Single crystal Raman spectra of forsterite, fayalite, and ... · American Mineralogist, Volume 76, pages 110L1109, 1991 Single crystal Raman spectra of forsterite, fayalite, and monticellite

American Mineralogist, Volume 76, pages 110L1109, 1991

Single crystal Raman spectra of forsterite, fayalite, and monticellite

A. CnopnrasMax Planck Institut fiir Chemie, Postfach 3060, 6500 Mainz, Germany

Ansrn-lcr

Polarized single crystal Raman spectra of the fundamental modes of forsterite (MgrSiOo),olivine (Mgorr,Feo,r), fayalite (FerSiOo), and monticellite (CaMgSiOo) are presented. SevenIow energy modes (<450 cm-') in forsterite differ from those of all previous studies. Allmodes predicted by symmetry for forsterite and monticellite were observed; 34 out of 36modes were observed for fayalite. Assignment of the modes was determined by systematicsin frequency changes resulting from cation substitution. Although the lattice modes aregenerally mixed, likely mode assignments are made using the following observations. Thelowest energy modes are assigned to SiOo translations and appear to be mixed with thecation translations. The lattice modes between 330 and 435 cm-' in forsterite that changedthe least with composition were assigned as SiOo rotations. The modes from 300 to 390cm-' that showed the greatest variation with composition or showed signs of two-modebehavior in the olivine Mg* were assigned as M2 translations. The SiOo internal stretchingand bending modes were assigned to the highest frequencies; they vary little from forsteriteto monticellite to fayalite and appear to depend more on cation mass than volume. Theseassignments are consistent with previous single-crystal infrared studies of forsterite andfayalite and with mode Griineisen parameters 7, measured vs. pressure in that the highest'y, values should be associated with the M2 cations and the lowest with the SiOo internalmodes.

INrnonucrroN

The vibrational modes of olivines, important geophys-ical and cosmochemical phases, have been studied exten-sively by Raman spectroscopy (Iishi, 1978; Servoin andPiriou, 1973; Piriou and McMillan, 1983; Stidham et al.,I 976; Hohler and Funck, I 973; Chopelas, I 990), infraredspectroscopy (Hofmeister, 19871. Tarte, 1963; Paques-Ledent and Tarte, 1973: Kovach et al.. 1975: Hofmeisteret al., 1989; plus some references given above for Ramanspectroscopy), inelastic neutron scattering (Rao et al.,1988), and lattice dynamical calculations (Price et al.,1987a, 1987b). Study of these properties yields insightinto the interatomic forces within the crystal structureand a basis for understanding the effect ofcation substi-tutions on the thermodynamic properties. For example,the heat capacity and entropy can be estimated to betterthan 5olo over a moderate temperature range (-500 K,Kieffer, 1979) from the mode frequency information ob-tained by infrared and Raman spectroscopy. The accu-racy in estimating these quantities can increase to betterthan 0.50/o over a larger temperature range (> 1000 K) ifall of the infrared and Raman modes are enumerated andassigned to atomic motions. The detailed mode assign-ments provide an accurate method for estimating the fre-quencies of inactive or unobserved modes, thereby yield-ing more precise information on the frequency distributionor density of states (see Hofmeister, 1987; Hofmeisterand Chopelas, l99la; Chopelas, 1990, l99l). The most

important modes are those below 450 cm-r, as the esti-mates of heat capacity and entropy vs. temperature atambient temperatures and below are very sensitive to thenumber of these modes and their distribution. These are,however, the most difficult to measure because of exten-sive overlapping, breadth ofpeaks and two-mode behav-ior in solid solutions, and low intensities in Raman spec-tra because of the low polarizabilities of the octahedralstructural units.

The polarized Raman spectrum of forsterite has beenpreviously described (Hohler and Funck, 1973; Servoinand Piriou, 1973; Iishi, 1978), but none of the resultsagree for the frequencies of the low intensity modes. Theonly other olivine for which a (nearly) complete single-crystal Raman spectrum has been described is tephroite(MnrSiOo) (Stidham et al., 1976); partial data are avail-able for Ca-bearing phases (e.g., Hohler and Funck, 1973;Piriou and McMillan, 1983). This study was prompted,in part, by the general lack of Raman data in the lowfrequency range for other olivines and, in part, by dis-crepancies with the previously reported data for forsterite(Chopelas, 1 990).

In this study, single-crystal polarized Raman spectra offorsterite, olivine (Mgorr,Feo,2)2SiO4, monticellite, andfayalite are presented. Mode assignments to molecularmotions are made by comparison of analogue modes inthese olivines and previous results oftephroite (Stidhamet al., 1976) and ̂ y-CarSiOo (Piriou and McMillan, 1983).

0003-004x/9 l/0708-l I 0 I $02.00 1 1 0 1

ForsteriteAg (xx)

e: tTI

€ l i ls: lls r ll- i i l . i / \

A9 {yy)

r1,r /i )

Bzs (xz)

II

A9 lzzl

F -r s l n * ;

l l l l l l , l ; )

Brq(yz)

- [

I 102 CHOPELAS: RAMAN SPECTRA OF OLIVINES

F

v)z.UFz.

U

!

E

200 100 600 800 ?00 100 600 800 1oo0FRE0UENty (crir1)

Fig. l. Polarized Raman spectra of forsterite (MgrSiO.). Po-larizations and symmetries are indicated. Features not labeledin the B symmetries correspond to intensity leaked from otherpolarizations, allowed by the polarizing limit of the analyzer(0.9999). Polarization symbols do not represent sampling ge-ometries as (xz): (zx), for example. The spectra are not smoothedor base line corrected.

The new spectral data are shown to be consistent withthe single-crystal infrared results for forsterite and fayal-ite of Hofmeister (1987)r the data also show that modeswith the same assignments have similar mode Griineisenparameters (Chopelas, I 990).

The thermodynamic parameters of olivines are calcu-lated in a sequal paper (Chopelas and Hofmeister, inpreparation) where the Raman and inliared data arecombined to yield a complete set of vibrational frequen-cies for the above-mentioned olivines.

ExpBnrrvrnNTAL DETAILS

Synthetic end-member forsterite described by Suzukiet al. (1983), synthetic end-member and natural(Feono,Mno06)2SiOo fayalite described by Hofmeister(1987), and natural monticellite Ca (Mgn,,Feoon)SiOo de-scribed by Sharp et al. (1986) were used. Single crystalsof forsterite, monticellite, and synthetic fayalite were pol-ished on the crystallographic faces, and the natural fayal-ite specimen was a thin (-10 pm) {100} cleavage plate.These were mounted on the optical bench, and final align-ment of the crystals was made by observing the extinctionof the A, modes under crossed polarization (analyzer per-pendicular to the laser polarization). These were not foundto extinguish until the crystal was aligned to better than0.5'. The spectra were either taken in a standard 90" Ra-man configuration or in a backscattering configuration,in which the laser light enters the sample at a 45o angleand the Raman spectrum is collected from the same face.The backscattering configuration did not change the rel-ative intensities ofthe peaks.

The Raman spectra were excited by the 488.0-nm lineof a Spectra Physics 2025-5 Ar ion laser, focused to 10rrm diameter in the sample. For the A, modes of forsteriteand the other olivines, powers of 20 to 200 mW sufficedto obtain the spectra. However, for the forsterite off-axismodes (B", modes, x: 1,2, or 3), up to I W of power atthe sample was required to bring the signal of the weakestmodes above the minimal base line noise level. No shiftor broadening of the Raman lines from the effects of heat-ing was observed. An f : 2 lens collected the Ramansignal and an f : 8 lens focused the image of the sampleon the entrance port of the monochromator. The collec-tion of the Raman signal over a large solid angle did notappear to mix the polarizations to a significant extent, asshown by the nearly complete extinctions of the modesin the other polarizations (see Figs. l-3). Any spilloverintensity from the other symmetries can be accounted forby the polarizing limit of the analyzing polarizer (0.9999).The Raman signal was analyzedwith an ISA U1000 dou-ble monochromator equipped with a photon-countingdetection system. The spectral resolution was 2 cm ', but

TABLE 1. Classification of the 81 optic modes of olivine by site group to factor group analysis

1 1 B1e TBzs 78* 10A, 98,, 138,, 1383,

SiO4 internalv1

!2

Vg

Lattice'SiO4 rotSiO4 transM1 transM2 trans

Activity.-

b

112

51202R

61122

1202R

3n1I

14210IR

t

01'l

14210'I

R

30II17213'l

0

301116203'I

tr

o'|12271132lr

b

112271132tr

Nofer From Farmer and Lazarev (1974); see Hofmeister (1987) for complete analysis.* Abbreviations: rot : rotation; trans: translation.** R : Raman active; 0 : not spectroscopically active; ir : infrared active.

CHOPELAS: RAMAN SPECTRA OF OLIVINES 1 103

200 100 600 E00 200 100 600 800

FREOUENCY (cm-1)

Fig. 3. Polarized Raman spectra of monticellite (CaMgSiO")analogous to those in Figure t. These were obtained with thesame spectrometer settings and laser power as those of olivine,Figure 2.

e.9., Hofmeister, 1987); the 8l optic modes are listed bysymmetry in Table l.

The olivine structure contains isolated SiOo units linkedby octahedrally coordinated M2* cations. The cations arein two crystallographically distinct sites, the smaller Ml(C, symmetry) site and largerM2 (C, symmetry) site. TheMl octahedron shares six edges with neighboring poly-hedra. two with SiO, tetrahedra. The M2 octahedra sharethree edges with neighboring polyhedra but only one withan SiOo tetrahedron. From the greater extent ofedge shar-ing between SiOo and Ml0u polyhedra, one might expectthat the Ml cation has a greater influence on the SiOointernal mode frequency. This does not appear to be thecase (see the mode assignment section below).

By site $oup to factor group analysis (e.g., Farmer andLazarev, 1974), one can determine the total number ofmodes of each motion type by assuming that the SiOo"molecules" retain their internal modes. This approxi-mation is useful for determining frequency ranges forunobserved and inactive vibrational modes. In this anal-ysis, shown in Table l, no Raman active M2* translationsresult from the Ml cation. The following sections de-scribe new spectroscopic results listed in Table 2, corre-lated by analogous modes in each of the symmetries.

Forsterite

The Raman spectra of pure forsterite taken in six po-larizations, presented in Figure l, have well-formed peakswith a flat base line (no stray light, plasma lines, or flu-orescence). The spectra as shown are not smoothed or

F

z.UFz.

U

F

dE

Faz.lrJ

z.I.LJ

ku-JE.

200 400 600 800

FREOUENTY (cm-1)Fig.2. Polarized Raman spectra of olivine (Mgorr,Feo,r)rSiOo

for the B symmetries obtained with the same spectrometer set-tings as for data in Figure I but with 100/o of the laser power.These differ from data in Figure I by the significant broadeningof the peaks, increased intensity under the base line, and theappearance ofbroad difuse features below 220 cm-t.

the spectra were sampled at 0.8 cm-' (-0.2 A) intervals.The range of frequencies for the spectra was 40 to 1040cm-I. All spectra were taken at 293 + | K.

SpncrnoscoPrc RESULTS

Olivines are of orthorhombic (Pbnm) symmetry con-taining 4 MrSiOo formula units per unit cell. Thus, oliv-ines have 84 normal modes. By a symmetry analysis ofthe invariant atoms, the 84 vibrational modes belong tothe irreducible representations of the point group Dro (see,

MonticettiteAg {xx) B.- lxvl

Brn

o

I 104 CHOPELAS: RAMAN SPECTRA OF OLIVINES

Tlele 2, Mode frequencies* in cm-' of olivines and assignments

Fo, oo Fo* Fa "y-Caz Assignment

Ae965856824608545422339329304226183

B"(xrt975866838632582434383351318274220

Brs (xz)881s864393653232421 a E

8"" (yzl

Nofe: Fo : forsterite, this study; zr: mode Gruneisen parameter from Chopelas (1990a); Fos: (Mgrr,Fe,JrSiO4, this study; Mo: monticellite, thisstudy; Fa : fayalite, this study; Te : tephroite, taken at 14 K by Stidham et at. (1976); a-Ca, : o-6".9'O4, piriou and McMillan (1983); M: averageof M,* masses (see Fig. 6).

. The uncertainties for the freouencies of this work are 1 cm '.'- Ouoted from Sharp et al. (1986).

0.66o.440.480.700.531.481.871 . 1 61.630.672.1

0.661 . 4

849

935840808c / c

5 1 5389256291244167't24

820588546393307288271203155

ccrt

4013192741881 1 9

93284081456250536923728925917' l1 1 9

860553405309290189102

900549

949851818589534402275307258172'145

954855828600560407333303266215164

879572411327263243141

961854822606542417334326301222181

973864836630578429379348314

215

880582433355314236

917589427404368312282

9258398 1 4

Yg

v . ! v "

v , l v "

!2

M2 translationSiO4 rotationM2 translationSi04 translationSi04 translation

Yg

4 ( r v )v , ( I 4 lVq

!2

M2 translationM2 translationSiOl rotationSiOi translationSiOn translation

V3

Y2

mix (SiOl rot)mix (M2 trans)mix (SiO4 rot)mix (SiO4 trans)

Vg

l4

mix (SiO4 rot)U2

mix (M2 trans)mix (SiOi rot)mix (SiO1 trans)Wo (cm3 mol 1).*1AaM

9205924354 1 037431528643.650.203 0.189

89957833239926625121651.560.176

947851822577524384312277?260193't54

3762811861 1 346 .15

0.1 34

892ccc

30437827622313748.610.1 35

887

59 .110.158

o.44

1 . 6

1 . 2 1

0.38

0.991 .75

base line corrected. The other three off-axis polarizationsyielded identical results to those shown and are not pre-sented; thus, (xy) : Ox).On the other hand, the Ramanspectra of mantle-relevant olivine (Forr,Fa,r) have broad-er peaks and uneven base lines, especially below 500 cm I,shown in Figure 2 for the B,, (x : l, 2, or 3) modes.Additional broad features appeared in the spectra ofFo*below 200 cm-' that do not appear to be fundamentalRaman modes or related to two-mode behavior (wheretwo modes appear in intermediate compositions, the in-tensity of each reflecting the relative proportions of thecations). Similar features were found in the Raman ofpyrope (Mgn.) (Hofmeister and Chopelas, l99lb) at lowfrequencies and may represent some forbidden latticemodes appearing because of the reduction of symmetryby the substitution of other elements in the cation sites.The frequency shift from the substitution of l2olo Fe forthe Mg is used to help determine mode assignments in a

following section, while keeping in mind that any two-mode behavior would not lead to proportional shifts forsome of the modes. All but the two weakest fundamentalmodes were found in the olivine (Forr).

Although the forsterite spectra in Figure I appear to besimilar in relative intensity for the higher intensity modesto those previously published (e.9., Iishi, 1978; Hohlerand Funck, 1973),the lowest intensity modes in the threeB,, symmetries differ from those of any previous work.In B,r, clear modes were found a1352 cm I and 383 cm-',and a weak mode was found at 27 4 cm-t instead of modesat 165,192,260, and 418 cm-r as found by Iishi (1978)or Servoin and Piriou (1973). Of all 36 Raman modes inthe spectrum, only the 274 cm' mode had less than a3:l signal to noise ratio. This value is supported as afundamental mode by the appearance of a low-intensityanalogue B,, mode in monticellite (next section) andtephroite (Stidham et al., 1976). In B,,, a weak but clear

mode was found at 175 cm-'instead of 142 cm 'as re-ported by Iishi (1978). In Br", clear modes were found at286 and 435 cm-rinstead of those reported a| 226 and.272 cm' by Iishi (1978). The source of the previouslyreported modes may have been incomplete extinction ofmodes in other polarizations or impurity effects (men-tioned above), as suggested by a comparison ofthe peakwidths and base lines of the spectra of Iishi (1978) withthose in Figure l. These new modes were confirmed byseveral repeat spectra in different configurations, i.e., thosefor both (xy) and. (yx) configurations for B,", and thosewith a slight rotation of the crystal that caused relativeintensity changes among the modes.

The new modes are supported by analogous modes inthe other olivines and the similarity of the forsterite sin-gle-crystal infrared results of Hofmeister (19g7), whereonly two modes were found below 268 cm 1. This is con-sistent with the number of modes expected for this fre-quency range by factor group analysis (see the mode as-signment section below). The results of this studv decreasethe number of modes below rhis value from eight to fivein the Raman spectrum. This may seem trivial at first,but the calculation of the heat capacity and entropy isvery sensitive to the number of modes below 300 cm r(Chopelas and Hofmeister, in preparation).

Thirty-three of the 36 mode frequencies in Table 2 arealso accurately predicted by lattice dynamical calcula-tions that did not use the spectral data to tune the inputparameters (Price et al., 1987a, 1987b). The only dis-crepant values are the three lowest frequency modes inB.r. For these modes, the trends of frequency vs. com-position suggest extensive mode mixing for this polaiza-tion (see the mode assignment section below).

Monticellite

The crystal quality and purity of the natural monticel-lite was sufrcient to produce sharp, well-formed peakseven in the low energy range (Fig. 3). The small amountof Fe present in this sample is not expected to affect sig-nificantly the results, as (l) the high-energy modes are inagreement with those of a pure synthetic monticellitesample (Piriou and McMillan, 1983) and (2) Ca2* occu-pies essentially all the M2 sites and the Ml translationsare not Raman active. The greater intensity of the lowenergy analogue modes compared with forsterite reflectsthe increased polarizability of the CaOu structural units.The same effect was found for the Ca garnets (Hofmeisterand Chopelas, 1991b). Caution must be used in deter-mining analogous modes for the olivines because the rel-ative intensities vary with composition.

All of the modes predicted by symmetry in each of thepolarizations were easily found and are listed in Table 2with their forsterite counterparts. The high-energy modesare in agreement with previous powder Raman data (pi-riou and McMillan, 1983). Notice that polarized single-crystal studies are required to resolve and assign the sixmodes between 534 and 600 cm r and four modes be-tween 399 and 4ll cm ' shown as broad bands in the

CHOPELAS: RAMAN SPECTRA OF OLIVINES I 105

powder data of Piriou and McMillan (1983). This alsooccurs for tephroite (Stidham et aI., 1976) and fayalite(see below).

The three A* polarizations help correlate the monticel-lite modes to those of forsterite. In d (xx) in forsterite,the 304 cm ' mode is very intense and the 339 cm-,mode disappears; in A"UD, the opposite is true. Theanalogous behavior in monticellite results in a correlationof the 258, 307 , and 276 crn ' modes in monticellite withthe 304, 329, and 339 cm-, modes in forsterite, respec-tively. A similar correlation of the modes might occur inB,, since this symmetry represents modes that have splitdue to lowering of symmetry (Davydov splitting). For theremaining two symmetries, analogous modes in the twominerals were assumed to appear consecutively as a firstapproximation.

Fayalite

Laser powers in excess of 20 mW caused heating ormelting of the dark synthetic fayalite. This resulted inspectra with lower signal-to-noise ratios, especially forthe B* modes (see Fig. 4). The laser power limitation alsoprevented the resolution of the seventh Br, mode and theeleventh B,, mode. A feature at 277 cm ', appearing inseveral repeat spectra of Brs, may be the missing modein this configuration, but it was not as clearly resolvableas the other peaks.

There are two high-energy broad features in ,\ sym-metry that are not fundamental modes, as they are muchbroader than the other modes and have no analogy in theother olivines. In addition, the intermediate modes at365-405 cm-r and 505-580 cm I are broader than theircounterparts in the other olivines. These effects have alsobeen observed for the Raman spectra of almandine (Hof-meister and Chopelas, l99lb). It has been shown recentlythat the intermediate modes become significantly nar-rower at lower temperatures, an efect ascribed to anhar-monicity (Sharma and Cooney, 1990). The broad, high-energy features appear to be related to the Fe3- contentof the fayalite (S. K. Sharma, personal communication,l 990).

The natural fayalite (Feono,Mnoou)rSiOo sample was al0-pm thick x 30-pm x 30-pm {100} cleavage plate.Only unpolarized spectra aligned along the y and z axeswere obtained; Figure 5 shows the A\6)D or A"(zz) I Bs"polarizations. Some of the other modes in Br, and Br,were also shown as either shoulders on the high energymodes or weak modes in the low-frequency ranges byspectra taken as the sample was rotated about the collec-tion (crystal's X) axis. The results, shown in Figure 5,show that the observed mode frequencies for the naturalfayalite are very similar to those observed for the syn-thetic fayalite, as would be expected by the similarity inmass and cation radii of Mn2* and Fe2t. The peaks in thenatural sample are also broader, as observed for the nat-ural olivine Fo* in this study.

For three high-energy Raman modes in Fe-Mg solidsolutions, i.e., modes at 920,856, and 824 cm r in for-

(t)z.uJz.U

F

5LU

r 106

400 600 800 200 400 600 800

FREQUENCY ( cm -')

Fig. 4. Polarized Raman spectra of synthetic fayalite (FerSiOo)analogous to those in Figure l. These were obtained with thesame spectrometer settings as those of olivine, Figure 2, but laserpower was limited to 20 mW at the dark sample. Broad, highenergy features marked with an asterisk (*) are not fundamentalmodes.

sterite, it has been shown that the frequency varies lin-early with Fe content to 800/o Fe (Guyot et al., 1986). Theresults for fayalite (Table 2) lie at the extrapolated valuesfor l00o/o Fe. Powder infrared data also show that theSiOo internal modes also vary linearly with compositionwithin a solid solution (Burns and Huggins, 1972), so itis expected that the values for Fo* in Table 2 should lieintermediate to those for forsterite and fayalite. Dis-counting modes with two-mode behavior, this appears tobe the case (see next section).

Moor AssrcNMENTs

The frequency changes due to cation substitution arefundamental to understanding changes in certain mac-roscopic physical properties such as heat capacity, entro-py, and compressibility. The first step to understandingthe connection between vibrational spectra and thesephysical properties is the assignment of the modes toatomic motions. In this case, this is done by cross com-parison of the analogous modes for the various olivinespecies. Cation substitution for Mg2* in forsterite servesto cause a decrease in mode frequencies, mainly becauseof increased mass or increased volume. Other effects mightinclude coupling and mode mixing.

In addition to the present measurements for forsterite,monticellite, and fayalite, the single-crystal Raman studyof tephroite by Stidham et al. (1976) is complete in the

CHOPELAS: RAMAN SPECTRA OF OLIVINES

6z.trJ

z.lrj

-)lrJd.

180 360 s40 720 900

FRE0UENCY (cm-1)Fig. 5. Unpolarized Raman spectra of fayalite (Feo ,oMno ou)r-

SiOo obtained from a {100} cleavage plate. Modes other thanthose in A" and Br, were found by rotating the crystal about thecollection (X axis of the crystal). The spectra pictured representa composite of 18 different spectra taken in different orienta-tions.

low-frequency range. Their results are interpreted usingthe results of this study and listed in Table 2. The efectsof cation mass and volume on the mode frequencies aredistinguished by comparing the effect of the largest cation(Ca'?*) vs. the heaviest (Fe'?*) on the mode frequencies'

The mode Grtineisen parameter, ?,, derived from thepressure shift of the modes should also correlate veryclosely, because the volume change during compressionis caused by compression of the voids and MOu octahedrabut not the SiO4 tetrahedra. Therefore, it is expected thatthe lattice modes would have higher 7, values than theSiOo internal modes, as appears to be the case (see Table2). Exceptions are discussed below.

SiOo internal modes

In the factor $oup method (e.9., Farmer andLazarev,1974\, the four internal SiOo frequencies are assumed tobe retained in the spectra but slightly modified by thecrystal environment, e.g., symmetry of the site and near-est neighbor distances. This is a viable approximationwhen the SiO" internal mode frequencies are significantly

* E i a s

e:(Fe f i f ,aB3o (yz ) 5

Foyotite ( Fo or, ) gAg (zz) * B,n(yz)

A9(yy) + B3n(yz)

higher than the lattice modes, as appears to be the casefor olivines.

The symmetric stretching frequency z, should vary theleast with changing composition. However, the two in-tense high-energy A, modes vary by about the same smallamount for the range of compositions. This is conststentwith the suggestion that these modes contain both z, andasymmetric stretching z. character (paques-Ledent andTarte, 1973;' Piriou and McMillan, 1983). In B,,, the twointense high-energy modes vary more with compositionthan do the corresponding A.s modes but the fact that theyboth vary by the same amount suggests the same type ofmode mixing. The remaining high-energy modes are as-signed z. and are in accord with the number and sym-metry expected from the symmetry analysis.

The frequency variation of the high-energy modes forthe olivines (data given in Table 2) is quite small but isobviously affected by the cation substitution. A plot offrequency vs. lrFM, wherc M represents the average ofthe two cation masses, shows that most of the modes varylinearly with this parameter (see Fig. 6). This parameterrepresents the frequency change ofan oscillator, resultingfrom a change in mass, from z a. y,Em, where z is thefrequency of an oscillator, k the force constant, and mthe mass. There have been extensive discussions ofwhether the two intense d high-energy mode frequenciesdepend on the volume of the Ml site (piriou and Mc-Millan, 1983) or on O-O distances that are distorted fromideal symmetry (Lam et al., 1990) in response to Ca2*substitution in the M sites. If tephroite or fayalite areincluded in this analysis, the heavier but relatively smallcations cause a decrease in the mode frequencies by aneven larger amount. However, it is clear from Figure 6that all modes do not fall on linear trends, e.g., those at965 and 920 cm' in forsterite, indicating some depen-dence offrequency on something else, such as cation vol-ume or coupling effects.

If the SiO" bending modes are assigned to the nexthighest frequencies (except for the 435 83. mode in for-sterite), the number and symmetry of the bending modesfor all four symmetries agree with those predicted bysymmetry analysis. The 435 cm-r 83* mode in forsteritedid not fall on the trends for data from the other olivines;it was of much weaker intensity, and it shifted by a largeramount than the other bending modes by substitution ofl2o/o Fe for Mg and thus was assigned to a lattice mode.Even though the bending modes are very similar in fre-quency for all of the symmetries, they generally occur inthe same frequency order for the olivines for which dataare reported in Table 2; that is, none of the lines shownin Figure 6 crosses another. The same general small shiftsas a function of composition found for the SiOo stretchingmodes were found for the bending modes, except that themonticellite /2 modes were below the lines connectingdata points for the other olivines, indicating either somedependence of these on volume or mixing with othermodes. The latter is more likely because the mode Gri.i-neisen parameters for these modes in forsterite are sig-

CHOPELAS: RAMAN SPECTRA OF OLIVINES

800

620

sio 4 TNTERNAL MoDESvl and v3 modes

1 1- l,--n

2--2--2

v2 modes

.18 .20

I 107

980

960

940

920

900

880

860

840

820

600

580

560

540

520

500

TE3oz.LUfaLUELL

430

410

390

370,13

Te ycaz Mo Fou, Foroo

1/-/T

Fig. 6. Plots of the SiOn internal modes vs. the parameterl/yfM (listed in Table 2 for the various olivines), representingthe change in vibrational frequency with mass. M is the averageof the cation masses; for example, for monticellite M : (24.3 +40.l)/2. The symbols represent the symmetries of the observedmodes as follows: O : O., I : B,r; 2: Br"i 3 : Brr; minerals:Fa : fayalite; Te : tephroite; ̂ yca2:7-CarSiOn; Mo : monti-cellite; For, : (Mgo rr,Feo,r).SiOo; Fo,oo : forsterite.

Fa

I 108

nificantly greater than for the other internal modes. Theextent of the mixing might be resolved by studies of solidsolutions.

Lattice modes

The variation of the remaining lattice modes with com-position is much larger than for the SiOo internal modes.Among the lattice modes, the SiO4 rotations are expectedto have the highest frequency and vary the least; the SiOotranslations, to be the lowest in frequency; and the SiOoand M2 translations to be mixed, as observed for theorthosilicate, garnet (Hofmeister and Chopelas, l99lb).These appear to be the case for the olivines. For the A,modes of forsterite and monticellite, the 329 cm ' for-sterite mode correlated with the 307 cm-' monticellitemode and the 291 cm-' tephroite mode. Since it variedthe least among the lattice modes, this was assigned toan SiOo rotation (see discussion on rotational modes inHofmeister and Chopelas, l99lb). The 339 and 304 cm-'modes in forsterite were then assigned to M2 translations;they are in agreement with the number predicted by sym-metry analysis and have the highest mode Griineisen pa-rameters in this range. The remaining 183 and 226 cm I

modes in forsterite were assigned SiOo translations. Sim-ilar trends were found for B,, and were likewise assigned.The mode Griineisen parameter for the 183 cm-' for-sterite mode is consistent with those observed for othersilicates (diopside, enstatite, Chopelas, in preparation;

B-MgrSiO", Chopelas, 199 l).It is not expected or observed that the mode frequen-

cies measured for Fo* lie proportionately between thosefor fayalite and forsterite. Observations of two-mode be-havior of the cation translations for pyrope-almandinesolid solutions (Hofmeister and Chopelas, l99lb) indicatethis might occur for the forsterite-fayalite solid solutionseries as well. Recall that two-mode behavior occurs whentwo modes, one representing each end-member, appearin the spectrum of a binary solid solution. The frequen-cies of these modes are nearly the same as those observedfor each end-member, and the intensities of the two modesrepresent the relative proportions ofeach cation present.Thus, those lattice modes showing the least frequencyshift may be part of two-mode behavior for the cationtranslations; the Fe counterpart in the spectrum is prob-ably too weak to be seen because of the low Fe contentof the olivine. This appears to be nearly the case in A,especially considering that the Fe2* preferentially substi-tutes at the large M2 site and a proportionate shift of theM2 cation translations should be about l0 to 15 cm-',which is clearly not observed.

The Br, and Br, lattice modes appear to be mixed tovarying degrees in the olivines since from forsterite tofayalite the frequency changes from 50 to 75 cm-' in Br,and from ll0 to 175 cm-' in Brr. In addition, the mon-ticellite modes are not intermediate in frequency, sug-gesting a strong dependence on volume or other effectsfor these modes. Interpretation of the spectra would re-quire Raman spectra of olivines of intermediate compo-

CHOPELAS: RAMAN SPECTRA OF OLIVINES

sitions and a single crystal study of ^y-CarSiOo to definethe frequency trends and reveal any two-mode behavior.These are interpreted as mixed modes but are estimatedto have the largest contribution (noted in brackets in Ta-ble 2) by comparison with modes in other symmetries,in the absence of further experiments that could betterexplain the observations.

In comparing the frequencies of the various mode cat-egories, the frequency ranges for forsterite and fayalitefound in this study are seen to be similar to those foundfor the infrared spectra of Hofmeister (1987). These arealso the frequency ranges that lead to the best match ofthe calculated heat capacity and entropy with calorimet-ric data (see Hofmeister, 1987; Chopelas, 1990), suggest-ing that not only can accurate spectral data yield good

estimates of thermodynamic properties but the oppositemay also be true: that accurate thermodynamic proper-

ties can be used to estimate spectral properties. Moredetails regarding the thermodynamics of olivines will bepresented in a subsequent paper (Chopelas and Hofmeis-ter, in preparation).

AcrNowr.BncMENTS

I thank A.M. Hofmeister for valuable discussions and contribution of

the monticellite and natural fayalite samples for this study; R.J. Hemley

for contributing the synthetic fayalite; and Ph. Gillet, R. Boehler, and an

anonymous reviewer for helpful comments on the manuscript.

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MaNuscnrsr RECETVED Mev 29, 1990MaNuscnrrr ACcEFTED Apxrl 9, l99l

CHOPELAS: RAMAN SPECTRA OF OLIVINES