Single-crystal elasticity of hydrous wadsleyite and implication for the Earth’s

transition zone

Zhu Mao1, Steven D. Jacobsen1, Fuming Jiang1, Joseph R. Smyth3, Christopher Holl2, Daniel J. Frost4

Thomas Duffy1

1Princeton University, Department of Geosciences, Princeton, NJ, 085402Northwestern University, Department of Geological Sciences, Evanston, IL 60208

3University of Colorado, Department of Geological Sciences, Boulder, CO 803094Bayerisches Geoinstitut, Universität Bayreuth, 95440 Bayreuth, Germany

2

Estimate of water content in the mantle

MORB source from 0.005 to 0.02 wt% (e.g. Saal et al.2002)

OIB source from 0.03 to 0.1 wt% (e.g. Dixon et al.2002)

Shear wave velocity anomaly 0.3 wt% from 300-500 km in central and eastern Europe (Nolet and Zielhuis 1994)

Width of 410-km discontinuity 0.02-0.07 wt% (Wood 1995; van de Meijde et al., 2003)

Transition zone electrical conductivity 0.1-0.2 wt% (Huang et al., 2005)

3

Model for global water circulation

Ohtani 2005

4

transition zone

Li et al., 2001Fei and Bertka 1999

ri

5

Wadsleyite ( -Mg2SiO4)

• Has the greatest hydrogen storage capacity among the olivine polymorphs (e. g., Smyth 1987).

• Including ringwoodite, transition zone could contain a large water reservoir perhaps exceeding the mass of the hydrosphere (Smyth et al., 2006).

• Small amounts of water can strongly influence physical properties of mantle minerals (e. g., Wood 1995).

• The bulk modulus of hydrous wadsleyite was studied by static compression studies (Yusa and Inoue 1997; Smyth et al., 2005; Holl 2006).

• Pressure derivatives of bulk and shear moduli are needed to extrapolate elastic moduli to high pressures.

6

1. Ambient conditions measurements:

0.37 wt%, 0.84 wt% and 1.67 wt% H2O content

2. High-pressure measurements to 12 GPa:

0.84 wt% H2O content

Single-crystal elasticity measurements for hydrous wadsleyite by Brillouin scattering:

7

Example of Brillouin spectrum at ambient conditions for sample containing 0.84 wt% H2O.

-10 -5 0 5 10

LA LA

TA2 TA2TA1

Velocity (km/s)

R

TA1

1. Ambient conditions measurements

8

RMS: 49 m/s0.84 wt% water:

0 50 100 150

6

8

10

(0.56, 0.42, 0.71)

0 50 100 150

6

8

10

(0.84, 0.36, 0.42)

0 50 100 150

6

8

10

(0.15, 0.90, 0.42)

0 50 100 150

6

8

10

(1.00, 0, 0)

Azimutha angle (degree)

Velocity (km/s)

(b)

Measured compressional and shear wave velocities as a function of direction by Brillouin scattering.

9

Single-crystal elastic moduli of Mg2SiO4 hydrous wadsleyite as a function of water content.

Elasticity of anhydrous wadsleyite:

Sawamoto et al., 1984

Zha et al., 1997

110

100

90

80

70

60

Cij (GPa)

1.51.00.50.0

Water (wt%)

C13

C23

C12

120

110

100

90

1.51.00.50.0Water (wt%)

C55

C44

C66

400

350

300

250

Cij (GPa)

1.51.00.50.0

C22

C11

C33

10

is the water weight percent.OHX 2

OHOHS XGXK22

)1(9.7)1(8.111)6(4.12)7(3.1700 −=−=

180

160

140

120

100

80

Modulus (GPa)

2.52.01.51.00.50.0

Water (wt%)

KS

G

Yusa and Inoue 1997 Smyth et al., 2005. Wa II Zha et al., 1997 Sawamoto et al., 1984

11

VP and VS calculated for three olivine polymorphs at ambient conditions

Sawamoto et al., 1984; Zha et al., 1996 Inoue et al., 1998; Jackson et al., 2000 Li et al., 2003; Wang et al., 2003; Sinogeikin et al., 2003

See also: Fe-bearing hydrous ringwoodite Jacobsen et al., 2004.

0.0 0.4 0.8 1.2 1.6 2.0 2.48.4

8.6

8.8

9.0

9.2

9.4

9.6

9.8

10.0

Vp (km/s)

H2O (wt%)

olivine

Wadsleyite

Ringwoodite Mg#100

0.0 0.4 0.8 1.2 1.6 2.0 2.4

5.0

5.2

5.4

5.6

5.8

olivine

Wadsleyite

Ringwoodite Mg#100

Vs (km/s)

H2O (wt%)

12

2. High-Pressure measurements

Photo of hydrous wadsleyite crystal at 12 GPa

mμ250

ruby

ruby

13

450

400

350

300

250

Modulus (GPa)

14121086420

Pressure (GPa)

C22C11 C33

Open symbol: Zha et al., 1997Filled symbol: This study

140

130

120

110

100

90

Modulus (GPa)

14121086420

Pressure (GPa)

C55C44 C66

160

140

120

100

80

60

Modulus (GPa)

14121086420

Pressure (GPa)

C12 C13 C23

Single-crystal elasticity of wadsleyite with 0.84 wt% H2O as a function of pressure

14

240

220

200

180

160

140

120

100

80

Modulus (GPa)

14121086420

Pressure (GPa)

KS

G

KS'=4.2(1)

G'=1.4(1)

Aggregate bulk and shear moduli as a function of pressure

Anhydrous wadsleyite (Zha et al., 1997)

Wadsleyite with 0.84 wt% H2O (this study)

15

Application to the Earth’s mantle

1. Velocity jump at 410-km depth

2. Velocity gradient in the transition zone

16

)()()()( 0000 TTT

KTKTK P

SSS −

∂∂

+=

)]4(2

31[)21)((3 '2

5

0 SS KfTfKP −−+=

]1))(

)([(

2

1 3/2

0

−=TT

fρρ

∫=

−T

T

dTT

eTT 0

')'(

000 )()(α

ρρ

GVGKV SSP =+= 22 3/4 ρρ

Hydrous olivine

Hydrous wadsleyite

PS

T

K)(

∂∂

(GPa/K)

-0.0164(5)

-0.0175(3)

SS

P

K)(

∂∂

4.2(2)

4.2(1)

)10( 15 −−× Kα

WX

T

162.04.3

1022.273.2 3

−×+ −

Table. Thermal elastic parameters

Liu et al., 2005; Mayama et al., 2004;

Zha et al., 1996;

Inoue et al., 2004

0 200 400 600 800 10005

6

7

8

9

10

11

12

VP (km/s)

Depth (km)

AK135)]35(1)[()21( '0

2/5SSS KfTKfK −−+=

17

wdolP

seisPfrac V

Vol

−

−

ΔΔ

=

200 300 400 500 600

8.0

8.4

8.8

9.2

9.6

10.0

VP (km/s)

Depth (km)

VP at 410 km

Wadsleyite

olivine

200 300 400 500 600

8.0

8.4

8.8

9.2

9.6

10.0

AK135

VP (km/s)

Depth (km)

VP at 410 km

18

1. Velocity jump at 410-km depth

360 400 440 4806.6

6.9

7.2

7.5

0.8 wt% H2O

410 km

olivine

wadsleyite

VB (km/s)

Depth (km)

VK= 7.7%

VK= 6.7%

VK= 5.7%

dry conditions

0.4 wt% H2O

Frost and Dolejš 2007

19

360 380 400 420 440 460 480

4.6

4.8

5.0

5.2

5.4

0.8 wt% H2O

0.4 wt% H2O

Dry conditions

Olivine

Wadsleyite

410 km

VS (km/s)

Depth (km)

VS=12.1%

VS=10.8%

VS=9.4%

20

Olivine fraction as a function of water in wadsleyite

0.0 0.4 0.8 1.2 1.6

40

50

60

70

80

90

100

olivine volume fraction %

H2O in wadsleyite (wt%)

Pyrolite

determined by VB contrast at 410 km

reference seismic model: AK135

21

Olivine fraction as a function of water in wadsleyite

0.0 0.4 0.8 1.2 1.6

40

50

60

70

80

90

100

olivine volume fraction %

H2O in wadsleyite (wt%)

Pyrolite

determined by VB contrast at 410 km

reference seismic model: AK135

wdolS

seisS

V

V

−−

−

ΔΔ

22

2. Velocity gradient in the transition zone

Speziale, unpublished

23Li et al., 2001

24

Litasov and Ohtani 2003

Demouchy et al. 2005

~0.9 wt%~0.3 wt%

25

AK135 : 0.24 wt%

njpb: 0.4 wt%

PA5: 0.7 wt%

TNA-GCA: 0.5 wt%

SNA-S25: 0.8 wt%

Estimates of the reduction of water content:

Grand and Helmberger 1984; Walck 1984; Lefevre and Helmberger 1989

Kennett et al., 1994; Kennett et al., 1995; Gaherty et al., 1996

400 425 450 475 500 525 550

7.0

7.2

7.4

7.6

wd with 0.1 wt% H2O

VB (km/s)

Depth (km)

AK135

dry wd

wd with 0.34 wt% H2O

26

AK135 : 0.25 wt%

njpb: 0.4 wt%

PA5: 0.7 wt%

TNA-GCA: 0.5 wt%

SNA-S25: 0.8 wt%

Estimates of the reduction of water content:

Grand and Helmberger 1984; Walck 1984; Lefevre and Helmberger 1989

Kennett et al., 1994; Kennett et al., 1995; Gaherty et al., 1996

400 420 440 460 480 500 520

7.2

7.3

7.4

7.5

7.6

VB(km/s)

Depth(km)

AK135

njpb

TNA-GCA

SNA-S25

PA5

27

Conclusions

• Aggregate bulk and shear moduli of hydrous wadsleyite vary linearly as function of water content:

• For iron-free olivine polymorphs, water has a greater (or similar) effect on the elasticity of wadsleyite than the other two polymorphs.

• The high pressure measurements of hydrous wadsleyite show pressure derivative of bulk modulus, KS’ and shear modulus, G’ is similar to its anhydrous phase: KS’ = 4.2(1), G’ = 1.4(1).

OHOHS XGXK22

)1(9.7)1(8.111)6(4.12)7(3.1700 −=−=

28

Conclusions

• For a pyrolite upper mantle (60 vol% olivine), 0.8 wt% H2O in wadsleyite is required to match the velocity contrast given by seismic model AK135.

• Transition zone seismic velocity gradient (AK135) can be matched by ~0.3 wt% H2O reduction in wadsleyite from 410 to 520 km. Regional model needs more water reduction to match the velocity gradient than AK135.

29

30

Frost and Dolejš 2007

31

120

110

100

90

80

70

60

Cij (GPa)

1.51.00.50.0

C55

C44

C66

wadsleyite

olivine

400

350

300

250

200

Cij (GPa)

1.51.00.50.0

C22

C11

C33

olivine

wadsleyite

110

100

90

80

70

60

Cij (GPa)

1.51.00.50.0H2O (wt%)

C13

C23

C12

olivine

wadsleyite

32

0.0 0.4 0.8 1.2 1.6 2.0 2.4

80

90

100

110

120

G (GPa)

H2O (wt%)

0.0 0.4 0.8 1.2 1.6 2.0 2.4120

140

160

180

Forsterite

Wadsleyite

rw Mg#90

Ringwoodite(rw) Mg#100

H2O (wt%)

KS (GPa)

33

Table. Water storage capacity of olivine polymorphs with pressure and temperature

Litasov et al., 20030.8021.51200

Ohtani et al., 20000.2918.51600rw

0.2918.51600

0.4618.51400

Litasov et al., 20030.72161400

0.93151400

Demouchy et al., 20052.68141200wd

0.40121400

Smyth et al., 20060.89121200ol

ReferenceH2O (wt%)P (GPa)T (oC)

Litasov et al., 20030.8021.51200

Ohtani et al., 20000.2918.51600rw

0.2918.51600

0.4618.51400

Litasov et al., 20030.72161400

0.93151400

Demouchy et al., 20052.68141200wd

0.40121400

Smyth et al., 20060.89121200ol

ReferenceH2O (wt%)P (GPa)T (oC)

34

200

180

160

140Bulk Modulus (GPa)

4.44.24.03.83.63.43.2

Density (g/cm3)

Ringwoodite

Wadsleyite

Olivine

T=300K

P=10-4

GPa

Mg#100

Mg#90

120

100

80

60Shear Modulus (GPa)

4.44.24.03.83.63.43.2

Density (g/cm3)

Olivine

Ringwoodite

Wadsleyite T=300K

P=10-4

GPa

Mg#100

Mg#90Effect of composition and structure on the elasticity of olivine (Mg, Fe)2SiO4 polymorphs

Birch’s plot

35

200

180

160

140

120

KS (GPa)

4.44.24.03.83.63.43.2

Density (g/cm3)

Ringwoodite

Wadsleyite

Olivine

Chondrodite

Clinohumite

hy-ol hy-wa this study hy-ri

120

100

80

60

G (GPa)

4.44.24.03.83.63.43.2

Density (g/cm3)

RingwooditeWadsleyite

OlivineClinohumite

Chondrodite

hy-ol hy-wa this study hy-ri

Effect of hydration

36

• Elasticity of hydrous olivine Jacobsen et al., 2006.

• Elasticity of hydrous ringwoodite Inoue et al., 1998 and Wang et al., 2003

• Assuming a linear relationship between aggregate moduli and water content for three olivine polymorphs.

Effect of water on the elasticity of iron free olivine polymorphs

Thus, water has a greater (or similar) effect on the elastic moduli of wadsleyite than the other two polymorphs.

14

12

10

8

6

4

2

0

G/G

2.01.51.00.50.0

Water (wt%)

olivine

ringwoodite

wadsleyite

1.6%

5%

7.1%

14

12

10

8

6

4

2

0

K0S

/K0S

2.01.51.00.50.0

Water (wt%)

wadsleyite

ringwoodite

olivine2.9%

4.5%

7.3%7.4%