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