Pressure Scales & Hydrostaticity

1. Pressure Scales & Hydrostaticity TAKEMURA Kenichi National Institute for Materials Science (NIMS), Tsukuba, Japan COMPRES workshop on pressure scales, Geophysical Lab., CIW, U.S.A., January 28, 2007.

2. Outline • Basic consideration • Examples: Au, Nb • Conclusions Effect of nonhydrostatic stress Acknowledgments : A. K. Singh, A. Dewaele

3. more serious ! Nonhydrostatic stress • Stress inhomogeneity • Uniaxial stress (signal) pressure gradients broadening (signal) lattice distortion shift

4. Deformation under uniaxial stress K. Takemura, JAP 89, 662 (2001).

5. t = - (3 M1)/ (aM0 S) M0 = ap { 1 + (at /3) (1-3 sin2 q ) [(S11 - S12 ) - (1- a-1 ) (2 Gv )-1 ] } M1 = - apat S / 3 G(hkl) = ( h2 k2 + k2 l2 + l2h2 ) / (h2 + k2 + l2 ) S = S11 - S12 - S44 / 2 G-plot am (hkl) = M0 + M1 [ 3 (1-3 sin2 q ) G(hkl)] Deviatoric stress Singh & Takemura, J. Appl. Phys.90, 3269 (2001). Takemura & Singh, Phys. Rev. B73, 224119 (2006).

6. Nonhydrostatic stress conditions are difficult to reproduce ... “Pressure” is meaningful only under hydrostatic conditions.

7. single crystal broadening polycrystalline single crystal local stress ! (+ grain boundaries, dislocations, twins, ...) Idealhydrostatic conditions can only be achieved witha fluid pressure medium and a perfect single crystal. Local stress

8. Au

9. x-ray beam ( 40 mmf ) He loading Dia. anvil (300 mmf) 9.9 GPa ruby ( 4 mmf ) He 180 MPa Regasket ( 52 mmt ) Aufoil ( 1 mmt ) Before (114 mmf) After (60mmf)

10. Au in He at 74.5 GPa He ruby ( 4 mmf ) Au foil ( 1 mmt ) Re gasket ( ~10 mmt ) 80 mm 300 mm

11. Ruby spectra R1-R2 separation R1 fwhm

12. Au in He at 74.5 GPa Photon Factory l= 0.6198 Å

13. EOS of Au Fig. by T. Duffy

14. Error in pressure or d-value? DP ~ 4 GPa @ 65 GPa DP/P ~ 6% Dd/d0 Dd/d0 ~ 0.002 D(d/d0 )/(d/d0 ) ~ 0.2% DP D(V/V0 )/(V/V0 ) ~ 0.6% Ruby scale: Mao (1986)

15. px (mm/pixel) x (pixel), L (mm) l (Å) d = l/2sinq tan2q = X/L = pxx / L Uncertainty in d-value Dq = tan2q/2(1+tan22q)[(Dpx/px)2+(Dx/x)2+ (DL/L)2](1/2) ~ ±0.05% ~ ±0.05% ~ ±0.05% Dd/d = [ (Dl/l)2 + (Dq/tanq)2](1/2) ~ ±0.07% ~ ±0.05%

16. expanded t = - (3 M1)/ (aM0 S) (powder) compressed (foil) G-plot & deviatoric stress s3> s1 t = s3- s1 70 GPa (Dewaele) s3< s1 66 GPa (Takemura)

17. Both data approach, but (111) Experiments should be done again to see the reproducibility and consistency ...

18. Nb

19. A B 150 mmf C nb1100, DA: 150/300 mmf ,7° Re (31 mmt, 50 mmf) After He loading 125 GPa 14.4 GPa Before He loading 50 mmf A B C ruby 4 mmf 30 mmt 〜8 mmt sample 5 mmt

20. Luminescence spectra of three rubies at the same pressure in a He-pressure medium

21. Ruby R1-R2 splitting is sensitive to uniaxial stress & crystallographic orientation R1 R2 K. Syassen (private commun.) Chai & Brown, GRL 23, 3539 (1996). He & Clarke, J. Am. Ceram. Soc. 78, 1347 (1995).

22. Ruby spheres • merit • demerit well-defined size (thickness) avoid bridging anvils 2 ~ 40 mm crystallographic orientation unknown effect of nonhydrostatic stress unclear

23. Proposal: pressure standard (like the length and mass standards) • Prepare ruby and Au (or any standard) in a DAC with He and stabilize the pressure at “50 GPa”. • Use the sample (ruby and Au) in this particular DAC as a pressure standard common to high-pressure community. • Check the wavelength of ruby and the d-values of Au at each institute. Round-robin (Don’t change the pressure!)

24. Conclusions • Importance of realizing good (quasi)hydrostatic conditions. • Need for orientated thin tiny ruby disks to check the magnitude of uniaxial stress. • Need for common pressure standards prepared in a DAC for high-pressure community. Check always how large the uniaxial stress component is.