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# Elasticity of lower-mantle bridgmanite

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## References

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## Author information

Authors

### Contributions

J.-F.L. initiated the project. Z.M. performed the data processing using the covariance matrix. J.Y. and S.F. performed the sensitivity test analysis. Z.M. and S.F. performed elasticity modelling and error analysis. S.F. prepared the draft Supplementary Information. J.-F.L. wrote the manuscript and all authors participated in the manuscript revision.

### Corresponding author

Correspondence to Jung-Fu Lin.

Declared none.

## Extended data figures and tables

### Extended Data Fig. 1 Relationship between the uncertainties of the reported elastic constants and our calculated sensitivity of wave velocities for a chosen crystallographic (100) orientation as well as the number of measured phonon directions.

ad, The azimuthal angle between two adjacent phonon directions is 10°. Error bars in bd represent standard deviations (1σ) of the elastic constants. Data on the elastic constants are from ref. 6.

### Extended Data Fig. 2 Modelling the acoustic velocity of bridgmanite to derive Cij at 11.66 GPa.

Error bars are not shown when smaller than the symbols. Filled data points are the velocity data from Kurnosov et al.3; the dashed lines are velocity-fitting curves from Kurnosov et al.3; and the solid lines are velocity-fitting curves using the Cij derived from the covariance matrix analysis in this study. Red, VP; green, VS1; blue, VS2. The orientations of the crystal platelets are given in parentheses.

### Extended Data Fig. 3 Modelling the acoustic velocity of bridgmanite to derive Cij at 31.76 GPa.

Vertical lines represent standard deviations (+1σ) and are not shown when smaller than symbols. Solid data points are velocity data from Kurnosov et al.3; the dashed lines are velocity-fitting curves from Kurnosov et al.3; and the solid lines are velocity-fitting curves using the Cij derived from the covariance matrix analysis in this study. Red, VP; green, Vs1; blue, Vs2. The orientations of the crystal platelets are given in parentheses.

### Extended Data Fig. 4 Adiabatic bulk modulus and shear modulus of bridgmanite (Mg0.9Fe0.1Si0.9Al0.1)O3 at high pressure.

a, KS; b, G. Red data points are results using our obtained full elastic constants (Cij); black data points are data reported in Kurnosov et al.3. Black and red dashed lines are the best fits to data from Kurnosov et al.3 and this study, respectively. Error bars represent standard deviations (1σ) and are not shown when smaller than the symbols. In this study, the adiabatic bulk modulus at ambient conditions (KS0) is 250(1) GPa, with the pressure derivative of KS at 300 K (KS) = 3.2(2), while the shear modulus at ambient conditions (G0) is 159(1) GPa, with the pressure derivative of G0 at 300 K (G′) = 2.2(1).

### Extended Data Fig. 5 Comparison of elastic constants of single-crystal bridgmanite as a function of pressure.

Bgm, MgSiO3 bridgmanite; Fe10-Al10-Bgm, (Al,Fe)-bearing bridgmanite with a composition of (Mg0.9Fe0.1Si0.9Al0.1)O3. Error bars represent standard deviations (1σ) and are not shown when smaller than the symbols. Symbols indicate experimental results from the literature; lines indicate theoretical calculations3,6,7,16,17,18,19,20. The filled red circles represent the derived elastic constants in this study using the raw velocity data in Kurnosov et al.3.

### Extended Data Fig. 6 Comparison of aggregate compressional and shear wave velocities of single-crystal and polycrystalline bridgmanite at high pressure.

Symbols and solid lines represent experimental results from the literature; dashed lines indicate theoretical calculations3,6,7,8,9,10,11,16,17,18,21,22. The solid red circles are the calculated velocities of (Al,Fe)-bearing bridgmanite using the elastic constants derived in this study (Extended Data Fig. 5), while open black circles are from Kurnosov et al.3. Error bars represent standard deviations (1σ) and are not shown when smaller than the symbols.

## Supplementary information

### Supplementary Methods

The Supplementary Methods consist of calculation on the sensitivity of wave velocity to variation of elastic constants, uncertainty evaluation on the derived elastic constants, derivations of elasticity from single crystals to aggregates

### Supplementary Table 1

Derived full elastic constants of bridgmanite (Mg0.9Fe0.1Si0.9Al0.1)O3 at high pressure in this study using the raw velocity data in Kurnosov et al.3 and the covariance matrix analysis

### Supplementary Table 2

Covariance matrix (in GPa2) of elastic constants at 0.48 GPa

### Supplementary Table 3

Covariance matrix (in GPa2) of elastic constants at 11.66 GPa

### Supplementary Table 4

Covariance matrix (in GPa2) of elastic constants at 15.89 GPa

### Supplementary Table 5

Covariance matrix (in GPa2) of elastic constants at 21.25 GPa

### Supplementary Table 6

Covariance matrix (in GPa2) of elastic constants at 25.06 GPa

### Supplementary Table 7

Covariance matrix (in GPa2) of elastic constants at 31.76 GPa

### Supplementary Table 8

Covariance matrix (in GPa2) of elastic constants at 35.44 GPa

### Supplementary Table 9

Covariance matrix (in GPa2) of elastic constants at 40.17 GPa

## Rights and permissions

Reprints and Permissions

Lin, JF., Mao, Z., Yang, J. et al. Elasticity of lower-mantle bridgmanite. Nature 564, E18–E26 (2018). https://doi.org/10.1038/s41586-018-0741-7

• Accepted:

• Published:

• Issue Date:

• DOI: https://doi.org/10.1038/s41586-018-0741-7

• ### Experimental elasticity of Earth’s deep mantle

• Hauke Marquardt
• Andrew R. Thomson

Nature Reviews Earth & Environment (2020)

• ### Kurnosov et al. reply

• A. Kurnosov
• H. Marquardt
• L. Ziberna

Nature (2018)