Elasticity of single crystal and polycrystalline MgSiO 3 perovskite by Brillouin spectroscopy

Transcription

1 GEOPHYSICAL RESEARCH LETTERS, VOL. 31, L06620, doi: /2004gl019559, 2004 Elasticity of single crystal and polycrystalline MgSiO 3 perovskite by Brillouin spectroscopy Stanislav V. Sinogeikin Department of Geology, University of Illinois, Urbana, Illinois, USA Jianzhong Zhang 1 Mineral Physics Institute, State University of New York at Stony Brook, Stony Brook, New York, USA Jay D. Bass Department of Geology, University of Illinois, Urbana, Illinois, USA Received 22 January 2004; revised 27 February 2004; accepted 3 March 2004; published 26 March [1] The elastic moduli of MgSiO 3 perovskite have been measured on both single-crystal and polycrystalline samples by Brillouin spectroscopy at ambient conditions. The aggregate elastic moduli calculated from measured singlecrystal elastic moduli and from the average polycrystalline velocities are in excellent agreement. This convincingly demonstrates that accurate values of elastic moduli can be obtained for polycrystalline samples of dense anisotropic materials by Brillouin spectroscopy. Our new values of the bulk modulus (K S = 253(3) GPa) and shear modulus (m = 175(2) GPa) are 4% and 1% lower than commonly accepted values for end-member MgSiO 3 perovskite (K S = 264 GPa, m = 177 GPa). These lower elastic moduli suggest that the pressure, temperature, and compositional dependence of elastic moduli and wave velocities for magnesian silicate perovskite must be reevaluated in order to obtain reliable constraints on the mantle chemistry and thermal structure. INDEX TERMS: 3909 Mineral Physics: Elasticity and anelasticity; 3919 Mineral Physics: Equations of state; 3934 Mineral Physics: Optical, infrared, and Raman spectroscopy; 8124 Tectonophysics: Earth s interior composition and state (1212). Citation: Sinogeikin, S. V., J. Zhang, and J. D. Bass (2004), Elasticity of single crystal and polycrystalline MgSiO 3 perovskite by Brillouin spectroscopy, Geophys. Res. Lett., 31, L06620, doi: /2004gl Introduction [2] (Mg, Fe, Al)(Si, Al)O 3 perovskite (where Mg and Si are the dominant cations) is likely the most abundant phase in Earth s lower mantle. Therefore, knowledge of its elastic properties is of first-order importance for constructing reliable compositional and mineralogical models of the lower mantle, and addressing its thermal structure. The P-V and P-V-T equations of state (EOS) of silicate perovskite, both the Mg end-member and solid solutions, have been investigated and reported in numerous papers [e.g., Mao et al., 1991; Wang et al., 1994; Funamori et al., 1996; Fiquet et al., 1998]. The average value of the isothermal 1 Now at LANSCE Division, Los Alamos National Laboratory, Los Alamos, New Mexico, USA. Copyright 2004 by the American Geophysical Union /04/2004GL bulk modulus (K T0 ) of MgSiO 3 reported in these recent studies is 261 GPa. Although static compression measurements can provide accurate lattice parameters and cell volumes at high pressures, the well-known tradeoff between K T0 and its pressure derivative can introduce considerable uncertainty in the values of K T0 derived from fitting P-V data to an equation of state [e.g., Bass et al., 1981; Bina, 1995]. In contrast, acoustic techniques such as Brillouin scattering and ultrasonic interferometry provide direct values of the adiabatic bulk modulus (K S ), as well as the shear modulus (m), compressional acoustic velocities (V P ), and shear (V S ) velocities. Unfortunately the number of such acoustic measurements reported to date is extremely limited. There are only two determinations of single-crystal elastic moduli (C ij s) of MgSiO 3 perovskite by Brillouin scattering [Yeganeh-Haeri et al., 1989; Yeganeh-Haeri, 1994]. The K S and m reported in these two studies differ by 7% and 4%, respectively. The later study was claimed to be more accurate by the author, and yielded a value of K S = 264(5) GPa, in agreement with the average K T0 = 261 GPa measured by compression if the difference between isothermal and adiabatic moduli is accounted for ((K S =K T (1 + agt), where a is thermal expansivity, g is the thermodynamic Gruneisen parameter, and T is the absolute temperature). These values of K S and K T0 have been adopted in some studies of the pressure, temperature, and compositional derivatives of the bulk modulus [e.g., Bina, 1995; Jackson and Rigden, 1996; Shim and Duffy, 2000], and in studies of lower mantle composition and thermal structure [e.g., Jackson and Rigden, 1998; Trampert et al., 2001]. [3] The bulk modulus of MgSiO 3 perovskite is, however, still controversial and uncertain. A wide range of values have been reported. Several P-V EOS studies suggest a value of K T0 3 4% lower than 261 GPa [e.g., Ross and Hazen, 1990; Fiquet et al., 2000]. A lower value of K T0 is also supported by Jackson and Rigden s [1996] analysis of the available P-V-T data for MgSiO 3 perovskite. These authors found that when K T0 is left unconstrained, its best-fit value is several percent lower than 261 GPa. Such ambiguity in the bulk modulus of Mg end-member perovskite warrants further study of its ambient-condition elasticity, preferably by independent measurement techniques. In this study we present the results of new Brillouin measurements at ambient conditions performed on both L of5

2 polycrystalline and single-crystal samples of MgSiO 3 perovskite, with the goal of obtaining more accurate values for the bulk and shear moduli. A second objective of this study was to further investigate the possibility of using polycrystalline samples to obtain accurate elastic moduli by Brillouin scattering. Brillouin scattering is a well-established technique for measuring elastic moduli on single crystals, and on polycrystalline samples in the special case of materials with very low elastic anisotropy [e.g., Sinogeikin and Bass, 2002]. In this study we demonstrate that Brillouin scattering measurements on well-sintered polycrystalline specimens with pronounced elastic anisotropy can yield accurate values for the bulk elastic properties V P,V S,K S, and m. 2. Experiment 2.1. Sample Synthesis and Characterization [4] The perovskite sample was synthesized from homogeneous MgSiO 3 glass at 25 GPa and 1873 K for one hour (run #3815) in a Kawai-type split-sphere apparatus (USSA-2000) at the Mineral Physics Institute, SUNY at Stony Brook. Previous studies indicate that the maximum solubility of water in pure MgSiO 3 perovskite is not more than 100 wt. ppm, even if synthesized under hydrous conditions [e.g., Litasov et al., 2003]. No water or flux was used in our sample synthesis. The starting glass was kept in a desiccator, and was heated in an oven at 110 C for about 24 hours before the synthesis at high P and T. The resultant sample was a colorless, clear polycrystalline aggregate with exceptionally well-sintered grains. The grain size was typically in the range of 5 to 20 mm, although some grains had lateral dimensions of up to 150 mm. The absence of preferred orientation of crystallites in the sample was confirmed by angle-dispersive X-ray measurements and visual observations under an optical microscope in cross-polarized light. [5] Angle-dispersive X-ray spectra were collected over a 2q range of 2.5 to 110 degrees. A LeBail refinement of the x-ray pattern in the Pbnm space group produced lattice parameters of a = (4) Å, b = (4) Å, c = (4) Å, and V = (5) Å 3. The molar volume and density are 24.45(1) cm 3 /mol and (1) g/cm 3, respectively, in agreement with literature values [e.g., Ross and Hazen, 1990; Mao et al., 1991; Fiquet et al., 2000]. The X- ray pattern revealed four small non-perovskite reflections, which could be attributed to stishovite. However, stishovite was not found in Raman spectra (which has about the same scattering volume as a Brillouin measurement). The Raman and x-ray measurements suggest that the quantity of stishovite grains was small (<2%) and should not noticeably affect the polycrystalline velocity measurements Brillouin Measurements [6] Brillouin scattering measurements were performed using an Argon ion laser (l = nm) as a light source, and six-pass tandem Fabry-Perot interferometer [Sinogeikin et al., 1998]. Significantly, all measurements were performed with a platelet scattering geometry and a 90-degree external scattering angle. This is an important difference from previous measurements on MgSiO 3 perovskite [Yeganeh-Haeri et al., 1989; Yeganeh-Haeri, 1994]. The measurements and the Brillouin system were calibrated Figure 1. Stacked Brillouin spectrum of polycrystalline MgSiO 3 perovskite. Peaks marked as V P and V S correspond to compressional and shear acoustic modes, respectively. Only portions of the spectra above the horizontal baseline were used for the analysis. using an MgO single-crystal standard to reduce geometric or other possible systematic errors in velocity determinations. MgSiO 3 perovskite is metastable at ambient conditions and can twin or amorphize due to heating or interaction with laser light [e.g., Yeganeh-Haeri, 1994]. Therefore very low laser power (8 12 mw on single crystals and mw on polycrystalline samples) was used in all measurements. Both polycrystalline and singlecrystal samples were carefully examined by optical microscopy before and after each set of measurements. We did not detect any sample alteration for the measurements reported here Measurements on Polycrystalline Samples [7] For polycrystalline Brillouin measurements two samples with lateral dimensions of mm and mm were polished into plates with parallel faces to a thickness of 30 mm, and mounted on glass fibers. [8] In our polycrystalline measurements each Brillouin spectrum is a superposition of the light scattered from all grains within the scattering volume. MgSiO 3 is elastically anisotropic, so an average velocity from a single spectrum measured on a small number of grains may not represent the true aggregate velocity of MgSiO 3. We therefore performed a large number of measurements on different parts of the sample, sampling many grains with different orientations. On the first sample we collected 18 Brillouin spectra varying the collection spot position and laser power. On the second sample we performed three different sets of measurements (15 17 measurements in each set) varying collection spot position, orientation of the sample, laser power, and input laser polarization. All spectra were normalized by the integration time, and stacked into composite spectra (Figure 1) Measurements on Single-Crystal Samples [9] MgSiO 3 perovskite is orthorhombic with nine independent single-crystal elastic moduli. The small size of the single crystals made it unfeasible to pre-orient the samples before polishing. Therefore, three samples with general crystallographic orientations were prepared by polishing in a way that preserved the maximum cross-sectional area. The 2of5

3 Figure 2. Typical Brillouin spectrum of single-crystal MgSiO 3 perovskite. Peaks marked as V P, V S1, and V S2 correspond to compressional and two shear acoustic modes, respectively. final sample dimensions were about 100 to 150 mm laterally with thicknesses of 7 20 mm. The samples were glued to glass fibers and mounted on goniometer heads. Lattice parameters and orientations of the samples were determined with a four-circle x-ray diffractometer. The lattice parameters were identical to those measured on the polycrystalline sample within experimental uncertainties. [10] Even though the single crystals were not optically perfect (each crystal contained some small inclusions, and a number of cracks, mostly along cleavage directions) all Brillouin spectra were of excellent quality with sharp peaks and low background. Most of the spectra exhibited two shear modes (Figure 2). 3. Results 3.1. Polycrystalline Samples [11] Each set of polycrystalline spectra was analyzed in three ways: 1) the mean V P and V S velocities were measured from each spectrum, and averaged for each set of measurements; 2) time-normalized spectra in each set were stacked, the background was subtracted, and V P and V S velocities were calculated as mean peak positions (the position that divides the area under the peaks into two equal parts); 3) the mean velocities were calculated from stacked spectra using the slowness (inverse of velocities). Our results show that the aggregate acoustic velocities (and therefore the elastic moduli) are relatively insensitive to the type of analysis performed, with K S and m varying by less than 1%. Moreover, the four sets of measurements yielded K S and m values all within 0.6% of the average value, indicating the precision, or statistical variation of the measurements. The resulting average K S and m are 253(5) and 172(3) GPa, respectively. The 2% uncertainty in the elastic moduli takes into account likely errors due to photoelastic effects (anisotropy of the photoelastic coupling) and the possible effect of stishovite contamination Single-Crystal Samples [12] Single-crystal Brillouin measurements were performed on three samples, the faces of which have direction cosines of (0.942, 0.320, 0.099), (0.463, 0.765, 0.448), Figure 3. Measured velocities as a function of angle in the (0.463, 0.765, 0.448) scattering plane. c = 0 corresponds to [0.776, 0.598, 0.200] direction. The open symbols are velocities, measured on different samples, but within 5 of this scattering plane. Solid lines show acoustic velocities calculated from the best fit single-crystal elastic moduli. The uncertainties in measured velocities are within the size of the symbols. and (0.715, 0.106, 0.691) with respect to the orthonormal coordinate system. For each sample the acoustic velocities were measured over an angular interval of 180 from both sides of the sample (Figure 3). Velocities were measured in 65 distinct crystallographic directions. The final dataset consisted of 172 mode velocity measurements, many of which are averages of two or more redundant measurements in identical directions. [13] Acoustic velocities were inverted for the C ij s using the linearized inversion method of Weidner and Carleton [1977]. Inversions were performed with different initial values of C ij s to ensure that the result is insensitive to the starting model. The final best-fit elastic constant model yields a 43 m/s RMS (root mean square) error with respect to the observed velocity data. The best-fit single-crystal elastic moduli of MgSiO 3 perovskite are given in Table Discussion [14] The polycrystalline and single-crystal Brillouin measurements resulted in identical values of the bulk modulus (K S = 253(3) GPa, Voigt-Reuss-Hill average), and values for the shear modulus that agree within mutual Table 1. Single-Crystal Elastic Moduli of MgSiO 3 Perovskite a C ij This Study Yeganeh-Haeri [1994] C (4) 482(4) C (3) 537(3) C (4) 485(5) C (2) 204(2) C (2) 186(2) C (2) 147(3) C (3) 144(6) C (3) 147(6) C (3) 146(7) a All single-crystal elastic moduli are given in GPa. Numbers in parentheses represent 1 s.d. uncertainties in the last digit. 3of5

4 Table 2. Aggregate Elastic Properties of MgSiO 3 Perovskite a Parameter Polycrystalline, This Study Single-Crystal, This Study Single-Crystal b K S 253(5) 253(3) 264(5) m 172(3) 175(2) 177(4) V P 10.84(10) 10.88(6) V S 6.47(6) 6.53(3) 6.57 a All elastic moduli are given in GPa, and the acoustic velocities are in km/s. Aggregate elastic moduli and velocities for single-crystal studies are given as Voigt-Reuss-Hill averages calculated from single-crystal elastic moduli. b Yeganeh-Haeri [1994]. uncertainties (172(3) GPa and 175(2) GPa, respectively). This remarkable level of agreement demonstrates that accurate values of the aggregate elastic moduli can be obtained from Brillouin measurements on polycrystalline samples, even if the samples posses significant elastic anisotropy. [15] The results of this study are in agreement with a number of P-V measurements of the bulk modulus [e.g., Ross and Hazen, 1990; Fiquet et al., 2000]. In contrast, our measured values of K S and m are lower than that of Yeganeh-Haeri [1994] by 4% and 1%, respectively (Table 2). Moreover, all the C ij s, reported by Yeganeh- Haeri [1994] (except C 66 and C 23 ) are higher than our values (Table 1), and the differences in C 22,C 33, and C 12 exceed the stated mutual uncertainties. These discrepancies are likely explained by differences in experimental approaches. All of our measurements were performed using a platelet symmetric scattering geometry, in which the Brillouin shift and measured velocities of an optically isotropic material are independent of the sample refractive index (V i = Dw i l/2sin(q*/2), where V i is an acoustic mode velocity, Dw i is the Brillouin shift, l is the laser wavelength, and q* is an external scattering angle). We approximate MgSiO 3 perovskite as optically isotropic because its birefringence is very small (d 0.01), and the uncertainties in velocities due to such small birefringence are well within the stated experimental errors. Also, extreme care was taken to ensure a well-controlled scattering geometry. In contrast, the measurements of Yeganeh-Haeri [1994] were performed on unpolished samples immersed in a high refractive index fluid, using a non-symmetric geometry in which the velocity depends on the refractive index (V i = Dw i l/ 2nsin(q/2), where n is the refractive index of the sample, and q is an internal scattering angle). In this geometry uncertainties in the refractive index of the sample, the refractive index mismatch between the fluid and the sample, and errors in the orientation of crystal growth faces, all contribute to errors in the scattering angle and phonon velocity. [16] Our single-crystal measurements indicate that MgSiO 3 perovskite exhibits significant elastic anisotropy. Despite significant differences in the absolute values of the C ij s, the acoustic anisotropy (A Vi = 100(V i,max V i,min )/ V i,aver, where V i is compressional or shear mode) from this study (A Vp = 7.7%, A Vs = 15.3%) and Yeganeh-Haeri [1994] (A Vp = 7.4%, A Vs = 16.2%) are similar. Our results also indicate significant anisotropy in the axial compressibilities, with the b-axis being least compressible and the c-axis being most compressible. This result is in agreement with single-crystal static-compression measurements [e.g., Kudoh et al., 1987; Ross and Hazen, 1990] and calculations [e.g., Wentzcovitch et al., 1998; Kiefer et al., 2002]. [17] Under lower mantle conditions Mg-silicate perovskite has higher velocities than Fe-periclase ((Mg, Fe)O), which is generally viewed as the second most abundant phase [Jackson and Rigden, 1998]. Therefore, smaller values for the elastic moduli of Mg-perovskite, as from this study, generally imply that lesser amounts of magnesiowustite would be needed to match lower mantle velocity profiles such as PREM (Dziewonski and Anderson, 1981). However, any quantitative conclusions require knowledge of the pressure, temperature, and compositional derivatives of (Mg, Fe, Al)(Si, Al)O 3 perovskite. Most calculations of such derivatives have thus far been based on the assumption that K T0 = 261(1) GPa [e.g., Bina, 1995; Jackson and Rigden, 1996; Fiquet et al., 2000; Shim and Duffy, 2000]. A value of K T0 = 251(3) GPa (this study) will significantly modify temperature, compositional, and pressure derivatives of perovskite, and require a reinterpretation of the chemical and thermal structure of the Earth s lower mantle. [18] Acknowledgments. This research was partially supported by NSF grant EAR and COMPRES, the Consortium for Materials Properties Research in Earth Sciences under NSF Cooperative Agreement EAR Any opinions, findings, and conclusions or recommendations expressed in this material are those of the authors and do not necessarily reflect the views of the National Science Foundation. We thank J. M. Jackson, S. Speziale, and two anonymous reviewers for helpful comments. References Bass, J. D., R. C. Liebermann, D. J. Weidner, and S. J. Finch (1981), Elastic properties from acoustic and volume compression experiments, Phys. Earth Planet. Inter., 25, Bina, C. R. (1995), Confidence limits for silicate perovskite equations of state, Phys. Chem. Miner., 22, Fiquet, G., D. Andrault, A. Dewaele, T. Charpin, M. Kunz, and D. Hausermann (1998), P-V-T equation of state of MgSiO 3 perovskite, Phys. Earth Planet. Inter., 105, Fiquet, G., A. Dewaele, D. Andrault, M. Kunz, and M. 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