Elastic properties of pyrope - Springer Link

Phys Chem Minerals (1991) 17:617-621

PHYSICSCHEMISTRY NMIflERALS 9 Springer-Verlag1991

Elastic Properties of Pyrope Bridget O'Neill ~ *, Jay D. Bass 1, George R. Rossman z, Charles A. Geiger 3 * * and Klaus Langer 3 1 Department of Geology, University of Illinois, 1301 W. Green St. Urbana, IL 61801, USA 2 Division of Geological and Planetary Sciences, California Institute of Technology, Pasadena, CA 91125, USA 3 Institut ffir Mineralogie und Kristallographie, Technische Universitfit Berlin, Ernst Reuter Platz 1, W-1000 Berlin 12, Federal Republic of Germany Received May 6, 1990

Abstract. Brillouin spectroscopy was used to measure the single crystal elastic properties of a pure synthetic pyrope and a natural garnet containing 89.9 tool% of the pyrope end member (MgaAlzSi3OI2), The elastic moduli, ci~, of the two samples are entirely consistent and agree with previous estimates of the elastic properties of pyrope based upon the moduli of solid solutions. Our results indicate that the elastic moduli of pyrope end-member are c11=296.2-t-0.5, c12=111.1_+0.6, c,~4= 91.6 _+0.3, Ks = 172.8 _+0.3, g = 92.0 +_0.2, all in units of GPa. These results differ by several percent from those reported previously for synthetic pyrope, but are based upon a much larger data set. Although the hydrous components of the two samples from the present study are substantially different, representing both 'dry' and 'saturated' samples, we find no discernable effect of structurally bound water on the elastic properties. This is due to the small absolute solubility of water in pyrope, as compared with other garnets such as grossular.

Introduction The elastic properties of garnet are of key importance for constraining appropriate models for upper mantle mineral assemblages. Garnet lherzolite models of the upper mantle contain about 15 vol% garnet, principally the pyrope end-member (Mg3A12Si3Olz), although assemblages containing greater amounts of garnet are generally compatible with seismic velocity data (Bass and Anderson 1984; Anderson and Bass 1984). Pyrope has been shown to be stable to pressures above 20 GPa (Liu 1977) and thus is of importance when modelling the transition region as well. In order to account for the * Present address: Department of Geology and Geophysics, University of California, Berkeley, CA 94720. FAX no. (415) 643-9980 ** Present address: Bayerisches Forschungsinstitut fiir Experimentelle Geochemie und Geophysik, Universit/it Bayreuth, Postfach 101251, W-8580 Bayreuth, FRG

wide compositional variations observed in garnets it is necessary to know the elastic properties of the major end-members, and to formulate mixing relations which accurately estimate the properties of garnet solid solutions. Natural pyrope samples from lower crustal highgrade metamorphic rocks or ultrabasic igneous rocks generally contain a maximum of 70-80 tool% pyrope end-member. Due to the unavailability of pure natural samples the only previous study of pyrope elasticity was performed using a synthetic sample (Leitner et al. 1980). The elasticity of pyrope has, however, been estimated by extrapolating data from natural garnets of intermediate compositions to the pure Mg end-member, following the assumption that the moduli of garnet solid solutions are linearly related to the end-member properties (Babuska et al. 1978; Isaak and Graham 1976; Leitner et al. 1980). The maximum pyrope content in the natural garnets to which this mixing model has been applied is 73.1%, rather far from the end-member. Given the scarcity of measurements on pyrope and the great abundance of this component in garnets of upper mantle origin, we have undertaken a thorough experimental study of its elastic properties. Moreover, we have chosen to measure the elastic properties of both synthetic and natural samples which have, undoubtedly, crystallized under different pressure and temperature conditions, and which have been characterized by other laboratories, particularly in terms of their volatile (e.g., H20, CO2) content. We report in this paper the single crystal elastic constants, c~j, measured by Brillouin spectroscopy, of a natural pyrope of 90% purity and compare the results with new measurements of a synthetic pyrope sample. Experiment The natural pyrope, sample GRR1266, is a water clear crystal from the Dora Maira Massif, Italy. It is part of the sample used by Rossman et al. (1989) in their study of the hydrous components in natural pyrope. Electron probe microanalysis by Rossman et al. showed a slight variation in the chemistry of the Larger sample

618 from the center to the rim, with the Fe z+ content ranging from 5.1% (rim) to 6.0% (center). The average of the three analyses reported by Rossman et al. yields a garnet composition of (Mgo.899Feo.ov6Cao.o24)A12SiaO12, and we take this to be representative of the chip used in our Brillouin experiments. A small ( ~ 2 0 0 gm) part of the Brillouin sample was used for determination of b o t h the lattice parameter and refractive index (Table 1). For comparison, the lattice parameter of a garnet solid solution can be calculated from the regression analysis of Novak and Colville (as reported by Meagher 1982). The measured and calculated lattice parameters thus obtained are in perfect agreement if the average composition given above is used, indicating that this chemical composition is appropriate for the sample we studied.

Table 1. Properties of pyrope samples GRR1266

Lattice parameter

P51

measured

reference

measured reference

11.490 (3)

11.492 (10)" 11.457 (2) 11.459 b

era- 8

Density g/cm 3 Refractive indices, nD n514

3.604 (9) ~

1.717 (5) 1.727 (5)

3.567 (1)

7.717 (5) d

1.717 (5) 1.720 (5)

1.714 b

Calculated from the regression analysis of Novak and Colville (as reported by Meagher 1982) b From Skinner (1956) c This uncertainty takes into account possible compositional variance d Calculated from: no =~nDixi, where nDi is the index of refraction of garnet end-member i (Skinner 1956), and x~ is the mole fraction present of end-member i

The index of refraction was measured for both yellow, nD, and green, ns14, light by the oil immersion method. It is necessary to measure the refractive index at the wavelength used in the Brillouin measurements in order to accurately calculate acoustic velocities and to correct for the effects of refraction at the surfaces of the crystal. Sample GRR1266 was observed to be optically isotropic except for two small inclusions that exhibited localized birefringence. Because our sample G R R I 2 6 6 is a chip from a larger sample it originally had irregular surfaces. This necessitated grinding and polishing artificial faces on the crystal which was done in such a way as to maintain the maximum volume. The final size was approximately 0.9 x 0.9 x 1.0 mm. The final crystallographic orientation of the prepared sample was obtained using a Syntex P21 four-circle x-ray diffractometer. Pyrope sample P51 was synthesized from an oxide mix at 1000 ~ C and Pn~o=23.5 kbar. The oxide mix contained ten mole percent excess silica and the garnet should therefore be saturated with respect to SiO2. Electron microprobe analysis yielded a composition of Mg3.o3Alt.gvSi2.99O12based upon 12 oxygen. P51 is a single euhedral crystal approximately 0.9 x 1.2 x 1.2 m m in dimension with natural dodecahedral growth faces. The sample is clear and shows no birefringence. The lattice parameter, determined by powder x-ray diffractometry, is listed in Table 1 along with the density calculated from the measured value of ao, and the indices of refraction. The indices of refraction, nD and n~14, were measured by oil immersion. On the basis of previous studies it is possible to estimate the hydrous content of both pyrope samples used in this study. From a detailed examination of the infrared absorption spectra of several crystals from the Dora Maira locality Rossman et al. (1989) found the hydrous component to vary between 0.00016% and 0.0035% (expressed as weight percent H20). Sample GRR1266 yielded the lowest value and was chosen for this study as the 'driest' pyrope for which single crystals are available. In contrast, pyropes synthesized under conditions of high Pn o typically contain much larger . 2 hydrogarnet components (Gelger et al. 1990). In particular, infrared absorption spectra of pyrope P51 yields an estimated H 2 0

9Table 2a. Velocities for Pyrope P51 Velocities Calculated b (km/s)

Velocities Observed b (kin/s)

Wave Normal a N~

Nb

N~

Vp

-0.676 -0.721 -0.480 -0.115 0.106 0.224 0.442 0.636 0.794 0.863 0.954 0.995 0.982 0.915 0.723 -0.994 -0.105 -0.033 -0.635 0.756 - 0.139

-0.491 -0.416 -0.594 -0.677 -0.678 -0.665 - 0.609 -0.516 --0.393 -0.285 --0.145 0.014 0.180 0.341 0.522 -0.020 0.731 0.734 0.510 0.332 0.894

-0.549 -0.554 -0.646 -0.727 -0.728 -0.712 - 0.659 -0.574 --0.464 --0.417 -0.264 -0.100 0.063 0.214 0.452 0.106 0.674 0.678 0.580 -0.565 0.426

9.11 9.09 9.08 9.05 9.15 9.13 9.15 9.10 9.06 9.11 9.11 9.10 9.10 9.1 l 9.06 9.11 9.10 9.11 9.02

Vsl

Vs2

Vp

Vsl

9.10 5.15 5.11 5.09 5.11 5.12 5.11 5.08 5.08 5.08 5.06 5.05 5.05 5.05 5.06 5.01 5.09 5.13 5.08 5.04

9.10 9.10 9.10 9.10 9.10 9.10 9.10 9.I0 9.11 9.12 9.11 9.11 9.07 9.12 9.10 9.10 9.10 9.11

a The acoustic wave normal is given in terms of direction cosines with respect to the three crystallographic axes b Shear wave polarizations are known

5.08 5.09 5.10 5.10 5.09 5.09 5.08 5.08 5.07 5.07 5.07 5.07 5.07 5.08 5.07 5.10 5.08 5.09 5.08

Vs2

619

Table

2b.

Velocities for Pyrope GRRI266 Velocities Calculated b (km/s)

Velocities Observed b (km/s)

Wave Normal a N,

Nb

- 0.637 - 0.637 -0.550 - 0.429 -0.313 0.031 0.172 0.377 0.432 0.427 - 0.546 - 0.607 -0.611 0.061 0.628 0.915 0.976 0.384 -0.539 0.122 -0.637 0.628 0.395 0.981 0.545 0.595 -0.333 0.524 - 0.482 -0.567 -0.607 - O.554 -0.178 -0.451 0.578 -0.718 0.045 -0.036 0.997

- 0.627 - 0.486 -0.117 O.144 0.333 0.720 0.818 0.886 0.851 0.887 -0.835 - 0.749 -0.312 -0.628 0.437 0.025 0.049 -0.775 -0.587 -0.968 - 0.627 0.437 -0.193 0.029 0.123 0.276 -0.876 0.288 - O.864 -0.822 - 0.749 - O.128 0.511 -0.881 -0.638 -0.668 -0.993 0.661 0.080

Nc 0.449 0.599 0.827 O.892 0.890 0.693 0.549 0.268 0.299 0.176 0.069 0.266 0.727 -0.776 -0.644 -0.403 -0.212 -0.502 0.604 -0.218 0.449 -0.644 -0.899 -0.192 -0.829 -0.755 -0.348 0.801 - O.144 0.049 0.266 O.823 0.841 -0.147 -0.510 0.194 -0.109 0.749 -0.023

Vv

Vsl

Vs2

Vp

Vsl

Vs2

9.06 9.08 9.18 9.20 9.22 9.07 9.09

5.11 5.09 5.16 5.13 5.13 5.07 5.10 5.09

5.12

9.06 9.06 9.07 9.07 9.07 9.07 9.07

5.10 5.10 5.10 5.09 5.09 5.07 5.07 5.09

5.09

9.02 9.04 9.03 9.10 9.15 9.16 9.17 9.14 9.16 9.09 9.11 9.06 8.91 9.04 9.24 9.22 9.14 9.13 9.17 8.87 8.97 8.91 9.01 8.93 9.00 9.07 8.99 9.01 8.91 9.09

9.07 9.07 9.07 9.07

5.09 5.09 5.06 5.10 5.09 5.11 5.12 5.07 5.18 5.16 5.14 5.11 5.01 5.06 5.14 5.17 5.14 5.13 5.02 5.05 5.08 5.01 5.02 5.02 5.04 5.03 5.07 5.04 5.10

5.14 4.99 5.07

9.07 9.06 9.08 9.08 9.07 9.06 9.08 9.06 9.06 9.08 9.08 9.07 9.07 9.07 9.07 9.07 9.07 9.07 9.07 9.07 9.07 9.06 9.07 9.09 9.07 9.09

5.09 5.10 5.10 5.10 5.07 5.10 5.09 5.08 5.08 5.09 5.07 5.10 5.10 5.09 5.08 5.10 5.10 5.09 5.10 5.10 5.10 5.10 5.07 5.09 5.09 5.10 5.07 5.07 5.07

5.10 5.07 5.08

a The acoustic wave normal is given in terms of direction cosines with respect to the three crystallographic axes b Shear wave polarizations are known

content of 0.018%, approximately two orders of magnitude greater than GRR1266 (Rossman, unpublished data; Geiger et al. 1990). Moreover, P51 did not show evidence of free water from inclusions in the IR spectrum. Although the details of the IR spectra for these two samples differ, making the nature of the hydrous component in GRR1266 somewhat problematic, these samples represent quite different levels of water content. For both samples, optical goniometry was used to determine the orientation of the crystal faces relative to the crystallographic axes in order to correct the Brillouin data for refraction effects (Vaughan and Bass 1983). The Brillouin scattering technique is described in detail by Vaughan (1979) and Sandercock (1982). An Ar-ion laser operated at a wavelength of 514.5 nm served as the light source, and a scattering angle of 90 ~ was used. Light scattered from the sample was analyzed by a plane-parallel piezoelectrically driven Fabry-Perot interferometer operated in four-pass configuration (Sandercock 1982). Further details on the spectrometer and methods used for our velocity measurements are given by Bass (1989).

Results

F o r t h e s y n t h e t i c p y r o p e , P51, a t o t a l o f 37 m o d e v e l o c i ties w e r e m e a s u r e d in 21 c r y s t a l l o g r a p h i c d i r e c t i o n s w i t h each mode velocity being an average of four velocity m e a s u r e m e n t s ( T a b l e 2 a ) . M e a s u r e m e n t s o f 78 m o d e velocities, in 39 c r y s t a l l o g r a p h i c d i r e c t i o n s , w e r e t a k e n o n G R R 1 2 6 6 , t h e n a t u r a l p y r o p e ( T a b l e 2 b ) . T h e initial data taken on GRR1266 showed a larger scatter than for the synthetic pyrope which may have resulted from s e v e r a l effects i n c l u d i n g s l i g h t c o m p o s i t i o n a l v a r i a t i o n s in t h e s a m p l e , l i g h t s c a t t e r i n g f r o m t h e t w o i n c l u s i o n s , a n d , to a lesser d e g r e e , c u r v a t u r e o f t h e a r t i f i c i a l l y c u t surfaces. W e t h e r e f o r e c o l l e c t e d a l a r g e r n u m b e r o f m e a s u r e m e n t s o n this c r y s t a l a n d a v o i d e d t a k i n g m e a s u r e ments hear the included areas of the sample. The velocity m e a s u r e m e n t s , f o r e a c h s a m p l e w e r e c o r r e c t e d f o r re-

620 Table 3. Elastic properties of pyrope

Pure pyrope This study, measured a Leitner et al., measured b Babuska et al., calculated r Pyrope solid solution This study, measured a This study, calculated e

C 11(GPa)

C44

C12

Ks

/.t

296.2 (5)

91.6 (3)

111.1 (6)

172.8 (3)

92.0 (2)

295 (2)

90 (3)

117 (1)

177 (1)

89 (1)

296.3 (14)

91.9 (5)

111.3 (12)

173.0 (9)

92.1 (5)

297.6 (12)

92.7 (7)

109.8 (8)

172.4 (7)

93.2 (5)

297.5

92.2

110.5

172.8

92.7

" Sample P51 b Synthetic pyrope (Leitner et al. 1980) ~ From intermediate composition garnets (Babuska et al. 1978) d Sample GRR1266 From the composition of GRR1266, (Mgo.s99Feo.o76Ca0.o24)A12SiaO12,using the relation C = ~ C~xi, where C is a clj, Ci is the value of that cij for garnet end-member i, and xi is the mole fraction present of end-member i

fraction effects (Vaughan and Bass 1983) and then inverted to obtain the best-fit set of elastic moduli, cij, (Weidner and Carleton 1977) which are given in Table 3. The adiabatic bulk modulus, Ks, and the shear modulus, ~t, also given in Table 3, were calculated using both Voigt-Reuss-Hill averaging and Hashin-Shtrikman bounds (Watt et al. 1976) with the results from the two methods being in complete agreement. The uncertainties for the moduli in Table 3, are one standard deviation calculated from the RMS error in velocity for the 78 and 37 mode velocities for GRR1266 and P51, respectively. Previous calibration experiments (Bass 1989) have determined that the accuracy of elastic moduli obtained from velocity measurements on samples with artificially prepared surfaces is approximately two standard deviations. We have since improved our polishing techniques so that curvature o f the crystal surfaces introduces less of an error in velocity and elastic modulus. Nevertheless, the true errors for sample G R R I 2 6 6 are probably about two standard deviations due to uncertainties in the chemical composition (density) and refractive index of the sample. Since sample P51 is synthetic and euhedral, its surfaces are perfectly flat and the composition is well defined. The accuracy of the reported moduli should therefore be superior for sample P51, approximately at the one standard deviation level.

Discussion Of all previous experimental studies on garnet elasticity our results are most directly compared with those of Leitner et al. (1980). These authors determined the elastic constants o f a synthetic pyrope which was synthesized under conditions similar to those for sample P51, and

these values are listed along with those measured in the present study in Table 3. Although cll and c44 from the two studies agree within mutual uncertainties, we have obtained a significantly lower value of c12. Inasmuch as c12 is an off diagonal modulus, it cannot be directly measured and at least three distinct mode velocities must be measured in order to constrain this modulus. In order to obtain a high degree of redundancy, velocities were measured in 21 crystallographic directions in the present study. This large data set should effectively average out r a n d o m experimental errors as well as uncertainties in crystallographic orientation, and, although the entire data set was used to constrain each of the moduli (cij), such redundancy checks are particularly important for off-diagonal moduli (c~2). Since the data set o f Leitner et al. (1980) consists o f measurements in three directions only, we place greater confidence in the results of this study. As a result of the differences in the two sets of single-crystal moduli, we obtain a substantially lower bulk modulus, Ks, and larger shear modulus, ~t, for pure end-member pyrope than was obtained by Leitner et al. (1980). A comparison of the elastic moduli measured for the natural, solid solution, pyrope and the synthetic, end-member, pyrope from this study (Table 3) shows them to be in agreement within the experimental uncertainties. The similarity of the ci~'s is expected because the differences in elastic moduli among the garnet endmembers thus far measured are small. This point is emphasized by calculating the elastic properties of the solid solution GRR1266 from the end-member moduli. A given modulus for a solid solution is obtained as an average o f the end-member moduli weighted by the mole fraction o f the end-member present. This linear mixing approach has been shown to accurately represent the elasticity of

621 complex garnet solid solutions, with the possible exception of those on the grossular-andradite join (O'Neill et al. 1989; Bass 1989). For the properties of pyrope we use the moduli of sample P51 from this study, whereas the moduli of almandine (Fe3Al/Si3Oa2 , cll =309, c12=111, c ~ = 9 6 , K s = 1 7 7 , ~t=97) and grossular (Ca3A12Si3012, Cla =321.7, c12=91.4, c4~= 104.6, K s = 168.4, g = 108.9) are taken f r o m Bass (1989). The difference between the calculated and measured moduli of garnet G R R 1 2 6 6 (Table 3) are well within the uncertainties of the data, and are, indeed, unresolvable using our experimental techniques. F r o m the above discussion it is clear that the endm e m b e r moduli can be used to calculate the properties of a garnet with arbitrary composition. In the absence of measurements of actual end-members, several authors have previously attempted to estimate the moduli of the end-members from a linear regression analysis of natural solid solutions. It is interesting to compare our new measurements with one of the more recent analyses of garnet elasticity by Babuska et al. (1978). Their estimates for the moduli of pure pyrope (Table 3) are seen to be indistinguishable f r o m the actual measured values for P51. The remarkable consistency between the calculated and measured values are an additional indication that our results for the elasticity of pure pyrope (sample P51) are to be preferred over the earlier results o f Leitner et al. (1980). The agreement of the elastic moduli obtained for the natural and synthetic pyrope samples investigated in this study indicate that there is no discernable effect of a hydrous c o m p o n e n t in pyrope. Although the elastic properties of grossular has been shown to be profoundly effected by a hydrous c o m p o n e n t (O'Neill et al. 1988), the absolute H 2 0 content of our ' w e t ' sample (P51) is relatively low c o m p a r e d to those for some grossular and spessartite garnets (Aines and Rossman 1984; Lager et al. 1989). Due to the limited capacity of pyrope to a c c o m m o d a t e a hydrous c o m p o n e n t in its structure (Aines and R o s s m a n 1984), the elastic properties of m a n tle pyrope will not be sensitive to the fo 2 under which the garnet equilibrated. Acknowledgements. Three of the authors (J.D.B., B.O'N. and G.R.R.) were supported in this research by the National Science Foundation. Additionally, B. O'N. gratefully acknowledges the support of the NSF Research Experiences for Undergraduates program.

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