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.

Outline

Basic consideration

Examples: Au, Nb

Conclusions

Effect of nonhydrostatic stress

Acknowledgments : A. K. Singh, A. Dewaele

more serious !

Nonhydrostatic stress

•Stress inhomogeneity

•Uniaxial stress

pressure gradients

lattice distortion

broadening

shift

(signal)

(signal)

Deformation under uniaxial

stress

K. Takemura, JAP 89, 662 (2001).

-plot-plot am (hkl) = M0 + M1 [ 3 (1-3 sin2 ) (hkl)]

t = - (3 M1)/ (M0 S)

Singh & Takemura, J. Appl. Phys. 90, 3269 (2001). Singh & Takemura, J. Appl. Phys. 90, 3269 (2001).

Deviatoric stress

(hkl) = ( h2 k2 + k2 l2 + l2h2 ) / (h2 + k2 + l2 )(hkl) = ( h2 k2 + k2 l2 + l2h2 ) / (h2 + k2 + l2 )

M0 = ap { 1 + (t /3) (1-3 sin2 ) [(S11 - S12 ) - (1- -1 ) (2 Gv )-1 ] }

M0 = ap { 1 + (t /3) (1-3 sin2 ) [(S11 - S12 ) - (1- -1 ) (2 Gv )-1 ] }

M1 = - ap t S / 3M1 = - ap t S / 3

S = S11 - S12 - S44 / 2 S = S11 - S12 - S44 / 2

Takemura & Singh, Phys. Rev. B 73, 224119 (2006). Takemura & Singh, Phys. Rev. B 73, 224119 (2006).

“Pressure” is meaningful only under hydrostatic conditions.

Nonhydrostatic stress conditions are difficult to reproduce ...

Ideal hydrostatic conditions can only be achieved with a fluid pressure medium and a

perfect single crystal.

Local stress

single crystal

single crystal(+ grain boundaries,

dislocations, twins, ...)

polycrystalline

broadening

local stress !

Au

He loading

Before ( 114 m ) After ( 60 m

)

He180 MPa

ruby ( 4 m )

Au foil

( 1 mt )

Re gasket

( 52 mt )

Dia. anvil ( 300 m )

9.9 GPa

x-ray beam

( 40 m )

300 m

80 m

Au foil

( 1 mt )

Heruby( 4 m )

Au in He at 74.5 GPa

Re gasket

( ~10 mt )

Ruby spectraR1-R2 separation

R1 fwhm

Au in He at 74.5 GPaPhoton Factory

= 0.6198 Å

EOS of Au Fig. by T. Duffy

Error in pressure or d-value?

P

d/d0

P ~ 4 GPa @ 65 GPa

d/d0 ~ 0.002

P/P ~ 6%

d/d0 )/d/d0 ) ~ 0.2%

V/V0 )/V/V0 ) ~ 0.6%

Ruby scale: Mao (1986)

Uncertainty in d-value

d = / 2 sin tan 2 = X / L = px x / L

d / d = [ (/2 + (tan ) 2 ](1/2)

= tan 2 2 (1+ tan 2 2)[ (px/px2

+ (x/x2 +

(L/L2 ](1/2)

~ ±0.05%~

±0.07%

~ ±0.05%~ ±0.05%

~ ±0.05%

px (mm/pixel)x (pixel), L (mm) (Å)

-plot & deviatoric stress

66 GPa (Takemura)

70 GPa (Dewaele) t = -

t = - (3 M1)/ (M0 S)

>

<

compressed

expanded

(foil)

(powder)

Both data approach, but

Experiments should be done again to see the reproducibility and consistency ...

(111)

Nb

nb1100, DA: 150/300 m ,7°

Re (31 mt, 50 m)

ruby 4 m

After He loading 125 GPa

14.4 GPa

30 mt〜 8 mt

sample 5 mt

Before He loading

A B

C

150 m

50 m A B C

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

Ruby R1-R2 splitting is sensitive to uniaxial stress & crystallographic

orientation

Chai & Brown, GRL 23, 3539 (1996). He & Clarke, J. Am. Ceram. Soc. 78, 1347 (1995).

R1

R2

K. Syassen (private commun.)

Ruby spheres•merit

•demerit

well-defined size (thickness)

avoid bridging anvils

crystallographic orientation unknown

effect of nonhydrostatic stress unclear

2 ~ 40 m

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-robin

(like the length and mass standards)

(Don’t change the pressure!)

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.