Post on 19-Jan-2016
description
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