Shear Waves in the Diamond-Anvil Cell Reveal Pressure-Induced Instability in (Mg,Fe)O

Shear waves in the diamond-anvil cell reveal pressure-induced instability in (Mg,Fe)O

Steven D. Jacobsen*†, Hartmut Spetzler‡§, Hans J. Reichmann¶, and Joseph R. Smyth§

*Bayerisches Geoinstitut, Universita¨ t Bayreuth, 95440 Bayreuth, Germany; ‡Cooperative Institute for Research in Environmental Sciences, University of Colorado, Boulder, CO 80309-0216; §Department of Geological Sciences, University of Colorado, Boulder, CO 80309-0399; and ¶GeoForschungsZentrum Potsdam, Telegrafenberg, 14473 Potsdam, Germany

Communicated by Russell J. Hemley, Carnegie Institution of Washington, Washington, DC, March 5, 2004 (received for review February 15, 2004) The emerging picture of Earth’s deep interior from seismic tomog- compositional variation or phase changes in (Mg,Fe)O are raphy indicates more complexity than previously thought. The ongoing (16). presence of lateral anisotropy and heterogeneity in Earth’s mantle Megahertz-frequency ultrasonics measurements in the mul- highlights the need for fully anisotropic elasticity data from min- tianvil press are a leading resource for experimental thermoelas- eral physics. A breakthrough in high-frequency (gigahertz) ultra- tic data on polycrystalline samples at simultaneous high pres- sound has resulted in transmission of pure-mode elastic shear sures and temperatures relevant to Earth’s mantle (17). waves into a high-pressure diamond-anvil cell using a P-to-S However, single-crystal experiments giving elastic anisotropy elastic-wave conversion. The full elastic tensor (cij) of high-pressure (cij) in the multianvil press are relatively few (18). Also at minerals or metals can be measured at extreme conditions without megahertz frequencies, ultrasonic interferometry has been ap- optical constraints. Here we report the effects of pressure and plied successfully to single-crystal samples in the gas- or liquid- composition on shear-wave velocities in the major lower-mantle pressurized piston-cylinder apparatus (19) and the Paris– oxide, magnesiowu¨ stite-(Mg,Fe)O. Magnesiowu¨ stite containing Edinburgh cell (20), but these frequencies still limit the Ϸ more than 50% iron exhibits pressure-induced c44 shear-mode minimum sample size to Ϸ1 mm. For microcrystals less than softening, indicating an instability in the rocksalt structure. The Ϸ0.5 mm in size, as most available synthetic high-pressure Ϸ oxide closer to expected lower-mantle compositions ( 20% iron) mantle phases are, the DAC is the preferred pressure cell, shows increasing shear velocities more similar to MgO, indicating capable of hydrostatic pressures to Ϸ10 GPa with liquid pressure that it also should have a wide pressure-stability ﬁeld. A complete media, and to much higher pressures when loaded with a gas such sign reversal in the c44 pressure derivative points to a change in the as helium or neon. Brillouin scattering in the DAC is a powerful Ϸ topology of the (Mg,Fe)O phase diagram at 50–60% iron. The method for measuring single-crystal elasticity to pressures now relative stability of Mg-rich (Mg,Fe)O and the strong compositional in excess of 50 GPa (21) and temperatures to 1,500 K (22), but ٢͞ ٢ dependence of shear-wave velocities (and c44 P) in (Mg,Fe)O as an optical method it is limited to fairly transparent single implies that seismic heterogeneity in Earth’s lower mantle may crystals. Another novel method, impulse-stimulated scattering result from compositional variations rather than phase changes in (23), has been extended recently to include acoustic surface- (Mg,Fe)O. wave measurements (24) from which shear velocities in opaque minerals or metals are obtained but without P-wave velocities dense oxide of iron and magnesium is expected to coexist needed for the complete elastic tensor. Awith magnesium silicate perovskite-(Mg,Fe)SiO3 in Earth’s By extending the ultrasound to gigahertz frequencies, we lower mantle at 660- to 2,900-km depth (1). The physical reduce acoustic wavelengths in minerals to Ϸ1–10 ␮m. Pure- properties of (Mg,Fe)O have been studied extensively by using mode ultrasonic shear waves have been transmitted into a both static (2–5) and dynamic methods (5–9), but there remains high-pressure DAC. To resolve some of the questions surround- considerable uncertainty surrounding the structure and behavior ing (Mg,Fe)O stability, we measured the pressure dependence of of (Mg,Fe)O in the lower mantle. Periclase (MgO) has the S-wave travel times in (Mg,Fe)O crystals ultrasonically to ex- rocksalt structure to at least 227 GPa (10). On the other hand, ϭ␳ 2 amine the behavior of the c44 elastic constant ( VS͓100͔)asa wu¨stite (FeO) undergoes a displacive phase transition to a Ϸ function of composition. This pure-shear mode is the elastic rhombohedral distorted B1 structure at 17 GPa and subse- parameter most sensitive to the rhombohedral distortion ob- quently to the B8 or NiAs-type structure above 100 GPa (11). served in FeO before the B1–B8 phase transition (11) and Differences in the high-pressure behavior of MgO and FeO therefore should be a useful predictor of (Mg,Fe)O stability. imply a change in topology of the (Mg,Fe)O phase diagram, Shear-mode softening (i.e., decreasing shear velocities with GEOPHYSICS requiring there to be a two-phase field or exsolution gap, but increasing pressure) in FeO (25) is the result of strong magne- where in composition between ferropericlase (Mg-rich) and toelastic coupling driving the B1 (paramagnetic) to rhombohe- magnesiowu¨stite (Fe-rich) this should occur is not clear yet. dral (antiferromagnetic) phase transition (26). Mode softening Iron-rich compositions (Mg0.1Fe0.9)O and (Mg0.25Fe0.75)O dis- in FeO has also been deduced from lattice strain in nonhydro- play the rhombohedral distortion above 20 and 60 GPa, respec- static x-ray diffraction experiments (27), but uncertainties in the tively (12, 13). At 80–90 GPa and 1,000 K, (Mg Fe )O and 0.50 0.50 magnitude of c from such methods are on the order of 15–20%. (Mg Fe )O were reported to separate into ferropericlase ij 0.60 0.40 Our direct (ultrasonic) observations of shear elasticity in plus FeO in the externally heated diamond-anvil cell (DAC) (Mg,Fe)O were carried out by using an acoustic shear-wave (14). But in a similar study using a laser-heated DAC, both interferometer for the DAC. The methodological advance not (Mg Fe )O and (Mg Fe )O were stable in the B1 struc- 0.39 0.61 0.25 0.75 only has broad application to high-pressure research in Earth ture at 100 GPa and 2,500 K (13). A high-spin to low-spin Ϸ transition in Fe was reported for (Mg0.83Fe0.17)O between 50 and 60 GPa (15) but without evidence for a volume change or Abbreviation: DAC, diamond-anvil cell. phase stability. Thus, despite concerted efforts to elucidate the †To whom correspondence should be addressed at: Carnegie Institution of Washington, structure and stability of (Mg,Fe)O at lower mantle conditions, Geophysical Laboratory, 5251 Broad Branch Road NW, Washington, DC 20015. E-mail: experiments thus far have led to conflicting results. The search [email protected]. for wave-speed discontinuities in Earth’s lower mantle related to © 2004 by The National Academy of Sciences of the USA www.pnas.org͞cgi͞doi͞10.1073͞pnas.0401564101 PNAS ͉ April 20, 2004 ͉ vol. 101 ͉ no. 16 ͉ 5867–5871 Fig. 1. Making waves in the DAC. (A) The P-to-S acoustic wave converter (between a pair of tweezers) before sputtering the P-transducer. (Scale bar, 3 mm.) The gem is an oriented single crystal of yttrium aluminum garnet (Y3Al5O12), hand-faceted to tolerances of Ϯ0.1° (H. Schulze, Bayerisches Geoinstitut). It produces pure-mode elastic shear energy with 1- to 10-␮m wavelengths and well deﬁned polarization direction for high-pressure elasticity experiments in the DAC. (B) Shear waves are introduced into the DAC through one of the anvils (shown schematically, not to scale). Echoes are produced at each major impedance contrast and labeled as follows: the buffer rod echo, diamond echo, and sample echo. S-wave travel times are determined from acoustic interface spectra produced in the combined diamond and sample echoes by scanning the frequency (29). and materials sciences but also for development of an absolute transducer. The entire round trip through the system is typically pressure scale (21, 28). Ϸ3 ␮s. The time difference between the diamond and the first sample echo is usually very short (8–20 ns) compared with the Experimental Methods width of the input signal (Ϸ100 ns). An interference pattern is The acoustic interferometer is based on our first-generation produced by measuring the amplitude of the combined signal at gigahertz-ultrasonic delay line (29). In its initial form, gigahertz- a position where there is first-order interference (between the ultrasonic interferometry was well suited for high-pressure ex- diamond and sample echoes) and scanning the frequency (Fig. periments in the DAC (30, 31) but limited to P-wave experiments 2). Shear-wave travel times are determined from each fitted by the absence of commercially available shear-wave transducers frequency maxima and minima of interference (29). operating at gigahertz frequencies. Here we describe an acoustic The samples are prepared as oriented single-crystal plates: P-to-S conversion buffer rod for high-pressure shear elasticity polished with parallel faces and flat to Ϸ1͞10␭ with thicknesses experiments in the DAC, pictured in Fig. 1. The buffer rod works ranging from Ϸ20 to 40 ␮m. The plates have a finishing polish on the principle of Snell’s Law. A P-wave traveling in the [100] of optical quality and are placed directly on the culet of the direction of an yttrium aluminum garnet crystal buffer rod (Fig. acoustic transmitting anvil. A small force is applied to the sample 1A) is incident on a conversion facet, cut at a special angle to by adding silica aerogel to a liquid 16:3:1 methanol͞ethanol͞ produce a converted S-wave at 90° to the incident P (Fig. 1B). For water pressure-transmitting medium. The aerogel has a very high cubic materials, the angle of incidence producing an orthogonal porosity (Ͼ90%) and acts as a spring to gently press the sample ϭ ͓100͔͞ ͓100͔ conversion from Snell’s Law is given by tan(i) VP VS . against the anvil. In this way, we avoid the use of messy glues or For optical yttrium aluminum garnet, we determined i ϭ 59.5° foils to achieve acoustic coupling between the sample and the from bench-top measurements of VP and VS. The initial com- diamond. We presume that a very thin layer of the fluid pressure pression waves are produced by a ZnO thin-film P-transducer, medium is present under the sample to an extent determined by sputtered directly onto the side of the buffer rod. The P- the equilibrium between the relative magnitudes of the normal transducer (and conversion to shear) is operable over a very force transmitted from the aerogel and the surface tension of the broad bandwidth, typically from Ϸ0.5 to Ͼ2.0 GHz. By forcing fluid. Pressures Ͼ10 GPa were routinely reached, but the the conversion to occur at 90°, the direction of particle motion aerogel-alcohol mixture is hydrostatic to only Ϸ9 GPa, where the is preserved across the conversion. Both P- and S-waves prop- glass transition was observed by the onset of shear-wave trans- agate in pure-mode directions [100] of the single-crystal buffer mission completely through the sample chamber (i.e., a diamond rod, and therefore the polarization is precisely known. Shear culet-to-culet reflection was detected around this pressure but waves produced in this way are of much higher quality than those always before the sample bridged the anvils). Pressures were usually generated (at megahertz frequencies) by shear-wave determined by using the ruby fluorescence scale (32). transducers, because there is no P-wave contamination. We Shear-wave travel times were measured as a function of suggest that shear-wave generation by this method might be a pressure in [100]-oriented single-crystal (Mg,Fe)O. The samples useful replacement for traditional shear-wave transducers alto- were synthesized by the interdiffusion of Fe and Mg between gether in other ultrasonic applications. single-crystal MgO and prereacted magnesiowu¨stite powders The interferometer uses a continuously running, highly stable (5). Sample nomenclature is FeX, where X gives the atomic ratio frequency synthesizer that provides phase coherence throughout Fe͞(Fe ϩ Mg). The crystal of pure iron-wu¨stite has the non- a measurement. This is akin to the use of a laser in an optical stoichiometric formula Fe0.95O. interferometer and allows us to measure ultrasonic travel times to a small part of an interference fringe or Ϸ1 part in 105 if the Results and Discussion round-trip travel-time through a sample is Ϸ100 ns (sample Measured shear-wave travel times for (Mg,Fe)O are plotted in Fig. thickness of 300–500 ␮m) and to 1 part in 103 if it is an order of 3A. The velocities shown in Fig. 3B are calculated from the travel magnitude shorter (sample thickness of 30–50 ␮m). The con- times by using the sample thicknesses. The initial sample thick- tinuous signal is gated with a pulse generator, allowing the nesses were determined in each case by measuring the zero- introduction of short tone bursts. Impedance contrasts at the pressure travel time and converting to thickness by using the buffer-rod–diamond interface, diamond–sample interface, and bench-top velocities (5). The change in length with pressure was sample–pressure medium interface produce reflections, which calculated from their equations of state over the same pressure return and reconvert to P, and are finally detected by the source range (5). Shear velocities along [100] decrease with increasing

5868 ͉ www.pnas.org͞cgi͞doi͞10.1073͞pnas.0401564101 Jacobsen et al. pressure for wu¨stite-FeO and magnesiowu¨stite samples Fe78 and Ѩ ͓100͔͞Ѩ ϭϪ Ϯ Ϫ Ϯ Ϫ Ϯ Fe56, with VS P 42 ( 1), 26.9 ( 0.4), and 15.2 ( 0.2) msϪ1⅐GPaϪ1. However, for ferropericlase containing Ϸ24% iron, Ѩ ͓100͔͞Ѩ Ϯ Ϫ1⅐ Ϫ1 the sign of VS P switches and is 11( 1) ms GPa . The results demonstrate that increasing Mg content in (Mg,Fe)O acts to stabilize the B1 structure at high pressures. The c44 elastic constants were calculated from the shear velocities as a function of pressure. The results are plotted in Fig. 4, with polynomial fits given in Table 1. For the cubic structure, this term of the elastic tensor provides an important proxy for the cubic body diagonal stiffness (11). The second-order displacive phase transition observed at room temperature for FeO at Ϸ17 Ϸ GPa (11), for (Mg0.1Fe0.9)O at 20 GPa (12), and for Ϸ (Mg0.25Fe0.75)O at 60 GPa (13) is a rhombohedral distortion of the B1 structure. The distortion occurs by elongation of the body diagonal [111] and therefore should be revealed by mode softening in c44. Polynomial fits to c44 with pressure indicate significant reduction in this elastic constant for FeO and Fe78 on the order of 20% and 13%, respectively, over this pressure range. Although we still observe decreasing c44 with pressure in Fe56, it is Ͻ2% at 10 GPa, thus the change in topology of the (Mg,Fe)O high-pressure phase diagram is expected to occur at iron con- Ϸ tents higher than 60% FeO or (Mg0.4Fe0.6)O, consistent with recent in situ high P-T diffraction studies (13). The spin state of iron in (Mg,Fe)O at lower-mantle conditions has major implications for the density, composition, and seismic structure of Earth’s lower mantle. A transition from the usual high-spin state of iron to the low-spin state in (Mg0.83Fe0.17)O was reported at pressures above Ϸ50 GPa by using x-ray emission spectroscopy (15). The authors postulate that the spin-state transition influences Fe–Mg partitioning between magnesiowu¨stite and (Mg,Fe)SiO3-perovskite enough to nearly deplete the perovskite of iron at depths below the transition. Although the authors were unable to report associated volume changes in the (Mg0.83Fe0.17)O in situ, the spin-state transition is expected to decrease effective ionic radius of Fe by as much as 10%. Therefore, even with only 10–20% Fe in (Mg,Fe)O, a rather large (Ϸ2–5%) volume change is expected to occur. The decrease in mean M–O bond distances (and shortened O…O interatomic distances) in the rocksalt structure containing low-spin iron therefore should exhibit increased compressional and shear-wave velocities as the strong O…Ore- Fig. 2. Ultrasonic shear-wave interference spectrum from inside the DAC. pulsive forces become highly incompressible. In this study, we have (A) The acoustic interference spectra (here for magnesiowu¨ stite-Fe78 at 9.1 shown that there is a strong dependence of shear velocities on the GPa) are produced by measuring the amplitude of the returning echo from iron content in (Mg,Fe)O, especially at higher pressures. Given that the diamond culet in lapped contact with the sample at two different a change in the spin state of iron should also influence the Mg–Fe positions in the time domain (Inset, shown at 1,025 MHz). The smooth curve partitioning in the mantle, it is not clear yet how a high-spin to was measured at a position before the sample echo arrives, whereas the low-spin transition in iron will effect seismic wave velocities in the curve showing Ϸ50-MHz modulation was measured at a position in which there is ﬁrst-order overlap between the diamond and sample. (B) Shear- lower mantle, but any increase in the shear elastic moduli brought wave travel-time data are calculated from the frequency of the maxima on by the volume change might be dampened by reduced shear ͞ and minima (29). We solve for the phase experimentally by calculating the velocities associated with an increasing Fe Mg ratio in (Mg,Fe)O. GEOPHYSICS travel time for several values of m(1), the number of whole-integer wave- The advent of acoustic shear waves in the DAC has made lengths in the round-trip (sample) distance for the ﬁrst maximum. The possible direct observation of shear-mode softening in major consequence of choosing the wrong m is illustrated here by plotting the lower-mantle phase (magnesiowu¨stite) and tripled the pressure best m(1) ϭ 16 plus and minus one integer. range over which similar behavior has been measured in FeO.

Table 1. Variation of the c44 elastic constant of (Mg,Fe)O with pressure

Composition c44, GPa Pmax, GPa Ref.

FeO 45.5(1) Ϫ 1.03(2)P Ϫ 0.014(3)P2 3 (ultrasonic) 25 FeO 46.09(7) Ϫ 0.86(4)P Ϫ 0.024(4)P2 8.4 (ultrasonic) This study Fe78 63.42(6) Ϫ 0.91(3)P Ϫ 0.004(3)P2 9.1 (ultrasonic) This study Fe56 83.44(4) Ϫ 0.14(2)P Ϫ 0.003(2)P2 8.8 (ultrasonic) This study Fe24 123.3(2) ϩ 1.24(5)P 7.2 (ultrasonic) This study MgO 155.7(5) ϩ 1.09(7)P Ϫ 0.0047(16)P2 55 (Brillouin) 21 MgO 155.8(2) ϩ 1.11(1)P Ϫ 0.016(3)P2 3 (ultrasonic) 19 MgO 154.4(20) ϩ 0.84(20)P ϩ 0.003(10)P2 18.6 (Brillouin) 37

Jacobsen et al. PNAS ͉ April 20, 2004 ͉ vol. 101 ͉ no. 16 ͉ 5869 Fig. 4. A complete sign reversal in the pressure derivative of the shear elasticity (Ѩc44͞ѨP) in (Mg,Fe)O indicates a pressure-induced structural instability for Fe-rich compositions. Elastic constant data from this study are shown by filled circles with dashed-line fits (given in Table 1). Also plotted are previous ultrasonic data to 3 GPa (solid curves) for MgO (19) and FeO (25) as well as data for MgO from Brillouin scattering [dash-dot (21) and dotted (37) curves]. Shear-mode softening in (Mg,Fe)O may be due to strong magnetoelastic coupling [as in FeO (26)], driving potential magnetic and structural phase transitions. The results indicate that B1-structured ferropericlase is expected to have a similar pressure-stability field as MgO, which is stable at pressures throughout Earth’s lower mantle (10).

complete switching in the high-pressure elastic behavior of (Mg,Fe)O points to a change in the topology of the (Mg,Fe)O phase diagram at Ϸ50–60% iron, consistent with previous in situ x-ray diffraction studies (13). The observed shear-mode soften- Fig. 3. Pressure-induced shear instability is detected in Fe-rich (Mg,Fe)O. (A) ing in Fe-rich (Mg,Fe)O is likely due to strong magnetoelastic The observed ultrasonic travel times (ﬁlled circles) are plotted against pres- coupling [as in FeO (26)] and indicates an instability in the sure. The FeO is wu¨ stite-(Fe0.95O), and otherwise the labels (FeX) indicate the rocksalt (B1) structure at high pressure. However, the high- atomic ratio X ϭ Fe͞(Fe ϩ Mg). (B) Fe-rich (Mg,Fe)O exhibits decreasing shear velocities with increasing pressure. Previous ultrasonic results for FeO (25) are pressure shear elasticity of ferropericlase closer to expected plotted with a solid curve. lower-mantle compositions is more similar to MgO, indicating that it should have a similarly wide pressure-stability field (10). However, shear-wave velocities in (Mg,Fe)O at high pressures Ѩ ͞Ѩ Although we detect a structural instability in Fe-rich magnesio- strongly depend on composition, with c44 P switching between Ѩ ͞Ѩ Ϸ wu¨stite, the elastic derivative c44 P switches (becoming posi- positive for compositions with less than 50% iron to negative tive) for ferropericlase (Fe24) and is more similar to MgO than for iron-rich magnesiowu¨stites (Fig. 4). Therefore, it is possible magnesiowu¨stite Fe56 (Fig. 4 and Table 1). Because of the nature that wave-speed discontinuities and heterogeneity in Earth’s of the high-pressure rhombohedral distortion in magnesiowu¨s- lower mantle (16, 33–36) result from compositional variations tite (body-diagonal elongation), the results provide direct evi- driven by a high-spin to low-spin transition in iron rather than a dence for a systematic increase in the high-pressure stability of structural phase transition in ferropericlase. the B1 structure for (Mg,Fe)O with increasing Mg content. Previous static compression experiments (5) indicate that We thank Hubert Schulze, Klaus Mu¨ller, Georg Hermannsdoerfer, there is a small initial increase in the bulk modulus (and ѨK͞ѨP) Heinrick Ohlmeyer, Sven Lindenhardt, Kurt Klasinski, Jeffrey Cooper, Ϸ and Stephen Mackwell for their assistance. We also thank Jung-Fu Lin, for (Mg,Fe)O with iron contents up to 25% FeO, consistent Russell Hemley, Ho-kwang Mao, and Ian Jackson for useful discussions with theoretical predictions for stoichiometric (Mg,Fe)O (6). and critique of the manuscript. This work was supported by the Deutsche Ѩ ͞Ѩ Here we observe an increase in the derivative c44 P by almost Forschungsgemeinschaft, the National Science Foundation, and the 13% between MgO and (Mg,Fe)O containing Ϸ25% FeO. A Alexander von Humboldt Foundation.

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Jacobsen et al. PNAS ͉ April 20, 2004 ͉ vol. 101 ͉ no. 16 ͉ 5871