Single-Crystal IR Spectroscopy of Grossular-Andradite Garnets

American Mineralogist, Volume 80, pages I 145-1 156, 1995

Single-crystalIR spectroscopyof grossular-andraditegarnets

B. P. McAlooN Department of Geology, University of California, Davis, California 95616, U.S.A. A. M. florurrsrnn Department of Earth and Planetary Sciences,Washington University, St. Louis, Missouri 63131, U.S.A.

Ansrnlcr Fe3+-Al3+substitution in the octahedral site of 14 natural garnet sampleswas investigated through measurement of complete single-crystal infrared (IR) reflectancespectra across the grossular-andradite[Car(Al,Fe,-")rSirO,r] binary. Frequenciesof all 17 IR- active fundamental modes depend nearly linearly on composition. Two peaksassigned to translations of the octahedralcations againstthe O framework exhibit two-mode behavior. Observation of similar frequenciesfor bands involving Al and Fe3+and of much larger intensities for bands associatedwith Fe3+suggests that the Fe-O bond has greaterstrength, which compensatesfor the greater mass of Fe. The nearly linear behavior of the modes indicates that mixing should approach ideality for this series,as was previously observed in thermodynamic studies. The existence of ideal mixing suggeststhat high degreesof ordering are not present, and thus that ordering might not causethe anomaious birefrin- genceassociated with this series.

Iwrnooucrrorv Frequenciesof the l7 garnet IR-active fundamentals(lat- The garnet structure(e.g., Novak and Gibbs, l97l) is tice vibrations) depend approximately linearly on com- ideal for the study of solid-solution behavior of vibra- position, which is consistentwith ideal mixing. tional modes owing to its high (i.e., cubic) symmetry and to the variety of chemical substitutions possible.Spectro- ExpnnrunrtrAt- METHoDS scopic studies of solid solutions are motivated by (l) the Compositional analyseswere obtained with a Cameca observation that macroscopicproperties vary nonlinearly SX-50 electron microprobe using a 15 keV acceleration with some compositional series(e.g., Ganguly and Sax- voltage, 20 nA sample current, and 40 s counting times. ena, 1987),(2) the existenceof modelsthat allow for cal- Natural mineral standardswere used. Compositional maps culation of macroscopicproperties from microscopic be- based on microprobe data were drawn for samples dis- havior (e.g., Kieffer, 1979), and,(3) the insight provided playing zonation; such samples were used for IR mea- by infrared (IR) vibrations into the nature of the chemical surementsonly if a homogeneousarea of at least 150 x bond. The grossular-andradite[Car(Al,Fe,,)rSirO,r] bi- 150 pm existed. nary is of interest becausefor this seriesthe bulk modulus Infrared reflectancespectra were obtained at ambient appearsto be nonlinear (Bass,1986), yet shearmodulus temperatureand 1.0 or 2.0 cm-I resolution using an (Bass,1986) and lattice parameterdepend almost linearly evacuated Bomem DA3.02 Fourier Transform Interfer- on composition (Huckenholz et al., 1974), and other ex- ometer (FTIR) equipped with a mercury cadmium tel- perimental and theoretical studiessuggest essentially ide- luride detector and a KBr beamsplitter for the range450- al mixing (e.g.,Holdaway,1972; Ganguly, 1976; Perchuk 4000 cm-' and with a Si bolometer and various Mylar and Aranovich, 1979;Bird and Helgeson,1980). beamsplitters for wavelengthsbelow 600 cm '. Spectra Previously,McAloon and Hofmeister(1993) obtained were collected from singly polished sampleswith random spectra from three end-member samples and an inter- crystal orientation and sizesranging from -0.25 x 0.25 mediate, upon which crystallographic refinements had x 0.03 mm to -12.0 x 14.0 mm using a Spectratech been performed, to investigate the effect of ordering on FTIR microscope.Doubly polished sectionswere not used IR spectra of garnets. This study presents complete IR to avoid multiple reflections.A Kramers-Kronig analysis reflectancedata for 14 natural samplesthat lie closeto or (e.g.,Andermann et al., 1965)was performedon merged on the grossular-andradite(Gr-An) binary. Natural sam- reflectancespectra [see Hofmeister and Chopelas(1991) ples were used despite some uncertainties in the site oc- for procedural detailsl. Longitudinal optic (LO) peak po- cupancy, becausereflectance measurements from single sitions were obtained from minima in the imaginary part crystalsare complete and quantitative. It is not necessary of the dielectric function im[/(e, + ier)], and transverse to obtain absorption spectra becausethese data can be optic (TO) peak positions were obtained from maxima in extracted from reflectancespectra (e.g., Wooten, 1972). the dielectric function er. Absorptivity was calculated from 0003-o04x/95l1I l2-l 145$02.00 tt45 tr46 MCALOON AND HOFMEISTER: IR SPECTRA OF GARNETS

TlaLe 1. Sampledescriptions

Thick- Approx. Retardation. ness Source,cat. Sample comp. Color of hand sample (mrm) (mm) Birefringence* Locality no."

43 Gr, yellow-green 950 0.658 0.001undulatory Stanley Butte, Graham 1, bulk "Anr.. Co., AZ 19 G16Ane4t dk. brown 0.0051 Sonoma Mt. Range, NV 2I 33 GrBAne2 green-brown 50 0.01 0.005spotty Franklin,NJ 3, 9925 25 G11r7Ans3+ green 1700 0.697 0.002spotty Santa Rita Peak, San 3,24144 Benito Co.. CA 41 G1122An67 r+ yellow-green 1100 0.284 0.004spotty Clear Creek. San Benito 1, bulk Co., CA 44 Gr*Anr, green 1100 0.395 0.003spotty Dan rin Mine District, 4, OA593 Inyo Co., CA 52 Gr""Anu, pale green cloudy$ 0.897 0.01 Dan /in Mine District, 4,203 Inyo Co., CA Gr4eAn51 dk. brown deepcolor$ 0.871 $ Garnet Hill, Calaveras 3, bulk Co., CA M GrqAn6ll green 0.01ll Munam, North Korea 5, GRR1411 27 GrrlAn2e dk. brown deepcolor$ 1.s3s $ Bishop, Inyo Co., CA 3,5183 28 GrsoAn20 It. brown, orange 330 0.841 0.0004undulatory Mussa Alp, Piedmont, 3, s1s3 Italy 51 Gr.,An. white, colorless 300 1.073 0.0003spotty Lake Jaco, Mexico 6, SM888 24 Gr.uAnu white, colorless 1100 1.089 0.001undulatory Cerro los Muertos, 3, bulk Chihuahua,Mexico 12 GrseAnr# white, colorless 160 0.540 0.0003undulatory Asbestos, Quebec, 7# Canada

Note.' Compositionsare normalizedto end-members(Ca2+,Mn2+,Fe,+,M9,+)3A12(Si,Ti)3O1r-Cas(Fe3*,Cr3+)r(Si,Ti).O,". See text tor discussion. - Retardation and biretringenceare average values from unorientedsamples. Birefringencevalue for sample 52 is from Eastman(1980). ** Source referencesare as follows: 1 : J. de Mouthe, Califomia Academy of Sciences,San Francisco,CA; 2 : J. Downs, Ohio State University, Columbus, OH (sample obtained from Ernest G. Ehler's personal collection at Ohio State University);3 : A. Kampf and D. Eatough, Los Angeles County National History Museum, Los Angeles,CA; 4 = H. Eastman, Bond Gold, Denver,CO (a descriptionof the sample is given by Eastman,1980); 5 : G. Rossman, California Institute of Technology, Earth and Planetary Sciences Division, Pasadena,CA; $ : Universityot Califomia, Davis, CA; 7 : F. Allen, EngelhardCorporation, Edison, NJ. Uncatalogedmaterials are referredto by "bulk." t Kingmaand Downs(1989). f More figures are reported than are significantto differentiatesamples 25 and 41. $ These samples were too darkly colored or opaque (cloudy)with fluid inclusionsto ascertain retardation. ll G.R. Rossman(personal communication). See also Takeuchiet al. (1982)and Rossmanand Aines(1991). # Allenand Buseck(1988).

a(v) : 2me,(v)/n(v) (l) Crrpvrrclr coMposrrloN where d is absorptivity, ,4is the index of refraction (cal- Fifty-two natural singlecrystals were obtained from the culated from the reflectivity; see,e.g., Wooten, 1972), and individuals listed in Table I and in the Acknowledgments z is frequency. An ambient-temperature, deuterated or from the University of California, Davis, collec- triglycine sulfate detector and a 6 or 12 p.m Mylar beam- tion. Only samples with minimal (<30/o total) pyrope- splitter were used to obtain supplementary far-IR ab- almandine-spessartine[(Mg,Fe,Mn), Al, Si, O,, ] and sorption data from powder dispersed in petroleum jelly uvarovite (CarCrrSirO,r) components were used for IR on a polyethylene card. Uncertainties in peak positions study. Fourteen of the samples (Table l) met these of + l-0.01 cm-r are relatedto peak widths (or estima- criteria and adequately covered the grossular-andradite tions of shoulder positions) becausethe accuracy of the binary. Average chemical analysesare reported in Table FTIR spectrometeris an order of magnitude smaller. 2. [Previously published analyses are summarized in Crystals were polished and examined with a petro- Table l. The Munam sample is slightly off the binary graphicmicroscope. Average optical retardation(A in units with a reported composition of (Ca, n,Mnoor- of 10-6 mm) was estimated visually by comparison with F{.S"XAI,rrFefljrTioor)(Si2e7Al0o3)O,2: Takeuchi et al., a Michel-Levy interference color chart. Becauseof the 1982.1Individual microprobe analysesand data for the variable and undulatory nature of birefringence,a more other samplesmay be obtained from the authors. One of precise quantitative measurementof the small amounts the 14 samplesinvestigated may be problematic: sample of retardation using a Berek compensatorwas not possi- 25 is Si deficient and has a low total weight percent. ble. Birefringence (D)was calculatedwith the formula Small amounts of H have been detected in samples from some of the same localities investigatedhere. From 6 : nz - l06Nt (2) \: the study of Rossmanand Aines (1991), it is probable (e.9.,Kerr, 1977),where n is the index of refractionand that sample5l has 0.04 wto/oH2O, M has 0.08 ttrto/o,24 / is the thickness in millimeters. Thicknesseswere mea- has0.1 | wto/o,44and 52 have0.20 vto/o,28has 0.37 wto/o sured with a digital micrometer. H,O, and l2 has 0.08-0.38 wto/oHrO. From the study of MCALOON AND HOFMEISTER: IR SPECTRA OF GARNETS tt47

TABLE2. Average microprobe analyses

Sample 43 33 25 41 44 52 3s 27 28 51 24 Pointssampled 96223433 43 53 31 10 14 Orides (wto6). sio, 34.s4(15)35.07(20) 33.07(30)34.44(36) 36.32(39) 36.10(8) 37(9) 37.50(48)38.34(24) 38.93(15)39.73(24) Tio, o.o2(2) 0.10(5) 0.02(2) 0.06(6) 0.69(25) 0.38(14) 0.61(16) 0.78{12) 0.s0(13) 0.70(10) 0.01(3) Al,o3 0.31(22) 1.58(26) 2.45(12) 2.53(15) 5.96(96) 8.31(45) 10(2) 15.56(26)17.42(411 20.13(20)20.89(17) CrrO" 0.02(3) 0.01(2) 0.01(2) 0.02(2) 0.03(2) 0.03(2) 0.03(4) 0.03(3) 0.01(2) 0.01(1) 0.01(2) FerO. 30.75(29)28.92(47) 27.55(21)27.3q19) 22(11 19.58(76) 1s(4) 8.56(45) 6.42(59) 3.15(17) 1.78(30) Mgo 0.03(2) 0.03(2) 0.19(3) 0.175(5) 0.14(8) 0.10(3) 0.08(3) 0.06(2) 0.23(6) 0.81(8) 0.37(3) CaO 32.34(23)33.01(31) 34.05(21)32.90(44) 32.76(221 34.74(18) 33(s) 34.06(38)35.49(40) 37.11(18)37.02(31) MnO 0.15(5) 0.73(31) 0.06(6) 0.02(4) 0.44(3) 0.35(9) 0.76(22) 1.12(19) 0.33(7) 0.10(2) 0.08(8) FeO-' 1.03(36) 0.22(26) 1.23(36) 0.98(34) 0.47(431 0.87(13) 0.7(5) 1.35(38) 0.40(31) 0.04(5) 0.00(0) Total e9.s7(69) 99.69(s6)98.62(59)98.46(27) 98.76(24)100.46(24) 97.28(58) e9(1) 99.13(49)100.97(39) 99.90(39) Cation3t si 5.953 5.929 5.692 5.876 6.007 s.854 6.030 5.919 5.957 5.871 6.007 Ti 0.003 0.012 0.002 0.007 0.086 0.046 0.075 0.093 0.058 0.096 0.002 AI 0.063 0.316 0.497 0.508 1.161 1.589 1.917 2.895 3.190 3.577 3.724 Cr 0.003 0.0015 0.002 0.002 0.003 0.003 0.003 0.003 0.001 0.001 0.001 Fe3+" 4.088 3.711 3.745 3.649 2.799 2.507 2.019 1.195 0.803 0.362 0.203 Mg 0.007 0.008 0.048 0.045 0.035 0.025 0.020 0.015 0.053 0.182 0.083 Ca 5.903 5.979 6.279 6.015 5.806 6.036 5.799 s.761 5.908 s.995 5.998 Mn 0.021 0.105 0.009 0.003 0.061 0.048 0.107 0.150 0.043 0.012 0.014 Al+Cr+Fe3+ 4.154 4.029 4.244 4.159 3.963 4.099 3.939 4.093 3.994 3.940 3.928 Ca+Mg+Mn 5.931 6.092 6.336 6.063 5.902 6.109 5.926 s.926 6.004 6.189 6.095 Component3(mol%)" Uv 0.1 0.04 0.0s 0.05 0.08 0.07 0.1 0.1 0.02 o.o2 0.03 An 98.4 92.1 88.2 87.7 70.6 61.2 51.3 29.2 20.1 9.2 5.0 Gr 1.0 6.0 10.8 11.4 27.7 37.6 46.5 67.9 78.3 87.6 93.4 Py 0.1 0.1 0.8 0.74 0.6 0.4 0.3 0.3 0.9 2.9 1.4 Sp 0.3 1.7 0.1 0.06 1.02 0.8 1.8 2.5 0.7 0.2 0.2 'The mean and standard deviation are reported. ". The algorithm used for our microprobe program provides for some Ferr*(by filling the dodecahedralsite before filling the octahedralsite). t In the recalculation.all Fe was assumed to be F€P+.Se€ t6xt for discussion.

Santa Rita Peak garnersby Lager et al. (1989), it is prob- the problematic chemistry of sample 25,we decided that able that sample 25 has more OH, with -0.4-2.9 wto/o it was not worthwhile to pursue further measurementsof HrO (estimated using extinction coemcientsappropriate the sample's OH signature. to grossular).For comparison, absorptivities were calcu- Site occupancieswere assumedto be as follows: (l) For lated from our reflectivity data. Intense absorptions were simplicity, Ti was assignedto the tetrahedral site. The Ti seenat 3553 and 3597 cm ' in the OH stretching region of sample 25 (Fig. l). The intensity pattern and peak 000 positions are similar to those observedfor samplesfrom HrO Region the same locality (Lager et al., 1989) and to those observed for two other andradite samples(Armbruster and 800 E Geiger, 1993).OH stretchingbands were not resolved for tr any of our other samples:Figure I shows the spectrum 600 - for sample 27, which is typical. It appearsthat the low * .= HrO contents (less than about 0.4 wt0/oHrO) previously 4oo.= garnets (Rossman measuredfor from theselocalities and CL Aines, l99l) are difficult to detect from reflectivity measurements.The HrO content for sample 25 obtained from zoo8 lt the calculated reflectance(Fig. l) using the calibration of Rossmanand Aines (1991)for grossularitewas absurdly 000 high, l8 wto/oHrO, compared with the content of l 4 wto/o ...-tr*,'^."""';7^ HrO surmised from the microprobe analysis of this an- 00 (its An is Table 2). The dradite content 880/0, extinction 3000 3200 3400 3600 3800 4000 coefrcient for OH in andradite is possibly an order of Frequency, cf,-l magnitude larger than that in grossularite.Given the bi- modal appearanceof the OH spectra (strong OH peaks Fig. 1. SingJe-crystalreflectance spectra and calculated ab- for sample 25 vs. negligible absorptions for the others), sorptivities in the near-IR region for representativesamples. Sol- the lack of a suitable calibration for OH in andradite, and id line. samole 25. Dotted line. sample 27. I 148 MCALOON AND HOFMEISTER: IR SPECTRA OF GARNETS may be located in the octahedral site with Al in the tet- an optical figure was difrcult to seebecause of the spatial rahedralsite for chargecompensation (e.g., Dowty, l97l; variation of the birefringence. Complex optical textures Deer et al., 1982 Huggins et al., 1977a, 1977b; Schwartz have been previously reported (Akizuki, I 984), including et al., 1980);however, for the low TiO, contentsencoun- bow-tie patterns(Allen and Buseck,1988). Thus, the op- tered here (about one-half of the sampleshave between tical properties of these samples appear to be typical of 0.4 and 0.8 wt0l0,and the remainder have below 0.I wto/o), grossular-andradite. partitioning of Ti among any of the sitesnegligibly affects A weak dependenceof birefringenceon composition is the recalculation. (2) All Fe was assumedto be Fe3+in indicated for this suite. Grossular-rich sampleshave the the octahedral site, except in the case of a few samples lowest values,0 : 0.0004-0.001;andradite-rich garnets with overfilled octahedral sites (discussedbelow). Fer* have moderatevalues, d : 0.001-0.0050; and samples was not determined from spectralmeasurements because near the midpoint of the binary have the highest bire- we were not equipped to measure Fe2+ d-d transitions fringences,d : 0.0100 (seeTable 1; Foord and Mills, near 1000 nm. High concentrations of Fe2+are not sug- 1978;Kingma and Downs, 1989).This correlationis ten- gestedby the color; the yellow-greencolor ofgrandites is tative owing to the small number of samplesinvestigated. due to Fe3+, whereasthe dark brown and orange colors of hand specimensare associatedwith high Mn contents Rrsur,rs (G. R. Rossman, 1993 personal communication). Speci- IR reflectancespectra ation as exclusively Fe3+ appears reasonable for most All 14 garnet samplesexamined have intensity patterns samplesbecause the dodecahedralsite is filled by the di- (Fig. 2) characteristicof IR reflectancespectra for silicate valent cations Ca, Mg, and Mn (Table 2). Samples43, garnets(cf. Hofmeister and Chopelas,l99l). [Spectraof 25,41, and 27 could have some Fe2+because the octa- samples 19 and 12 are found in McAloon and Hofmeister hedral site is overfilled in comparison with the dodeca- ( I 993). Theseare not repeatedhere because they are nearly (Table hedral site 2). If we set the sum of Al + Cr * Fe3+ the sameas thoseof samples24 and 43.1All l7 IR bands equal to 4 and assignexcess Fe to the dodecahedralsite, expectedfrom symmetry analysisare observedin andra- then the An contents of the three Fe-rich sampleschange dite-rich samples(sample 43 has l5 strongbands and two (for negligibly sample 43, An becomes 98.35 molo/oin- shoulders). whereas 15 obvious modes and one weak steadof 98.42; for sample41, An becomes87.25 molo/o shoulder (at 425 cm-t) are seenin grossular-richsamples. insteadof 87.73;and for sample25, An becomes87.53 Peaksare labeled accordingto the nomenclatureof Tarte molo/oinstead of 88.24). However, allowing for Fe2+for (1965)and Moore et al. (1971). the Fe-poor sample27 changesthe An content from29.20 The weak peaks in Figure 2 were confirmed in far-IR to 27.55 molo/0. powder absorbance spectra. These data are not shown The samples(Table 2) are closeto the grossular-andra- becauseno new featureswere revealed. Similarly, single- dite binary. To arrive at the binary compositions of Table crystal absorbancespectra previously obtained from sam- l, the uvarovite and andradite contents ofTable 2 were ples 12 and 19 (McAloon and Hofmeister, 1993) also summed. This approximation is reasonablebecause all agreewith the reflectivity spectraof thesesamples. samples contain <0.03 wto/oCrrO. and becauseCr and The signal-to-noise ratio of the reflectancespectra is Fe are similar in mass. Also, pyrope, almandine, and generally very high (Fig. 2). The small amount of noise spessartinecontents were added to the grossularcontent seenin most spectranear 100 cm I is due to low absolute of Table 2 to arrive at the binary representationof Table transmission near the spectral limits of the detector and l. The approximationof our seriesas (Ca2*,Mn2*,Mgr*, beamsplitter. The spectrum of sample 19 is noisy near + +,Cr3+,Al)r Fe' )rAlr Si,O, rCa,(Fe3 Si,O,, is reasonable 600-650 cm I becausea small area was sampled during pyrope, becausethe sums of the almandine, and spessar- acquisition of mid-IR data. Noise below 200 cm-' for tine components are all <3.1 mol0/0,and most are below sample 4l is the result of diffraction becausethe sample's (although I .5 molo/o sample 27 could have up to 5.7 molo/o 100 pm dimension is near the wavelengths of the im- if Fe2+ is truly present), and becausethe focus of this pinging light. study is on Al-Fe substitution in the octahedral site. The dielectric functions obtained through Kramers- The effect of impurities on our spectral data and the Kronig analysis (Fig. 3) are well behaved (see,e.g., the above uncertainties in site occupancy will be accounted ideal casespresented by Wooten, 1972) and, similar to for in the subsequentanalysis. those measured previously for garnets.l Figure 3 shows representativecases and the samplesfor which the intensity patterns varied the most. The andradite-rich samples Orrrcar. pRopEnrrEs (43, 19, and 33) have dielectric functions that are similar All samplesare birefringent (Table l). The degreevar- ies by two orders of magnitude: Dranges from 0.0004 to ' 0.01. The values for the birefringenceare comparable to A copyof Figure3 in its entiretymay be obtainedfrom the authors request.It may previous measurements(see summary by Meagher, upon alsobe orderedas Document AM- 1982). 95-601from theBusiness Ofrce, Mineralogical Society of Amer- The Darwin garnetsare biaxial (Foord and Mills, 1978; ica, 1015Eighteenth Street Nw, Suite 601, Washington,DC Eastman,1980); however, for most of the other samples 20036,U.S.A. Please remit $5.00in advancefor the microfiche. MCALOON AND HOFMEISTER: IR SPECTRA OF GARNETS rt49

2. 2.5

.= = .= o (tz g -9 o iFo E E 1. 1.5

0.5 0.5

0 2000 400 600 8001000 0 200 400 600 8001000 Frequency,cm'1 Frequency, cm'l

Fig.2. Single-crystalreflectance spectra for grossular-rich (a) and andradite-rich (b) binary samples. Grossular (Gr) content (center)is given for each sample number (far right). Fundamental modes are labeled for representativesamples. Noise is presentin somespectra near 100,200, or 600 cm-r. to those of sample 25 but with sharper peaks. The gros- intense for this garnet. The amount of impurity ions may sular-rich samples(28, 51, 24, and 12) have dielectric enhance the resonancesgiven that sample 5l has the functions that are similar to those of sample 27 but with strongestcombination bands and the highest sum of py- sharperpeaks. Spectra from samples12, 19, and M shown rope and spessartinecontents (3.10/o),whereas the other in McAloon and Hofmeister(1993) are not repeatedhere. samplesthat show strong combination peaks(samples 27 Their dielectric functions are similar to those of samples and 35) have the secondhighest sums (2.8 and 2.lo/o). 24,43, and 35, respectively. Sample 25 has an overtone at 672 cm-t , but this peak All samplesbetween 8 and 92 molo/oGr display a fea- appearsto be the result ofa different set ofcombinations, ture near 750 cm-'. This feature is probably an overtone e.g.,368 + 292 : 660,343+ 326 : 669,and 432 + 250 becausecombinations of lower frequency fundamentals : 682 cm-t; thus, the overtone of sample 25 should not in affected samplesare found yielding such a feature. In be compared with those of the remaining samples. sample 27, for example, possible combinations are 407 dependenceof IR modes + 351: 758,381.8 + 381.8:763.6,461.8 + 290.2: Compositional 752.0, and 611.8 + 151.5: 763.3 cm-t; similar com- For the most part, the intensity pattern gradually binations hold for the other samplesas well. For sample changesfrom that of andradite to that of grossular(Figs. 51, the peakat 758 cm-' is more intensethan is generally 2 and 3). Different peaks are affectedto varying degrees. expectedfor an overtone. However, overtones superim- Specifically,the high-frequencystretching modes are little posedon the stretchingpeaks near 900 cm-' are also very affected. Peaks near 400-500 cm-' become better sepa- l 150 MCALOON AND HOFMEISTER: IR SPECTRA OF GARNETS

60 50 0.5 0 E50 0 C' c40 E -rE Eco -0.5 J teo lr -2 ,i -l ,, 3o u2o -3 '= -1.5 E20 o -4E Ero -2 L5ro 6o -2.5 -5 0 -10 -3 200 400 600 800 1000 1200 200 400 600 800 1000 1200 Frequency, cm'1 Frequency, cm't

30 25 0 =25 -l o 820 820 (, -2 E 5 ts -3 ,i 1s GrrnAn' L (' -4 .3ro E10 o -5 o5 -g .9 OE -6 o0 ct -7 -5 0 200 400 600 800.1000 1200 200 400 600 800 1000 1200 Frequency, cm't Frequency, cm'l

30 30 1 .25 0 'l/ o 52s 3s ll im(l/e) im(1/e) -1 -2 Ezo 2zo c -2 f Il E rs GrorAnu, -4 -3 ., 15 '3 L ro -6 (, -4 E 10 OE o .9 -5 -8 i5s E" o0 -6 0 -10 -5 -7 0 200 400 600 800 1000 1200 0 200 400 600 800 10001200 Frequency, cm-l Frequency,cfi'l

Fig. 3. The dielectric functions e, and imaginary parts im(l/e) of the grossular-andraditesamples. Grossular (Gr) content is given for each sample number (upper left). Sample numbers 12, 19, and M can be seen in McAloon and Hofmeister (1993). Sample numbers 12,24, 51,28,M,33, 19, and 43 have beendeposired. rated as the An content increases.Intensity generally in- middle of the binary. Another very weak mode (Jo) is creasesnear 300-375 cm-r from sample35 (490loGr) to presentin grossularbut cannot be tracedcompletely across andradite. Intensity of the low-frequency peaksdecreases the binary. We attempted to quantify the above relation- from grossular to the middle of the binary and then in- ships from both the raw data (Fig. 2) and the dielectric creasesagain. Two modes (Joand O) decreasein intensity functions (Fig. 3) but did not find a strong correlation as Gr content increases,eventually disappearingnear the between relative or absolute intensity and composition. McALOON AND HOFMEISTER: IR SPECTRA OF GARNETS I l5l

Tlele 3. High-frequencylR peak positions(cm-1) of Ca.(Fe,Al)rSi.O12garnets

ModeBCDOvertoneEF Assiqnment:. 13 - Normailzeo Sample comp. (% Gr) LO TO LO TO LO TO 43 1.5 981.7* 879.7 819.5 825.2 857.9 807.4 590.7 589.s 531.9506.1 19 6 988.0 884.6 823.8 830.s 861.6 811.9 594.6 590.7 536.1 510.6 338 983.6 880.3 822.4 826.3 860.8 806.7 593.2 592.0(0.2)533.9 507.5 25 11.71 980.5 879.9 821.0 -818 859.5 804.3 671 672.7(0.31590.6 588.5 533.6 502.7 41 12.21 987.8 883.7 819.5 821.0 859.5 810.7 745 744 591.3 s90.0(0.5)536.0 509.1 44 29 988.7 886.4 827.4(0.5) 82s.3(0.5)863.2 813.7 743.8(0.3)743.9 597.5 s96.0 540.3 514.8 52 39 989.4 888.2 828.3 833.2 865.9 814.9 745.s(0.21746 600.2 597.8 541.8514.6 35 49 994.5 893.8 836.3 837.s(0.5)873.8 818.3 751.2 751.1(0.2) 607.9 604.5 551.3521.9 M (Munam)64 1000.3 900.3 -841 841.0 878(2) 825.6 752.4 752.3 612(2)607.8 558.4 529.2 27 71 1001.0 903.5 845 846.1(0.5) 880.5 829.5 758.7(0.21758.0(0.5) 615.9 611.8 562.8 532.4 28 80 1001.0 902.4 846.1 848.5 880.9 829.3 758.5(0.2)758.6 617.6 613.2 566.5 532.9 51 91 1007.8 903.9 849.1(0.s) 8s0(1) 882.7 833.2 758.7 757.8 620.1 614.9 572.4 536.3 24 95 1004.9 905.4 850.0 854.0 883.7 835.1 622.2 617.0 574.6 538.8 12 99 1007.4 907.8 851.4 8s6.3 884.7 837.7 623.8 618.0 576.2 539.8 the SiOl 'Assignments are based on those lor grossular by Hofmeister and Chopelas (1991), where /3 is the asymmetric stretching motion of tetrahedron,and zois the asymmetric bending motion of the SiOl tetrahedron. -- The uncertainty in the last digit is +1 unless indicateddifferently' t More figures are reported than are significantto differentiatesamples 25 and 41.

The intensities display a zig-zagpattern with composition dinated Fe2+,and thus their compositionsmay not be (not shown) possibly becauseof changes in mixing of correctly representedby the approximations in Table l. modes acrossthe binary. Some of the departures from linearity in Figure 4 could Peak positions (Tables 3-5) increasealmost uniformly result from differences between the true and assumed with grossular content. kast-squares analysesindicate that site occupancies. the TO mode frequencies depend linearly on g,rossular content (Fig. a). Thus, frequencyalso dependslinearly on Drscussrox AND coNclusroNs Al or Fe content or on the Al/(Al + Fe3+) ratio. The slopesrange from 0. l8 to 0.69 cm-'/molo/oGr, but most Two-mode behavior lie near 0.3 cm-'/mol0/oGr (Table 6). The highestslopes For some solid solutions, IR peak positions vary as well as the greatestdepartures from nonlinearity occur smoothly with composition along the seriesmuch like the for the closelyspaced, intense bands near 250-450 cm-', Vegard law behavior in X-ray diffraction (one-mode be- which probably interact and henceare mixed modes. The havior). In other solid solutions, bands appear that are three peaks that cannot be traced completely acrossthe characteristic of each end-member. These may vary in series (Jo, Jo, and O) also depend linearly on peak position, but the main changeis in relative intensity composition. with composition along the series(two-mode behavior). Sample 25 at ll.7 molo/oGr lies below the trends of Two-mode behavior originates in local modes and is ex- virtually all peaks. The much lower frequenciesof this pected if substantial differencesexist betweenthe masses sample compared with those of sample 41, with similar of substituting ions or betweenthe force constants(Chang grossular content (12.2 molo/o),are seen both in the di- and Mitra. 1968)and if end-memberbands do not over- electric functions obtained from Kramers-Kronig analy- lap (Fertel and Perry, 1979).ln complex structures(e.9.' ses (Fig. 3) and in the raw data (Fig. 2). Sample 25 ap- perovskites)some bands may exhibit one-modebehavior parently includes a substantial hydrogarnet substitution while other bands exhibit two-mode behavior (Barker et as shown in the near-IR spectrum (Fig. l) and because al., 1968). Two-mode behavior was reported for trans- the amount of Si detecteddoes not fill the site (Table 2). lations of the SiO4tetrahedron in solid solutions between The amount of OH- cannot be quantified from spectros- grossular and pyrope (or almandine) garnet (Hofmeister copy becauseto our knowledgean appropriate calibration and Chopelas,l99l) and for the stretchingmodes and is not available. We attribute the lower frequenciesfor translations of the tetrahedra for solid solutions between sample 25 to its departure from the grossular-andradite Y3Al2Al3Or2and MnrAlrSirO,, (Lu et al., 1993)' binary. In particular, the OH- substitution servesto ex- For grossular-andraditesolid solutions' large mass dif- pand the lattice, even for percent-levelconcentrations (see, ferencesbetween Al and Fe could cause two-mode be- e.g., Lager et al., 1989, and the following discussion). havior. The disappearancesof modes O' Jo, and Jo as Hence the observed low frequencies for sample 25 ate composition progressesare compatible with two-mode consistent with a significant hydrogarnet substitution. behavior. The two higher frequency and higher intensity Some of the remaining samplescould also have tetra- peaksconstitute one pair. Mode O in andradite-rich com- hedrally coordinated Al or Fe3+or dodecahedrallycoor- positions is probably correlated with mode N in grossu- lt52 MCALOON AND HOFMEISTER: IR SPECTRA OF GARNETS

T^BLe4' Intermediatefrequency lR peakpositions (cm-l) of ca.(Fe,Al)rsi.o12garnets ModeGHl Assignment' vr Normalized T(oct) u2 Sample comp. (% cr) LO TO LO TO LO TO 43 1.5 484.3f 477.4 455.9 431.6 415.6 374.4 19 6 488.3 480.3 461.3 435.2 419.9 378.6 33 8 486.8 479.O 462.4 434.0 42't.4 375.8 25 11.7+ 488.1 473.7 460.6 432.7 417.1 368.0 41 12.2+ 486.8 478.9 461.6 436.5 420.5 377.7 44 29 470.4 482.9 429.3 442.6 491.1 400.6 52 39 473.7 483.5 434.5 441.7 493.9 396.1 35 49 485.3 488.7 447.7 451.2 501.5 408.3 M (Munam) 64 494 494.3 456.9 459.2 510.8 419.8 27 71 497 494.1 458.9(0.2) 461.8 513.9 424.1 28 80 498 498 462.4 464.3 518.3 425.7 51 91 502.1 501.6(0.2) 465.2 467.0 523.5 431.8 24 95 503.8 503.8 467.8 469 526.2 433.9 12 99 506.0 506.0 469.5 470.6 529.4 434.9

)hopelas (1991), where zn is the asymmetric bending motion of the SiOl loct) is a translation of the octahedrallycoordinated cations against the O

25 and 41. lar, which was inferred to be a doublet from comparison (Hofmeisterand Chopelas,l99l) for modes H, I, K, N, with the other aluminous garnets (Hofmeister and Cho- R, Q, P, and O in andradite be revised (Tables 4 and 5). pelas, l99l). All other peaksfollow classicalone-mode The old assignmentswere made by pairing peaksin gros- behavior. The reasonfor different behavior ofthe various sular and andradite,which was difrcult becausetwo peaks garnet modes in is explicit in the band assignments,as are missing for grossular.The connection of IR peaks to discussedin the following sections. atomic motions is a first approximation in which mode mixing is assumedto be negligible.We do not imply Band assignrnents that the contributions of atomic motions from individual sites Assignments of the observed IR peaks to atomic mo- in garnet representlocalized vibrations. tions are basedon symmetry analysis(Moore et al., 197l), Two-mode behavior (discussedabove) is observed for previous IR data on chemical substitutions among gar- two bands only. This behavior is consistent with assign- nets(Hofmeister and Chopelas,I 99 I ), and our data (which ment of these particular bands (J and O) to translations directly link andradite and grossular peaks). The corre- of the octahedral cation (Tables 4 and 5). Other motions lation of Figure 4 requires that previous assignments predicted by symmetry analysis lack the requisite large

Trele 5. LowJrequency lR peak positions (cm-r)of Ca3(Fe,Al),Si3O12garnets ModeMONpeR Assignment- T(sioo) T(oct) T(dod) T(dod) T(dod) T(sio4)" Nonrarized _ sample comp.(% Gr) Lo To Lo To Lo ro Lo ro Lo ro Lo ro 43 1.5 279(2ll 280(2) 245.4 244.7 214.7 212.7 190.7 187.3 151.9 151.1 132.3 -284 -279 131.4 19 6 247.5 246.4 216.7 214.0 192.1 188.4 154.2 153.0 134.7 133.7 33 8 280 ? 246.9(0.3) 216.6 213.9 192.1 188.0 154.1 153.3 134.8 133.8 25 11.7+ 274(2) 268(2) 255(21 -250 214.s 211.3 189.3 184.2 148.7 148.2 129.7 129.1 41 12.2+ 300 275 250(2) 248.6 216.2 215.3 191.2 189.0 152.0 151.8 135.2 134.8 44 29 292 287 255 -254 220.7 218.8 194.1 190.1 158.9 158.4 136.4 135.8 52 39 293 284.0 225.3 220.2 195.2 190.9 161.1 160.3 138.3 136.6 35 49 29.t(2) 287(2) 23.t.8 226.7 197.2 193.2 167.0 165.3 144.5 (Munam) 142.8 M 64 292.8 288.5 238.3 232.7 200.5 197.0 175.0 172.4 147.6 146.7 27 71 291.9(0.s)290.2 239.7 234.2 200.4 197.4 177.0 174.6 151.8 151.5 28 80 296.5 293.8 243.0 236.0 203.0 199.8 180.4 177.5 152.0 150.3(0.3) 51 91 299.0 298.0 245.7 239.5 204.3 202.2 18i,.9 181.5 153.7 153.0 24 't2 95 301.1 299.2 247.0 240.6 205.9 203.5 186.6 183.4 155.7 154.6 99 302.9 300.6 248.75 241.49 248.79 241.49 207.4 204.5 188.8 184.0 157.5 155.6 'Assignments are based on_those grossular for by Hotmeister and Chopelas (1991), where T(oct) indicates a translation of the cations in the octahedrally coordinated site, T(dod) indicates translaiions of the cations in'tne obdecdiredralinterstice, and T(sioo) indicates a translation tetrahedron. of th€ .'This mode is probabty mixed with T(dod). t The uncertainty in the last digit is +1 unless indicateddifferenfly. * More figures are reported thin are significantto differentiatesampres 2s and 41. $ Inferred to be a doublet. MCALOON AND HOFMEISTER: IR SPECTRA OF GARNETS I 153

Trete 4.-Continued

Mode K L Assignment* T(oct) R(SiO.) R(SiO.) T(oc0 Sample TO 43 355.4 348.1 322 321.s(0.5) 329.0 297.7 19 359.5 351.6 323 324.0 332.5 301.0 33 359.9 350.5 324.7(0.s| 332.8 296.9 25 353.9 343.2 330 326(2) 324.6 292.4 41 358.0 351.5 -323 -322 330.0 -302 44 400(2) 383 364.3 360.0 335.9 319.8 310(2) 305.4 52 3e4e) 368.3 357.9 339.3 -325 312(1 ) 303.9 35 -390 379.9 366.8 346.3 3i!5.9 327(2) 317(2) M (Munam) -400 390.6 377.4 354(2) 345.9 332(21 314.1 27 433(2) -407 393.0 381.8 353 3s1(2) 28 -412 396.4 383.6 3s3(2) 349.7 51 438(21 -41 6 400.0 388.4 356(1) 357(1) 24 441(21 - 419 402.8 390.0 355.8 355.7 12 450(2) 425(2\ 404.9 389.8 356.0 355.0 mass or force-constantdiference in the grossular-andra- Frequency,composition, and structure dite series.Symmetry analysis predicts that three translations involving the octahedral site should occur. The Frequency dependson atomic mass, bond length, and third octahedral translation (mode H at 432 cm-r in an- the strength ofthe chemical bond. In a series,the change dradite and 47 1 cm-r in grossular) does not meet the in the bond strength should be gradual and dependenton criteria of nonoverlapping peaks becausethe end-mem- the bond length. Hence, the observed,approximately lin- ber peaksoverlap (ifthe dependenceoffrequency on lat- ear dependence of frequency on composition (Fig. 4) tice constant is accountedfor). should be related to structural changesin the seriesbe-

44 T(oct) \, 900

800 36 'Eg2 : tTooE c) j > 928 o E c o o 5 - -- o T(oct' AN) J '41 44 52--T --: 8'600 8zq lr 25 Vc lJ. 20 500

40 20 40 60 80 100 20 40 60 80 GrossularContent, mol % GrossularContent, fF-Ol o/o

Fig. 4. IR frequencies ofglossular-andradite fundamental TO monds : T(oct), downward pointing triangles : vz, solid circles modes as a function of composition. Uncertainties in frequency : T(AD, open diamonds : T(Fe), plus signs : R, solid squares are smaller than the symbol. (a) High-frequencymodes. (b) Low- : T, Xs : T(dod). Least-squaresfits are shown as solid lines for frequency modes. Symbols: open squares : zr, squares with bands exhibiting one-mode behavior or dashed lines for two- crosses: overtone, upward pointing triangles : zo, solid dia- mode behavior. Small labels are sample numbers. I 154 MCALOON AND HOFMEISTER: IR SPECTRA OF GARNETS

Tlale 6. Linearrepresentation- ofgrossular-andradite lR modes 2.08 12.1 dvldX (cm-'/mol% Mode Assignmenr 2.06 t"rl1't GOR o B U3 879.3 0.300 0.98 2.04 o !s 821.3 0.334 0.96 < E D Ug 805.3 0.313 0.98 (! Overtone 739.4 0.223 0.95 -:o2.02 12h E 587.7 0.311 0.99 c A F 504.2 0.363 0.98 u 475.0 0.293 0.98 -9 (,o H e.oo T(oct) 430.5 0.413 0.99 t I l2 371.8 0.679 0.98 <- I O ------D ro T(AD 362.2 0.611 0.99 5 r.ge J K R 345.1 0.472 0.98 o 1.9 L n 318.4 0.391 0.95 Jo T(Fes*; 295.6 0.317 0.87 9 t.go M T 275.1 0.244 0.92 T(Fe3+) 244.6 0.334 0.97 N T(dod)-" 210.7 0.316 0.99 1.94 o' f T(dod) 185.5 '148.4 0.181 0.98 NM o r(dod) 0.362 0.99 R T 130.1 0.258 0.98 1.92 1.8 * 0 20 40 60 80 100 These parameters were obtained from least-squaresanalysis: /o is o/o the gJossularposition, dzldX is the slope, and R is the goodness Grossular Content, fitol -'For of fit. Gr-rich samples this peak is probably degeneratewith T(Al). Fig. 5. Summaryof crystallographicdata on grossular-andradite.Symbols: open squares : single-crystaldata from Novak cause the mass difference directly influences only three and Gibbs (1971);open circles : single-crystaldata from Tak- modes and is accounted for in the existence of two- euchiet al. (1982),labeledas K: Kamaishi,M : Munam,and mode behavior. NM : North Moravia;solid diamond: single-crystaldata from : Most of the existing crystallographicdata on grossular- Allen and Buseck(1988); solid triangles single-crystaldata (1989);plus : powder andradite garnets (Fig. 5) are derived from powder dif- from Kingmaand Downs signs data of Huckenholzetal. (1974);open triangles : single-crystaldata on fractometry of synthetic samples.The compositions are hydrousSanta Rita andraditeby Lageret al. (1989).Open tri- thus precise, but the data do not include bond lengths. anglesare labeledwith their OH contents(as wto/o HrO, deter- Severalsingle-crystal studies involve birefringent garnets, mined from X-ray refinements).Dashed and dotted lines are and most of these refinements utilized lower symmetry least-squaresfits to all the data.(Allen and Buseck,1988, did spacegroups. The variation in spacegroup presents no not reportY-O bondlengths.) The solidline is thetrend defined obstaclein the comparison of measurementsbecause the by andradite-richsamples. reduced-symmetry unit cells were metrically cubic or could be closely approximated by a pseudocubiccell. The study of Santa Rita andradite (Lager et al., 1989) pro- does not correlate well with the departure from linearity duced lattice constants differing considerably from the becausethe most highly ordered sample (Kamaishi gar- series(Fig. 5). The data suggestthat the lattice constant net) lies on the line (Fig. 4). The crystallographic data of sample 25 is at least as large as that of end-member appear compatible with a slight difference in slope be- andradite, which is consistent with the measuredvalues tween andradite- and grossular-rich compositions. Fre- for its frequencies(Fig. 4). The OH contents of the two quency vs. composition may also show a slight flattening Santa Rita Peak samplesshown are estimated as 0.4 and near the grossularend-member. Thus, it appearsthat fre- 2.9 wto/oHrO (Lager et al., 1989), such that the more quency correlatesdirectly with the lattice parameter and hydrated sample has the larger lattice constant.The trend that the relationship is approximately linear. clearly indicates the strong influence of OH on the struc- Cation-O bond lengths (such as those ofthe octahedra tural parametersof garnets. shown in Fig. 5) may depend linearly on grossular con- Least-squaresanalysis of all garnetsexcept the San Be- tent. However, the data are not sufficient to establish a nito samplesshows that the cubic lattice parametervaries relationship, and therefore it is premature to attempt a roughly linearly with composition (Fig. 5). The fit gives correlation offrequency with bond lengths. The linear correlation between IR peak positions lattice parameter (A) and composition of grandite gamets allows estimation : 12.055- 0.00215.cr content(molo/o) (3) of composition from vibrational spectra,given that the gar- with a goodnessoffit equalto 0.997.The departurefrom net in question is determined to be a grandite (and not linearity in Figure 5 may be associatedwith the compo- significantly hydrated) using an independentmethod (e.g., sitionsofrhe garnetsofTakeuchi er al. (1982)lying slight- color, association, or semiquantitative chemical analy- Iy off the binary becausethe Munam sample, which is sis). The most reliable indicator modes are the peaksthat situated farthest from the trend, has the largest amounts are both well resolved and fairly intense, e.g., modes B of impurities (Mn, Ti, and Fer+). The degreeof ordering or F. If powder measurementsare made, the far-IR modes MCALOON AND HOFMEISTER: IR SPECTRA OF GARNETS I 155 would serve well as tracers becausethe absorption fre- these differencesaffect compressibility, but also this par- quencies of these weak modes lie close to the TO com- ticular sampleis so far offthe binary that it simply should ponent, and thus particle size and scatteringaffect the far- not be used to establish mixing properties. IR modesthe least. Birefringence in grossular-andradite Chemical bonding Optical anomalies are present in the suite investigated The frequencies of the Fe local modes in grossular here (Table 1), as are commonly observed for grossular- should be related to the Al modes either by (mor/mr")' : andradite (Meagher, 1982). Yet, our IR data are com- 0.688, assumingthe cations vibrate againstthe O sublat- patible with the cubic garnet structure. One possibility is tice, or by Qto,-o/ttr"-")u' : 0.897,assuming the O anions that the IR spectraare not sensitiveto the Al-Fe ordering participate (p is reduced mass). (By comparing the local inferred from the crystallographicrefinements (Takeuchi modes, we eliminate the need to consider bond lengths.) et al., 1982;Allen and Buseck,1 988; Kingma and Downs, The observedratios are 0.776 for mode J couple, l.l4 1989) but visible measurementsare. The higher sensitiv- for mode O-N couple,and 1.00 for mode H (which fol- ity in the visible could be related to differencesin chem- lows one-mode behavior). Two of the Fe modes (O and ical bonding becausethe metal-O chargetransfer that oc- H) have higher frequenciesthan expected,suggesting that curs in the ultraviolet has a tail into the visible region. their bond strengths are larger. The larger intensity for However, we favor the hypothesisthat ordering may not the translations of Fe3+in andradite in comparison with be present (symmetry reduction should have increased the Al translations in grossular also suggestsstronger the number of IR bands) and strain causesthe birefrin- chemical bonding of Fe. This can probably be explained genceas discussedby McAloon and Hofmeister (1993). by the fact that the larger Fe ion fills the octahedral site (For a discussion of hypothesesother than strain or or- more fully. dering, seeMeagher, 1982.)The relationship of structural strain to composition is discussedin detail by Armbrus- Mixing properties ter and Geiger (1993); in particular, they observed that present The observed,approximately linear dependenceofthe the same amount of strain is in 11 as in la3d previous vibrational frequencieson composition (and similar be- garnets.In addition to the arguments,the ideal (e.g., havior for the lattice parameters)suggests that thermo- mixing previously observed Ganguly, 1976; Bird dynamic properties such as heat capacity and entropy and Helgeson, 1980) and inferred in this work may not follow ideal mixing laws becausethese quantities are in- be compatible with the degreesof ordering of up to 650/o (Takeuchi tegralsofvarious functions involving the vibrational fre- reported for the intermediate compositions et quencies(Kieffer, 1979). This inference agreeswith con- al.. 1982). previous (e.g., clusions of workers Holdaway, 1912; Acrt.TowLEDGMENTs Ganguly, 1976;Perchuk and Aranovich, 1979;Bird and Helgeson, 1980) that grossular-andraditebehaves essen- We heartily thank F. Allen (Engelhard Corporation, New Jersey),P. Buseck(Arizona State Universit , J. DeMouthe (California Academy of tially as an ideal ionic solution. Sciences,San Francisco),H.S. Eastman(Bond Gold Company, Colorado), Similarly, bulk moduli calculatedusing the vibrational A.R. Kampf and D.L. Eatough(Los AngelesCounty Natural History Mu- data for this seriesin Hofmeister's(1991) model would seum), K. Kingma (Johns Hopkins University), J. Downs (Ohio State also vary linearly with composition. The predicted linear University), and G.R. Rossman (California Institute of Technology)for providing dependencediffers considerably from the inference of a their help in samples.We also thank T. Fagan,S. Roeske,and R. Schaal(University ofCalifornia, Davis) for obtaining microprobe data. minimum near 22 molo/ogrossular (Bass, 1986). Even if Many thanks also to N. Winter (University of Califomia, Davis) for help we account for the slight departuresin frequencyand lat- in sample preparation. B.P.M. wishes to thank P. Kelly (University of tice parameter from a linear relationship with composi- California, Davis) for helpful comments and discussion. E. Libowitsky tion, the resultant calculatedminimum would still be less (California Institute of Technology), G.A. Lager (Jniversity of Inuis- (Swedish Natural History) are thanked propose ville), and H. Skogby Museum of than one-tenth as deep as that observed.We that ville), and H. Skogby(Swedish Museum of Natural History) are thanked the observed minimum in bulk modulus, which is de- for helpful reviews. Support was provided by the David and Lucile Pack- fined by only one sample,is an artifact resulting from the ard Foundation. variance of that particular sample'scomposition from the The sample in question is a black andradite with binary. RrrnnnNcns crrED 2.69 wto/oTiO, (Babuskaet al., 1978).Ti'* is probably octahedrally coordinated, with Al in the tetrahedra to Akizuki, M. (1984) Origin of optical variations in grossular-andradite provide charge compensation. This large amount of Ti garnet. Arnerican Mineralogist, 69, 328-338. Allen, F.M., and Buseck, P.R. (1988) XRD, FTIR, and TEM studies of (and substitution of Al for Si) is sufficient to alter the optically anisotropic grossular garnets. American Mineralogist, 73, 568- vibrational frequencies(note that sample 25 of the pres- 584. ent study with a smaller Si deficiency, Table 2, has fre- Andermann, G., Caron, A., and Dows, D.A. (1965) Kramers-Kronigdis- quenciesthat are lower than the linear trend of Fig. a). persion analysis of infrared reflectance bands. Journal of the Optical 55, 1210-1216. indicates inter- Society of America, The black color of Babuska'ssample that Armbruster, T., and Geiger, C.A. (1993) Andradite crystal chemistry, valencecharge transfer is occurring, and thus the bonding dynamic X-site disorder and structural strain in silicate garnets.Eu- may also differ for the garnet in question. Not only could ropean Journal of Mineralogy, 5, 59-7 1. 1156 MCALOON AND HOFMEISTER: IR SPECTRA OF GARNETS

Babuska,V., Fiala, J., Kumazawa, M., Ohno, L, and Sumino, J. (1978) taining silicate garnets:L The distributrion ofAl, Fe!*, and Tia+ be- Elastic properties of garnet solid-solution series.physics of the Earth tween octahedral and tetrahedral sites. American Mineralogist, 62,475- and Planetary Interiors, 16, 157 -17 6. 490. Barker, A.S., Jr., Ditzenberger,J.A., and Guggenheim,H.J. (1968) Long- - (1977b)Titanium-containing silicategarnets: II. The crystalchem- wavelength optical lattice vibrations in mixed KMg\-KNiF, crysrals. istry of melanites and schorlomites.American Mineralogist, 62,646- PhysicalReview, 175, I 180-l 190. 665. Bass,J.D. (1986) Elasticity ofuvarovite and andradite garnets.Journal of Kerr, P.F. (1977) Optical mineralogy, 492 p. McGraw-Hill, New York. GeophysicalResearch, 9 l, 7 505-7 5 16. Kiefer, S.W. (1979) Thermodynamics and lattice vibrations of minerals: Bird, D.K., and Helgeson,H.C. (1980) Chemical interactions of aqueous III. 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