Raman spectroscopy of superionic solid solutions of alkaline-earth and rare-earth halides

PHYSICAI. REVIK% 8

Raman spectroscopy of superionic solid solutions of alkaline-earthand rare-earth halides

D. J. Oostra and H. %. den HartogSolid State Physics Laboratory, University of Groningen, l Melktveg, 9718 EP -Groningen, The Netherlands

(Received 23 August 1983)

%c present experimental results of Raman scattering of several fluorite-type materials doped with

trivalent rare-earth ions in the temperature range 300—1400 K. In all of the solid solutions we ob-

scrvc R Raman pcRk, which 18 Rssoc1Rtcd with thc cxcltRtlon of a T2g phonon. In heavily doped

Ba, „LR„F,+. samples we obser e an additional Raman peal, which we tentatively ascribe to the

excitation of local-modc vibrations in the vicinity of an interstitial fluoride ion. These defects are

present in considerable concentrations in these materials as a result of charge compensation. In

agreement with theoretical predictions, we do not observe this local-mode excitation peak in concen-

trated solid solutions Srl „La„F2+„.Clustering turns out to influence the Raman scattering spectracoQ81dcrably. Th18 CRQ bc scen from thc Icsults obtained for thc saITlplcs SI'l ~Yb~F2+~. Herc~

apart from the T2g-phonon peak we observe for heavily doped samples an extra peak, which is as-cribed to the excitation of a local-mode vibration in the neighborhood of an anion vacancy; these va-

cancies are present in clusters containing more than one Yb + impurity. The width of the Ramanpeak is broadened appreciably by jumping defects, which are present in large numbers, especially in

heavily doped samples. fhe behavior of this contribution to the width of the Raman peak has been

analyzed for R large QUIIlbcr of so11d solutions 3fl ~A~F2+@ OI' Ml xE~C12+~. FIOIYl this analy818

we have found values for the activation energies associated with the jump frequencies of the defects1nvolvcd,

I. INTRODUCTION

Solid solutions of alkaline-earth halides with the fluor-ite lattice structure and rare-earth halides have receivedconsiderable attention in recent literature. First, becauseit is possible to prepare crystalline materials with the rath-er simple fluorite structure containing very large numbersof rare-earth impurities, and second because fluorite-typealkaline-earth halides show an interesting order-disorderphase transition well below thc melting po1nt. Above thcphase-transition temperature T, the disorder in the anionsublattice appears to be very large; the long-range order ofthese materials is maintained by t4e cation sublattice,wh1ch turns out to bc very stable.

The defect structure of the solid solutions Mi „R„Fz+„and Mi „R„Clz+„has been studied with many differentexperimental techniques. Also, theoreticians have paidattention to the above-mentioned features of the materialsunder consideration. Recently, we have studied somevery heauily doped materials by means of EPR, ionic ther-mocurrents (ITC), dielectric loss, ionic conductivity, andRaman scattering. From these results we were ableto propose a model for the ionic conductivity processes inthese heavily doped materials. This conductivity model isbased upon a percolat1on-type mechan1sm In whIch theatomically dispersed defect centers play a very importantrole. "

It appears thRt there Rrc cons1dcr able dcvlat1ons be-tween the different types of solid solutions, although theproperties of the ions involved are not much different.Solid solutions Sr& „Ia~F2+~ have been shown to contain

mainly isolated complexes consisting of a trivalent impur-ity and a nearby interstitial fluoride ion. Clusters withmore than one trivalent La ion are, even if they arepresent, of minor importance (see Ref. 18).Sr, „Yb„F2+, samples, however, show appreciable clus-tering at relatively small values of x. This has been foundby Meuldijk and den Hartog from combined ionic conduc-tivity and ITC experiments. As a consequence the ionicconductivity of the two series of solid solutions mentionedabove are completely different. While for Sri „La„Fz+„the ionic conductivity increases with x the ionic conduc-'tivity of tlie solid sollltloiis Sii ~Yb~F2+» shows a verycomplicated behavior as a function of x. It appears that,in general, one can say that for solid solutionsSri „R„F2+„clustering is important if R is chosen in thesecond half of the series of rare-earth elements, whereasclustering is of minor importance if R is one of the firstions in this series. Significant deviations of the defectstructure of these two groups of solid solutions have alsobeen indicated by Brown et al. ' who carried out EPR ex-periments on Sr, „CC„F,+~ and Sr) ~Er„F,+„crystals.

In the present paper we concentrate on the behavior ofthe Raman spectra of the above-mentioned groups of solidsolutions. In addition we have investigated solid solutionsBal „Ia F2+„and SrI „I.a„F2+„. In an earlier paperwe have shown that with Raman experiments at high tern-peratures (i.e., close to T, ) one can obtain informationabout the jump behavior of the defects. ' Here, we followa similar appx'oach. From thc cxpcriIIlcntal I'csults wcfind the values of the activation energies associated withthe jumping defects at high temperatures.

gc1984 The Anmrican Physical Society

2424 D. J. OQSTRA AND H. W'. den HARTOG

Wc fllnd tllat, tllc SRIllplcs SI"I » La» FI+» Rnd

Ba& „La„F2+„behave similarly in the sense that the ac-tivation energy of the jumping defects decreases graduallywith increasing values of x. This behavior is explained interms of two possible mechanisms: (a) an increasedbroadening of activation energies of the jumping defectswith increasing RF& concentrations, and (b) the existenceof two con1peting jurnp mechanisms in heavily doped ma-terials. The first jump Inechanism is dormnated by thedissociation of dipolar complexes and the jump e~e~gy offree interstitial fluoride ions; the second jump mechanismis determined by the jump energy of a reorienting dipolarcomplex. The latter mechanism is a percolation-typen1echanism which has been described in some detail byden Hartog and Langevoort, ' and Meuldijk et aL' Interms of this mechanism we expect the activation energyto vary between two extreme values: The higher value isassociated with dilute solid solutions and the lower valuewill be observed for very heavily doped samples. It ap-pears that both the broadening of activation energies andthe percolation jump mechanism play a role if we want toexplain our observations.

The observed Raman peak in pure fluoride crystals isdue to the excitation of a phonon which is of the T2g type.Ill t111s IIlodc two Ilclgllbor111g substltut1011al fluorid lollsmove into opposite directions. The total dipole momentof this excitation is 0, as expected for a Raman-activemode. Depending upon the type of solid solution, we haveobserved, in some cases apart from the intrinsic T2g pho-non, additional Ran1an modes. A general trend observedfor these modes is that the intensity increases with in-creasing concentrations of trivalent impurities. Addition-al bands have been observed for solid solutionsBa~ „La„F2+, and Sr& „Yb„F2+„. In contrast, we didnot observe any additional Raman peaks in the solid solu-tions Sr) ~ La~F2+„and Sr( „La„C12+~.

From the behavior of the intensity of the additional Ra-man peaks as a function of the concentration of trivalentcations we conclude that these bands are due to some kindof local mode, and from the fact that the additional peaksare located in the neighborhood of the T2g-phonon peakwe will tentatively conclude that these bands are associat-ed with vibrating F ions. For the interpretation of theextra Raman peaks we shall use the theoretical resultspublished by Nerenberg et al. These authors have calcu-lated the positions and widths of a large number of localmodes in the three alkaline-earth fluorides CRFI, SrFI,and BaF2. There is a local-mode excitation in the vicinityof an interstitial fluoride ion which is in close agreementwith the additional band in Ba~ La„F2+ samples. Onthc other hand~ wc have found I Sr) @Yb@F2+~ sanlplcswith large values of x an additional Raman peak, which isvery close to the frequency of a local-mode excitation fre-quency of a vacancy in SrF2.

mm/h; for the chloride crystals a growth rate of 6 mm/hwas chosen in order to obtain monocrystalline materials.

The chloride-based solid solutions are highly hygro-scopic and need special attention in order to avoiddeterioration of the crystal surface. These materials werepolished under silicon oil; after this treatment the sampleswere introduced into a glovebox containing less than 0.2ppm HzO vapor, where the surfaces of the samples werecleaned very carefully. Without exposing the sample tothe outside atmosphere it was mounted into the Ramanhigh-temperature measuring cell, containing a Ta furnace,which consists of a wire attached up to an alumina tube.After closing the Raman cell it was removed from theglovebox, attached to a high-vacuum system(10 —10 ' Torr), and placed in a Spex Ramalog Ramanspectrometer. The fluoride-based samples could be han-dled in air because they are not hygroscopic. For both thefluoride and chloride samples very careful polishing isnecessary, because insufficiently polished satnples show avexy poor signal-to-noise ratio.

In the temperature range T ~ 1100 K we have employedphase-sensitive detection in order to suppress the largeamount of noise coming from the heat radiation of thefurnace. Although phase-sensitive detection improves thesituation considerably, the experiments in the very high-'tcIllpcl'Rtlllc Icg1011 Rrc st111 I'Rtllcl' diff lclll't bccRllsc of thcincreasing noise, background signal, and the decreasingsignal intensity resulting from the appreciable broademngof the Raman peaks in this temperature range.

The observed Raman spectra were analyzed with a corn-puter program. The two line spectra were also analyzed;difficulties are encountered at high temperatures, wherethe lines are very wide and where it is impossible to recog-nize the two peaks. Extrapolating the results from thelow-temperature spectra we were able to obtain, in a largenumber of cases, good fits of our two-line Raman spectraat high temperatures. From these fits we have obtainedvalues for the position of the Raman peaks and the widthsat half-height.

The behavior of the halfwidths of the Raman peaks hasbeen analyzed with a theoretical formula, which has basi-cally been given by van der Marel and den Hartog. '

Frotn this analysis we obtain values for the activation en-ergy associated with the jump processes in pure and heavi-ly doped matenals.

The compositions of the solid solutions have been deter-mined by means of x-ray fluorescence. In some cases thefluorescence lines of the alkaline-earth and rare-earth ionsare so close to each other that it is difficult to analyzesamples with small RF& concentrations. This is, for ex-ample, the case for solid solutions BaI „La„F2+„. Forthese solid solutions RF3 concentrations can be deter-mined down to approximately 1 mol %. In the other casesit is often possible to determine RF3 concentrations of afew tenths of 1 mol%.

The crystals used for this investigation have been grownin our laboratory. Details of the procedures and crystal-growing facility have been published in earlier papers byour group. ' '" The growth rate for all fluorides was 6

III. EXPERIMENTAL RESUI.TS

In this section we shall present results of Ramanscattering experiments on a large number of solid solu-tions of the tyPes MI „R„Fz+„and M, „R„el&+„. In

29 RAMAN SPECTROSCOPY OF SUPERIONIC SOLID SOLUTIONS. . . 2425

earlier investigations we have shown that the ionic con-ductivity of these solid solutions may behave very dif-ferently from one another. An important parameter con-trolling the ionic conductivity phenomena is the clustenngof the trivalent rare-earth ions. Clustering is importantin the solid solutions Sr& „Yb„F2+„(Ref. 16),Sr& „Dy„Fz+„,and Sr& „Er„F2+„(Ref.21), but it is rel-atively unimportant in the solid solutions Sr& „La„F2+„(Ref. 18), Sr&,Ce„Fz+„, Sr& „Pr„Fz+„(Ref. 22),Sr, ,Nd Fz+„(Ref. 13), and also Ba~ „La„F2+„(Ref.12). Because we expect that the Raman results will alsobe strongly affected by the eventual clustering we shallpresent our results obtained for the various types of solidsolutions separately.

LaF3

lhC

C

LaF3

LaF3

La F3

LaF3

LaF3

I

200I

260

Energy (cm )

I

320I

380

FIG. 1. Survey of Raman experiments on solid solutionsBa~ „La„F~+„. The measurements have been carried out atroom temperature.

A. Bag „La„Fg+„

In an earlier paper van der Marel and den Hartog'have given the first results of Raman scattering experi-ments on solid solutions Ba& „La„F2+„overa wide rangeof temperatures. In this paper we shall expand the con-centration range investigated considerably. In Fig. 1 wepresent the results of a number of Raman scattering ex-periments on solid solutions Ba~ „La F2+„carried out at

1.0-

O

0L

M 05I

V)CCD

C

theory

0.00 5 10

Conc. LaF3 (mol'&Oj

I

&5

FIG. 2. Results for the ratio of the intensity of the Ramanpeak at about 260 cm ' and the T2g peak in solid solutionsBa~ „La„F2+„asa function of the LaF3 concentration.

room temperature. It can be seen immediately that inpure BaF2 the T2g Raman peak is located at about 238cm '. If we increase the amount of LaF3 added to thecrystal an additional peak at about 260—270 cmdevelops. For LaF3 concentrations higher than about 25mol % the T2s peak almost disappears and the band locat-ed at about 270 cm ' is the main band.

In Fig. 2 we have plotted the intensity ratio of the extraRaman line and the Tz~ band as a function of the LaF3concentration, and it can be seen that above 7.5 mo1% theratio increases very rapidly with increasing values of x.For concentrations larger than 15 mol% the intensity ofthe peak at about 260—170 cm ' is larger than that of theTpg band.

We have investigated the solid solutions in a wide rangeof temperatures, analyzed the shape of the peaks, andfound values for the positions and widths of each of theindividual peaks. Well below the superionic phase-transition temperature, which for BaF2 is located at 1275K, the linewidth of the Raman peak increases very rap-idly and in addition a strong background signal develops.These phenomena make a proper analysis of the results inthe neighborhood of T, very difficult. We note that thesedifficulties are not encountered for BaF2 andBa~ „La„F2+„crystals alone. These effects have alsobeen observed for crystals with relatively low melting tem-peratures. We assume that the increasing background iscaused by the fact that at high temperatures the mobilityof the ions in the imperfect crystal induces a breakdownof the conservation law for the wave vector. In additionwe have observed that it is very important to work withhigh-quality optical samples with well-polished faces inorder to reduce the scattering due to imperfections of thecrystalline material and the surface.

In Fig. 3 we have presented a plot containing the resultsof the peak position and width of the T2s band in pureBaF2 as a function of the temperature. The T2g peakshifts to lower energies with increasing values of T andupon proceeding to the range T & T, we see that the ener-

gy associated with the Raman peak decreases very rapidly.The corresponding behavior of the linewidth shows alinear increase with T in the low-temperature range. Inthe neighborhood of T, the linewidth increases very rapid-ly with T.

2426 D. J. OOSTRA AND H. %. den HARTOG 29

pure Ba F2

200—XUE

LL)

160—

200-

240,—

p--p- Q~ 0-~ 0 O~~p Q,

\

b

150—

1 x x Z+x

E

100—

.O

Q)C

0 s

400I

800T(Kj

1200

FIG. 3. Behavior of the position and the linewidth of the T2g

Raman peak in pure BaF~ as a function of the temperature.

I

400I

800

T(K}

I

1Z00

FIG. 5. Behavior of the linewidth of the T2g Raman peaks invarious solid solutions Ba~ „La„F2+„asa function of the tern-

perature.

Solid solutions Ha~ „La„F2+ have been investigated ina wide range of temperatures. An example has been givenin Fig. 4; here we are dealing with a BaF2 sample dopedwith 9.5 mol% LaF3. In the Raman spectrum obtained atabout room temperature we can distinguish two peaks:the T2g peak, which is also observed in pure BaF2, and anadditional band at about 260—270 cm '. From a least-squares-fitting method we find values for the intensity,position, and width of the two Raman peaks. Results of

BaF2 95mol% LQF3

5K

these analyses have been given in Fig. 5 together withthose of a number of other solid solutions Ba& „La„Fz+„and the results for pure BaFz. It can be seen that the in-crease of the linewidth is very steep for pure BaF2,' for thesolid solutions the additional increase of the linewidth isobserved at lower temperatures if x is increased. On theother hand, the increase of the linewidth is less drastic forsolid solutions than for pure BaFz. We have analyzed theresults given in Fig. 5 with the model proposed by van derMarel and den Hartog according to this model the ex-cess linewidth due to the jumping defects can be written as

I d =CT exp( E, /kT ) . —

» Eq. (1), E, is the jump energy of the defects which in-fluences the width of the Raman peak and C is a propor-tionality factor, which has been given by van der Mareland den Hartog. '

In Table I we have compiled the values of the activationenergy E, as determined from the additional linewidth fordifferent solid solutions Ba& „La„Fz+„. Because of therapidly increasing intensity of the band at 260—270 cmwith increasing values of x for x p0. 10, it was not possi-ble to obtain reliable analyses for the T2g band in this con-centration range.

B. Sr) „La„F2+„

Solid solutions of SrF2 and LaF3 behave similarly toBa& „La„F2+„.For pure SrF2 the T2g peak is located at283.6 cm '. For solid solutions this band has shifted

TABLE I. Activation energy E, for solid solutionsBa& „La F2+„.

100I

2001

Energy (cm j

I

300 400

FIG. 4. Survey of the results of Raman experiments on aBaFq sample containing 9.5 mol% LaF3. The experiments havebeen carried out in the temperature range 300—1150K.

0.0150.0450.0750.095

E, (eV)

0.800.660.500.36

RAMAN SPECTROSCOPY OP SUPERIONIC SOLID SOLUTIONS. . .

TABLE II. Activation energy E, for solid solutions

Sr~ „La„F2+„.

0.0490.152

0.810.14

EO

~ 100-V

C

slightly to higher energies. An advantage of this group ofsolid solutions is that the extra Raman peak occurring inBaI „La„F2+„does not exist in Sr~ „La,F2+ crystalswith LaF& concentrations up to 15.2 mol%. The resultsof the analysis of the Raman experiments have been com-piled in Table II.

C. Sri „Yb„p

50-

000l

800. 1200

FIG. 7. Behavior of the width of the Tq~ Raman peaks invarious solid solutions Sr( „Yb„F2+„asa function of the tem-perature.

Pol solKI solUtlons Sli ~ Yb~F2+~ wc have carflcd OUt

Raman experiments in the concentration range0&x &0.13. In Fig. 6 we have given a few examples ofthe results obtained at room temperature. %C observe thatin contrast with the results found for Sr1 „La„F2+„thereis a weak band at slightly higher energies than the T2sband for YbF3 concentrations x & 0.1. The Raman spec-tra observed for Sr, „Yb„F2+„samples resemble thoseobserved for Ba1 „La„F2+„.There is, however, a differ-ence: The additional band is far stronger in theBal „La„Fz+~ samples.

The behavior of the linewidth as a function of T ob-

pure SrF&

10.5 rnoI '/o YbF3

served for the solid solutions Sr1 „Yb„Fz+„differs fromthat observed for Sr1 „La„Fz+„and Ba1 „La„F2+„sam-ples. This can be seen from the results presented in Fig. 7.The samples of pure SrF2 and the one containing 2.2mol%%uo YbF1 behave quite similar to the correspondingsamples of the series of solid solutions Ba1 „La„F2+„(seeFig. 5). A very different result is obtained for the samplewith 4.3 mol % YbF&. Here the defect-induced additionallinewidth increases very rapidly at rather low tempera-tures, indicating that the activation energy for this samplehas a relatively large value as compared to the samplescollta111111g 10.5 aIld 12.7 11101%YbFs.

In addition we note that for the samples containing 10.5and 12.7 mol % YbF3 the linewidth in the low-temperature region is slightly larger than for pure SrF2.The slopes of the plots of the hnewidth versus T are, how-ever, the same as for pure SrF2. The results of theanalysis of the plots in Fig. 7 using Eq. (1) have been com-piled in Table III. Whereas the activation energy for thesystems Ba& „La F2+„and Srl La F2+„decreases con-tinuously with increasing values of x, the results for Z, ofSrl „Yb F2+„show a broad minimum.

D. Sr) „La„C12+„

12.7 ma I '/o YbF3

Thc SrC12-based solid solUtlons al c hygroscopic andthey need attention in order to obtain samples of sufficientoptical quality for reliable experiments. Samples of pooroptical quality show a lot of surface scattering, whichreduces the signal-to-noise ratio drastically.

The T2s peak in carefully treated SrC12 samples is more

o/o YbF3

TABLE III. Activation energy E, for solid solutionsSr( „Yb„F2+„.

E, {eV)

I

2001

3001

&00

Energy Icrn

500

FIG. 6. Raman results of some solid solutions

Sr) „Yb„F2+„.

0.0220.0430.0820.0860.1050.127

3.20.600.420.460.550.95

D. J. QQSTRA AND H. %. den HARTQG

TABLE IV. Activation energy E, for solid solutionsSr) „La„C12+„.

0.0120.043

0.240.93

I

E~ 100

a50

600

contribution of the defect-induced linewidth increases. Incontrast with the results obtained for the solid solutions

Ba& ~I.a Fz+, Sr& „La~F2+„, and SrI ~Yb„F2+„,where the deviation between the curves associated withsolid solutions and those of the pure-fluorite samplesoccurs at lower temperatures with increasing values of x,for Sr) „La„C12+„wefind that the dominant effect is theincreasing activation energy with increasing x. In TableIV we have compiled the activation energies of two solid

soluttons of the type Sr& „La„Clq+„.

IV. DISCUSSIQNFIG. 8. Behavior of the position and vridth of the T2g Raman

peak as a function of the temperature as observed in pure SrCl2.

intense than in the SrF2- and BaFz-based solid solutions.This is probably due to the fact that the polarizability ofCl is significantly larger than that of F . In pure SrC12the Tzs peak is situated at 181.4 cm ' (for T=290 K). InFig. 8 we present two plots showing (a) the behavior of theposition of the T2g peak, and (b) the width of this band asa function of the temperature. At low temperatures thepeak shifts to lower energies with increasing T; in the vi-

cinity of the superionic phase transition the shift of thepeak position with increasing T becomes larger and larger.The behavior of the width of the Raman peak as a func-tion of T shows a linear part in the low-temperature re-

gion; in the neighborhood of T, the width increases ex-ponentially.

In Fig. 9 we have plotted the behavior of the li.newidthof the T2g peak as a function of the temperature for pureSrClq together with the results obtained for two solid solu-

tions Sr, „La„C12+„. With increasing values of x the

A. Activation energy

The Raman scattering experiments carried out in thisinvestigation have demonstrated that for al/ solid solu-tions investigated the addition of trivalent impurities tothe cubic alkaline-earth halide crystals leads to anenhanced broadening of the T2s peak. There are, howev-

er, remarkable differences between the various solid solu-

tions if we look more closely at the details of the behaviorof the additional contributions to the linewidth. In an ear-lier paper we have proposed that the extra contributionto the linewidth is due to the rapidly jumping defects,which are present in large amounts in heavily doped ma-terials.

In Fig. 10 we have presented a survey of the activationenergies obtained for the f1uoride solid solutions investi-gated. The solid solutions Ba~ „La„F2+„andSri „La„pz+„behave similarly. The activation energydecreases with increasing values of x; this behavior agrees

Sr.Yb

O 5--

50-.

6OO 7OO SO0

TEMPER&TuRE(&)

I I I

5 tO tSCONCENTRATION (lno('I. )

FIG. 9. Behavior of the width of the T2g Raman peak Isolid solutions Sr& „La„Cl2+„asa function of the temperature.

FIG. 10. Plots of the activation energies obtained for thevarious fiuoride solid solutions as a function of the rare-earthconcentration.

29 RAMAN SPECTROSCOPY OF SUPERIONIC SOLID SOLUTIONS. . . 2429

qualitatively with what is expected on the basis of a modelwith interacting defects. According to this model the ac-tivation energy of the defects does not have a uniquevalue, but it is broadened by a distribution function. Thisdistribution of activation energies for example, can, bewritten as

N(E) = exp1

p 77

(E E )2

instead of the usual one given by

v=voexp( —E, /kT) .

Equation (4) indicates that the activation energy which iscalculated from an Arrhenius plot is for a process with abroadening parameter p equal to

E,'=E, p14kT—.The activation energy which is measured in this wayshould be corrected, as shown in Eq. (5). The apparantactivation energy is smaller than the average value E, .The effects of broadened jump energies have been investi-gated with the ITC method and ionic conductivity, andit was found that the broadening of activation energiesleads to observable effects on the experimental results. Inorder to explain the reductions of E, observed in this pa-per it is necessary to assume that the value of p is quitelarge.

Another possible origin of the reduction of E, for in-creasing values of x is that the jump frequency of the de-fects depends on more than one mechanism. Clues for theexistence of a jump mechanism consisting of two compet-ing terms have been given in a series of papers dealingwith space-charge relaxation phenomena in solid solutionsof the type M~ „R„F2+ . ' ' ' In order to explain theobserved results it was necessary to assume that the relax-ation time associated with the depolarization process, denHartog and Langevoort' have proposed the followingorm:

1 —a a(6)

where a is the probability of a dipolelike jump to contri-bute to the conductivity process. This probability hasbeen shown to increase drastically with the concentrationof trivalent impurities present in the sample. ' ' ' In theextreme cases where a is 0 or 1 the activation energies areequal to the one associated with the extrinsic conductivityprocess (Ef ) and the dipole-jump mechanism (E~), respec-tively. This means that, although the process is morecomplicated, an interpretation in terms of one thermallyactivated process will lead to a decrease of the activationenergy from Ef to E~. For the system Sr& „La„F2+„wehave found these parameters to be approximately 1.2 and

where p is a measure for the width of the distributionfunction. In accordance with the distribution function (2)we calculate, for the jurnp frequency,

2

v=3 exp +4k T

0.6 eV, respectively. ' Unfortunately it is not possible todetermine the additional contribution to the linewidth forsmall values of x, which is associated with jumps of de-fects produced by the existence of trivalent impurities, be-cause the numbers of these defects are rather small. Con-sequently, the extra contribution is also rather small. TheRaman technique can be used to detect deviations betweenthe results of pure and doped materials for values ofx )0.01.

In Fig. 10 we see that the activation energy for smallvalues of x, for Ba& „La„F2+„,is about 0.8 eV, which isin close agreement with the values from our ITC experi-ments on the space-charge relaxation band. ' The corre-sponding value for solid solutions Sr& La F2+ is about1.1 eV; also, this value is in close agreement with the valueobtained from ITC experiments by Meuldijk and den Har-tog. ' The deviating behavior of the solid solutionsSr&,Yb F2+„probably has something to do with the ex-tensive clustering, which has been found by Meuldijk andden Hartog' from combined ITC and dc ionic conductivi-ty experiments.

Catlow et al. have observed that in some solid solu-tions of the type M& „R„Fz+„andMr „R„C12+„the su-perionic phase transition shifts to lower temperatures withincreasing values of x. For Cap 9~Y009F209 a shift ofmore than 200 K as compared to the value of T, of pureCaF2 has been reported. Catlow et a/. have suggestedthat this shift of T, is due to the trapping of interstitialF ions by impurity-interstitial F -ion complexes, i.e.,the formation of some kinds of clusters. We note that thevery strong increases of the linewidths observed forSr& Yb„F2+ and Sr& La„C12+, as shown by Figs. 7and 9 strongly suggest that here too the superionic phase-transition temperature has shifted to lower temperatures.Preliminary differential scanning calorimetry (DSC) mea-surements on solid solutions Sr& „La„C12+„made it clearthat the phase transition shifts to lower temperatures withincreasing values of x. By analogy we expect that alsoin solid solutions of the type Sr~ La„C12+ clustering oftrivalent impurities and interstitial anions plays an impor-tant role. At the moment no combined ionic conductivityand ITC experiments, which provide us with informationabout eventual clustering in these solid solutions, areavailable. These experiments are planned for the near fu-ture in our laboratory. At the moment, unfortunately, noDSC data on solid solutions Sr&,Yb F2+„are available.This data would show the eventual shift of the phase tran-sition (these experiments are in progress).

The complicated behavior of the activation energy as afunction of the concentration of Yb impurities is probablyrelated to the presence of different types of clusters. Ithas been shown by several authors that in solid solutionsof rare-earth fluorides (of the second half of thelanthanides series) and SrF2 contain different types ofclusters. ' ' These clusters may contribute to thelinewidth of the Raman scattering peak, because at hightemperatures they probably reorient very rapidly. Theymight also contribute to the conductivity at very highYbF3 concentration, because charge carriers (interstitialF ions) may jump from one cluster center to anotherwithout dissociation. This conduction mechanism is quite

2430 D. J. GOSTRA AND H. Vf. den HARTOG

similar to the percolation conduction model proposed forsolid solut1ons Bai » La» F2+» (Ref. 12) andSr&,Nd F2+„(Ref. 13). This has also been suggested byMeuldijk and den Hartog' as a conclusion from theircombined ionic conductivity and ITC results.

For the sample containing 2.2 mol% YbF3 we have ob-served a very large value of the activation energy. The er-ror bar of this particular result is relatively large becausethe extra contribution to the linewidth is determined bysubtracting the linewidths observed for pure SrF2 fromthose obtained for the solid solutions. It can be seen thatdeviations between the two corresponding curves (see Fig.7) occur in a temperature range where we observe for bothsamples a considerable curvature in the plots of thelinewidth versus temperature. On the other hand, weknow that in samples which contain a few mole percent ofYbF3 clustering affects the ionic conductivity appreciably(see Ref. 16). In this concentration range, interstitials,which carry the current in an ionic conductivity experi-ment, are probably trapped by some types of clusters.This leads to higher values of the activation energy.

B. Interpretation of the Raman spectra

The Raman spectra of solid solutions Ba& „La„F2+„clearly show two peaks. The first peak located at about240 cm ' (as measured at 300 K) is ascribed to the T2gexcitation. A schematic representation of this excitation,in which only the lattice F ions are involved, has beenshown in Fig. 11. Our observations are in agreement withthose published earlier for pure BaF2. ' The secondpeak located at higher energies has been discussed in a re-cent paper by our group. ' %'e assume that the additionalband in Ba~ La„F2+„ is associated with the Eg Ramanexcitation of the corresponding local mode of an intersti-tial I' ion. This mode has been shown in Fig. 12. Ac-cording to Nerenberg et aL this local mode should havean excitation frequency of about 284 cm ', which is veryclose to the frequency of the extra Raman peak. Also, thewidth of this peak as calculated by Nerenberg et al. israther narrow. It is interesting to note here that the corre-sponding peaks in solid solutions Ca& „La F2+, andSr& „La„F2+„are located at significantly lower energies;in addition, the peaks are expected to be considerably wid-er than for Ba& „La„F2+„.Experimental results obtainedin our laboratory strongly suggest that clustering oftrivalent lanthanide impurities only plays a minor role. '

I

I

I

I

I

0 cation

anion

FIG. 11. Schematic representation of the T2g-phonon modein the fluorite lattice structure.

I

I

I

I

I

!

IIII

0 cation

anion

I interstitial anion

FIG. 12. Schematic representation of the Eg local mode of aninterstitial fluoride ion in the fluorite lattice.

The dominant defects in these solid solutions are simpledip oles, mostly next-nearest-neighbor — (NNN —) typeR +-F; complexes. The local modes of the interstitialfluoride ions in Ba~ »La»Fq+» are therefore easy todetect.

A completely different situation occurs for solid solu-tions Sr~ „La Fz+ and Sr& Yb„F&+„. First, we knowthat the Eg mode of the interstitial fluoride ion will showa relatively large linewidth and the positions of the corre-sponding Raman peak is expected to be 151 cm '. %ehave not been able to observe a Raman peak in this region,indicating that due to the large linewidth the intensity ofthe peak is reduced to values below the signal-to-noise ra-tio. In solid solutions Sr~ „La„F2+ we have not ob-served any additional Raman peak, which is in contrastwith the results obtained for Sr) Yb F2+ . In the lattersolid solutions we have found that for very heavily dopedmaterials (x )0.1) a weak line at the high-energy tail ofthe T2g peak is present. Although the spectra observedfor very heavily doped Sr~ „Yb„F2+„crystals are rathersimilar to the ones found for Ba& „La„F2+„,containing3—7 mol% LaF3, we assume that the extra band in thecrystals Sr~ „Yb„F2+, is not due to interstitial fluorideions. Apart from the interstitial fluoride ions there arealso anion vacancies present in these solid solutions.These vacancies are situated in clusters, which have beendiscussed by several authors in the literature. ' Neren-berg eI; al. have also calculated the frequencies of localmodes of anion vacancies. A narrow excitation, which isRaman active and sufficiently narrow, is located at an en-

ergy of 325.5 cm '. This frequency is rather close to theposition of the additional Raman line in heavily dopedsolid solutions Sr~ Yb Fq+ . The excitation under con-sideration has been given in Fig. 13.

We emphasize that the interpretation of the experimen-tal results as given here is a preliminary one. It needs in-dependent justification. Our interpretation is, however, inline with the general behavior of the defect structure ofthe solid solutions M, „R„F2 „,which has been studiedin detail in our laboratory ' ' ' ' it is also in linewith results of spectroscopic investigations which have

RAMAN SPECTROSCOPY OF SUPERIONIC SOLID SOLUTIONS. . .

0 cation

anion

Q anion vacancy

FIG. 13. Schematic representation of the T2 local-mode vi-

bration of an anion vacancy in the fluorite lattice.

been carried out on some particular types of MI „R„F2+„solid solutions. ' Further details about the defect struc-ture will be obtained from combined Rmxan and ir-absorption experiments on solid solutions MI „E.,F2+„containing H probes, which will be introduced into thesamples. The first preliminary ir-absorption experimentshave already been carried out and they show appreciabledifferences between samples which are known to have astrong tendency towards clustering and tho, se in whichclustering of trivalent impurities only plays a minor role.

From Fig. 2 we see that the intensity of the additionalRaman peak, which has tentatively been associated. withthe Eg excitation of an interstitial F ion, increases withincreasing LaF3 concentrations. This can be understood,

because for each La + ion in the crystal one compensatinginterstitial F ion is present. From detailed. ITC andEPR experiments we know that clustering is not impor-tant in Bal „La„F2+„.' Simple charge-compensatingcomplexes containing the interstitial fluoride ions are theorigin of the Eg peak. If the concentration of these com-

plexes increases the corresponding Raman peak will in-

crease in intensity. Qn the other hand. , the T2g-phononpeak d8creQseS slglllflcantly with lllcl'eas111g LRFI concell-trations. Extreme situations, where the T2g peak is dimin-

ished, may occur for LRF& concentrations higher than 25mal% (see Fig. 1). Comparing the schematic representa-tions of the T2s-phonon mode and the Es local mode, we

conclude that the F ions contributing to the Eg localmode do not contribute anymore to the T2g-phonon mode.If we assume that the F ions, independent of the mode,contribute with equal amounts to their Raman peaks, weare able to calculate the intensity ratio of the T2s and EsRaman peak as a function of the concentration of LaF3.Results of these calculations have been shown in Fig. 2;we see that there is qualitative agreement between thepredicted and observed intensity ratios.

ACKNO%'LEDGMENTS

The authors wish to thank Mr. P. Wesseling for grow-ing the crystals and technical assistance, Dr. I.. G. P. Dal-molen for helping us with the Raman scattering setup,and Mr. J. F. Goldstein for his assistance with electronicproblems. This work is part of the research program ofthe Stichting Fundarnenteel Onderzoek der Materie[Foundation for Fundamental Research on Matter(FOM)] and has been made possible by financial supportfrom the Nederlandse Organisatie voor Zuiver —Weten-schappeiijk Onderzoek [Netherlands Organization for theAdvancement of Pure Research (ZWO)].

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