First crystal-structure determination of olivine in diamond: Composition and implications for provenance in the Earth's mantle

Earth and Planetary Science Letters 305 (2011) 249–255

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Earth and Planetary Science Letters j o u r n a l h o m e p a g e : w w w. e l s ev i e r. c o m / l o c a t e / e p s l

First crystal-structure determination of olivine in diamond: Composition and implications for provenance in the Earth's mantle Fabrizio Nestola a,b,⁎, Paolo Nimis a,b, Luca Ziberna a, Micaela Longo a, Andrea Marzoli a, Jeff W. Harris c, Murli H. Manghnani d, Yana Fedortchouk e a

Department of Geoscience, University of Padua, Via Giotto 1, 35121 Padova, Italy IGG-CNR, UO Padova, Via Giotto 1, 35121 Padova, Italy Department of Geographical and Earth Sciences, University of Glasgow, G128QQ Glasgow, UK d Hawaii Institute of Geophysics and Planetology, University of Hawaii, 1680 East-West Road, Honolulu, USA e Department of Earth Sciences, Dalhousie University, Halifax NS, Canada B3H 4J1 b c

a r t i c l e

i n f o

Article history: Received 26 October 2010 Received in revised form 1 March 2011 Accepted 7 March 2011 Available online 31 March 2011 Editor: L. Stixrude Keywords: diamond inclusion olivine diffraction pressure

a b s t r a c t We report for the first time a complete X-ray diffraction in-situ crystal-structure refinement of a single crystal of olivine still trapped in a diamond (Udachnaya kimberlite, Siberia). A two-step experimental procedure, consisting of accurate crystal centering using a four-circle diffractometer equipped with a point detector and subsequent collection of complete intensity data using a second diffractometer equipped with a CCD detector, allowed us to overcome previously reported experimental problems and to refine the crystal structure without extracting the inclusion from the diamond host. The data allowed us to obtain the cation distribution over the two crystallographic M2 and M1 sites, which provided composition of olivine inclusion as Fo92.7(4). A novel experimental calibration of the pressure–volume equation of state for such composition was obtained using new in situ high-pressure X-ray data on a Fo92 olivine single-crystal and new established compositional effects on olivine unit-cell volume. Such equation of state allowed us to determine the internal pressure at the olivine inclusion, Pi = 0.40(1) GPa. The value for the internal pressure compares well with but has lower uncertainty than estimates obtained using micro-Raman spectrometry for similar olivine inclusions in diamonds from the same kimberlite. Taking into account elastic relaxation of the diamond–olivine pair to ambient P–T, we determined formation pressures of 3.5 GPa to 4.9 GPa, depending on the assumed temperature (800 °C to 1300 °C). These values suggest formation near the graphite–diamond boundary and are comparable to estimates from conventional and Raman thermobarometry for other peridotitic inclusions in Siberian diamonds. © 2011 Elsevier B.V. All rights reserved.

1. Introduction Diamonds and their inclusions are among the deepest materials originating from the Earth's interior. Their study plays a key role in understanding and interpreting the geodynamics, geophysics, petrology, geochemistry and mineralogy of the Earth's mantle from lithospheric to lower-mantle levels (Stachel and Harris, 2008, and refs. therein). Mineral inclusions in diamonds reflect the chemical composition and mineral assemblages of the two principal rock types occurring in the deep lithosphere, namely peridotite and eclogite (e.g., Meyer, 1987). Typical mineral inclusions of the peridotitic paragenesis are olivine, orthopyroxene, chromian diopsidic clinopyroxene, chromian pyropic garnet, magnesiochromite and iron–nickel sulfides, whereas typical

⁎ Corresponding author at: Department of Geoscience, University of Padua, Via Giotto 1, 35121 Padova, Italy. Tel.: +39 49 827 2009; fax: +39 49 827 2010. E-mail address: [email protected] (F. Nestola). 0012-821X/$ – see front matter © 2011 Elsevier B.V. All rights reserved. doi:10.1016/j.epsl.2011.03.007

eclogite minerals are omphacitic pyroxene, chromium-poor garnet, and iron-rich sulfides. All of these mineral phases have been identified by X-ray diffraction or electron microprobe analysis since the 1950s (e.g., Harris, 1968, Harris et al., 1970, Meyer, 1987, Mitchell and Giardini, 1953) and by micro-Raman spectroscopy more recently (e.g., Liu et al., 1990; Nasdala et al., 2003). However, in many cases the inclusions were studied after extraction from the diamonds. A non-destructive in-situ investigation of an inclusion in diamond is useful and important because: (a) some mineral inclusions under pressure could have a different crystal structure, and thus different petrologic significance compared to that at ambient pressure; (b) the internal pressure on the inclusion can provide information about the formation pressure of the diamond (e.g., Izraeli et al., 1999; Sobolev et al., 2000); (c) the morphology and growth relationships of the inclusion with the host diamond can provide indications about its protogenetic vs. syngenetic and/or epigenetic nature (e.g., Sobolev, 1977); and (d) preservation of the diamond surface growth features can maintain clues on late oxidation processes (Fedortchouk and Canil, 2009).

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Even though identification of the mineral phase is often relatively simple by optical microscopy, X-ray diffraction (XRD) or microRaman spectroscopy, detailed compositional data cannot generally be extracted. This can be particularly relevant for those minerals that are characterized by significant cation substitutions in their crystal structure (e.g., garnet, pyroxene and olivine). To our knowledge, the only direct chemical data for inclusions still trapped in the diamonds have been thus far obtained on a single diamond by micro X-ray fluorescence using synchrotron radiation (Brenker et al., 2005). In that case, the estimated uncertainties of Ca measurements on Casilicate minerals were ±5–6 wt.%. More recently, Yasuzuka et al. (2009) proposed a method to estimate the Mg# value [= 100 Mg / (Mg + Fe)mol] of olivine inclusions from their Raman spectra with an uncertainty ±0.8. In both cases, the errors in the resulting major element data were much larger than in conventional electron microprobe analyses, i.e., much larger than generally required for detailed petrologic and thermobarometric studies. In principle, compositional data on samples showing limited cation substitutions (e.g., olivine and enstatite) can be indirectly retrieved from a complete crystal-structure refinement of the inclusions (cell parameters, bond lengths and atomic site occupancies) by singlecrystal XRD analysis. High-quality XRD analysis, however, requires accurate centering of the crystal in the path of the X-ray beam. In routine XRD practice, this is done through a simple visual procedure, which requires observation of the crystal from various orientations. This can hardly be achieved when the crystal is included in a host with high refraction index and complex morphology such as diamond. In fact, non-destructive, single-crystal XRD analyses of inclusions in diamonds have generally been restricted to the determination of the unit-cell parameters (Harris, 1968; Harris et al., 1970; Mitchell and Giardini, 1953) and, to the best of our knowledge, high-quality crystal-structure refinements have never been obtained. For example, Kunz et al. (2002) obtained crystal-structure data on inclusions of majoritic garnets using single-crystal synchrotron XRD, but an accurate structure refinement was not possible due to experimental difficulties associated with (a) the lack of parallel faces on the diamond host, which made it difficult to center the crystal visually, (b) impossibility to apply specific crystal-offset centering procedures (King and Finger, 1979) due to the lack of a four-circle diffraction geometry, and (c) the very strong anisotropic absorption and extinction effects caused by the large diamond host. In this work, we followed a non-routine XRD experimental procedure to study inclusions in diamonds. This procedure, which has been previously used only for high-pressure, in-situ XRD analysis in diamond-anvil cells (Angel et al., 2000; Nestola et al., 2005), employs two different single-crystal four-circle diffractometers installed in the same laboratory and equipped with a point detector and a CCD detector, respectively. The first diffractometer is optimized for accurate crystal-centering under the X-ray beam and measurement of unit-cell parameters. The second diffractometer is optimized

for collection of diffraction peak intensity data necessary for reliable crystal structure refinement. This two-step procedure overcomes previously reported experimental problems and is capable of providing complete, accurate and precise unit-cell volumes and crystal structure data on inclusions with a crystal size potentially down to 30–40 μm. Here we have investigated two olivine inclusions in a diamond (Fig. 1) from the Udachnaya kimberlite, Siberia, and used the crystal structure refinement data of the largest inclusion to obtain its chemical composition (Mg#) and an indication of the pressure of its entrapment in the host diamond in order to determine the pressure of formation of diamond with a precision definitively higher than those reported so far in literature. 2. Experimental The inclusions studied in this work are two virtually colorless olivines included in a colorless Siberian diamond (0.08 carats). The diamond has a complex habit, with a prevailing octahedral form and longest dimension about 3 mm (Fig. 1a). The studied olivines are two of three inclusions within this diamond, all showing negative-crystal shapes. The largest olivine is a flattened, elongated cubo-octahedron with the longest dimension being about 360 μm (Fig. 1b). Two cracks parallel to diamond {111} propagate from two opposite corners of this inclusion and extend up to ca. 130 μm and 20 μm, respectively, into the adjacent diamond. The smallest olivine is an elongated cubooctahedron with the longest dimension being about 80 μm, and is crack-free (Fig. 1a). The third inclusion lies closer to the diamond external faces, is surrounded by several cracks (Fig. 1a), and was not studied in this work. Unit-cell parameters of these two olivine inclusions were determined by X-ray diffraction experiments on a STOE STADI IV four-circle diffractometer (installed at the Department of Geosciences, University of Padova) operating at 50 kV and 40 mA, equipped with a point detector and controlled by the software SINGLE (Angel et al., 2000). This diffractometer was optimized for measurement of unit-cell parameters following recommendations in Angel et al. (2000). Accurate centering of the crystal under the X-ray beam was achieved by iterative adjustment of the crystal offset calculated by the software SINGLE. Such procedure allowed centering of the sample even if the inclusion was not always visible due to the diamond morphology. Typical half-widths of the reflections were between 0.13(1) and 0.18(2)° in ω for the smaller crystal and 0.14(1) and 0.19(1)° in ω for the larger crystal. Therefore, the variations among the half-widths for different reflections are within 2 to 3 σ. Full details of the peak-centering algorithms are provided by Angel et al. (2000). During the centering procedure, the effects of crystal offsets and diffractometer aberrations were eliminated from the refined peak positions by the eight-position centering method of King and Finger (1979). Such procedure allowed us to perfectly center the crystal under the X-ray beam and avoid the experimental problems

Fig. 1. a) Expanded view of the inclusion-bearing diamond studied in this work. The inclusions studied by X-ray diffraction are the largest crystal of olivine in the center and the smallest olivine on the right side of the diamond. b) Close-up of the largest olivine inclusion.

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encountered in previous studies (cf. Kunz et al., 2002). Unconstrained unit-cell parameters were obtained by vector least-squares (Ralph and Finger, 1982) centering 18 diffraction reflections up to 2θ max = 30°. The symmetry-constrained unit-cell parameters reported in Table 1 were found to be within one estimated standard deviation of the unconstrained ones. Optimization of the point-detector diffractometer for measurement of unit-cell parameters required specific modification of the diffractometer setup, which made it unsuitable for the collection of diffraction intensity data necessary for reliable crystal structure refinement useful to get information on the chemistry of the inclusions. Therefore, the sample was transferred along with its holder to a second four-circle diffractometer STOE STADI IV, equipped with a CCD detector from Oxford Diffraction, which allowed collection of complete intensity data. In this case, accurate centering of the crystal under the X-ray beam was achieved considering the known geometric relations between the two diffractometers. The data were acquired using a MoKα radiation operating at 50 kV and 40 mA and up to 86° in 2θ, using a 1° ω-scan with exposure time of 15 s and collecting 570 frames. The sample-detector distance was 60 mm. The program CrysAlis RED (Oxford Diffraction) was used to integrate the intensity data, applying the Lorentz-polarization correction, while the X-RED (Stoe and Cie, 2001) and X-SHAPE (Stoe and Cie, 1999) programs were used to correct for absorption. After correction, the Rint value changed from 14.4% to 10% (a typical Rint for intensity measurement in diamond anvil cell). Absorption due to the diamond host was not corrected for, owing to the very small absorption coefficient of diamond (μ = 0.20 mm−1 for MoKα) with respect to olivine (μ = 1.79 mm−1 for Fo92Fa8). Several works on silicates studied in diamond anvil cell clearly show that the effect of diamond absorption on atomic coordinates, atomic displacement parameters and site occupancies is minimal (e.g. Nestola et al., 2006, 2008). Weighted structural anisotropic refinement was performed in the Pbnm space group using the SHELX-97 program in WINGX package (Farrugia, 1999; Sheldrick, 1997), starting from the atomic coordinates of olivine Mg1.81Fe0.19SiO4 (i.e., ~Fo91Fa9) (Ottonello et al., 1990). The atomic scattering factors were taken from the International Tables for XRay Crystallography (Wilson, 1995). Neutral vs. ionized scattering curves were refined for the oxygen (O and O2−) and silicon (Si and Si4+) atoms. Fully ionized scattering factors were used for Mg2+ and Fe2+.

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Table 2 Unit-cell parameters and volumes at different pressures for olivines Fo92, unit-cell volume at ambient pressure for Fo80, and extrapolated volume V0 for our inclusion Fo92.7. P (GPa)

a (Å)

b (Å)

c (Å)

V (Å3)

Fo92 sample 0.00010(1) 0.469(8) 0.990(7) 1.463(6) 1.957(7) 2.233(8) 2.957(7) 3.490(9) 4.098(9) 4.614(9) 5.299(10) 5.907(9) 6.577(10) 7.265(14) 8.069(14)

4.7630(2) 4.7588(2) 4.7544(2) 4.7505(2) 4.7465(2) 4.7442(2) 4.7389(2) 4.7346(2) 4.7300(2) 4.7266(2) 4.7218(2) 4.7177(2) 4.7132(2) 4.7087(2) 4.7035(2)

10.2276(6) 10.2116(9) 10.1925(5) 10.1768(4) 10.1599(5) 10.1491(7) 10.1284(6) 10.1085(8) 10.0909(5) 10.0763(6) 10.0567(5) 10.0380(6) 10.0197(5) 10.0002(6) 9.9792(5)

5.9925(2) 5.9858(2) 5.9770(2) 5.9699(2) 5.9624(2) 5.9579(3) 5.9478(2) 5.9406(4) 5.9311(2) 5.9243(2) 5.9155(2) 5.9076(2) 5.8994(2) 5.8906(2) 5.8807(2)

291.92(2) 290.88(3) 289.64(2) 288.61(2) 287.53(2) 286.87(3) 285.48(2) 284.31(3) 283.10(2) 282.15(2) 280.90(2) 279.76(2) 278.60(2) 277.38(2) 276.02(2)

Fo80 sample 0.00010(1)

4.7711(2)

10.2623(7)

6.0080(3)

294.17(3)

Extrapolated V0 for our inclusion Fo92.7 sample P (GPa)

V (Å3)

0.00010(1)

291.73(2)

Anisotropic thermal parameters were obtained for all atoms. Very low residual electron-density maximum was observed in the differenceFourier map. Details of the refinement results are reported in Table 1 along with the cation distribution at M2 and M1 sites, from which it was possible to retrieve the composition for our larger olivine inclusion being Fo92.7(4). Tables containing observed and calculated structure factors are available in the on-line journal depository. Attempts to refine the crystal structure of the smallest olivine were unsuccessful, likely due to the limited size and the deep position inside the diamond. In order to estimate the unit-cell volume at room pressure for Fo92.7 we have performed X-ray diffraction measurements at ambient conditions on two single-crystals of natural olivine selected from the

Table 1 Unit-cell parameters of the larger and smaller olivine inclusion, crystal-structure refinement details, atomic coordinates, anisotropic thermal parameters and selected bond lengths (Å) for the larger crystal. Larger crystal a (Å) b (Å) c (Å) V (Å3) S.G. Radiation Total refl.ns Unique refl.ns Rint (%) R4σ (%) GooF N° parameters

4.7605(7) 10.2153(19) 5.9798(8) 290.80(2) Pbnm Mo Κα 4302 426 10.7 3.4 0.9 45

Smaller crystal

Mg and Fe cation distribution based on the refined electrons at M2 and M1 sites for the larger crystal

a (Å) b (Å) c (Å) V (Å3)

4.7580(7) 10.2015(18) 5.9904(9) 290.77(2)

M2 site

M1 site

Mg = 0.922(6) Fe = 0.077(6)

Mg = 0.932(6) Fe = 0.068(6)

Atomic coordinates and thermal parameters (Å2) for the larger crystal Site

x

y

z

U11

U22

U33

U23

U13

U12

Ueq

T M2 M1 O1 O2 O3

0.4268(2) 0.9903(2) 0 0.7662(6) 0.2211(6) 0.2784(4)

0.0942(1) 0.2775(1) 0 0.0923(3) 0.4480(3) 0.1632(2)

0.25 0.25 0 0.25 0.25 0.0335(3)

0.0081(6) 0.0127(8) 0.0074(7) 0.006(1) 0.010(1) 0.0090(9)

0.0042(5) 0.0048(7) 0.008(7) 0.007(1) 0.006(1) 0.0068(9)

0.0057(5) 0.0071(6) 0.0056(7) 0.008(1) 0.006(1) 0.0066(8)

0 0 −0.0009(4) 0 0 0.0009(8)

0 0 −0.0008(5) 0 0 −0.0012(8)

−0.0004(4) −0.0000(5) 0.0003(5) 0.0020(1) 0.0000(1) 0.0004(7)

0.0060(3) 0.0082(4) 0.0070(4) 0.0074(6) 0.0076(6) 0.0075(4)

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suite studied by Princivalle and Secco (1985) (samples LE8 and BO321) showing compositions Fo92 and Fo80, respectively. To ensure consistency with our data on the olivine inclusion, the unit-cell parameters of both samples Fo92 and Fo80 were re-determined in this work using identical equipment and procedures used for measuring the unit-cell volume of the inclusion. The data for V0 of Fo92 (LE8) and Fo80 (BO321) are reported in Table 2. Finally, the unit-cell parameters of sample Fo92 (LE8), which is a very close composition to our Fo92.7, were measured in situ at fifteen different pressures, from room pressure to 8.07 GPa. The sample was studied using a STOE STADI IV four-circle diffractometer and the SINGLE software (Angel et al., 2000). The crystal was loaded in an ETH-type diamond anvil cell (Miletich et al., 2000), using a steel gasket (T301), pre-indented to a thickness of 90 μm and with a hole of 250 μm in diameter. A single-crystal of quartz was used as an internal diffraction pressure standard (Angel et al., 1997) and a 16:3:1 mixture of methanol:ethanol:water was used as hydrostatic pressure medium, which is demonstrated to be hydrostatic up to the maximum pressure reached in this work (Angel et al., 2007). Unit-cell parameters were determined at high pressure by the method of eight-position diffracted-beam centering (Angel et al., 2000; King and Finger, 1979). The unit-cell volumes measured at different pressures are reported in Table 2. 3. Results and discussion 3.1. Crystal-structure and chemical composition The crystal structure of the largest olivine inclusion was determined with a remarkable agreement factor R1 = 3.4%, a typical value for a structure determination performed with the crystal in air. The quality of the data collected allowed us to refine the crystal structure anisotropically and all the atoms gave positive atomic displacement parameters (see Table 1). As a consequence, we obtained with high precision the mean number of electrons at M2 and M1 crystallographic sites, i.e., 13.08 (± 0.22) and 12.95 (± 0.24) electrons, respectively (errors here and in the following are 1-s.d. uncertainties). These values allowed us to obtain the cation distribution at M2 and M1 reported in Table 1, which provides a bulk composition Fo92.7(4) for our olivine. Such composition is reliable even if we did not consider any electron contributions from potential Ca, Ni, Ti, Mn, Na, Cr and K impurities. In fact, based on data reviewed by Stachel and Harris (2008) for 831 samples of olivine inclusions in diamond, the content of Ni is around 0.007 a.p.f.u., while the total content of other minor elements is negligible (only 0.001 a.p.f.u. on average). In terms of electrons, the entire corresponding contribution from all minor elements is only 0.17 (0.35 using mean + 2 s.d. values reported in Stachel and Harris, 2008) electrons, a value within the error of the structure refinement. The composition determined is well within the compositional field for Yakutian mantle olivine (Fo91 to Fo94; Sobolev et al., 2009). Using the subdivision of peridotitic inclusions into harzburgitic, lherzolitic and wehrlitic parageneses originally proposed by Sobolev et al. (1973), the composition of our sample is typical of a harzburgitic olivine inclusion of the peridotitic paragenesis, which based on the review of Stachel and Harris (2008) falls in the range Fo90.2–95.4 (mean Fo93.2, mode in class Fo93.0), although significant compositional overlap exists with lherzolitic olivines (range Fo90.1–93.6, mean Fo92.0, mode in class Fo92.0–92.5). 3.2. Evaluation of the internal pressure The formation pressure of an inclusion (Pf) can be estimated from the residual internal pressure exerted by the host diamond (Pi), assuming elastic relaxation of the diamond–inclusion pair to ambient P–T (e.g., Barron, 2005; Izraeli et al., 1999; Rosenfeld and Chase, 1961;

Zhang, 1998). The internal pressure on the inclusion can be obtained from its unit-cell volume (Vi) and the P–V equation of state calibrated for its particular composition. We determined the P–V equation of state for a natural olivine with composition Fo92, i.e. close to the composition of our inclusion, using a diamond anvil cell and measuring the unit-cell volumes at varying P by single-crystal X-ray diffraction (Fig. 3). The results (Table 2) allowed us to determine the bulk modulus KT0, and its first pressure derivative K′, using a 3rd-order Birch-Murnaghan equation of state (Birch, 1947) calculated using the software EOSFIT5.2 (Angel, 2000): V0 = 291.92(2) Å3, KT0 = 123.4(9) GPa, K′ = 5.5(3). These elastic parameters are within the range of previous estimates for Mg-rich olivine (Andrault et al., 1995; Hazen, 1976; Smyth et al., 2006). Recent experimental data obtained on natural samples of olivines with varying compositions and using the same experimental laboratory and setup used in this work (Nestola et al., submitted for publication) indicate that variations of up to at least 10% in forsterite content have negligible effect on KT0 and K′ values. Accordingly, the equation of state we obtained for sample Fo92 can safely be applied to our inclusion Fo92.7. It is well known that the forsterite–fayalite solid solution shows no excess volume of mixing (e.g., Princivalle and Secco, 1985). Therefore, the unit-cell volume at ambient pressure and temperature (V0) of our inclusion can be calculated by linear extrapolation to our composition Fo92.7 of the unit-cell volumes determined for Fo92 and Fo80 at ambient P–T, using identical experimental procedures and equipment (Table 2). As reported in Table 2 the extrapolated V0 for our olivine is 291.73(2) Å3. Knowing the V0 and the Vi, and the above equation of state coefficients, we calculate an internal pressure Pi = 0.40(1) GPa. The estimated internal pressure is within the range (0.13–0.65 GPa) obtained using the Raman shift technique on sixteen similar olivine inclusions in three diamonds from the same kimberlite (Izraeli et al., 1999). The small error of ±0.01 GPa (calculated by normal propagation of errors on Vi, V0, KT0 and K′) can be compared with the much larger errors of ca. ±0.15 GPa with the Raman shift technique (Izraeli et al., 1999). 3.3. Diamond formation pressure Izraeli et al. (1999) used bulk moduli and thermal expansion data for olivine and diamond from the literature to devise a simple barometer for olivine inclusions, assuming perfect elastic behaviour. Unfortunately, the authors did not perform an accurate evaluation of the uncertainties of their barometric calibration. In order to evaluate the formation pressure along with its uncertainties, we have calculated Pf for our olivine inclusion, following the procedure described in Howell et al. (2010), using thermal expansion data for olivine from Gillet et al. (1991) and compressibility data from this work. The temperature dependency of olivine compressibility was assumed to be equal to that of pure forsterite (Isaak et al., 1989). Thermoelastic parameters for diamond were the same as in Howell et al. (2010). Assuming mantle temperatures between 800 °C and 1300 °C, we obtained a pressure of formation Pf between 3.5(2) and 4.9(2) GPa, respectively (Fig. 2). The quoted errors were estimated by numerical propagation of errors (1 s.d.) on Pi and thermoelastic parameters. The error on our measured Pi contributes negligible errors (less than ±0.02 GPa) on Pf, whereas uncertainties in olivine thermal expansion coefficients are by far the largest source of error. By comparison, typical uncertainties on Raman-based measurements of Pi alone would propagate errors of ca. ±0.2 GPa on calculated Pf (cf. Izraeli et al., 1999). The obtained estimates of Pf are within error of the diamond stability field and suggest formation close to the graphite–diamond boundary (Fig. 2). Using a temperature of 1200 °C for diamond formation (i.e., the same T as that estimated by Izraeli et al., 1999, for two Udachnaya olivine-bearing diamonds based on nitrogen

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Fig. 2. Estimated pressures of formation for the Udachnaya olivine inclusion (horizontal bars = ± 1 s.d.), calculated at 100 °C increments of T in the range 800–1300 °C. The half-tone band is the graphite–diamond boundary according to thermodynamic calculation by Berman (1979; lower P limit) and Chatterjee (1991; upper P limit). The Chatterjee curve is in excellent agreement with reversed experiments by Kennedy and Kennedy (1976) at T = 1100–1625 °C. Dashed lines are reference conductive geotherms at different surface heat flow (mW m−2) after Pollack and Chapman (1977). P–T conditions for Siberian peridotite xenoliths (calculated following recommendations in Nimis and Grütter, 2010) and inclusions in diamonds are shown for comparison. P–T estimates for inclusions in peridotitic diamonds: chromian diopside — single-Cpx thermobarometry (Nimis, 2002, Nimis and Taylor, 2000); garnet — strain birefringence analysis and nitrogen-aggregation thermometry (Howell et al., 2010); olivine — micro-Raman spectroscopy and nitrogen-aggregation thermometry (range for 16 inclusions in 3 diamonds, Izraeli et al., 1999) and this work. Source of data for Siberian xenoliths: Boyd (1984), Boyd et al. (1976, 1997), Canil and O'Neill (1996), Griffin et al. (1996), Pearson et al. (1994), Pokhilenko et al. (1977, 1991, 1993), Rodionov and Sobolev (1985), Solovjeva et al. (1995a,b, 1997).

aggregation state), a Pf of 4.6(2) GPa is calculated. This value is within the range (4.4–5.2 GPa) (if the same procedure adopted here is applied to Pi data from Izraeli et al. (1999), the range for Pf becomes 4.2–5.0 GPa) of the Pf values estimated by Izraeli et al. (1999), based on micro-Raman spectrometry at the same T for sixteen olivine inclusions in three Udachnaya diamonds (Fig. 2). If lower temperatures of 850 to 1100 °C are assumed, the calculated pressures (Pf) lie within the errors of conditions estimated by Nimis (2002) for isolated inclusions of chromian diopside in Siberian diamonds using singleCpx thermobarometry (Fig. 2). The small cracks surrounding the largest olivine inclusion indicate potential depressurization by non-elastic processes and, consequently, possible underestimation of the formation pressure. The nearly identical unit-cell volume measured on the smallest, crack-free inclusion (Table 1) suggests that their effect on pressure estimates is small compared to errors derived from uncertainties in the thermal expansion of olivine (note that multiple olivine inclusions in the same diamond almost invariably show similar compositions (typically within ±1 in Mg# value; e.g., Promprated et al., 2004; Sobolev et al., 2008), hence the same P–V equation of state can reasonably be adopted also for the smallest olivine inclusion). The observation by Izraeli et al. (1999) that similar cracks around their olivine inclusions did not cause systematic deviations in measured Pi relative to crackfree inclusions corroborates this conclusion.

3.4. Evaluation of differential stress on the olivine inclusions The unit-cell edges of the investigated olivine inclusions have been compared with the unit-cell edges of olivine Fo92 measured at variable pressure in a diamond anvil cell by single-crystal X-ray diffraction under hydrostatic conditions (Fig. 3). To ensure data consistency, the experimental values for Fo92 at variable pressure have been extrapolated to Fo92.7 (the composition of the olivine inclusion) using the same linear relation observed at ambient P–T (see “Diamond formation pressure”). All data measured at 15 different pressures (Table 2) lie within three times their nominal standard deviations of

the respective third-order Birch–Murnaghan equations of state determined for a, b and c edges (Fig. 3). The larger olivine inclusion has slightly lower c edge than expected at the estimated internal pressure of 0.40 GPa, whereas a and b edges are within errors of the predicted values at this pressure (Fig. 3). The smaller olivine inclusion shows an opposite behavior, with slightly higher c edge and slightly lower b edge than expected and a edge within errors of the predicted value. The observed discrepancies suggest possible deviations from perfectly hydrostatic conditions. The calculated deviatoric strain (defined as the change in unit-cell parameters from hydrostatic to non-hydrostatic conditions at the same average stress; cf. Zhao et al., 2010) is ε11 = + 3.36(5) × 10−4, ε22 = + 3.92(5) × 10−4, and ε33 = − 9.69(8) × 10−4 for the larger olivine and ε11 = + 1.89(4) × 10−4, ε22 = + 9.60(7) × 10 −4 , and ε33 = − 8.02(6) × 10−4 for the smaller one. Non-hydrostatic conditions can be ascribed to anisotropic pressure release at the inclusion during post-entrapment processes. Differential pressure release due to oriented fracturing of the host diamond can reasonably be excluded, because no volume increase is observed on the larger olivine inclusion relative to the crack-free smaller inclusion. Moreover, the opposite deviations exhibited by the two inclusions indicate that the observed deviations were not controlled only by anisotropic relaxation of the orthorhombic olivine lattice to ambient P–T. Other potentially significant factors are plastic deformation of the diamond, which, however, is probably of minor importance in upper mantle rocks (cf. Cayzer et al., 2008), and shape of the inclusions. Indeed, the two inclusions exhibit very different shapes (flattened ca. perpendicular to olivine [010] vs. slightly elongated ca. along olivine [001]), so that variable finite expansion along olivine a, b and c axes may have induced deviatoric stress at the host–inclusion interface. Evaluation of shape effects would require complex computational procedures and, to the best of our knowledge, no quantitative model is presently available for negative crystal-shaped inclusions such as those here studied. We only note that the strongest observed discrepancies concern the olivine crystallographic directions characterized by the largest compressibility (b and c axes), which are evidently more sensitive

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(only slightly greater than the experimental errors) and should not have significantly affected evaluation of the remnant pressure at the inclusions. 4. Conclusions The present work shows that it is possible to retrieve the depth of provenance of inclusion-bearing diamonds using non-destructive techniques with a precision higher than with previously proposed insitu methods (e.g., micro-Raman spectroscopy). This is particularly relevant for included minerals that have thermoelastic properties which tend to retain relatively small internal pressures when the host diamond is brought to ambient conditions (e.g., olivine, garnet, and pyroxenes; cf. Barron, 2005). The same experimental procedure adopted here can potentially be extended to minerals other than olivine, provided the relative P–V equation of state is independent of composition or the composition can be adequately estimated. For mantle minerals that are characterized by simple substitution mechanisms (e.g., orthopyroxene, ringwoodite, magnesium–perovskite, and ferropericlase) the composition can be easily determined by X-ray diffraction crystal-structure refinement, as done here for olivine. An X-ray diffraction procedure capable of obtaining sufficiently precise compositional data on chemically more complex minerals such as garnet and clinopyroxenes, including eclogitic varieties for which no reliable barometric method is currently available, is under development. The minimum size of the inclusion required to obtain high-quality data will vary depending on its composition. From present data, a minimum size of ca. 100 μm can reasonably be estimated for typical mantle olivine. This limit can probably be reduced to 60–70 μm for minerals with higher contents of heavy elements characterized by high X-ray scattering power. Acknowledgments Fig. 3. Evolution of the unit-cell parameters as a function of pressure for the sample Fo92 compressed under hydrostatic compression in a diamond-anvil cell (black symbols). In blue and red colors the unit-cell parameters of the large and small olivine inclusions, respectively, are shown at their internal pressure of 0.40 GPa. The dashed curves fitting the experimental data up to more than 8 GPa represent the equations of state for each unit-cell parameter relative to the Fo92 hydrostatically compressed.

to small deviations from hydrostatic conditions, while a edge is virtually identical in both inclusions and in the experimental data at 0.40 GPa (Fig. 3). Internal compensation of olivine lattice strain along the b and c crystallographic axes allowed to maintain the overall unitcell volumes of the two inclusions essentially equal. A rough evaluation of the potential bias on estimates of formation pressure caused by anisotropic pressure release can be obtained considering the edge values showing the largest negative deviations from predicted (hydrostatic) values. Using elastic constants for Fo90 reported in Webb (1989) and the above strain tensors, we calculate an overpressure of 0.23 GPa on the c edge of the larger olivine and of 0.19 GPa on the b edge of the smaller olivine. Adding these values to the average internal pressure of 0.40 GPa determines an increase of only ~0.3 GPa in estimated source P. Complementary information on the deviatoric stress on the olivine inclusions is provided by the analysis of the widths of the diffraction peaks. The widths of diffraction reflections representative of variably oriented crystallographic planes were measured using a point detector for both olivine inclusions. The average peak width showed only small spread among different reflections (cf. experimental section). No systematic variation in peak width with crystallographic orientation was observed in either inclusion, suggesting no major deviation from uniform strain conditions. In addition to the above considerations, the virtually identical unit-cell volumes of the two olivine inclusions in spite of their different size and shape, suggest that deviations from hydrostatic conditions were of minor importance

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