Temperature derivatives of elastic moduli of MgSiO3 perovskite
Yoshitaka Aizawa, Akira Yoneda, Tomoo Katsura, Eiji Ito1, Toshiaki Saito, Isao Suzuki2
1 Institute for Study of the Earth’s Interior, Okayama University, Misasa, Tottori 682-0193, Japan.
2 Department of Earth Sciences, Okayama University, Okayama 700-8530, Japan.

Abstract. Elastic properties of polycrystalline MgSiO3 perovskite were determined bymeans of resonance sphere technique at temperatures from 258 to 318 K underatmospheric pressure. The temperature derivatives of adiabatic bulk (∂KS/∂T)P and shearmoduli (∂G/∂T)P are –0.029(2) GPa/K and –0.024(1) GPa/K, respectively. Applying thepresent results in interpretation of seismological observations, we suggest that thechemical composition of the earth’s lower mantle is pyrolitic at the potential
temperature of 1600 K.

1. Introduction
It is widely recognized that Mg-rich silicate perovskite is the most abundant mineralin the earth’s lower mantle [e.g., Ito and Takahashi, 1989; Jeanloz and Knittle, 1989;
Jackson, 1998]. Therefore, its elastic properties are of prime importance to constrain thechemical composition and temperature profile in the lower mantle. The elastic moduli
of silicate perovskite at ambient conditions have been determined with Brillouinscattering [Yeganeh-Haeri, 1994]. However, the pressure and temperature derivatives ofthe elastic moduli are poorly constrained. Most previous experiments using diamondanvil cell were suitable for obtaining a static compression curve yielding onlyisothermal bulk modulus (KT), its temperature derivative, and thermal expansion (α)
with relatively large uncertainty [e.g., Mao et al., 1991; Wang et al., 1994; Funamori et1

al., 1996; Fiquet et al., 2000].
Sinelnikov et al. [1998] reported the pressure and temperature derivatives of shear
modulus using elastic wave velocity measurements at pressures as high as 8 GPa andtemperatures up to 800 K. Their temperature derivatives, however, were derived fromthe shear moduli measured at various P-T conditions. Therefore, their results may beconstrained by the uncertainties not only of temperature but also of pressure.
In this study, we conducted measurements to obtain temperature derivatives for bothbulk and shear moduli of polycrystalline MgSiO3 perovskite using resonant spheretechnique [Suzuki et al., 1992] at atmospheric pressure. Relatively high precision in
determining temperatures and resonance frequencies in this technique enabled us todetermine the temperature derivatives of the elastic moduli even for small temperature
variations.

2. Experimental
A polycrystalline sample of MgSiO3 perovskite was synthesized with the Kawai-typehigh-pressure apparatus at pressures and temperatures around 23 GPa and 1800 K for arun duration of 1 hour. The recovered sample was confirmed to be pure aggregate ofperovskite by micro-focus X-ray diffraction spectra. It was carefully made into aspherical shape by means of the two-pipe method [Fraser and LaCraw, 1964] with adiameter of 1.303 (6) mm. The bulk density was determined to be 4.10(6) X 103 kg/m3
which was close to 4.108 X 103 kg/m3 taken from the literature [Ito and Matsui, 1979].
The resonance spectra were acquired from 3.8 to 8.0 MHz at 10 K intervals between
258 and 318 K. An example of the spectra is shown in Figure 1. Nine resonant modes(0T2, 0S2, 1S1, 0T3, 0S3, 0S0, 1S2, 0S4, 0T4) were recognized. However, the peaks of toroidal2

(0T2, 0T3 and 0T4) modes are highly sensitive to the distortion in the sample shape fromthe sphere, which results in the substantial peak splitting (Figure 1). Therefore, weomitted those peaks and also adjacent spheroidal modes (0S3, 0S4) which can not be
distinctively recognized. The rest of 4 spheroidal modes (0S2, 1S1, 0S0, 1S2), being lesssensitive to shape irregularity and thus showing slight peak splitting, were used in theanalyses followed. It should be noted that even if we considered the average value ofthe substantially scattered but identified peaks (0T2 mode) which was omitted from theconsideration, the resulting variations are as small as ~1 % for absolute value and within~6 % for the temperature derivatives. At ambient pressures, it is known that silicate
perovskite becomes amorphous at around 400 K [Wang et al., 1994]. The highest
temperature of the present measurements was 318 K, low enough to avoid
amorphization of the sample. Although the temperature variation was limited to be only60 K, the temperature was controlled within 0.1 K and we observed the resonant
frequencies clearly shifted with changing temperatures (Figure 2).

Results and Discussion
The elastic wave velocities (VP and VS) at 298 K were determined to be 10.7 and 6.51
km/s, respectively, using a least-square analysis based on the results obtained from four
spheroidal modes. The results were consistent being within 3 % of the commonly
accepted data calculated from Brillouin scattering (Table 1). The bulk and shear moduli
were computed from those velocities for each temperature interval (Figure 3). The
temperature derivatives of elastic moduli were calculated with a linear fitting (Table 1).
The errors at each data point are mostly caused by the uncertainty of the diameter.
Therefore, the errors of the temperature derivatives are not constrained by them, but

3

instead, reflect the variations of resonant frequencies at each measurement. The
temperature derivative for shear modulus thus obtained ((∂G/∂T)P = -0.024(1) GPa/K)
was somewhat smaller in magnitude than the data by the ultrasonic measurements(-0.029(3) GPa/K) [Sinelnikov et al., 1998]. On the other hand, the temperature
derivative of KS ((∂KS/∂T)P = -0.029(2) GPa/K) was in good agreement with thetemperature derivative of KT determined by the static compression [Funamori et al.,1996]. Although the shear modulus (G=174.1(5)) agreed well with other studies[Yeganeh-Haeri, 1994] within 2% (Table 1), the bulk modulus (KS=237.7(8)) differedby 4 to 10% compared with the literature values as shown in Table 1 [Yeganeh-Haeri,1994; Andrault et al., 2001]. The discrepancy is mainly caused by disagreement in VP.
Relatively low KS in the present study suggests that a small amount of pores exists
within the specimen. Even if the present specimen may be porous, however, it has beenrecognized that shear moduli in resonance experiments are less sensitive to the porosity
compared with bulk moduli [Suzuki et al., 1992; Katsura et al., 2001].
Previous ultrasonic experiments at high pressures (~8 GPa) [Sinelnikov et al., 1998]
were conducted in the temperature range of up to 800 K. The ultrasonic velocity
measurements were performed in a solid pressure-medium and at various P-T
conditions outside the thermodynamic stability field of MgSiO3 perovskite. Therefore,
they had difficulty in determining the temperature derivatives at constant pressure,which requires corrections of the pressure fluctuations associated with temperaturechange. In addition, in a solid pressure-medium, the effect of deviatoric stresses causes
the uncertainty of pressure, which may affect the ultrasonic velocity measurement athigh pressure.
We calculate the VP and VS for possible mantle models at high temperature and4

atmospheric pressure and compare them with the values inferred for the adiabaticallydecompressed lower mantle [Jackson et al., 1998]. The lower mantle is assumed to be a
mixture of perovskite (Pv) and magnesiowüstite (Mw) with XPv ranging from 0.67 to 1.0(XMw=0.33-0) in molar ratio. The total iron content, Fe/(Fe+Mg) was fixed at 0.12. The
partition coefficient (k) of Fe and Mg between Pv and Mw phases represented byk=(XMg/XFe)Pv/(XMg/XFe)Mw. Because the experimentally determined values of k range
widely, we adopted 0.25 [Katsura and Ito, 1996], and somewhat higher value 0.45
[Kesson e al., 1998] is also employed in the following analysis. As the elastic moduli(M0) of perovskite phase, we used KS =260 (±5) and G=177 GPa, which are commonlyaccepted values. Temperature corrections were applied to the elastic properties by
M=M0+ (∂M/∂T)P·(Tp-300) and to the density of both phases based on the present results,
together with recent studies [e.g., Trampert et al., 2001; Kung et al., 2002]. The elastic
wave velocities of the lower mantle are computed at a potential temperature (Tp) of
1600 K, which is plausible in order to account for the depths of major seismic
discontinuities interpreted as phase transitions [Ito and Katsura, 1989; Jackson, 1998].
Our model calculations at 1600 (±100) K (Figure 4) demonstrate that the elastic wave
velocities of pyrolitic composition (XPv=0.67) are preferable in order to account for
those estimated from the seismological observations [Dziewonski and Anderson, 1981;
Kennett et al., 1995], even if the effect of Fe-Mg partitioning is considered. On the otherhand, pure perovskite model yields velocities too fast to reconcile with the observations.
Unlike the estimates based on the previous results of the temperature derivatives[Sinelnikov et al., 1998], which favors the more perovskite-enriched composition thanpyrolite (XPv=~0.75 in Fig. 4), the present results suggest uniform chemical composition
throughout the mantle. In order to provide a tighter constraint for the chemical and5

thermal model of the lower mantle, the effect of Fe and Al on the elasticity of silicate
perovskite should be considered [Zhang and Weidner, 1999; Andrault et al., 2001;
Kiefer et al., 2002] in the future.

Acknowledgments.
We thank Prof. I. Jackson and an anonymous reviewer for constructing comments.

References
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6

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Kennett, B. L. N., E. R. Engdahl and R. Buland, Constraints on seismic velocities in the Earth fromtraveltimes, Geophys. J. Int. 105, 429-465, 1995Kung, J., B. Li, D. J. Weidner, J. Zhang, R. C.
Liebermann, Elasticity of (Mg0.83, Fe0.17) ferropericlase at high pressure: ultrasonic measurements inconjunction with X-radiation techniques Earth Planet. Sci. Lett. 203, 557-566, 2002.
Kesson, S. E., J. D. Fitz Gerald and J. M.G. Shelly, Mineralogy and dynamics of a pyrolite lower mantle.
Nature 393, 252-255, 1998.
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Res. 96, 8069-8079, 1991.
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Suzuki, I., Y. Inoue, J. Hirao, H. Oda, T. Saito and K. Seya, The resonant sphere technique formeasurements of elasticity and anelasticity of a small specimen : An application to olivine, Zisin 45,213-228, 1992.
Trampert, J., P. Vacher and N. Vlaar, Sensitivities of seismic velocities to temperature, pressure andcomposition in the lower mantle. Phys. Earth Planet. Inter. 124, 255-267, 2001.
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perovskite: constraints on composition of the lower mantle. Phys. Earth Planet. Inter. 83, 13-40, 1994.
Yeganeh-Haeri, A., Synthesis and re-investigation of the elastic properties of single-crystal magnesium
silicate perovskite. Phys. Earth Planet. Inter. 87, 111-121, 1994.
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Figure captions
Figure 1. An example of resonant spectra at 258 K. Data was obtained at 100 Hzintervals.

Figure 2. Temperature dependence of resonant frequencies in MgSiO3 perovskite for
0S2 and 0S0 resonant modes. The temperature was controlled within 0.1 K during themeasurements at 10 K intervals. Circles and diamonds represent heating and coolingprocesses, respectively.

Figure 3. Adiabatic bulk and shear moduli of MgSiO3 perovskite as a function oftemperature. Relatively large errors resulted from uncertainty of the diameter.

Figure 4. Estimated elastic wave velocities of (Mg, Fe)SiO3 perovskite plus (Mg, Fe)O
magnesiowüstite mixtures at around 1600 K at atmospheric pressure. For comparison,decompressed seismic wave velocities [Jackson, 1998] based on the seismologicalmodel [Dziewonski and Anderson, 1981; Kennett et al., 1995] are shown by open square.
Note that the temperature at atmospheric pressure designates potential temperature in
the earth’s interior. The velocities are calculated for various bulk compositions of XPv
and at temperatures 1600±100 K. Solid black and gray diamonds represent the VP andVS for the model lower mantle (XPv = 0.67-1.0) with k of 0.25 and 0.45, respectively.
Open diamonds exhibit the velocities calculated based on the previous study [Sinelnikov
et al., 1998]. Error bars correspond to the uncertainties of the potential temperature(±100 K) and the value of Ks (±5 GPa).

9

Table 1. Bulk and shear moduli and their temperature derivatives of magnesium silicate perovskite
Reference

KS (GPa)

K’G (GPa)

VP (km/s) VS (km/s)(∂KT/∂T)P(∂G/∂T)P#This study

237.7(8)174.1(5)

10.70

6.51

<a>

264(5)

177(3)

11.03

6.56

<b>

249(3)

4.0fixed<c>

253(9)

3.9-0.017(2)<d>261(4)

4.0fixed-0.05(1)<e>261

4.0fixed-0.023(11)

<f>

261

4.0fixed-0.028(3)<g>

175(6)-0.032(2)-0.024(1)-0.029(3)<a> Brillouin-scattering measurements for MgSiO3 single crystal; Yeganeh-Haeri, 1994; <b>-<e> Static
compression in DAC; <b> Andrault et al., 2001; <c> Fiquet et al., 2000; <d>* Fe-bearing MgSiO3
perovskite (Mao et al., 1991); <e> Wang et al., 1994; <f> Static compression in Kawai-type apparatus;
Funamori et al., 1996; <g> Ultrasonic interferometry for polycrystalline samples; Sinelnikov et al., 1998.
KS is converted into KT using the relation of KT=(1+αγT)KS, where γ is assumed to be constant, 1.3.

#10

Aizawa et al. Fig. 10T2

Amplitude (arbitrary)

0

S2

4.0
0

4.5

T30

S1

5.0

5.5
0

S30

6.0

1S0
6.5

10

S2

7.0

7.5

T4S4

8.0

Frequency (MHz)Figure 1. An example of resonant spectra at 258 K. Data was obtained at 100Hz intervals.

Aizawa et al. Fig. 24.26004.25500S2Frequency (MHz)4.25004.24504.2400

250

260

270

280

290300310

320280290300310

320

6.45006.4450
6.44006.435006.43006.4250

250

260

S0270

Temperature (K)Figure 2. Temperature dependence of resonant frequencies of MgSiO3 perovskite for 0S0 and 0S2
resonant modes. The temperature was controlled within 0.1 K during the measurements at 10 K
intervals. The circles and diamonds represent the heating and cooling processes, respectively.

Aizawa et al. Fig. 3

240.0

179.0
Bulk modulus

178.0

238.0

177.0

237.0

176.0

236.0

175.0

235.0

174.0

234.0
250

Shear modulus
260270280

290300310

Shear modulus (GPa)

Bulk modulus (GPa)

239.0

173.0
320

Temperature (K)Figure 3. Adiabatic bulk and shear moduli of MgSiO3 perovskite as a function of temperature.
The relatively large errors resulted from uncertainty of the diameter.

Aizawa et al. Fig. 4

6.00
XPv=1

Tp=1600 K
VS (km/s)

5.90

XPv=0.80

XPv=0.67(pyrolitic)
k=0.455.80
DecompressedLower mantle
k=0.255.70

XPv=0.75
XPv=0.67

5.60
9.80

9.90

10.0

10.1

VP (km/s)
Figure 4. Estimated elastic wave velocities of (Mg, Fe)SiO3 perovskite plus (Mg, Fe)O
magnesiowustite mixtures at around 1600 K at atmospheric pressure. For comparison,decompressed seismic wave velocities [Jackson, 1998] based on sesimological models[Dziewonski and Anderson, 1981] are shown by an open square. Note that temperature
at atmospheric pressure designates potential temperature in the earth's interior.
The velocities are calculated for various bulk compositions of XPv and at temperaturtes
1600+100 K. Solid black and gray diamonds represent the VP and VS for the model
lower mantle (XPv=0.67-1.0) with k of 0.2 and 0.45, respectively. Open diamonds exhibit
the velocities calculated based on the previous study [Sinelnikov et al., 1998]. Error bars
correspond to the uncertainties of the potential temperature (+100 K) and the value ofKS (+5 GPa).