Reduced-adiabat Isotherms of  Metals and Hard Materials at  100 GPa Pressures and Finite

Temperatures

W. J. Nellis

Department of Physics

Harvard University

Adiabatic Compression

• Sufficiently slow that the sample is in thermal equilibrium

and • Sufficiently fast that negligible heat flows

out of the sample during the lifetime of the experiment.

• Dynamic compression is adiabatic

• Shock or Hugoniot compression– P reaches its maximum quickly (~ ps)

Dynamic Compression I

Dynamic Compression II

• Isentropic and quasi isentropic (multiple shock) compression

– P reaches its maximum slowly (~ ns)

Adiabatic Temperature Increase

• Temperature T increases are relatively large in shock compression.

• Temperature increases are relatively small in isentropic compression.

Temperature increases in all adiabatic compressions

Dynamic Compression

• Induces lattice defects in solids:– Increases shear strength/stress at lower P and T– Defects anneal out at higher T and P

• Stress ( is measured in dynamic compression:

= −P + s (s=stress deviator)• Strength (s) increases are relatively small in shock

compression because of high Ts.• Strength s increases are relatively large in

isentropic compression because of lower Ts.• For a fluid s = 0 at all P.

Pressure Corrections

P0() = PD - (PD, ) - Pth()

Accuracies

P0() = PD - (PD, ) - Pth() (at 300 K isotherm)1

• PD is needed to 1%

(purely experimental; in hand for some metals)

• Pth/ PD < 30%

(purely theoretical; small minimizes systematic

uncertainties)

• / PD < 5%

(mixed experiment/theory; small minimizes uncertainties)

• Similar for other isotherms (T > 300 K)1Chijioke et al., J. Appl. Physics 98, 073526 (2005).

Pressure Limits• Single shock compressions are limited (/0~2 at ~100 GPa

in metals) because of high shock temperatures.

• Isentropic compressions are unlimited (/0~) because of low isentropic temperatures.

Establishing Pressure Standards I

• Based on accurate equation-of-state (EOS) data in the desired pressure range.

• Shock compression EOS data are the only primary experimental EOS data at 100 GPa pressures because they are based only on conservation of mass, momentum, and energy.

• Calculated thermal pressures to reduce dynamic EOSs should be as small as possible so that systematic uncertainties in the calculations have minimal effect on the accuracy of the calibration.

• Since dynamic compression is uniaxial, shear strength is included in the measured stress of a solid. Stress is the meaningful variable for a solid.

• In a hydrostatic pressure medium (DAC), compression is uniform for a cubic material. Shear strength is not important and pressure is the meaningful variable.

Establishing Pressure Standards II

• Extrapolations of B-M to ~100 GPa pressures using sound speed and its pressure derivative at P = 0.– In ~1950 Birch developed a phenomenological EOS model at high P

and in order to estimate high pressures in the Earth’s deep interior – before any laboratory experiments at 100 GPa pressures were performed. Extrapolation is not calibration.

• Extrapolate a ruby scale to higher pressures and modify it.• Assume a theoretically calculated P- isotherm as a standard.

The systematic uncertainty is unknown.

• Compare a shock-wave reduced isotherm with an isotherm measured in a DAC with Ps determined with ruby calibrated previously against a shock-wave reduced isotherm.

Approaches that cannot be used to qualify standards

Dynamic Compression Data Needed

• Dawaele et al., used Ta, Au, Pt, Al Cu, and W in measurements in DAC of ruby-line shift and X-ray density.

• Dynamic strength data and some Hugoniot data are needed to improve some SW-reduced isotherms.

• Pt is only one metal used to drive isotherms from Hugoniots by Chijioke et al.

• To get pressures above ~200 GPa, isentropes of metals should be measured and reduced to isotherms.

Systematic Differences

• Shock wave reduced isotherms for individual metals deviate systematically from the average of many.

• Pt, for example:

• Systematic uncertainties in this procedure need to be understood.

Concerns for DAC Pressure Calibration

• Stress gradients must be measured as functions of temperature and pressure.

• Positions of markers (e.g. ruby and metal chips) affect their responses.

• Positions of markers in DAC should be stated in publications

• Chemical reactions can occur at high T and P. One check is nature of samples recovered from high P/T.

Pressure Calibration at Finite Temperature I

• Choose pressure markers weakly sensitive to temperature and temperature markers weakly sensitive to pressure.

• P- Hugoniots and 0 K isotherms of hard materials are nearly identical (Pth/ PD ~ 0).

• Possible pressure standards for finite T are Diamond and BN.

• These can be calibrated for pressure against Chijoke et al.1

1Chijioke et al., J. Appl. Physics 98, 114905 (2005).

Isotherm and Hugoniot of Hard Materials

• Pavlovskii experiments

– Measured 4 Hugoniot points

for Diamond in 1971

(80 < PD < 80

GPa)

• Syassen et al. calculated 0 K isotherm.

• The two are virtually identical.

Pressure Calibration at Finite Temperature II• Hugoniot data for BN shows phase transition at 20

GPa and much data in 20 < PD < 80 GPa.

• Additional Hugoniot data are needed for BN and Diamond up to 200-300 GPa.

• Measurements of dynamic shear strengths of Diamond and BN are needed (no data now exists).

Conclusions• Pressure calibrations must be based on

experimental measurements at high pressures.• Shock wave reduced isotherms satisfy this

requirement.• Sound speed measurements on MgO in DAC up to

50 GPa (Mao et al.) satisfy this requirement.• Above ~200 GPa dynamic isentropes should be

used as reference curves rather than Hugoniots.