New accurate elastic parameters for the forsterite-fayalite solid solution

Transcription

1 American Mineralogist, Volume 96, pages , 2011 New accurate elastic parameters for the forsterite-fayalite solid solution F. NESTOLA, 1,2, * D. PASQUAL, 1 J.R. SMYTH, 3 D. NOVELLA, 4 L. SECCO, 1 M.H. MANGHNANI, 5 AND A. DAL NEGRO 1 1 Dipartimento di Geoscienze, Università di Padova, Via Gradenigo 6, I Padova, Italy 2 CNR-IGG, UO-Padova, Via Gradenigo 6, I Padova, Italy 3 Department of Geological Sciences, University of Colorado, Boulder, Colorado U.S.A. 4 Bayerisches Geoinstitut, Universität Bayreuth, D-95440, Bayreuth, Germany 5 Hawaii Institute of Geophysics and Planetology, University of Hawaii, 1680 East-West Road, Honolulu, Hawaii 96822, U.S.A. ABSTRACT Three natural olivines with Fo 80 Fa 20, Fo 71 Fa 29, and Fo 62 Fa 38 compositions were investigated in situ at high pressure by single-crystal X-ray diffraction using a diamond-anvil cell up to 8 GPa at room temperature. The bulk modulus, K T0, and its first pressure derivative, K, do not show any significant variation among the compositions investigated and, using the data on a further sample with Fo 92 Fa 8 composition recently investigated in the same laboratory and using the same experimental technique, we obtain, for the first time, a single equation of state for the entire Fo 92 Fa 8 -Fo 62 Fa 38 compositional range. The equation has the following coefficients: K T0 = 124.7(9) GPa and K = 5.3(3) and can be used for thermodynamic calculations involving the most common mantle olivine compositions. Keywords: Olivine, diffraction, pressure, elasticity INTRODUCTION Olivine [Mg 2 SiO 4 (forsterite, Fo)-Fe 2 SiO 4 (fayalite, Fa) solid solution] is one of the most studied minerals in Earth sciences due to its abundance in several geological terrestrial and extraterrestrial environments, and because it is therefore involved in geological processes at global scale. This phase is thought to constitute up to more than 50% of the Earth s upper mantle (e.g., Ringwood 1977) and between 36 and 38% of the whole-mantle (Ganapathy and Anders 1974; Morgan and Anders 1980). Olivine is stable down to 410 km where it transforms to its polymorph wadsleyite ( -olivine) at pressures dependent upon the Fe content and temperature. For example, at 1400 C for a pure Mg 2 SiO 4 composition the transformation occurs at about 14 GPa, while for (Mg 0.9 Fe 0.1 ) 2 SiO 4 it occurs in an interval between about 12.8 and 13.5 GPa but an increase of temperature would sharpen the olivine-wadsleyite transformation (Frost 2003 and references therein). This transformation is considered to be the cause of the seismic discontinuity at about 410 km depth in the mantle, and separates the upper mantle from the transition zone (e.g., Agee 1999). Thus, to evaluate the stability field and the interval of potential metastability accurately, it is crucial to determine its physical properties to construct correct thermodynamic models. For this reason, several previous studies tried to clarify the effect of the Mg Fe substitution on one of the most important thermodynamic properties, the room-pressure bulk modulus K T0 (inverse of compressibility ). In situ high-pressure X-ray diffraction experiments on a pure synthetic forsterite single crystal provided a K T0 = 132 GPa with the first pressure derivative K fixed to 4 (Hazen 1976). For a synthetic crystal of fayalite Hazen (1977) obtained a K T0 of 113 GPa, also assuming for the Fe end-member * fabrizio.nestola@unipd.it that K is equal to 4. Suzuki et al. (1983) used the Rectangular Parallelepiped Resonance method to determine an adiabatic bulk modulus K S0 = GPa for a synthetic forsterite that, using the conversion K S0 /K T0 = (1 + T) 1.01 (with = K 1, Fei 1995, and = 1.26, Isaak 1992), corresponds to a K T0 = GPa. Kudoh and Takeuchi (1985) also studied forsterite with same the experimental technique as Hazen (1976) and determined a K T0 of 123 GPa with K = 4.3. The authors also studied a natural sample of fayalite [containing 0.11 atoms per formula unit (apfu) of Mn and 0.04 apfu of Mg based on 4 O atoms] providing a K T0 = 132 GPa with K fixed to 4. Webb (1989), measured a San Carlos Fo 90 Fa 10 olivine by ultrasonic techniques and obtained a K S0 = GPa, corresponding to a K T0 = GPa, accompanied by K = Andrault et al. (1995) performed X-ray diffraction experiments on powder material samples up to 70 GPa for compositions (Mg 1 x Fe x ) 2 SiO 4 with x = 0, 0.17, 0.66, and 1, and found no differences in compressibility between them with a bulk modulus K T0, identical for all samples, equal to 131(6) GPa for K fixed to 4. Zha et al. (1996) found for pure forsterite a K S0 = 129 GPa corresponding to K T0 = GPa with a K = 4.2 by sound velocity measurements on a single crystal. Downs et al. (1996) measured pressure-volume data by single-crystal X-ray diffraction on a pure Mg 2 SiO 4 sample and calculated a K T0 = 125 GPa for K = 4.0. Speziale et al. (2004) studied a natural (Fe 0.94 Mn 0.06 ) 2 SiO 4 fayalite by Brillouin scattering and reported a K T0 = 136 GPa with K = 4.9. Poe et al. (2010) studied a single crystal of pure forsterite by single-crystal X-ray diffraction and obtained K T0 = GPa with K = 4.9. Nestola et al. (2011) measured the P-V curve of an olivine with composition Fo 92 Fa 8 by single-crystal X-ray diffraction and found K T0 = GPa with the first pressure derivative K = 5.6. It is evident from this brief review (see Table 1) that a significant degree of scatter is present among the bulk moduli of X/11/ $05.00/DOI: /am

2 NESTOLA ET AL.: COMPRESSIBILITY OF OLIVINE 1743 olivine obtained by different authors, with K T0 values determined for pure forsterite ranging between 123 and 132 GPa, with values between 128 and 129 GPa being in the majority. For fayalite the values of bulk modulus were observed to range between 113 and 136 GPa. Intermediate compositions have not been investigated as much, but the bulk modulus data also show marked differences ranging between 123 and 131 GPa. Among all of the data described above we should note that unfortunately the first pressure derivative of the bulk modulus, K, has often been fixed to 4, and when it has been determined it has a value close to 4 (in only one study is the K higher than 5). Fixing the K to 4 can result in an unreliable value for the bulk modulus since it is well known K T0 and K are strongly correlated in the fit of P-V data, often by more than 95% (e.g., Angel 2000). Thus, keeping the value of K constant could affect the calculation of the V/V 0 ratio at different pressures and hide the real effect of the Mg Fe substitution on olivine compressibility. Although olivine represents one of the most important and most studied phases for mantle mineralogy it is not clear whether, based on the present literature data for values of bulk modulus and its first pressure derivative, the Mg Fe substitution occurring along the forsterite-fayalite join increases or decreases the compressibility. The aim of this work is to clarify the effect of one of the most common cation substitutions in mineralogy, Mg replacing Fe, on the elastic properties of Mg-richer olivines by investigating three natural single-crystal olivines with compositions Fo 80 Fa 20, Fo 71 Fa 29, and Fo 62 Fa 38 by in situ high-pressure X-ray diffraction using a diamond anvil cell up to about 8 GPa at room temperature. The data obtained for these three compositions will be compared with the results obtained in a separate measurement on a Fo 92 Fa 8 olivine (Nestola et al. 2011) studied in the same laboratory using the same experimental setup. The aim of our work is to derive the equation of state parameters (both K T0 and K ) that will be useful in thermodynamic calculations for the most common olivine compositions at the pressures typical of upper mantle depths. Samples EXPERIMENTAL METHODS All of the crystals investigated were natural samples. The Fo 80 Fa 20 composition was selected from the same crystal suite studied by Princivalle and Secco (1985) and corresponds to sample BO321, whereas the Fo 71 Fa 29 and Fo 62 Fa 38 compositions correspond to the PU8 and samples described by Tarantino et al. (2003). Full characterization of these three compositions at room pressure and temperature by single-crystal X-ray diffraction and electron microprobe are provided in those references. The unit-cell parameters determined at room conditions in this work are in excellent agreement with those reported by Princivalle and Secco (1985) and Tarantino et al. (2003). In situ high-pressure single-crystal X-ray diffraction The three single crystals used in this work were free of twins and inclusions, with sharp optical extinction and sharp Bragg reflections. The crystal size ranged between m 3 and m 3. They were loaded in an ETHtype diamond-anvil cell in three separate experiments using T301 steel foils as gaskets, which were pre-indented to m with holes of 250 m in diameter and had crystals of quartz loaded as the internal pressure standard (Angel et al. 1997). Mixtures of methanol:ethanol:water with ratio 16:3:1 were used as pressure media, which remains hydrostatic up to the maximum pressure reached in this work (Angel et al. 2007). The high-pressure experiments were performed using a STOE STADI IV single-crystal diffractometer equipped with a point detector and automated by the SINGLE software (Angel and Finger 2011) allowing the use of the eight-position centering method (e.g., Angel et al. 2000; Nestola et al. 2005, 2006, 2010; Boffa Ballaran et al. 2009; Ullrich et al. 2009). Unit-cell parameters and volumes at different pressures for the olivines studied in this work are reported in Table 2. RESULTS Unit-cell parameter evolution and axial anisotropy In Figure 1, the evolution of the unit-cell parameters as a function of pressure is shown for different olivine compositions using the data from Table 2. For all compositions investigated, the b direction ([010]) is clearly the softest, whereas a ([100]) is the stiffest; the axial compressibility scheme is always b > c > a. In terms of compression, a, b, and c axes decrease by about 0.15(1), 0.30(1), and 0.23(1)% per GPa, respectively, at an identical rate for all of the investigated compositions, including the Fo 92 Fa 8 by Nestola et al. (2011). The unit-cell ratio at room pressure is a/a 0 :b/b 0 :c/c 0 = 1.00:2.15:1.26 for all compositions. To reliably calculate how this ratio changes as a function of pressure we needed to perform this calculation at the same elevated pressure values for all samples. Therefore, we determined the equations of state for each unit-cell edge using a third-order Birch-Murnaghan equation (BM3-EoS) (Birch 1947) with the EOSFIT5.2 software (Angel 2000). The data are reported in Table 3 including the values for Fo 92 Fa 8 by Nestola et al. (2011). Using the BM3-EoS coefficients of Table 3 we obtain, by an extrapolation, an identical anisotropy ratio at 10 GPa of a/a 0 :b/b 0 :c/c 0 = 1.00:2.12:1.25 for all compositions. TABLE 1. Literature data relative to the volumetric bulk modulus and its first pressure derivative for samples belonging to the forsterite-fayalite join Composition Volumetric bulk modulus, K T0 First pressure derivative, K Technique Reference Mg 2 SiO GPa 4 (fixed) X-ray diffraction (single crystal) Hazen (1976) Mg 2 SiO GPa Rect. Parall. Resonance Suzuki et al. (1983) Mg 2 SiO GPa 4.3 X-ray diffraction (single crystal) Kudoh and Takeuchi (1985) Mg 2 SiO GPa 4 (fixed) X-ray diffraction (powder) Andrault et al. (1995) Mg 2 SiO GPa 4.2 Sound velocity (single crystal) Zha et al. (1996) Mg 2 SiO GPa 4.0 X-ray diffraction (single crystal) Downs et al. (1996) Mg 2 SiO GPa 4.9 X-ray diffraction (single crystal) Poe et al. (2010) Mg 1.84 Fe 0.16 SiO GPa 5.6 X-ray diffraction (single crystal) Nestola et al. (2011) Mg 1.80 Fe 0.20 SiO GPa 4.66 Ultrasonic technique Webb (1989) Mg 166 Fe 0.34 SiO GPa 4 (fixed) X-ray diffraction (powder) Andrault et al. (1995) Mg 0.68 Fe 1.32 SiO GPa 4 (fixed) X-ray diffraction (powder) Andrault et al. (1995) Fe 1.89 Mn 0.11 SiO GPa 4 (fixed) X-ray diffraction (single crystal) Kudoh and Takeuchi (1985) Fe 1.88 Mn 0.12 SiO GPa 4.9 Brillouin spectroscopy Speziale et al. (2004) Fe 2 SiO GPa 4 (fixed) X-ray diffraction (single crystal) Hazen (1977) Fe 2 SiO GPa 4 (fixed) X-ray diffraction (powder) Andrault et al. (1995)

3 1744 NESTOLA ET AL.: COMPRESSIBILITY OF OLIVINE TABLE 2. Unit-cell parameters, volumes, and their standard deviations (in parentheses) measured at different pressures for the three olivine samples studied in this work P (GPa) a (Å) b (Å) c (Å) V (Å 3 ) Fo 80 Fa (1) (2) (7) (3) (3) 0.741(7) (2) (8) (3) (3) 1.206(8) (2) (7) (2) (3) 1.581(8) (2) (7) (3) (3) 2.353(7) (2) (7) (3) (3) 2.845(7) (2) (7) (3) (3) 3.639(8) (3) (10) (5) (4) 4.333(8) (2) (6) (3) (2) 5.278(12)* (2) (6) (4) (3) 5.901(11) (3) (6) (3) (3) 6.757(11) (2) (6) (4) (2) 7.426(14) (5) (16) (8) (6) Fo 71 Fa (1) (4) (4) (5) (3) 0.693(6) (3) (4) (4) (2) 1.556(6) (3) (4) (5) (2) 2.257(7) (3) (4) (5) (3) 2.711(9) (3) (4) (6) (3) 3.344(9) (3) (3) (6) (3) 4.141(10) (3) (3) (5) (3) 4.739(10) (3) (4) (6) (3) 5.200(10) (3) (4) (7) (3) 6.185(10)* (4) (4) (5) (3) 6.835(16) (4) (4) (5) (3) 7.635(11)* (4) (4) (5) (3) 8.197(11) (3) (4) (5) (3) Fo 62 Fa (1) (3) (3) (4) (2) 0.893(6) (3) (3) (4) (2) 1.736(6) (3) (3) (4) (2) 2.398(6)* (3) (3) (4) (2) 2.970(7) (3) (3) (5) (3) 3.801(7) (3) (3) (4) (2) 4.548(8)* (3) (3) (4) (2) 4.929(9) (3) (3) (4) (2) 5.653(9)* (3) (3) (4) (3) 6.259(9) (3) (3) (4) (2) 6.821(10) (3) (3) (4) (2) 7.596(10) (4) (4) (6) (3) * Data measured during decompression. VOLUME EQUATION OF STATE In Figure 2, the evolution of the unit-cell volume with pressure is shown for all samples investigated in this work with the Fo 92 Fa 8 sample by Nestola et al. (2011) for the purpose of comparison. The figure shows a very similar curvature in the pressure volume trend for all samples, and the data reported in Table 2 clearly indicate that the compression rate is almost identical regardless of the composition with a volume decrease of 0.68% per GPa for Fo 92 Fa 8 and Fo 80 Fa 20 and 0.67% per GPa for Fo 71 Fa 29 and Fo 62 Fa 38 compositions. To define the best equation of state that adequately describes the pressure-volume trends for our sample, we have constructed in Figure 3 an F E -f E plot (Birch 1978; Angel 2000 and references therein). The plot shows that data for the different compositions lie on positively inclined straight lines indicating that a BM3-EoS must be used to fit the experimental pressure volume data. The calculation has been performed, as for the unit-cell parameters, using the EOSFIT5.2 software (Angel 2000), and the data are reported in the last column of Table 3. We therefore refined simultaneously the unit-cell volume V 0, the bulk modulus K T0, and its first pressure derivative, K, for all compositions. The data for Fo 92 Fa 8 have also been added to Table 3. The quality of the EoS data is demonstrated by the small differences between the results obtained by the refinement and those obtained by the F E -f E plot. It is noteworthy that, even if there is a slight increase in the bulk moduli with increasing Fe content (see values in Table 3), these differences are within 2.5, making them almost negligible for thermodynamic purposes. At the same time, the values of first pressure derivative differ by less than 2. DISCUSSION In this paper, we have presented new elasticity data on the Mg-rich side of the forsterite-fayalite join. The necessity of these new high-pressure in situ experiments derived from the strong scatter in values for the bulk modulus found in literature. Here, TABLE 3. Equation of state coefficients for Fo 80 Fa 20, Fo 71 Fa 29, Fo 62 Fa 38 (this work) and Fo 92 Fa 8 (Nestola et al. 2011) fitted using a third-order Birch- Murnaghan equation Weighted linear fit from the F E -f E plot Fo 92 Fa 8 * a (1) Å b (6) Å c (2) Å V (2) Å 3 Ka 0 180(2) GPa Kb 0 94(1) Kc 0 122(1) K T (8) GPa 123.5(5) GPa K 9.7(7) K 4.2(3) K 5.4(3) K 5.6(2) 5.5(2) Fo 80 Fa 20 a (2) Å b (6) Å c (2) Å V (2) Å 3 Ka 0 182(3) GPa Kb 0 93(1) Kc 0 127(2) K T0 124(1) GPa 124.7(3) GPa K 10(1) K 4.2(4) K 4.6(5) K 5.4(3) 5.4(2) Fo 71 Fa 29 a (3) Å b (7) Å c (4) Å V (3) Å 3 Ka 0 186(4) GPa Kb 0 94(1) Kc 0 125(2) K T0 125(1) GPa 124.2(7) GPa K 7(1) K 3.3(3) K 6.4(6) K 5.1(3) 5.3(1) Fo 62 Fa 38 a (2) Å b (3) Å c (3) Å V (2) Å 3 Ka 0 186(4) GPa Kb (5) Kc 0 133(2) K T (8) GPa 126.6(4) GPa K 9(1) K 3.7(1) K 4.9(6) K 5.2(2) 5.2(1) Notes: Reported in the last column are the values of volumetric bulk moduli and their first pressure derivatives, obtained by the weighted linear fit of the F E -f E plot. * Calculated using the data in Nestola et al. (2011).

4 NESTOLA ET AL.: COMPRESSIBILITY OF OLIVINE 1745 FIGURE 1. Evolution of unit-cell parameters as a function of pressure for the samples studied in this work. The Fo 92 Fa 8 sample is from Nestola et al. (2011). The solid curves correspond to the BM3-EoS. (Color online.) FIGURE 2. Evolution of unit-cell volume as a function of pressure for the three samples studied in this work and for Fo 92 Fa 8 sample investigated by Nestola et al. (2011). The dashed curves represent the volume BM3- EoS. (Color online.) FIGURE 3. F E f E plot (Birch 1978; Angel 2000) (the normalized pressure stress F E F E = P/3f E (1 + 2f E ) 5/2 Eulerian strain f E f E = [(V 0 /V) 2/3 1]/2) for the olivine samples studied in this work and for Fo 92 Fa 8 by Nestola et al. (2011). (Color online.)

5 1746 NESTOLA ET AL.: COMPRESSIBILITY OF OLIVINE our experimental values, Table 3) and an error of for the V/V 0 ratio obtained from the error propagation considering an average error on the unit-cell volume of 0.03 Å 3 (based on the error of our experimental volumes in Table 3). The value of the isothermal bulk modulus K T0 obtained in this work corresponds to an adiabatic bulk modulus K s0 = GPa. This new value, thanks to the strong reproducibility of our results, can be used as a definitive value for Mg-richer olivines at least up to Fo 62 Fa 38. ACKNOWLEDGMENTS This study was possible thanks to the support of Progetto di Ateneo of University of Padova to F. Nestola (no. CPDA062139/06). S. Tarantino is thanked for providing the samples and for helpful scientific discussions. Two anonymous referees strongly improved this work by their helpful revisions. FIGURE 4. V/V 0 relative compression plotted as a function of pressure for all the samples of this work and for Fo 92 Fa 8 sample studied by Nestola Murnaghan equation of state (see text). (Color online.) we investigated by high-pressure single-crystal X-ray diffraction three olivine compositions Fo 80 Fa 20, Fo 71 Fa 29, and Fo 62 Fa 38 and compared our data with that of Fo 92 Fa 8 by Nestola et al. (2011). This latter sample was measured in the same laboratory with the same experimental methods. Our results clearly indicate that, at least in the range Fo 92 Fa 8 -Fo 62 Fa 38, both the values of bulk modulus and the first pressure derivative remain constant (within the standard deviations). In contrast to previous studies, we present for the first time values of K for compositions on which the first pressure derivative was never previously obtained. In terms of volume compression, fixing the value of K to 4, as often done in literature, can cause significant error: the V/V 0 ratio calculated at any pressure is the result not only of the value of K T0 but it also strongly depends on the K value (Bass et al. 1981). In general, our data in general show a lower value of bulk modulus with respect to all previous work (our data are close to GPa against an average of GPa of published data, see Introduction section) and a higher value of first pressure derivative ( for our data, for published data). The differences in the values of bulk modulus between our data and those reported in literature (at least those in which P-V data have been measured) are clearly related to the failure to determine the first pressure derivatives in previous studies. Figure 4 shows the V/V 0 relative compression data for all of the compositions we have measured along with the data on Fo 92 Fa 8 by Nestola et al. (2011). 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