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Baosheng Li ESS Building SUNY Stony Brook Stony Brook, NY 11794. Direct Pressure Measurements and Insights on Current Pressure Scales. This research is supported by NSF Elasticity Grand Challenge Grant. Simultaneous P - V-T Eos and Sound Velocity ( Vp , Vs ) Measurements. CCD/SSD. Press. - PowerPoint PPT Presentation
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Direct Pressure Measurements andInsights on Current Pressure Scales
Baosheng LiESS BuildingSUNY Stony BrookStony Brook, NY 11794
This research is supported by NSF Elasticity Grand Challenge Grant
CCD/SSD
PressIncident slits
Sample
X17B2
YAG and CCD Camera
X-ray Imaging
Ultrasonic Interferometer
Simultaneous P-V-T Eos and Sound Velocity (Vp,Vs) Measurements
NSLS
Experimental Techniques
Trigger
ComputerControl
Wave FormGenerator
DigitalOscilloscope
IEEE
i (t)
r(t)
Transducer
Buffer Rod
Sample
Ch1 SyncCh1
g(t)
Frequency
Amp
Ultrasonic Interferometry
cellassembly
TC
Pt NaCl
sample
C-heater
TC
Boron
Details of SAM 85
Cell assembly for ultrasonics at High P and T.
P and S wave travel times(tp, ts) inside the sample are measured at the same time
SEM Image of Hot-pressed MgO Polycrystalline sample
Bulk density: 3.57 g/cm3 (99.6% of theoretical density)
Unit Cell Volume:MgO Run #1 and Run #2
70
71
72
73
74
75
76
0 2 4 6 8 10 12
Sample Pressure (GPa)
Vo
lum
e (A
^3)
MgO_40
MgO_41
Results of Unit Cell Volume of MgO at High P and T
0.9
0.92
0.94
0.96
0.98
1
1.02
0 5 10 15 20
Pressure (GPa)
V/V
0
Fei99
This study
Speziale01
Utsumi98
D00
Yoneda90
Matsui00
J&N82
1073K
473K
5.5
5.6
5.7
5.8
5.9
6
6.1
6.2
6.3
6.4
6.5
0 2 4 6 8 10
Pressure (GPa)
VS (
km
/s)
This study
Isaak et al (1989)
Others' RT Values
300K
873K
673K
473K
1073K
9.1
9.3
9.5
9.7
9.9
10.1
10.3
0 2 4 6 8 10
Pressure (GPa)
VP (
km
/s)
This study
Compression
Others' RT Data
300K
873K
673K
473K
1073K
V(measured)-V(fit)
-0.04
-0.03
-0.02
-0.01
0
0.01
0.02
0.03
0.04
0 2 4 6 8 10
Vp
Vs
VP2 = (1-2)5/2(L1+L2) (1) VS2 = (1-2)5/2(M1+M2) (2)
with = [(1-(/o)2/3]/2 L1 = KS+(4/3)G; L2 = 5(KS+4G/3) - 3KS(KS’ + 4G’/3) M1 = G; M2 = 5G-3KSG’
Finite Strain Data Analysis
1. Finite Strain Equations
2. Solve for: KS0, Ks0’, G0, G0’,dKS/dT, dG/dT, d2K/dPdT, d2G/dPdT,
d2K/dP2, d2G/dP2 by minimizing Vmea-Vcal) 2
3. Calculation of sample pressureP = - (1-2)5/2(C1+0.5C22+ ….)withC1 = 3L1–4M1; C2 = 3L2–4M2+7C1
P and S wave Velocities: MgO
(b)
5.80
6.00
6.20
6.40
6.60
6.80
0.90.920.940.960.981
V/V0
Vel
oci
ty (
km/s
)
This study, P Dow n
This, study, P Up
ZHA00
Chopelas96
S&B98
Yoneda90
(a)
9.40
9.60
9.80
10.00
10.20
10.40
10.60
10.80
11.00
11.20
0.90.920.940.960.981
V/V0
Ve
loc
ity
(k
m/s
)
This study, P Up
This study, P Dow n
S&B 98
ZHA00
Chopelas 96
Yoneda90
Comparison of Elastic Properties from Selected Studies
KS
(GPa)
KS’ KS”
(GPa-1)
G(GPa)
G’ G”(GPa-1)
1(U) 163.0(6) 4.19(8) - 127.1(6) 2.46(6) -
1(U) 163.6(8) 4.17(10) - 129.4(6) 2.39(6) -
2(U) 162.5 4.13 -0.058 130.8 2.53 -0.066
3(U) 162.7 4.13 0.003 131.1 2.47 -0.079
3(U) 162.7 4.24 -0.030 131.1 2.41 -0.061
4(BS) 162.5(7) 3.99(3) 130.4(17) 2.85(9) -0.084(6)
5(BS) 163.2(10) 3.87 130.2(10) 2.21(10) -
5(BS) 163.2(10) 3.96(10) -0.044(20) 130.2(10) 2.35(10) -0.040(20)
6(SF) 162.0(10) 4.08(9) -0.036 130.9(5) 2.56(6) -0.030(10)
7(T) 162 4.15 128 2.44
8(T) 161 4.1 -0.028 131 2.4 -0.024
9(U) 162.2 4.5
10(Eos) 160a (4.15)
11(X-ray) 153a 4.15a
12(X-ray) 160.2a 3.99a
13(X-ray) 161a 3.94(20)a
1: This study, 2: Jackson & Niesler (1982); 3: Yoneda (1990); 4: Zha et al. (2000); 5: Sinogeikin and Bass (2000); 6: Chopelas (1992); 7: Karki et al. (1999); 8: Matsui (1999) ; 9: Anderson and Andreatch(1966); 10: Fei (1999); 11: Utsumi et al. (1998); 12: Speziale et al. (2001) ; 13 : Dewaele et al. (2000).
-1
-0.75
-0.5
-0.25
0
0.25
0.5
0.900.920.940.960.981.00
V/V0
DP
(GP
a)
Fei99, P(NaCl)
Utsumi98/NaCl
This study, Sample P
Speziale/Ruby
Yoneda90/Eos
This study/NaCl
This study/ Eos
S&B00/Ruby,Eos
Zha00/Ruby,Eos
Matsui
JAM82
Speziale/Ruby
J&S/Eos
V&A/ShockExp. Points Using NaCl/Ruby P scale
Comparison of V/V0 for MgO Collected Using Different P scales
10 20 GPa
Comparison with Previous Studies
Volume of MgO at P and T
10.2
10.4
10.6
10.8
11
11.2
11.4
0 5 10 15 20
Pressure (GPa)
Vo
lum
e (
A^
3)
BMD Eos /Speziale et al.(2001)Utsumi et al.(1998)
Fei(1999)/NaCl
This study/NaCl P
Fei(1999)/Au P
This study/ Abs P
1073K
300K
Difference Between Calculated Pressures on MgOand Those from NaCl (obs)
P(MgO) - P(NaCl)
-0.4
-0.2
0
0.2
0.4
0.6
0.8
250 450 650 850 1050 1250
Temeprature (K)
Pc
a l
- P
ob
s (
GP
a)
Expanding P T Range for P-V-VP-VS-T- Measurement
Pressure (GPa)0 5 10 15 20 25 30
Te
mp
era
ture
(K
)
500
1000
1500
2000
Transition Zone
Ultrasonics+X-ray
RUS
Brillouin Scattering P >50 GPa
Conclusions
• Unit cell volume, P and S wave velocities of MgO have been measured up to ~11GPa and 1073K.
• Combined analyses of the volume and velocity data yield direct determination of K, G, K/P, G/P, K/T, G/ T without relying on previous pressure scales (cross-derivatives and second order derivatives can be derived as well). The sample pressure can be directly calculated from the derived
• The discrepancies between previous EoS results likely results from pressure range and pressure scales.
• Comparison of the 300K isotherm of MgO suggests that MgO EoS from different studies are consistent within <1%.
• Direct pressures and those from NaCl/Ruby differ by an average of ~6% at the current experimental pressure range at room T. The difference becomes smaller at temperatures above ~1100k, within the claimed uncertainties of NaCl pressure scales (e.g., Brown, 1993).
Unit Cell Volume: MgO
70
71
72
73
74
75
76
0 2 4 6 8 10 12 14
Pressure (GPa)
Vo
lum
e (
A^
3)
Utsumi et al. (1998)
Fei(1999)
This study
zhang(2000)673K
1073K
(a)
9.30
9.50
9.70
9.90
10.10
10.30
10.50
10.70
10.90
11.10
0.920.940.960.981
V/V0
Vel
oci
ty (
km/s
)
This study #2
Compression
Others' RT Data
This study,P Up
This study, P Dow n
S&B 98
ZHA99
P wave velocities from Run #1 and Run #2
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