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Temperature derivatives of elastic moduli of MgSiO 3 perovskite

Temperature derivatives of elastic moduli of MgSiO 3 perovskite. Yoshitaka Aizawa and Akira Yoneda ISEI. Previous studies.

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Temperature derivatives of elastic moduli of MgSiO 3 perovskite

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  1. Temperature derivatives of elastic moduli of MgSiO3 perovskite Yoshitaka Aizawa and Akira Yoneda ISEI

  2. Previous studies • Extremely large coefficient of thermal expansion a=4 X 10-5 K-1 and large negative temperature derivative of the bulk modulus K/T=-6X 10-2 GPa/K: Mao et al. (1991), Stixrude et al. (1992) Pure perovskite lower mantle • Moderate coefficient of thermal expansion a=2 X 10-5 K-1 and temperature derivative of the bulk modulus K/T=-2X 10-2 GPa/K: Wang et al. (1994), Funamori et al. (1996), Fiquet et al. (1998) Pyrolitic lower mantle

  3. The temperature derivative of shear modulus was first reported by ultrasonic interferometry • Shear wave velocity measurement at high P-T conditions: Sinelnikov et al. (1998) Silica enriched lower mantle Technical Problems Their temperature derivative of G is determined based on the shear modulus obtained at various P-T conditions.

  4. Advantages of using Resonant Sphere technique • The relative high precision for determining the temperature and resonant frequencies. • The measurements are conducted under constant pressure. • Even though the stability field of MgSiO3 perovskite at atmospheric pressure is confined below 400 K, we can determine the temperature derivative for relatively small temperature modulations.

  5. Synthesis for MgSiO3 perovskite(23 GPa, ~1800 K) sample 1.0 mm MgO pressure medium

  6. How to make spheres?

  7. Block diagram of the resonant sphere technique amplifier oscillator transducer sample The data were obtained from 3.8 to 8.2 MHz at every 100 Hz and 10 K. The temperature was controlled within 0.1 K . Lock-in amplifier PC

  8. An example of resonant spectra at 258 K

  9. Effect of the distortion of the sample shape from sphere on the resonant frequencies The peaks of troidal modes are sensitive to the effect of the sample shape, which results in the peak splitting. Therefore we omitted those peaks and 4 spheroidal modes were used in the following analysis.

  10. Results of cooling (circles) and heating (diamond) processes 0S2 Frequency (MHz) The differences of the frequencies are within 0.1 % 0S0 Temperature (K)

  11. Bulk modulus (GPa) Bulk modulus (Ks) Shear modulus (GPa) Shear modulus (G) Temperature (K) Bulk and shear moduli of MgSiO3 perovskite

  12. Bulk modulus (K)の値が単結晶のデータに比べ、5-10%程度有意に小さい。試料の形状による共振周波数のシフト、あるいは直径の誤差を考慮してもまだ違いが残る。一方でShear modulus (G)は比較的よい一致を示した。

  13. 地球内部への適用 • 今回得られた弾性率の温度依存性を用いて下部マントル条件下における地震波速度を見積もった。Duffy & Anderson (1989), Trampert et al. (2001)にならい、Birch-Mahnaganの方程式により高圧下への外挿を行った。 • Potential temperatureが1600 K付近において観測データと整合的である。この温度は地震波速度不連続面の深さを相転移によるとする解釈とも矛盾しない。(Ito & Katsura, 1989, Akaogi, Ito & Navrotsky, 1989, Ita & Stixrude, 1992)

  14. Pyrolite modelは地震波観測データと整合的である。 VS (km/s) VP (km/s) Depth (km) Depth (km)

  15. さらに地球内部への適用 • 660 km不連続面がg-spinel → MgSiO3 perovskite + magnesiowüstiteによって生じると考えると、同様の計算により速度jumpが見積もられる。∆VS=6.1%, ∆VP=1.3%という結果が得られた。これは地震波による観測データ ∆VS=6-7%, ∆VP=2-5%と概ね整合的と言える。 • また、f=(∂logVf/∂T)Pとしたとき地震波速度の不均質を温度のみによるとした場合、dT=(dVf/Vf)/ fと表される。深さ1200 km付近での観測データdVf/Vfは1.4%程度とされ、上式によればdT=~400Kと推定される。* f= -(1/2)·a·(ds-1); ds=-(1/a)·(∂logKS/∂T)P

  16. 今後の課題 • 鉱物物理学的データによるRS/P= ∂logVS /∂logVPは 地震波による観測値と一致しない。 • Fe, Alの効果： Kは小さくなる。(Zhang & Weidner, 1999) Kは大きくなる。(Andrault et al, 2001) • ds = -(1/a)·(∂logKS/∂T)Pの圧力依存性？

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