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2.1.3 The measurement of high pressures

The Practical Pressure Scale at high pressures

For pressure measurements from atmospheric pressure up to 2.6 GPa primary standard pressure balances (also called piston gauges or dead weight testers) of different types are used. The typical measurement uncertainties of these balances¹ (at the 1σ level) are ± 10 ppm at 100 MPa, ± 100 ppm at 1 GPa and ± 1000 ppm at 2.6 GPa, increasing to some % at 10 GPa when piston-cylinder systems are used.

Beyond the range conveniently attainable by primary standards, there are several practical techniques for the measurement of pressure which are now recognized internationally: fixed points (phase transitions), equations of state and phenomena such as the ruby fluorescence shift. Some international conferences have issued recommendations on a practical pressure scale. At a symposium at the US National Bureau of Standards² N.B.S. (now National Institute of Standards and Technology N.I.S.T.), held in 1968, agreement was reached on the pressure values associated with certain phase transitions up to 10 GPa. A Task Group, appointed under the auspices of the International Association for the Advancement of High Pressure Science and Technology (AIRAPT) at its 6th Conference (Boulder, Colorado, 1977), is charged with making recommendations for an International Practical Pressure Scale; the first such recommendations were made at the 8th AIRAPT Conference (Uppsala, Sweden, 1981)³ and the second at the 10th AIRAPT Conference (Amsterdam, Holland, 1985).⁴

Different review papers^1,5,6 and books^7,8 have treated in detail the realization of the high pressure scale. As it is difficult to use primary standards for pressure measurements above 2 GPa, ‘reference points’ based on the phase transitions of pure substances are used. The phase transitions are frequently traceable to the primary pressure measurements and can be used as calibrants in the appropriate pressure ranges and are often associated with temperature fixed points.

Basic group of reference pressures associated with phase transition of pure substances

(Means of identification of transition: electrical resistance or volume change)

    * Values recommended at the NBS symposium, from reference 2.
    ^† Derived from V. E. Bean et al.⁴

The values given in the table represent the best estimate of the true transition pressure; the uncertainty associated with each value represents an estimate of how close the true transition pressure lies to the value given. It must be stressed that the degree of reproducibility of a transition pressure will depend on the experimental conditions and the method of realization of the transition. For detailed discussions of these topics see the review by Decker et al.,⁵ the review by Holzapfel,⁶ Chapter 3, by Bean, of reference 7 and Chapter 6 by Sherman and Stadtmuller of reference 8.

Mercury solid–liquid equilibrium at other temperatures

It has been recommended^3,4 that the best representation of the mercury melting curve up to 1.2 GPa is a third-order polynomial based on the work of Molinar et al.⁹ The equation, referenced to the International Temperature Scale of 1990 (ITS-90), is¹⁰:

      p = 1.932 845 10⁻²d + 1.833 3 10⁻⁶d ² + 5.979 1 10⁻⁸ d ³ GPa

where d = T – 234.3156, and T is the temperature in kelvin referred to the ITS-90 Temperature Scale.

   The residual standard deviation of this polynomial equation is 0.059 MPa and the estimated uncertainty of the mercury melting curve at the pressure of 1.2 GPa is ± 0.39 MPa. Extrapolation of the polynomial above 1.2 GPa is not recommended.

Additional reference pressures associated with phase transitions

These phase transitions have also been recommended,⁴ but they were calibrated as to pressure without the use of primary standards and frequently without a complete evaluation of the uncertainties; therefore such values should be used with caution and only when no other techniques are available.

    ^† Derived from V. E. Bean et al., reference 4.
    * Determined in the onset of forward transition only.
    ^ℵ Derived from V. E. Bean, Ch. 3, referenece 7.
     This value is under evaluation, other determinations found values close to 26.0 GPa (see next section).

Pressure scale as defined by the equation of state of sodium chloride

The AIRAPT Task Group reports of 1981³ and of 1985⁴ recommended that the Decker equation-of-state data for sodium chloride¹¹ be used as the practical reference standard in the pressure range below its phase transition to the CsCl structure (i.e. 29.6 GPa as originally determined by Decker’s equation,¹¹ now under revision).

Calculated pressures (rising values) versus compression for NaCl at 25ºC

The above table is based on that given by Decker in reference 5. These data are derived from more extensive input data than those previously published in reference 11 and cover a greater pressure range.

Data for other temperatures, namely 0°, 100°, 200°, 300°, 500° and 800 °C, may be found in reference 11. Pressure p = f (t, Δa/a₀) can also be computed by means of a polynomial representation of the Decker equation of state.¹² The NaCl equation of state is believed to represent the true pressure with an uncertainty of ± 1.1% up to 5 GPa, ± 1.7% up to 10 GPa and ± 2.4% up to 20 GPa. A more recent and precise redetermination of the NaCl equation of state¹³ up to a pressure of 3.2 GPa indicates that Decker’s equation of state overestimates pressure at 3.2 GPa by about 1.6%. At higher pressures, Ruoff et al.¹⁴ found, on the basis of shock data and Clapeyron thermodynamic data, that the NaCl phase transition at room temperature is 25.7 GPa, a value lower by 14.5% than the value (29.6 GPa) obtained with the use of Decker’s equation of state. It is therefore advisable to use Decker’s equation of state, a very important and useful equation, with some caution, until a complete verification of its limits of accuracy and also until more accurate and reliable equations of state of other substances, e.g. Cu, Ag, Au and particularly Pt, are available.

Pressure measurement using the ruby fluorescence shift

The shift in the wavelength of the R₁ fluorescence line of ruby is now used extensively as a pressure standard in diamond anvil cells. The following equations are taken from reference 3 and reference 6, where Δλ is the wavelength shift in nanometres:

(a) for pressures up to 29 GPa, based on the work of Piermarini et al.^{15, 16} who used the equation of state of NaCl as the pressure standard, the following linear relation gives the pressure versus the wavelength shift of ruby:

      p = (2.740 ± 0.016) Δλ GPa;

(b) for pressures from 6 to 100 GPa, based on the work of Mao et al.¹⁷ under non-hydrostatic conditions and of Mao et al¹⁸ in quasi-hydrostatic pressure media, who used as their pressure standard isothermal equations of state derived from shock wave experiments, the following non-linear relation is used:

where B = 5 for the non-hydrostatic case and B = 7.665 for the quasi-hydrostatic measurements.
   Δλ is again the wavelength shift of ruby expressed in nanometres and λ₀ = 694.24 nm is the wavelength of the R₁ line at atmospheric pressure.
   For the uncertainties associated with these data (ranging from few % to about 10% depending on the pressure range) reference must be made to the original sources.

Current developments in luminescence gauges

Other materials have recently been tested that exhibit more sensitivity to the luminescence effect than ruby, with the use, for example, of the sharp-line transition of Sm²⁺ in SrB₄O₇ (or BaFCl and SrFCl)¹⁹ and of Sm: YAG.²⁰
   Owing to their simple line shape, larger pressure sensitivity and reduced temperature sensitivity in comparison with the ruby characteristics, such substances are considered suitable candidates to replace the ruby line shift at pressures up to 50 GPa, expecially for, e.g., pressure measurements at high temperatures.

Pressure dependence of melting temperatures of some pure metals in the range 0–20 GPa

(Derived from Akella and Kennedy²¹)

References

G.F.Molinar

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