1. Pressure Scales & Hydrostaticity National Institute for Materials Science (NIMS), Tsukuba, Japan TAKEMURA Kenichi 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 pressure gradients lattice distortion broadening shift (signal)

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

5. G-plot a m ( hkl ) = M 0 + M 1 [ 3 (1-3 sin 2 q ) G( hkl )] t = - (3 M 1 )/ (aM 0 S) Singh & Takemura, J. Appl. Phys. 90, 3269 (2001). Deviatoric stress G( hkl ) = ( h 2 k 2 + k 2 l 2 + l 2 h 2 ) / ( h 2 + k 2 + l 2 ) M 0 = a p { 1 + (at /3) (1-3 sin 2 q ) [(S 11 - S 12 ) - (1- a -1 ) (2 G v ) -1 ] } M 0 = a p { 1 + (at /3) (1-3 sin 2 q ) [(S 11 - S 12 ) - (1- a -1 ) (2 G v ) -1 ] } M 1 = - a p at S / 3 S = S 11 - S 12 - S 44 / 2 Takemura & Singh, Phys. Rev. B 73, 224119 (2006).

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

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

8. Au

9. He loading Before ( 114 mm f ) After ( 60 mm f ) He 180 MPa ruby ( 4 mm f ) Au foil ( 1 mm t ) Re gasket ( 52 mm t ) Dia. anvil ( 300 mm f ) 9.9 GPa x-ray beam ( 40 mm f )

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

11. Ruby spectra R 1 -R 2 separation R 1 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? DPDP Dd/d 0 DP ~ 4 GPa @ 65 GPa Dd/d 0 ~ 0.002 DP/P ~ 6% D(d/d 0 )/(d/d 0 ) ~ 0.2% D(V/V 0 )/(V/V 0 ) ~ 0.6% Ruby scale: Mao (1986)

15. Uncertainty in d-value d = l / 2 sin q tan 2 q = X / L = p x x / L D d / d = [ ( D l / l ) 2 + ( D q / tan q ) 2 ] (1/2) D q = tan 2 q / 2 ( 1 + tan 2 2 q) [ ( D p x / p x ) 2 + ( D x / x ) 2 + ( D L / L ) 2 ] (1/2) ~ ±0.05% ~ ±0.07% ~ ±0.05% p x (mm/pixel) x (pixel), L (mm) l (Å)

16. G-plot & deviatoric stress 66 GPa (Takemura) 70 GPa (Dewaele) t = s 3 - s 1 t = - (3 M 1 )/ (aM 0 S) s 3 > s 1 s 3 < s 1 compressed expanded (foil) (powder)

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

18. Nb

19. nb1100, DA: 150/300 mm f,7° Re (31 mm t, 50 mm f ) ruby 4 mm f After He loading 125 GPa 14.4 GPa 30 mm t 〜 8 mm t sample 5 mm t Before He loading AB C 150 mm f 50 mm f ABC

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

21. Ruby R 1 -R 2 splitting is sensitive to uniaxial stress & crystallographic orientation Chai & Brown, GRL 23, 3539 (1996). He & Clarke, J. Am. Ceram. Soc. 78, 1347 (1995). R1R1 R2R2 K. Syassen (private commun.)

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

23. Proposal: pressure standard 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-robinRound-robin (like the length and mass standards) (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.