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Ultrasonics 44 (2006) e1495–e1498

Hypersonic velocity measurement using Brillouin scatteringtechnique. Application to water under high pressure and temperature

Frederic Decremps *, Frederic Datchi, Alain Polian

IMPMC – Physique des Milieux Denses, University of Paris VI, casier 77 Campus Boucicaut, 140 rue de Lourmel, 75015 Paris, France

Available online 9 June 2006

Abstract

This paper presents recent improvement on sound velocity measurements under extreme conditions, illustrated by the hypersonicsound velocity measurements of water up to 723 K and 9 GPa using Brillouin scattering technique. Because water at high pressureand high temperature is chemically very aggressive, these experiments have been carried out using a specific experimental set-up. Thepresent data should be useful to better constrain the water equation of state at high density. This new development brings high-qualityelastic data in a large pressure/temperature domain, which may afterwards benefit the understanding of many other fields as nonlinearacoustics, underwater sound, or physical acoustics from a more general point of view.� 2006 Elsevier B.V. All rights reserved.

Keywords: Speed of sound; Brillouin scattering; Extreme conditions

1. Introduction

For many years, inherent problems of carrying out elas-tic measurements in high pressure–high temperature cellshave prevented acoustics experiments under extreme ther-modynamic conditions. Consequently, little is knownabout experimental sound velocity of liquids and solids athigh density, data of major interest for physics, chemistryand geophysics. For example, understanding the Earthinterior is one of the most evident application of high pres-sure work in the (0–300 GPa) range (1 GPa = 10 kbar). Upto now, the deepest core sampling has been extracted at adepth of only few kilometers, and more than 99% of theEarth interior has to be studied by reproducing the thermo-dynamic conditions in the laboratory (Fig. 1). Beyond thisapplication, the study of matter under pressure is a fasci-nating field since pressure appears to be one of the mostpowerful thermodynamical parameter to tune propertiesfor understanding fundamental physics and chemistry. Asa matter of fact, the effect of pressure at room temperature

0041-624X/$ - see front matter � 2006 Elsevier B.V. All rights reserved.

doi:10.1016/j.ultras.2006.05.150

* Corresponding author. Fax: +33 1 44 27 44 69.E-mail address: frederic.decremps@upmc.fr (F. Decremps).

on the energetic of a crystal is much greater than the tem-perature change up to the melting point at room pressure[1]. Particularly, the measurement of sound velocity versuspressure of solids and liquids enables to probe with a highsensitivity the most unknown part of the interatomicpotential, say the repulsive one. Finally, the thermoelastic-ity of stressed material not only provides a way to studyfundamental physics, chemistry and geophysics, but alsogives crucial insight in the applied physics field through,for example, the structural stability of solids, the indirectdetermination of the piezoelectric properties and thethird-order elastic constants, or the mechanical propertiesof important material from a technological point of view.

When pressure and temperature are increased, liquidwater has a very interesting evolution, going from ahighly-structured molecular liquid with strong hydrogenbonds, to an ionic conductor and eventually to a metal.The knowledge of its thermodynamic properties at extremeconditions is of great importance for a number of scientificproblems in physics, chemistry, Earth and planetary phys-ics or biology. However, there exists rather few data thatbridges the gap between the extensive low pressure mea-surements made with piston–cylinder apparatuses in the

Fig. 2. Backscattering Brillouin scattering spectrum of water at 3 GPa and653 K. The central unshifted peak comes from the elastic scattering(Rayleigh peak). The frequency of the scattered light is increased in thecase of a phonon annihilation (Brillouin peak labelled B2), decreased inthe case of a creation (Brillouin peak labelled B1). In this geometry,knowledge of the refractive index n is necessary to calculate the soundvelocity v through the Eq. (1).

Fig. 3. Diamond anvil cell principle. A metallic gasket confines the samplewith the pressure gauge and the pressure transmitting medium. Diamondis chosen for its hardness and its transparency in a wide electromagneticradiation frequency range.

Fig. 1. Typical pressure range that can be reached in the laboratory withhigh pressure apparatus. Some examples from the Earth atmosphere to theinterior of planets give an idea of thermodynamical conditions.

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70s and the shock-wave experiments that explore the veryhigh pressure–temperature portion of the phase diagram.New speeds of sound experimental data are definitivelynecessary to accurately extend our knowledge of fluidwater.

We present here original experimental measurements ofthe sound velocity and a perspective of equation of statedetermination in liquid water up to 723 K and 9 GPa usingBrillouin scattering in a diamond anvil cell. This study is anexcellent example of what can only be achieved with theBrillouin technique [2], since, up to now, ultrasonic exper-iment in this (P,T) range cannot be performed on liquids.These state-of-the-art experiments will certainly be usefulin several applied problems and many other fields such asnonlinear acoustics, underwater sound, or physical acous-tics from a more general point of view.

2. High pressure and high temperature Brillouin scattering

technique

In Brillouin scattering, monochromatic light interactsinelastically with thermal acoustics phonons. These hyper-sonic waves produce a periodic modulation of the refrac-tive index in the material. The incident light undergoes aDoppler shift and is inelastically scattered with a frequencymodification depending on the sound wave velocity and theinteraction geometry. The energy range involved in Brill-ouin scattering from thermal excitations is of the order of10 GHz. The corresponding measured wave number shiftDr (in cm�1) is given by:

Dr ¼2nv sin h

2

� �

kcð1Þ

where v is the acoustic phonon velocity, n the refractive in-dex at k (the wavelength of the exciting light), c the speed oflight in vacuum and h the angle between the incident and thescattered light. Due to the small frequency shift and thesmall intensity of the inelastically scattered light (Brillouin)with respect to the elastically scattered one (Rayleigh), ahighly dispersive power spectrometer is used, namely theSandercock spectrometer, made of two Fabry–Perot inter-ferometers in tandem. A typical spectrum recorded onwater at high pressure and high temperature is shown inFig. 2. Combined with diamond anvil cell (DAC) [3], theBrillouin technique can be used to measure the high pres-sure sound velocity of small (dimensions on the order of10 lm) and (only) transparent materials [4].

The principle of high pressure generation with DAC isshown in Fig. 3 and can be briefly described as the follow-ing. A metal gasket (stainless, inconel or rhenium for exam-ple) is placed between the small flat parallel faces of twoopposed diamond anvils. The sample (with typically a vol-ume of 100 · 100 · 20 lm3) is confined in a hole (about200 lm in diameter) drilled in the pre-indented gasket

F. Decremps et al. / Ultrasonics 44 (2006) e1495–e1498 e1497

together with a pressure transmitting fluid (e.g., helium ornitrogen). Pressure is measured in situ with accuracy betterthan 3% using the fluorescence emission of a ruby ball [5]and/or SrB4O7:Sm2+ powder [6] placed into the gaskethole. The high quasi-hydrostatic pressure is generated onthe sample as a force pushes the two diamond anvilstogether. In our experiments, we used a membrane DAC[7], i.e., the force on the diamonds is applied through thedisplacement of the piston due to a membrane deformation(produced by a pressurized helium gas filling the mem-brane). The highest pressure attainable depends on the areaof the diamond anvil flat (with 0.03 mm anvil flats, pressureof about 300 GPa can be reached). The DAC can also befitted into a resistive cylindrical heater for high temperaturestudies up to 1000 K, a thermocouple being glued on oneend of the diamond anvil to determine the average temper-ature on the sample with an accuracy of a few K.

Fig. 4. Picture of the rhenium/gold gasket which confines H2O samples atthe liquid–ice VII transition (T = 572 K and P = 6.2 GPa).

Fig. 5. Pressure dependence of the sound

Because water at high pressure and high temperature ischemically very aggressive, these experiments have beencarried out using a specific experimental technique. Thediamond anvil cell, made of high temperature steel, washeated by a resistive external heater. The temperaturewas controlled by a thermocouple glued onto the side ofone anvil. The Brillouin scattering measurements were per-formed in the backscattering geometry (h = p), using the514.5 nm line of an argon laser. Water was confined in arhenium/gold composite gasket, rhenium being welladapted to high pressure–high temperature studies. Goldwas used to prevent chemical reactions between the watersample and the rhenium gasket on one hand, and the pres-sure gauge (SrB4O7:Sm2+) on the other hand, the latterbeing dissolved at temperatures above �500 K. A ruby ballserves as an additional in situ temperature gauge (seeFig. 4).

3. Hypersonic sound velocity of water up to 723 K and 9 GPa

by Brillouin scattering experiment in DAC

Brillouin spectra have been collected along several iso-therms between 300 K and 723 K. The measurementsextend to the solidification pressure, which usuallyoccurred less than 1 GPa above the melting point, unlessfor the 723 K isotherm where one of the anvils failed beforecompletion. The experimental data have been obtained inthe backscattering geometry which means that the soundvelocity can be extracted only if the refractive index isknown. For liquid water, the refractive index at 514.5 nmis accurately known at densities up to 1.06 g cm�3 and tem-peratures up to 773 K, which has been convenientlyexpressed in a simple formulation by Schiebener et al. [8]and Harvey et al. [9].

Direct and independent measurements of the refractiveindex in the visible range by Dewaele et al. [10] (using thesame method as in Ref. [11]) established that the latter

velocity in water at high temperature.

Fig. 6. Difference between the present sound velocity values (cexp) and those derived from the Saul and Wagner [13] equation of state (cSW).

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formulation remains valid in the P–T range spanned by ourexperiments. As can be observed in Fig. 5, the sound veloc-ity is a smooth and monotonous function of pressure in thestudied temperature range, showing that no first-orderliquid–liquid phase transition occurs such as, for example,the one observed in liquid phosphorous [12]. This workshows however that the state-of-the-art equation of state(EoS) of water (Saul and Wagner [13]) poorly describesthe sound velocity at high pressure and high temperature(Fig. 6). The difference can be represented by the followingpolynomial equation:

cexp � cSW ¼ a1P þ a2P 2 þ a3PT ð2Þwhere a1 = 8.5096 · 10�3, a2 = 9.9053 · 10�5 and a3 =�2.3143 · 10�5 (with the following unity for P, T and c:kbar, K and km/s).

4. Conclusion and perspective

Recent improvements to measure accurately hypersonicsound velocities of liquids under extreme conditions aredescribed. To illustrate the capability of this method, origi-nal results on sound velocity of water up to 9 GPa and723 K are given with an accuracy of about 1%.

To use the present data as a means to accurately deter-mine the EoS, we believe that different approaches shouldbe undertaken. This can be achieved for example by usinga model equation of state such as the one of Saul and Wag-ner [13], and use the present data to better constrain theparameters of the EoS. A similar method to get a decentequation of state is to use an iterative calculation with

the help of molecular dynamics computation using anempirical potential, such as the TIP4P model [14]: a trialvalue of the adiabatic to the isothermal bulk modulus ratio(c) is used to obtain the EoS which is then fitted to an adhoc potential. The second step is to use this potential torecalculate c which is finally used to correct the EoS.

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