 24, No. 11 RAMANSPE~PRLOP Cul 755

BetweenT, andT2, the crystal hasa hexagonal ed over as many as 42-sitesof the body-centered-structureand theRaman spectrumis shown in Fig. cubic lattice (spacegroup Im3m-0h

9). However,from crystal chemical considerations2°and from the

2. Two striking andsurprisingfeaturesareobserved peakof IRed9~the tetrahedrallybonded 1 2d-sitesofin this phase. First, the overall spectralline width is spacegroup Im3m-0h5 havebeensuggestedfor thenarrower in this phasethan in thezineblendephase location of the Ag-ion. More recent x-ray,2’just below T,, even though the dc conductivity in- EXAFS,22andneutron23diffraction resultsshowthatcreasesby a factor of 3 in this phase.14Second, indeedtheAg-ions areon the 1 2d-sites,with a smallthereis a sharpfeatureat 31 cm’. To understand displacement towards neighboring I 2d-sites~orthis spectrumin generaland the sharp feature in 6b-sites.23For a’-CuI, theI-ions areshownin Fig. 1.particular, onerecalls that for thewurtzite phaseof It hasbeen proposed4that for a’-CuI, the Cu-ionsAg! the zone center modes transform as the areon the8c-sitesof the Fm3m-0h5spacegroup, asA, +E,-F2E

2-l-2B2 irreducible representationsof the shownin Fig. 1. Thesesites are similar to the 1 2d-C6~point group. The B2 modesare neither Raman sites of thea-Ag! structurein that thepositive ion isor infrared active, while the other modesareexperi- tetrahedrallysurroundedby four I-ions. The Ramanmentally observed.’

5The high frequencyE2 modeis results are consistentwith this idea in two respects.

observedonly below liquid nitrogen temperatures, First, thepeak of the reducedRamandata still oc-while the low E2 mode(at 17 cm—’) is very sharp curs at a 125 cm’ in this phase,indicating thatandintense’

6andis alwaysobservableright up to the mostof theCu-ionsarestill surroundedtetrahedrallytemperaturewhere Ag! transforms from wurtzite by four I-ions, whereasif the Cu atomswere at thephaseto the a-phase,where the modeabruptly dis- octrahedralsite in this spacegroup a vibration fre-appears(reversibly).~ The LO partsof theA, andE, quencyof a 84 cm’ would be expected.’°Second,modesin Ag! becometoo weak to be observedwell we cancalculatetheRamanresponsefor the a’-CuIbelow room temperature9.Thus, in wurtzite Ag!, the phaseusing simple harmonic lattice dynamics,takinglow frequencyE

2 modeandthe TO partsof theA, the defect nature into account as was done forandE, modesremainup to the temperatureat which a-Ag!.

3 The defects breakthe normal Raman selec-the a-phaseoccurs. This is similar to our observa- tion rules and, as will be seen, most of the experi-tions in Cu! as discussedabove. We speculate, mentally observedfeatures can then be accountedtherefore, that in the narrow temperatureregion for.betweenT, and T

2 in Cu! we are observingthesesamemodesas in thewurtzitephaseof AgI. Taking For thea-Ag! calculation,only a bond stretchingthe ratio of the bond bending to bond stretching anda bond bendingforce betweentheAg andI-ionsforces’

7 from the roomtemperaturezincblendephase were needed,’3However, for Cu!, dueto the largerof Cu!, we calculatethe low frequencyE

2 mode to mass differences,sucha calculationresultsin a sepa-occur at 30.2 cm—’, in excellent agreementwith ex- ration betweentheacoustic andoptic branchesthatperiment. (This is thesameprocedurethatwas used is too large. A compressionalI-I force considerablyfor Ag!.’ 3) Alternately, using the three force con- stiffens theLA branch,so sucha forcewas addedtostant ~a’ ~Bandf7 which includesan I-! bond stretch- our model. Figure 3a shows the calculatedresultsing force as discussedbelow, we calculate33 cm’ for the density of statesof perfect zincblendeCulfor this mode. These results strongly suggestthat (solid line). These resultsare in reasonableagree-this phaseof Cu! also has the wurtzite structure. ment with neutron diffraction measurementsand aThe extra intensity observedbetweenthe E2 mode rigid-ion model.’

2 The calculation uses the ratherandthe main peak, still at 125 cm’, is similar, but straightforward equations of motion method24 tonot as strong as that for Ag!.9”8’19 By considering solvelargeclusters(1000-2000atoms)with periodicsomesmall amount of defects in this phaseof Cu!, boundaryconditions. To obtain these results, wethe spectralresponsecan easily be accountedfor.’3 took the ratio of the Cu-I bond bending to bondBetter x-ray and neutron diffraction investigations stretchingforce constants,f~/f~= 0.035 andfurthermight Drove interesting, since it appearsfrom our we used f /f = 0.15, where f is the I-I bondresults that thewurtzite phasemight be more highly stretchingiorce constant. A third relation is deter-orderedthan thezincblendeanda’-phases. mined by fixing the zonecenteroptic modeat 130

cm-’ (=2T0+1LO). The calculated Raman re-The resultsfor thehighest temperaturea’-phase, sponsefor the perfect zincblendelattice is a single

shown in Fig. 2, look very similar to thosein the modeat 130 cm’ with width 5 cm’ (fixed by thea-phaseof ~~ Again note that the line is resolutionof thecalculation).narrower than that which is observedin the zinc-blendephasejust belowT,, eventhough thedc con- For the a’-phase,we randomlyplace the properductivity is ten timeslargerin thea’-phase.’4 number of Cu-ions on the 8c-sites of the face-

centered-cubiclattice, shown in Fig. 1. Then usingThe earlyx-ray resultswith AgI’3 suggestedthat thesameforceconstantsas for thezincblendephase,

the a phasehas the two Ag-ions randomlydistribut- we calculate: the density of states(dashedline in

756 RAJW! SPECTRA OF Cul Vol. 24, No. 11

I I I I I I Fig. 3a); and the depolarized-bond stretching,- Cul depolarized-bond rotation, and polarized-bondw a PHASE stretchingRamanscattering(called d,, d2, and d, in

Fig. 3b); d3+(d,+d2)/2 and plot it in Fig. 3c alongwith theexperimentaldata. Note that, no new par-ameters wereusedfor the forcesin thea’-phase. As

!~ ~ I can be seen in Fig. 3a, the defect nature of thez

a’-phasebroadensthe density of states, having the

____________________________________ leasteffect on the longest wavelengthmodesas one3- would expect. Figure 3b showsthat the defectmod-

U) -‘ - el causesthe first order Raman intensity to occur

d, - perfectzincblendelattice, theRamanintensity occursthroughoutmost of thefrequencyrange,while in theI -

~ 0 only at 130 cm1. In Fig Ic, we addedthecalculat-

>zI - ~__._~_)r-._)1\.__ - ed polarized and depolarizedRaman scattering, as______ __________ we havedonefor Ag!, in amannerto reflect the fact4 ____ _____ _______

that polarizedscatteringis strongerthan the depolar-I-

0 I -$-‘‘~“~“~T- I d3 - ized scattering,although our experimentalsetupdoesI not allow us to determinethe ratio with any accura-

found in Ag!’7”9). As can be seen, the calculated

result displays many of the featuresof the experi-- CALC. i cy. (The same generalexperimentalobservationisz~ 2 -EXP. mental result. In particular, a peakat -~ 75 cm~,4

- found and a sharpdecreasein intensity at lower en-which is below the principal peak at 125 cm1, isWI- /0 ergies. If the model provided more intensity in the

/ d2 calculation (Fig. 3b), then the calculatedlower

,, II peakwould occur in the middle of the peak in theO 40 80 120 160 200

density of states of the acoustic branch at — 45EI”ERGY SHIFT (cm’~) cm’, which is quite close to what is experimentally

observed. However, we think that this is a minorFigure 3 Ca1culate~resultsas described in the

text. The resolution used in the compu— point and thus belive that thecalculation shows thatter calculations in (a) and (b) is about when disorder is taken into account, but still using5 cm~,while in (c) it is about 15 cm

1, simple harmonic lattice dynamics, most of the majorso that the results can better be con— features of the Ramanspectracan be understood.pared to the experiment as shown.

We would like to thankR. A. Figatfor help withthe sample preparation, and M. Foster and S. vonMolnar for their comments,

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Vol. 24, No. 11 RAMANSPECTRAOF Cul 757

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