Transcript Pressure Scales - MALTA

Pressure scales & gauges:
How to measure pressure:
adequately and accurately
Stefan Klotz
Université P&M Curie, Paris
Summary
 What is pressure?
 Primary & secondary pressure gauges
 Laboratory pressure gauges (bourdon, transducers, resisitive gauges):
« Fixed point » gauge
Optical gauges (ruby and others)
Diffraction gauges (x-rays and neutrons)
 Again: Primary pressure gauges: ultrasonics & shock waves
 Remarks and outlook: Precision in high P science & technology
What is pressure?
F
« P = Force/Area »
A
P
DV
P
DV
P
DV
Need more general expression for « pressure » and « deformation »
Stress and strain
(in a nutshell)
Strain (« deformation »):
U = (uij)
(3x3 matrix, symetric: 6 elements)
a
a
U=
*
a
0
*
U=
U=
0
*= 0
*
*
a
0
0
a
0 a
0 0
0 0
Remark:
Tr U = DV
s = (sij)
Stress (« pressure »):
(3x3 matrix, symetric: 6 elements)
F
s=
s=
s=
Remarks:
-p
-p
*
*
-p
0
*
0
*
p
0
0
p
0 p
0 0
0 0
- hydrostatic pressure: sij = -dij ∙ p
- hydrostatic component: p = ⅓ ∙Tr U
- Relation s ↔ U : Hook’s law: s = C U
*= 0
To remember:
 « Pressure » is a form of stress s=(sij)
 « Pressure » in physics means almost exclusively
hydrostatic pressure: s = -dij p
ex:
p = -(E/V)T
B= - (p/lnV)T
 importance of hydrostaticity in exp. studies
 Worthwhile to invest some time into theory of elasticity!
Primary pressure scales
(use only the definition of pressure)
High pressure balances
P = F/A
P-range: 0-5 kbar
Accuracy: 0.02%
High pressure balances to 3 GPa
- Technically difficult
- Not commercially available
- High exploitation costs
Accuracy: ~ 0.1%
Heydemann, J. Appl. Phys. (1967)
Secondary pressure scales
= Methods which:
 Are more adapted to a specific P range and device
 Have been calibrated to a primary standard
« Bourdon gauge »
« Heise » gauge, 0-6 kbar
reading precision: 2 bar
- Mechanic devices
- range: 0-1 GPa
- accuracy ~ 0.3%
Pressure transducer gauges
- Electronic devices:
detect change of resistance, capacity with p
- range: 0-1 GPa, commercially available ~ 1-3 k€
- accuracy ~ 0.5%
Manganine wire gauge
Manganine: alloy, 84% Cu, 14% Mn, 2% Ni
lnR/P = +0.023/GPa
Bridgman 1911
From: http://frustrated-electrons.ifs.hr/
- in form of coil. Small, simple, inexpensive
- range: 0-6 GPa, up to 250 °C; mainly in fluids, sometimes dynamic Ps
- accuracy ~ 0.5%
- need to be prepared and aged, « handwork » needed
- has non-negligible temp. dependence of resistance.
« Fixed point » gauges
Use phase transitions of certain elements & compounds
Usually detected resistively, sometimes volumetrically
Examples:
Hg liq-sol
Bi I-II
Tl II-III
Bi III-V
Pb I-II
GaAs
Bi
Bundy 1958
0.7569 GPa
2.556 GPa
3.67 GPa
7.69 GPa
13.4 GPa
17.5-18.5 GPa
Bi
Typical application: Multianvil cells
« Calibration curve »
= Pressure-load relationship
of a high P assembly
Courtesy: BGI, Bayreuth
Optical pressure gauges
= Gauges which use the pressure depencence of an
optical property of a material which is next to the
sample.
The ruby fluorescence gauge
Ruby: Al2O3:Cr 3+ (« corundum »)
Cr 3+: ~ 0.1-1 at%
0 GPa
20 GPa
Dl/DP = +0.365 nm/GPa
Piermarini et al. JAP 1975
K. Syassen, High Pres. Res. 28, 75 (2008)
The ruby 1986 calibration
(« Mao quasi-hydrostatic scale »)
Mao, Xu, Bell, JGR 91, 4673 (1986)
- Load DAC with Cu, Ag and ruby & Ar
- Measure V of Cu & Ag and determine P
from shock wave EoS
-Fit measured l(P) to a Murnaghan-function
and constrain it at low P to the
Piermarini coefficient
B

A   l 
   1
P

B   l0 


B


A  l 
   1
P

B   l0 


A = 1904 GPa
B = 7.665
Temperature dependence
- Line widths broaden considerably with T
P measurements more difficult at high T
Fluorescence at high P
- Fluorescence weaker at high P
need blue laser for very high Ps
Practical aspects
S. Klotz, unpublished
ruby
Ruby: easy to get, single crystalline, lowZ, unexpensive, strong fluorescence!
Can work with very small rubies: ~ 5 mm
(prefer ruby spheres)
laser
fiber
spectro
Optical set-up simple and compact,
relatively cheap (~ 5 k€)
Syassen, High Pres. Res. 28, 75 (2008)
How precise is the ruby scale?
 Below ~ 30 GPa, the Mao 1986 scale is accurate to ~ 1%.
 At 1-2 Mbar, it underestimates P by probably ~ 5-10%
 Many suggestions for revisons, but no general consensus
Other fluorescence gauges
Ruby:
Moderate dl/dp
Large dl/dT
Strontium borate
Matlockite
Chen et al., High Press. Res. 7, 73 (1991)
The « diamond edge » optical scale
Rule of thumb: (distance of the two edges in cm-1)/2 = P in GPa
« Use the diamond edge when you have nothing else to measure P »
Akahama & Kawamura, J. Appl. Phys 96, 3748 (2004)
Diffraction pressure gauges
= Gauges which use the pressure dependence of the
lattice parameter (unit cell volume) of a material in close
contact with the sample. Usually measured by a
diffraction experiment (x-ray & neutrons)
The Decker NaCl scale (1971)
• “Table”, semi-empirical (interatom. pot. + exp. input params)
• P-range: 0-300 kbar
• Accuracy: 0-5 % (!?)
Decker, J. Appl. Phys. 42, 3239 (1971)
Brown’s 1999 NaCl scale
PBrown-Pdecker (GPa)
M. Brown, J. Appl. Phys. , 1999
PBrown-PDecker/P  3%
Probably more accurate than Decker!
General observations
 « The Decker scale is the mother of the Ruby scale »
Mao, Xu, Bell, JGR 91, 4673 (1986)
Initial slope forced
to be coherent with
Decker scale
B

A   l 
   1
P

B   l0 


 Limited to 0-35 GPa (B1-B2 transition) Decker less frequently used
Other (more recent) diffraction gauges: metals
Dewaele et al., PRB 2004
Anzellini et al., JAP 2014
Dewaele & Takemura, PRB 2008
R
Re
PRuby (GPa)
 No tables: Take B0, B0’, V0 & plug into EoS form:
« Birch Murnaghan EoS »
« Vinet-Rydberg EoS »
X = (V/V0)
Primary standards at P>3 GPa?
 « Integration of bulk modulus »
 P 
B0   V 

 V T
V
B0 (V )
P(V )  P(V0 )   
dV
V
V0
Compress a sample and:
- Determine V by diffraction (precision : 10-4)
- Determine simultaniously compressibility by some technique
- Integrate
Ultrasonic measurements
Example: cubic system along [100]
r v2 = C11
l
B = (C11+2C12)/3
measure speed v of a pulse:
Precision: 10-4!
Problem: gives adiabatic B: « BS »
BT = BS/(1+agT)
agT  1% at 300 K
Feasible, but accuracy limited by precision in Grüneisen-parameter g !
 Shock wave measurements
shock front
r
P
E
Up
US
compressed (shocked)
material
r
r0
E0
uncompressed
Material: P=0
r 0U S
U S U P
P  r 0U PU S
« Rankine-Hugoniot equations »
U: speed
s: shock front, p: particle
Measure speeds  get P!
But:
Need to be « reduced » to T=const!
Mao, Xu, Bell, JGR 91, 4673 (1986)
Shock-wave reduced
EoS data
To remember:
Shock waves data provide (in theory)
a primary P gauge in the Mbar range
Outlook I: Accuracy in everyday life
Mass/weight:
1 g / 1 kg = 0.1%
Temperature:
0.1 K / 300K ~ 0.01 %
Length:
1 mm/1 m = 0.1 %
Time:
1 sec / 1 day = 0.001 %
Pressure:
0.1 bar / 2 bar
10 hPa/1000 hPa
Science, 3-10 GPa:
3-5% !!
5 % (tyre)
1% (atm. pressure)
Outlook II: High pressure metrology: A
boring subject?
Forman, Piermarini, Barnett & Block, Science 176, 285 (1972)
Piermarini, Block & Barnett, J. Appl. Phys. 44, 5377 (1973)
Barnett, Block & Piermarini, RSI 44, 1 (1973)
Piermarini, Block, Barnett & Forman, J. Appl. Phys. 2774 (1975)
Mao, Bell, Shaner, Steinberg, J. Appl. Phys. 49, 3276 (1978)
Mao, Xu & Bell, J. Geophys. Res. 91, 4673 (1986)
~ 4500 citation in total (2008)
K. Syassen, High Pressure Research (2008)
Thank you!