Transcript Document

Temperature derivatives of elastic
moduli of MgSiO3 perovskite
Yoshitaka Aizawa and Akira Yoneda
ISEI
Previous studies
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Extremely large coefficient of thermal expansion
a=4 X 10-5 K-1 and large negative temperature
derivative of the bulk modulus K/T=-6 X 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=-2 X 10-2 GPa/K: Wang et al. (1994),
Funamori et al. (1996), Fiquet et al. (1998)
Pyrolitic lower mantle
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.
Advantages of using Resonant Sphere
technique
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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.
Synthesis for MgSiO3 perovskite (23 GPa, ~1800
K)
sample
1.0 mm
MgO pressure medium
How to make spheres?
Block diagram of the resonant sphere technique
amplifier
transducer
oscillator
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
An example of resonant spectra at 258 K
Effect of the distortion of the sample shape from sphere on the
resonant frequencies
0 T2
0S2
10 m
20 m
30 m
3.85
3.90
真球
真球
3.95
4.00
4.05
4.10
4.15
Frequency (MHz)
3.85
3.90
3.95
Frequency (MHz)
4.20
4.25
4.30
4.30
4.35
Frequency (MHz)
4.00
4.05
4.15
4.20
4.25
Frequency (MHz)
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.
Results of cooling (circles) and heating (diamond)
processes
4.2600
4.2550
S
0 2
Frequency (MHz)
4.2500
The differences
of the frequencies are within 0.1 %
4.2450
4.2400
250
260
270
280
290
300
310
320
310
320
6.4500
6.4450
S
0 0
6.4400
6.4350
6.4300
6.4250
250
260
270
280
290
300
Temperature (K)
177.5
Bulk modulus (Ks)
239.0
177.0
238.5
176.5
238.0
176.0
237.5
175.5
237.0
175.0
236.5
174.5
236.0
235.5
250
Shear modulus (G)
260
270
280
290
300
174.0
310
Shear modulus (GPa)
Bulk modulus (GPa)
239.5
173.5
320
Temperature (K)
Bulk and shear moduli of MgSiO3 perovskite
Table 1. Bulk and shear moduli and their temperature derivatives of magnesium
silicate perovskite
Reference Ks (GPa)
This study 237.5
(1)
264 (5)
(2)
249 (3)
(3)
253 (9)
(4)
261 (4)
(5)
261
(6)
K'
G (GPa) V P (km/s) V S (km/s) ( K S /  T )P (GPa/K) ( G/  T )P (GPa/K)
174.4 10.70 6.51
-0.029 (2)
-0.023 (2)
177 (3) 11
6.56
4.0
3.9
4.0
4.0
-0.015 (2)
~-0.06 (1)
~-0.02 (1)
175 (6)
-0.029 (3)
(1) MgSiO3 single crystal Brillouin-scattering measurementsYeganeh-Haeri,
(
1994 ).
(2) Recent results from static compression, assuming K'=4.0Andrault
(
et al., 2001 ).
の値が単結晶のデータに比べ、5-10%程度有意に
(3) Fiquet et al., 2001
(4) Fe-bearing MgSiO3 perovskite (Mao et al., 1991 )
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
(5) Wang et al., 1994; Utsumi et al., 1995; Funamori et al., 1996
慮してもまだ違いが残る。一方で
は比較的よい一
(6)Ultrasonic measurements for polycrystalline samplesSinelnikov
(
et al., 1998
).
Bulk modulus (K)
Shear modulus (G)
gLiterature values of the temperature derivative of bulk modulus vary widely, depending on the chemical
致を示した。
composition of perovskite (6, 9, 10 -12 ) (see text ).
地球内部への適用
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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、BirchMahnagan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)
Pyrolite modelは地震波観測データと整合的である。
13.00
pyrolite
pure perovskite
PREM
ak135
7.200
7.000
VS (km/s)
VP (km/s)
12.50
12.00
11.50
11.00
10.50
600
6.800
6.600
6.400
6.200
6.000
800
1000
1200
1400
Depth (km)
1600
5.800
600
800
1000
1200
Depth (km)
1400
1600
さらに地球内部への適用
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660 km不連続面がg-spinel → MgSiO3 perovskite +
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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
今後の課題
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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？