pressure scales & hydrostaticity national institute for materials science (nims), tsukuba, japan...
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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.
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Outline
Basic consideration
Examples: Au, Nb
Conclusions
Effect of nonhydrostatic stress
Acknowledgments : A. K. Singh, A. Dewaele
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more serious !
Nonhydrostatic stress
•Stress inhomogeneity
•Uniaxial stress
pressure gradients
lattice distortion
broadening
shift
(signal)
(signal)
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Deformation under uniaxial
stress
K. Takemura, JAP 89, 662 (2001).
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-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).
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“Pressure” is meaningful only under hydrostatic conditions.
Nonhydrostatic stress conditions are difficult to reproduce ...
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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 !
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Au
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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 )
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300 m
80 m
Au foil
( 1 mt )
Heruby( 4 m )
Au in He at 74.5 GPa
Re gasket
( ~10 mt )
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Ruby spectraR1-R2 separation
R1 fwhm
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Au in He at 74.5 GPaPhoton Factory
= 0.6198 Å
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EOS of Au Fig. by T. Duffy
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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)
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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)
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-plot & deviatoric stress
66 GPa (Takemura)
70 GPa (Dewaele) t = -
t = - (3 M1)/ (M0 S)
>
<
compressed
expanded
(foil)
(powder)
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Both data approach, but
Experiments should be done again to see the reproducibility and consistency ...
(111)
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Nb
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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
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Luminescence spectra of three rubies at the same pressure in a He-pressure medium
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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.)
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Ruby spheres•merit
•demerit
well-defined size (thickness)
avoid bridging anvils
crystallographic orientation unknown
effect of nonhydrostatic stress unclear
2 ~ 40 m
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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!)
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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.