Physics of the Earth and Planetary Interiors 162 (2007) 22–31

The elastic properties of �-Mg2SiO4 from 295 to 660 K andimplications on the composition of Earth’s upper mantle

Donald G. Isaak a,b,∗, Gabriel D. Gwanmesia c, Derek Falde b,Michael G. Davis b, Richard S. Triplett c, Liping Wang d

a Institute of Geophysics and Planetary Physics, University of California, Los Angeles, CA 90095-1567, United Statesb Department of Mathematics and Physics, Azusa Pacific University, Azusa, CA 91702-7000, United Statesc Department of Physics and Pre-Engineering, Delaware State University, Dover, DE 19901, United States

d Mineral Physics Institute, Stony Brook University, Stony Brook, NY 11794-2100, United States

Received 30 November 2006; received in revised form 22 February 2007; accepted 28 February 2007

Abstract

New, high quality data are presented on the elastic properties of �-Mg2SiO4 (wadsleyite) from 295 to 660 K at ambient pressure.Elasticity measurements were carried out on a sintered polycrystal using resonant ultrasound spectroscopy (RUS). Room temperaturevalues for the adiabatic bulk (KS) and shear (G) moduli are 170.2(1.9) and 113.9(0.7) GPa, respectively. The KS data exhibit lineardependence on temperature (T) with (∂KS/∂T)P = −1.71(5) × 10−2 GPa K−1. Our result for (∂KS/∂T)P is consistent with a relativelyhigh magnitude for this derivative which contrasts with −1.20 × 10−2 to −1.30 × 10−2 GPa K−1 reported in some earlier studies.The average (∂G/∂T)P = −1.57(3) × 10−2 GPa K−1 over the temperature range studied. This result is consistent with most earliermeasurements of (∂G/∂T)P for wadsleyite. The (∂KS/∂T)P and average (∂G/∂T)P for wadsleyite over 295–660 K are not measurablyaffected by the presence of iron as seen from comparing our results with those from a RUS study on �-(Mg0.91Fe0.09)2SiO4. Further,our results for (∂KS/∂T)P and average (∂G/∂T)P are consistent with olivine content of 44–54% at 410-km depth in Earth, given other

assumptions made in recent studies about properties of the �- and �-olivine phases for P, T conditions at that depth. Our G(T) dataappear to exhibit small, but persistent, nonlinear behavior; the magnitude of (∂G/∂T)P increases with T. We discuss the importantimplications on upper mantle mineralogy if this nonlinear effect is confirmed and is demonstrated to apply when extrapolatingbeyond the temperature range of 295–660 K.© 2007 Elsevier B.V. All rights reserved.

nant ult

Keywords: Wadsleyite; Elastic properties; Mantle composition; Reso

1. Introduction

The elasticity of olivine [�-(Mg, Fe)2SiO4] and itshigh pressure polymorphs, wadsleyite (�) and ringwood-ite (�), are of significant interest because olivine is a

∗ Corresponding author at: Department of Mathematics and Physics,Azusa Pacific University, Azusa, CA 91702-7000, United States.

E-mail address: disaak@apu.edu (D.G. Isaak).

0031-9201/$ – see front matter © 2007 Elsevier B.V. All rights reserved.doi:10.1016/j.pepi.2007.02.010

rasound spectroscopy; Seismic discontinuities

primary mineral in many petrologic models of the Earth’supper mantle. Accurate data on elasticity of the olivineand wadsleyite phases are critical for investigating therole of the olivine [�-(Mg, Fe)2SiO4] to wadsleyite [�-(Mg, Fe)2SiO4] phase transition on the 410-km seismicdiscontinuity and for determining the olivine content of

the Earth’s upper mantle by comparing laboratory elas-ticity data for the �- and �-phases of (Mg, Fe)2SiO4 withthe seismic velocity jumps (discontinuities) at 410-kmdepth.

h and P

amaZeseivuatKre(aBKcmoasva1(ras(

dtsl(−(−2caL(Ko(nr

D.G. Isaak et al. / Physics of the Eart

The elasticity of the low pressure �-phase [Mg2SiO4nd (Mg, Fe)2SiO4] has received considerable experi-ental attention in the past few decades (e.g., Isaak et

l., 1989; Isaak, 1992; Zaug et al., 1993; Li et al., 1996;ha et al., 1996, 1998; Abrahamson et al., 1997; Darlingt al., 2004). However, precise modeling of the 410-kmeismic discontinuities also requires accurate data on thelastic properties of the wadsleyite phase. Several stud-es on end member wadsleyite (�-Mg2SiO4) agree onalues of the adiabatic bulk (KS) and shear (G) mod-li. Brillouin scattering measurements on single-crystalsnd ultrasonic interferometry studies using polycrys-alline specimens generally yield ambient values for

S and G in the range of 170–174 and 112–115 GPa,espectively (Sawamoto et al., 1984; Li et al., 1996; Zhat al., 1997; Li et al., 1998, 2001). Sinogeiken et al.1998) reported comparable values of KS = 170(3) GPand G = 108(2) GPa for Fe-bearing wadsleyite fromrillouin scattering measurements on single-crystal.atsura et al. (2001) and Mayama et al. (2004) both

onducted resonant ultrasound spectroscopy (RUS)easurements on a hot-pressed polycrystalline specimen

f �-(Mg0.91Fe0.09)2SiO4 and obtained KS = 165.7 GPand G = 105.4–105.7 GPa. Current data on the pres-ure dependence of the elasticity of wadsleyite indicatealues of (∂KS/∂P)T and (∂G/∂P)T cluster near 4.2nd 1.5, respectively (Zha et al., 1997; Li et al.,996, 1998, 2001). Liu et al. (2005), however, found∂KS/∂P)T = 4.56(23) and (∂G/∂P)T = 1.75(9), from aeanalysis of Li et al. (2001) data, which are near 4.8nd 1.7, respectively, found in the first direct mea-urements for these pressure derivatives of β-Mg2SiO4Gwanmesia et al., 1990a,b).

There are fewer and relatively more dispersedata of the temperature effects on KS and G forhe wadsleyite phase. Katsura et al. (2001) mea-ured KS and G for β-(Mg0.91Fe0.09)2SiO4 over aimited temperature range of 278–318 K, obtaining∂KS/∂T)P = −1.6(3) × 10−2 GPa K−1 and (∂G/∂T)P =1.2(1) × 10−2 GPa K−1. These results contrast with

∂KS/∂T)P = −1.2(1) × 10−2 GPa K−1 and (∂G/∂T)P =1.7(1) × 10−2 GPa K−1 reported by Li et al. (1998,

001) from ultrasonic interferometry studies on poly-rystalline �-Mg2SiO4 and with −1.29(17) × 10−2

nd −1.58(10) × 10−2 GPa K−1, respectively, cited byiu et al. (2005) from their reanalysis of Li et al.

2001) results. Mayama et al. (2004) re-measuredatsura et al. (2001) specimen over 298–470 K and

btained (∂KS/∂T)P = −1.75(3) × 10−2 GPa K−1 and∂G/∂T)P = −1.59(1) × 10−2 GPa K−1. There appearsear convergence in (∂G/∂T)P for a limited temperatureange if Katsura et al. (2001) data are discounted, and

lanetary Interiors 162 (2007) 22–31 23

there remain discrepancies in (∂KS/∂T)P for any temper-ature range.

Our purpose is to present new, precise data onthe temperature derivatives (∂KS/∂T)P and (∂G/∂T)P,of synthetic hot-pressed polycrystalline wadsleyite (�-Mg2SiO4) end member obtained by the resonantultrasound spectroscopy technique. These data are over295–660 K, thus, more than doubling the temperaturerange of previous RUS measurements for wadsleyite KSand G. We compare our data with those from previousstudies and discuss their implications on estimates of theolivine content of the Earth’s upper mantle.

2. Experimental procedures

The polycrystalline specimen of wadsleyite (�-Mg2SiO4) used in this study was hot-pressed inthe 1500-tonnes multi-anvil (Presnall Press) apparatus(Haemyeong et al., 2006) at the Geophysical Labora-tory of the Carnegie Institution of Washington, DC usinghot-pressing techniques described in Gwanmesia et al.(1990a, 1993). Starting material was very fine powder(<2 �m) obtained by crushing single crystal �-Mg2SiO4grown by Toru Inuoe at Ehime University in Matsuyama,Japan. The powder was first dried at 250 ◦C for 24 h andthen loaded into a Pt capsule. The capsule was cold-sealed in air and placed inside a NaCl sleeve. The samplewas hot-pressed at 14 GPa and 950 ◦C for 2 h inside the14/8 standard cell assembly. Synchrotron X-radiationdiffraction was used to verify complete transformationof the recovered sample to the wadsleyite structure. Thebulk density of the specimen (ρ = 3.468 g/cm3) mea-sured by the Archimedes’ immersion method was within99.9% of the X-ray density.

The original wadsleyite polycrystal was cylindrical inshape, about 3 mm in diameter and length. The specimenwas ground and polished into a precise right-rectangularparallelepiped using 9, 6, 3, 1, and 1/4 �m diamond com-pounds in succession. The final edge lengths (in mm) ofthe prepared rectangular parallelepiped specimen were2.167(1), 2.107(4), and 2.042(2), where the parentheticalnumbers indicate uncertainty in the last digit.

The adiabatic bulk and shear moduli of the preparedwadsleyite specimen were determined using the right-rectangular parallelepiped resonance (RPR) version ofresonant ultrasound spectroscopy. In RPR, the elasticproperties of a right-rectangular parallelepiped specimenare determined from measurements of its mechanical

resonance spectrum, edge lengths, and density (Ohno,1976). The parallelepiped wadsleyite specimen wasplaced between a pair of shear PZT transducers, touchingthe two transducers with specimen corners diagonally

h and P

24 D.G. Isaak et al. / Physics of the Eart

opposite each other. The transducers were held to thespecimen corners with a force equal to the weight of a fewgrams. One transducer provided mechanical vibration tothe specimen; the other monitored the vibration ampli-tude of the specimen. By scanning a range of frequencieswith a DRS Modulus II apparatus produced by DynamicResonance Systems, Inc., spectra of resonant frequen-cies at various temperatures were obtained. Samples ofthe spectra, depicting four modes in the 2.6–2.7 MHzrange at four temperatures, are provided in Fig. 1. Thetendency for some modes to invert, as seen in Fig. 1, iscommon in RUS and poses no problem for our analyses.These inversions are related to phase shifts associatedwith driven oscillators and are discussed in Chapter 1 ofMigliori and Sarrao (1997).

During data acquisition at elevated temperature, thespecimen was placed between transducers mounted onthe ends of corundum rods so that the transducers andspecimen could all be placed in a small furnace. Temper-ature in the furnace was measured with two Pt–Pt13%Rhthermocouples placed on opposing sides of the speci-men. The specimen temperature is known to within ±3◦at the highest temperature which propagates an uncer-tainty of about 1% to the temperature derivatives ofelasticity. Specimen edge lengths and density at elevatedtemperature were determined by the thermal expansiondata on wadsleyite provided by Inoue et al. (2004).

Frequency scans were performed during three

temperature excursions: run A, 295–640 K; run B,295–660 K; and run C, 295–620 K. We observed 12, 20,and 17 resonant modes at each temperature for the threerespective temperature runs. There are two exceptions.

Fig. 1. Sample of four resonant modes of �-Mg2SiO4 at different tem-peratures. The figure illustrates the gradual shift of each mode to lowerfrequency with increasing temperature. Arrows used to identify eachmode. At 600 K, the lowest two modes have shifted off scale. Occa-sional inversions of modes are due to acoustic phase shifts (see text forfurther discussion).

lanetary Interiors 162 (2007) 22–31

The two highest temperature (640 and 660 K) determi-nations of G in run B are based on only 9 instead of20 modes because several modes were not observed atthese two temperatures. The (∂G/∂T)P deduced from the9 modes at lower temperatures (600 and 620 K) where all20 modes were seen mimics that deduced from the 20-mode (∂G/∂T)P, so we are confident of reliably extendingthe results for G to 640 and 660 K based on these 9modes. A similar explanation applies to the highest tem-perature determination of G in run A. Also, during runA, an electrical problem prevented several modes frombeing seen at all temperatures; accordingly, that run usedfewer modes (12 instead of 20 or 17) throughout to deter-mine KS and G. This electrical problem also preventedretrieval of data in the middle temperatures (400–520 K)of run A, although signals at lower and higher tempera-ture than 400–520 K were generally very good.

An attractive feature of application of RUS to poly-crystals is that we obtain a check on whether or notthe specimen is isotropic. True isotropic specimens haveonly two unique elastic moduli, and they are determinedby fitting the resonance frequency spectrum. However,in the data reduction, a polycrystalline specimen can betreated as a single-crystal with assumed cubic symme-try. Thus, we consider the specimen to have the threeadiabatic second order elastic constants (Cij) as in cubicsingle-crystals. For a polycrystalline specimen, theseconstants are more appropriately considered effectiveelastic constants and labeled C∗

11, C∗12, and C∗

44 to dis-tinguish them from the real single-crystal Cij. If thepolycrystalline specimen is indeed isotropic, the fit offrequencies will give C∗

44 = (1/2)(C∗11 − C∗

12), a resultimplying there is only one unique shear modulus and twototal elastic moduli for the specimen. In other words, weallow 3 degrees of freedom, instead of 2, when fittingthe frequency spectrum to determine whether the elas-tic properties freely converge to the isotropic case (seealso Isaak et al., 1992 and Prikhodko et al., 2003). Theinherent isotropy of the specimen can be, therefore, con-firmed. We find very little anisotropy in our specimensince C∗

44 and (1/2)(C∗11 − C∗

12) agree with each otherto within 0.7 GPa for all mode combinations used in ouranalyses.

3. Results

The room temperature (295 K) KS moduli for the threeruns are 170.2(2.0), 170.7(1.9), and 169.7(1.9) GPa (see

Table 1). The corresponding G moduli are 114.0(0.8),114.1(0.6), and 113.9(0.7) GPa. Our results on poly-crystalline �-Mg2SiO4 are consistent with those fromBrillouin studies on single-crystals (Zha et al., 1997)

D.G. Isaak et al. / Physics of the Earth and Planetary Interiors 162 (2007) 22–31 25

Table 1Elasticity results from three temperature excursions (Run A, Run B, Run C) for wadsleyite Mg2SiO4 at ambient pressure (subscripted numbersshow experimental uncertainty)

T (K) KS (GPa) G (GPa)

Run A Run B Run C Run A Run B Run C

295 170.171.96 170.741.87 169.731.87 113.980.80 114.090.63 113.920.66

320 170.38 113.76340 169.47 170.17 113.37 113.49357 168.75 113.08360 169.74 113.18380 168.84 169.41 168.37 112.78 112.90 112.74400 169.09 112.60420 168.75 167.68 112.29 112.12440 168.43 111.98460 168.041.90 166.97 111.66 111.46480 167.69 111.33500 167.30 166.19 111.01 110.81520 166.96 110.67540 166.07 166.68 165.46 110.24 110.36 110.14560 166.30 110.05580 165.422.02 165.962.00 164.762.04 109.570.081 109.710.66 109.480.71

600 165.06 165.62 109.22 109.38620 165.27 164.07 108.88 109.03 108.79640 108.50 108.64660 108.25295a 170.081.91 170.291.82 169.591.99 113.900.78 113.930.61 113.920.70

a1eteoto

pfK(moas(lttrw2o

We also considered the possibility that the specimendehydrated during heating. But, the post-heating moduliwould increase, not decrease, if the specimen dehydratedduring heating. In any case, we fully account for this

Fig. 2. Measured temperature dependence of KS for polycrystalline

a After heating.

nd from ultrasonic studies on polycrystals (Li et al.,998, 2001) (see columns 2 and 3 of Table 2). Thearly Sawamoto et al. (1984) value of 174 GPa is a lit-le higher, but is nearly consistent with our results if anrror of 2 GPa is assigned to their result. Furthermore,ur results for G at room temperature are slightly higherhan 111.6(0.5) GPa reported by Liu et al. (2005) basedn a reanalysis of Li et al. (2001) data.

Results for KS and G at elevated temperature arerovided in Table 1 and illustrated in Figs. 2 and 3or all three temperature excursions. Also shown areS and G obtained for each run at room temperature

295 K) after heating. We observed a small hysteresisore prominently in KS. The 295-K moduli at the end

f a run are moderately lower than at the beginning. Were uncertain of reasons for this. Mayama et al. (2004)how virtually no hysteresis in their RUS study of �-Mg0.91Fe0.09)2SiO4, albeit, over a temperature rangeess than half that used in our study. Even though the hys-eresis we observed is small, it cannot readily be ascribedo random error in the calculation for K and G because

Sesonant frequencies systematically shift down slightlyhen comparing pre-heating and post-heating spectra at95 K. Subtle, irreversible changes in the specimen couldccur during heating. However, we carefully measured

the specimen dimensions after heating and obtained edgelengths identical to those measured prior to heating.

�-Mg2SiO4 from 295 to 620 K. Three separate temperature runs areshown. A representative error bar (±one sigma) is indicated. All datahave similar uncertainty. Lines are linear best-fits through data obtainedduring heating. Hysteresis in each temperature run is represented byopen symbols at 295 K.

26 D.G. Isaak et al. / Physics of the Earth and Planetary Interiors 162 (2007) 22–31

Table 2Summary of wadsleyite data at ambient pressure and temperature (Mg2SiO4 composition assumed unless noted otherwise)

ρ (g cm−1) KS (GPa) G (GPa) (∂KS/∂T)P (10−2

GPa K−1)(∂G/∂T)P (10−2

GPa K−1)(∂2G/∂T2)P (10−5

GPa K−2)Reference Comment

3.468 170.12.0 113.90.8 −1.670.03 −1.370.02 −1.250.10 This studya Run A, accounts forhysteresis

(−1.580.02) (Run A, 295–640 Kaverage)

3.468 170.81.9 114.00.6 −1.640.07 −1.370.03 −1.150.06 This studya Run B, accounts forhysteresis

(−1.570.03) (Run B, 295–660 Kaverage)

3.468 169.71.9 113.90.7 −1.750.03 −1.400.02 −1.210.08 This studya Run C, accounts forhysteresis

(−1.590.02) (Run C, 295–620 Kaverage)

3.468 170.21.9 113.90.7 −1.710.05 −1.370.03 −1.150.06 This studya Preferred values fromcurrent measurements

(−1.570.03) (Preferred 295–660 Kaverage)

3.474 1742 1142 Sawamoto etal. (1984)

Single-crystal,Brillouin

3.45 170 108 Li et al. (1996) Poly-crystal,ultrasonic velocities

−1.2 Jackson andRigden(1996)a

Internal consistencyanalysis

3.489 1702 1152 Zha et al.(1997)

Single-crystal,Brillouin

3.470 1732 1131 −1.20.1 −1.70.1 Li et al. (1998,2001)

Poly-crystal,ultrasonic velocities

3.470 170.71.1 111.60.5 −1.290.17 −1.580.10 Liu et al.(2005)

Reanalysis of Li et al.(2001) data

3.57 1703 1082 Sinogeiken etal. (1998)

Single-crystal,Brillouin,(Mg0.92Fe0.08)2SiO4

3.608 165.70 105.66 −1.60.3 −1.20.1 Katsura et al.(2001)

Poly-crystal, RUS,(Mg0.91Fe0.09)2SiO4

01

3.60 165.720.06 105.430.02 −1.750.03 −1.590.

a Values are referenced at 300 K.

hysteresis when determining values of (∂KS/∂T)P and(∂G/∂T)P and their uncertainties from our data.

Fig. 2 illustrates consistency in the temperaturedependence we observed for KS among runs A, B,and C. Chi-squared statistical tests reveal that KS(T)in runs A and B are appropriately described by linearexpressions. A second order fit is marginally justi-fied for KS(T) in run C, but we do not consider thisbecause it is not observed in all the runs, especiallyrun B which has about twice as many data points asthe others. The (∂KS/∂T)P values shown in Table 2 for

our results account for hysteresis described earlier. Forexample, the (∂KS/∂T)P = −1.64 × 10−2 GPa K−1 citedfor run B comes from −1.71 × 10−2 GPa K−1 (direct fitof data while heating) minus −0.007 × 10−2 GPa K−1

Mayama et al.(2004)

Poly-crystal, RUS,(Mg0.91Fe0.09)2SiO4

(−1.71 × 10−2 GPa K−1 times half the percent decreasein KS from hysteresis relative to total change in KS overthe temperature run). The uncertainties in (∂KS/∂T)P

listed for each run are based on the hysteresis andthe approximate 1% uncertainty in temperature mea-surements. Our final preferred value for (∂KS/∂T)P is−1.71(5) × 10−2 GPa K−1 (see Table 2); it comes froma weighted average of the three runs. Weighting is basedon both the number of data points and uncertainty in(∂KS/∂T)P for each of runs A, B, and C.

As seen in Table 2, our result for (∂K /∂T)

S P

is consistent with −1.75(3) × 10−2 GPa K−1 mea-sured for polycrystalline �-(Mg0.91Fe0.09)2SiO4using RUS (Mayama et al., 2004). The magnitudeof our (∂KS/∂T)P is, however, higher than that of

D.G. Isaak et al. / Physics of the Earth and P

Fig. 3. Measured temperature dependence of G for polycrystalline �-Mg2SiO4 from 295 to 660 K. Three separate temperature runs shown.A representative error bar (±one sigma) is indicated. Data within eachrun have similar uncertainty. Solid line shows linear best-fits throughrun B data obtained during heating. Dashed line shows second-orderfit through run B data. Slight hysteresis in each temperature run isr

−2ptbr(aMsin

wft(1e×aJ(domMosa

in random errors is observed. Secondly, similar curva-

epresented by open symbols at 295 K.

1.2 × 10−2 GPa K−1 reported by Li et al. (1998,001) from studies of ultrasonic wave velocities onolycrystalline �-Mg2SiO4, and also higher thanhe revised value of −1.29(17) × 10−2 GPa K−1

y Liu et al. (2005). Katsura et al. (2001)eport a (∂KS/∂T)P = −1.6(3) × 10−2 GPa K−1 forMg0.91Fe0.09)2SiO4 that is intermediate to our resultnd those of Li et al. (1998, 2001) and Liu et al. (2005).ayama et al. (2004), however, have remeasured the

ame specimen used by Katsura et al. (2001) and havendicated the Katsura et al. temperature derivatives areot sufficiently precise.

Jackson and Rigden (1996) estimated (∂KS/∂T)P foradsleyite by analyzing available P–V–T data using dif-

erent equation of state formulations. They concludedhat on average (∂KS/∂T)P = −1.9 × 10−2 GPa K−1 and∂KT/∂T)P = −2.8 × 10−2 GPa K−1 between 300 and600 K. These two derivatives are dependent onach other and consistent with (∂KT/∂T)P = −2.7(3)

10−2 GPa K−1 from X-ray diffraction measurementsnd analysis by Fei et al. (1992) on �-(Mg,Fe)2SiO4.ackson and Rigden (1996), however, concluded that∂KS/∂T)P and (∂KT/∂T)P are strongly temperatureependent and suggested a value for (∂KS/∂T)P at 300 Kf −1.2 × 10−2 GPa K−1. This result conflicts with oureasured value of −1.71(5) × 10−2 GPa K−1 on �-g2SiO4 at 300 K. The rapid increase in the magnitude

f (∂KS/∂T)P for β-(Mg,Fe)2SiO4 from 300 to 600 Kuggested by Jackson and Rigden (see their Fig. 6b) islso not evident in our measurements.

lanetary Interiors 162 (2007) 22–31 27

Fig. 3 shows G(T) for each temperature excursion.Chi-squared statistical tests indicate second order fitsin T are warranted for each run. The systematic cur-vature in G(T) is illustrated in Fig. 3; the dashedline shows a second order fit to run B. Determi-nations of the G(T) fit coefficients and uncertaintiesfor each run in Table 2 take into account hysteresis(considerably less than for KS) and uncertainty in mea-sured temperature, as in the analysis of KS. Values of(∂G/∂T)P and (∂2G/∂T2)P are interdependent for eachrun. We use run B to determine our preferred coeffi-cients at 300 K [(∂G/∂T)P = −1.37(3) × 10−2 GPa K−1;(∂G2/∂T2)P = −1.15(6) × 10−5 GPa K−2)] because Bhas 19 data points compared to 8 and 9, respectively,for runs A and C. However, we find remarkable agree-ment in (∂G/∂T)P and (∂2G/∂T2)P among the runs (seeTable 2).

Our average (∂G/∂T)P = −1.57(3) × 10−2 GPa K−1

from 295 to 660 K compares very well with (∂G/∂T)P =−1.59(1) × 10−2 GPa K−1 found by Mayama etal. (2004) on �-(Mg0.91Fe0.09)2SiO4. This aver-age is also consistent within mutual uncertaintieswith −1.7(1) × 10−2 GPa K−1 reported by Li etal. (1998, 2001) on �-Mg2SiO4 that was laterrevised to −1.58(10) × 10−2 GPa K−1 by Liu et al.(2005). Katsura et al. (2001) report a low mag-nitude of (∂G/∂T)P = −1.2(1) × 10−2 GPa K−1 for�-(Mg0.91Fe0.09)2SiO4, but this derivative, as withtheir (∂KS/∂T)P, was revised by Mayama et al. (2004).Li et al. (1998, 2001) and Mayama et al. (2004) donot consider systematic nonlinear temperature effectsin G(T). It is likely the Li et al. experiments, whichinvolved simultaneous pressure and temperature excur-sions do not have sufficient precision to identify smallnonlinear behavior in G(T). Mayama et al. (2004) dataextend from room temperature to 470 K. Inspection ofthe KS(T) and G(T) plots provided by Mayama et al.(2004) indicates the magnitudes of both (∂KS/∂T)P and(∂G/∂T)P increase with temperature. However, Mayamaet al. (2004) do not give quantitative analyses of secondorder T effects in their data.

The implications of a second order effect in G(T)are significant when extrapolating to temperatures ofEarth’s transition zone. Thus, it is important to discusswhy the observed nonlinearity cannot readily be ascribedto experimental uncertainty or degradation of the poly-crystalline specimen while heating. Error bars duringa temperature excursion remain constant; no increase

ture in G(T) was observed for all three runs. Very smallhysteresis (none for run C) in G(T) is seen when compar-ing pre-heating and post-heating values. Furthermore,

h and P

28 D.G. Isaak et al. / Physics of the Eart

the KS(T) data do not show these non-linear effects aswould be expected if the specimen were undergoing sub-tle degradation while heating. Finally, the curvature issystematic throughout the entire range of temperaturestudied. There is little change in the fitted second ordercoefficients when we reanalyze the G(T) data without thethree highest temperature points. It is also noteworthythat during depressurization in the hot-pressing of the �-Mg2SiO4 polycrystal, the sample is generally annealed attemperatures of up to 775 K (Gwanmesia et al., 1990a,b),thus, precluding sample degradation in this study carriedout to only 660 K.

Previous high-temperature RUS elasticity measure-ments on single-crystals of mantle phases have notdetected non-linear G(T) dependences as strong asimplied here for wadsleyite. For example, Isaak et al.(1989) find (∂G2/∂T2)P = −2.6(4) × 10−6 GPa K−2 forsingle-crystal �-Mg2SiO4 from 300 to 760 K, which isan order of magnitude smaller in absolute value thanour result for �-Mg2SiO4. Indeed, if the curvature seenin Fig. 3 is interpreted as actual second order depen-dence of G on T, we are confronted with the prospectthat temperature effects on G for �-Mg2SiO4 differsomewhat from �-Mg2SiO4 and other mantle phases forwhich precise high-temperature elasticity measurementshave been done. Accordingly, experimental confirmationof our results by measurements to higher temperaturesand with single-crystal �-Mg2SiO4, if available, shouldreceive experimental priority.

4. Discussion

In a recent study, Liu et al. (2005) suggested plau-sible olivine concentrations in Earth’s upper mantle bycomparing estimated differences in �- and �-olivineelasticity at transition zone pressure and temperature.Liu et al. (2005) presented new elasticity data onSan Carlos olivine at simultaneous high P (8.2 GPa)and T (1073 K), and then extrapolated the data andthose of the �-phase to 410-km P (13.8 GPa) and T(1673 K). Values for �-(Mg, Fe)2SiO4 P and T deriva-tives used by Liu et al. (2005) are (∂KS/∂P)T = 4.56,(∂G/∂P)T = 1.75, (∂KS/∂T)P = −1.29 × 10−2 GPa K−1,and (∂G/∂T)P = −1.58 × 10−2 GPa K−1. All thesederivatives come from a reanalysis of Li et al. (2001)report. Higher order derivatives, including the mixed P,T derivatives, were all considered to be negligible.

The Liu et al. (2005) study accounts for the prob-

ability that iron partitions preferentially to wadsleyite(Irifune and Isshiki, 1998) so that XFe(�) = 0.075 andXFe(�) = 0.115. This partitioning of iron affects densitiesand room-temperature G and KS values for the �- and �-

lanetary Interiors 162 (2007) 22–31

olivine phases. The temperature and pressure derivativesof G and KS, however, are assumed to be independent ofiron content (Liu et al., 2005). An important finding ofour study is experimental confirmation of this assump-tion as far as temperature effects on the elasticity of the�-olivine phase are concerned. This confirmation comesfrom comparing our results for (∂KS/∂T)P and (∂G/∂T)P

(average (∂G/∂T)P from 295 to 660 K) on �-Mg2SiO4with these derivatives for Fe-bearing wadsleyite, i.e., �-(Mg0.91Fe0.09)2SiO4 reported by Mayama et al. (2004)(see Table 2).

For XFe(�) = 0.075, XFe(�) = 0.115, and 410-km Pand T, Liu et al. (2005) find that �VP/VP = 10.9%and �VS/VS = 12.2% for the α- to β- transition, yield-ing olivine contents of 46 and 41% by volume inthe upper mantle when compared with 5% disconti-nuities in both VP and VS at 410 km depth (Nolet etal., 1994). These olivine percentages increase slightlyto 47 and 43% if latent heat (∼80 K) of the �–�phase transition is considered (Liu et al., 2005). Liuet al. (2005) study also considers effects of using(∂KS/∂T)P = −1.75 × 10−2 GPa K−1 (Mayama et al.,2004), instead of −1.29 × 10−2 GPa K−1, in modelingthe seismic discontinuities. Olivine percentages deter-mined from respective VP and VS discontinuities increaseto 53 and 42%, and to 54 and 44% when latent heat isaccounted for. The primary effect of increasing the mag-nitude of (∂KS/∂T)P of the � phase is to require moreolivine to satisfy the VP discontinuity; the VS amountis only marginally altered due to slight density changesat high pressure and temperature, and the disparity inolivine determined from VP and VS increases. Resultsof extrapolations based on different assumptions about(∂KS/∂T)P to transition zone temperatures are illustratedin Fig. 4.

Our (∂KS/∂T)P coincides with that obtained byMayama et al. (2004). Accordingly, our KS(T) data sup-port the conclusion that the jumps in VP and VS atthe 410-km depth are matched by 54 and 44% olivine,respectively, using assumptions other than (∂KS/∂T)P for�-olivine outlined by Liu et al. (2005). Mayama et al.(2004) arrive at slightly different conclusions, that 52and 42% olivine are required to match the respectiveVP and VS discontinuities, primarily because they makedifferent assumptions than do Liu et al. (2005) aboutparameters, such as (∂KS/∂P)T and (∂G/∂P)T for �- and�-olivine.

We now consider the effect of extrapolating appar-

ent nonlinearity in G(T) observed from 295 to 660 K,but proceed cautiously until these second order effectsare reproduced to higher temperatures and, if available,on single-crystals. By extrapolating this nonlinearity

D.G. Isaak et al. / Physics of the Earth and P

Fig. 4. Extrapolation of measured KS data to high temperature showingeffects of different assumptions about temperature derivatives on valueou3

tarsonbb

FeocAA

f KS at elevated temperature. Dashed lines show extrapolation ofncertainty associated with current data. The lines are referenced at00 K to our current run B data.

o 1673 K, G is about 8 GPa lower than by usinglinear extrapolation (see Fig. 5). The effect is to

educe both �VP/VP and �VS/VS for �- to �- tran-ition at elevated temperature, thus, requiring more

livine to model both VP and VS seismic disconti-uities at 410 km. In particular, �VP/VP and �VS/VSecome 7.7 and 7.5%, respectively, when G is reducedy 8 GPa at 1673 K. This suggests olivine contents of

ig. 5. Extrapolation of measured G data to high temperature showingffects of different assumptions about temperature derivatives on valuef G at elevated temperature. Dashed lines (barely visible boundingurve b) show ±0.01 × 10−2 GPa K−1 for a linear fit to current results.lso shown is an extrapolation of the second order fit to current data.ll lines are referenced at 300 K to our current run B data.

lanetary Interiors 162 (2007) 22–31 29

66 and 67%, respectively, are needed to satisfy �VP/VPand �VS/VS discontinuities at 410-km. Thus, extrap-olating the apparent second order effect in G resultsin increased estimates of the percentage of olivineand also reconciles the longstanding disparity in esti-mates of olivine content deduced from VP and VSprofiles. Previously, Gwanmesia et al. (1990b) suggested65% olivine content results from both �VP/VP and�VS/VS analyses if (∂KS/∂T)P = −1.8 × 10−2 GPa K−1

for �-olivine and there is a ‘high’ magnitude of(∂G/∂T)P = −2.0 × 10−2 GPa K−1. Interestingly, this isvery close to what is obtained when extrapolat-ing our (∂KS/∂T)P and (∂G/∂T)P to 1673 K. Our(∂KS/∂T)P = −1.71 × 10−2 GPa K−1, and the average(∂G/∂T)P from 300 to 1673 K is −2.1 × 10−2 GPa K−1

when extrapolating the measured curvature in G(T).In summary, our results show that (∂KS/∂T)P =

−1.71(5) × 10−2 GPa K−1 and the average(∂G/∂T)P = −1.57(3) × 10−2 GPa K−1 for �-Mg2SiO4over 295–660 K are indistinguishable from respec-tive values of −1.75(3) × 10−2 GPa K−1 and−1.59(1) × 10−2 GPa K−1 for �-(Mg0.91Fe0.09)2SiO4(Mayama et al., 2004). These comparisons confirmthat (∂KS/∂T)P and (∂G/∂T)P are practically unaffectedby incorporating iron in �-olivine for XFe = 0.00–0.09.Our (∂KS/∂T)P, however, contrasts with −1.20 × 10−2

to −1.30 × 10−2 GPa K−1 reported in some previousstudies (Li et al., 1998, 2001; Liu et al., 2005; Jacksonand Rigden, 1996). The higher magnitude of (∂KS/∂T)P

suggests estimates of olivine content in the upper mantleat 47% (VP) and 43% (VS) need upward revision to 54and 44%, respectively, given other assumptions in Liuet al. (2005) study. There appears near consensus onthe average (∂G/∂T)P for �-Mg2SiO4 over the first fewhundred degrees above room temperature. However, ourresults indicate that non-linear effects in G(T) may bepertinent when estimating olivine content in the uppermantle. By extrapolating nonlinearity in G(T) observedover 295–660 to 1673 K and using other assumptionsoutlined by Liu et al. (2005), we find that 66–67%olivine satisfies the 410-km velocity discontinuitiesand the disparity in the amounts of olivine required toreplicate the VP and VS jumps is eliminated.

Our discussion highlights the effect of assumptionsabout (∂KS/∂T)P and (∂G/∂T)P for �-olivine have on min-eral models of the mantle. Several factors reviewed byLiu et al. (2005) indicate a definitive solution as to theamount of olivine in the mantle is problematic even if

pressure and temperature derivatives of KS and G for theanhydrous �- and �-olivine phases are exactly known.There are still uncertainties about the temperature at410-km, the effect of water on the elasticity of olivine

h and P

30 D.G. Isaak et al. / Physics of the Eart

(especially wadsleyite) phases, the water content of themantle, and the exact nature of the observed seismic dis-continuities (Walck, 1984; Grand and Helmberger, 1984;Nolet et al., 1994; Shearer and Flanagan, 1999; Shearer,2000). Furthermore, we are not certain how far mea-surements made over 295–660 K warrant extrapolatingto higher T. This concern especially applies to the non-linearity in G(T) observed from 295 to 660 K. Additional�-Mg2SiO4 elasticity data to higher temperatures and onsingle-crystal specimens, if available, would be helpfulfor this purpose.

Acknowledgements

This work was supported by NSF under grants EAR-0409171 to DI at UCLA and EAR-0408751 to GDGat Delaware State University. This research was alsopartially supported by COMPRES, the Consortium forMaterials Properties Research in Earth Sciences, underNSF Cooperative Agreement EAR 01-35554. UCLAInstitute of Geophysics and Planetary Physics Publica-tion No. 6344.

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