1. Direct Pressure Measurements and Insights on Current Pressure Scales Baosheng Li ESS Building SUNY Stony Brook Stony Brook, NY 11794 This research is supported by NSF Elasticity Grand Challenge Grant

2. Experimental Techniques

3. Frequency Amp Ultrasonic Interferometry cell assembly TC PtNaCl 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

4. SEM Image of Hot-pressed MgO Polycrystalline sample Bulk density: 3.57 g/cm 3 (99.6% of theoretical density)

5. Results of Unit Cell Volume of MgO at High P and T 1073K 473K

7.  V P 2 = (1-2  ) 5/2 (L 1 +L 2  ) (1)  V S 2 = (1-2  ) 5/2 (M 1 +M 2  ) (2) with  = [(1-(  /  o ) 2/3 ]/2 L 1 = K S +(4/3)G; L 2 = 5(K S +4G/3) - 3K S (K S ’ + 4G’/3) M 1 = G; M 2 = 5G-3K S G’ Finite Strain Data Analysis 1. Finite Strain Equations 2. Solve for: K S0, K s0 ’, G 0, G 0 ’,dK S /dT, dG/dT, d 2 K/dPdT, d 2 G/dPdT, d 2 K/dP 2, d 2 G/dP 2 by minimizing  V mea -V cal ) 2 3. Calculation of sample pressure P = - (1-2  ) 5/2 ( C 1  + 0.5C 2  2 + ….) with C 1 = 3L 1 –4M 1 ; C 2 = 3L 2 –4M 2 +7C 1

8. P and S wave Velocities: MgO

9. Comparison of Elastic Properties from Selected Studies K S (GPa) KS’KS’ K S ” (GPa -1 ) G (GPa) G’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)162.54.13-0.058130.82.53-0.066 3(U)162.74.130.003131.12.47-0.079 3(U)162.74.24-0.030131.12.41-0.061 4(BS)162.5(7)3.99(3)130.4(17)2.85(9)-0.084(6) 5(BS)163.2(10)3.87130.2(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)-0.036130.9(5)2.56(6)-0.030(10) 7(T)1624.151282.44 8(T)1614.1-0.0281312.4-0.024 9(U)162.24.5 10(Eos)160 a (4.15) 11(X-ray)153 a 4.15 a 12(X-ray)160.2 a 3.99 a 13(X-ray)161 a 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).

10. Exp. Points Using NaCl/Ruby P scale Comparison of V/V 0 for MgO Collected Using Different P scales 10 20 GPa

11. Comparison with Previous Studies

12. Difference Between Calculated Pressures on MgO and Those from NaCl (obs)

13. Expanding P T Range for P-V-V P -V S -T-  Measurement RUS Brillouin Scattering P >50 GPa

14. 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).

17. P wave velocities from Run #1 and Run #2