REVIEW OF SCIENTIFIC INSTRUMENTS 80, 073902 共2009兲 Liquid mercury sound velocity measurements under high pressure and high temperature by picosecond acoustics in a diamond anvils cell F. Decremps,1,a兲 L. Belliard,2 B. Couzinet,1 S. Vincent,2 P. Munsch,1 G. Le Marchand,1 and B. Perrin2 1 Institut de Minéralogie et Physique des Milieux Condensés, Université Pierre et Marie Curie-Paris 6, CNRS UMR 7590, 140 rue de Lourmel, 75015 Paris, France 2 Institut des NanoSciences de Paris, Université Pierre et Marie Curie-Paris 6, CNRS UMR 7588, 140 rue de Lourmel, 75015 Paris, France 共Received 28 April 2009; accepted 5 June 2009; published online 8 July 2009兲 Recent improvements to measure ultrasonic sound velocities of liquids under extreme conditions are described. Principle and feasibility of picosecond acoustics in liquids embedded in a diamond anvils cell are given. To illustrate the capability of these advances in the sound velocity measurement technique, original high pressure and high temperature results on the sound velocity of liquid mercury up to 5 GPa and 575 K are given. This high pressure technique will certainly be useful in several fundamental and applied problems in physics and many other fields such as geophysics, nonlinear acoustics, underwater sound, petrology or physical acoustics. © 2009 American Institute of Physics. 关DOI: 10.1063/1.3160104兴 The determination of acoustic properties of solids and liquids under pressure is a powerful method to treat fundamental problems in physics of solid and liquid states since 共i兲 pressure is one of the most useful thermodynamical parameters to tune physical properties and 共ii兲 sound velocity v is very sensitive to subtle changes in local or long-range order as well as electronic properties of matter. From another viewpoint, the determination in laboratory of the pressure and temperature dependence of v is obviously pertinent for application in areas ranging from earth and planetary science to other applied fields such as petrology or material research. Up to recently, three types of techniques have been mainly used to measure the sound velocity of high density liquids in laboratory. The first one, usually denoted as the conventional pulse-echo ultrasonic technique, where the typical sample thickness has to be higher that several hundred of microns to avoid successive acoustic echoes to overlap. This last constraint is the main reason why such technique can only be performed combined with a large-volume cell1 共experimental volume of about 10 mm3兲 limiting the highest pressure that can be reached to about 20 GPa. Moreover, the huge technical difficulties to confine and insulate dense liquids at high pressure and high temperature in such large volume press overcome any sound velocity measurements of nonsolid compounds. Second, gigahertz interferometry has been implemented2 to measure the ultrasonic sound velocity in diamond anvils cell 共DAC兲. However the measurement of sound velocity at high pressure cannot be applied to dense liquids since the thickness between the two anvils is not measurable with a reasonable accuracy. The third well known method is the Brillouin scattering and can easily be adapted to be performed in a DAC 共Ref. 3兲, but transparent sample can exclusively be studied. Finally, in spite of many efforts, this array of constraints precludes a兲 Electronic mail: [email protected]. 0034-6748/2009/80共7兲/073902/3/$25.00 studying the viscoelastic properties in laboratory of opaque liquids under pressure above few kbars using a pistoncylinder systems. All these arguments have motivated the present work on the development of an high pressure laboratory approach to accurately measure sound velocity and attenuation in nontransparent liquids embedded in DAC. As a good candidate, picosecond acoustic is an optical pump-probe technique which enables the measurement of both mechanical and thermal properties of thin-film materials4–6 at ambient conditions. We have recently shown that the adaptation of this technique for measurements in diamond anvil cell allows the determination of v共P兲 and its attenuation in a single quasicrystal of AlPdMn in DAC.7 This method can be easily integrated in laboratory and overcomes all the drawbacks of traditional techniques. The present article is thus mainly devoted to the recent development of the picosecond acoustics in DAC in order to enable the sound velocity measurements in metal liquids under extreme conditions. Mercury has been taken as a prototypical case since 共i兲 some data on its properties at high pressure and high temperature can be found in the literature, 共ii兲 it is liquid over a large range of pressure at reasonable high temperatures that can be achieved using a classical resistive furnace. The price to pay is the high chemically reactivity of mercury which requires to take a special care for the choice of the gasket. We have used a pump-and-probe method associated with a conventional lock-in amplification scheme. The initial pulses are generated by a titanium:sapphire oscillator with a typical width less than 100 fs in the wavelength of about 800 nm. The output of this pulse laser is split into pump and probe beams. The pump is focused onto a small spot 共3 m兲 of the sample which creates a sudden and small temperature rise of about 1 K. The corresponding thermal stress generated by thermal expansion relaxes by launching a longitudinal acoustic strain field mainly along the direction perpendicular to the flat parallel faces of the sample. In our case, the 80, 073902-1 © 2009 American Institute of Physics Author complimentary copy. Redistribution subject to AIP license or copyright, see http://rsi.aip.org/rsi/copyright.jsp 073902-2 Decremps et al. probe beam, fixed on a piezoelectric stage from Physik Instrumente, is focused to a spot on the opposite surface of the sample with respect to the surface illuminated by the pump. The variation of reflectivity as a function of time is detected through the intensity modification of the probe delayed from the pump with a different optical path length. After propagation along the sample, the total contribution of both thermal and acoustic effects alter the optical reflectivity of the opposite surface of the sample. The photoelastic and the photothermal coefficients contribute to the change of both real and imaginary part of the reflectance,8 whereas the surface displacement only modifies the imaginary part. In this work we have only considered the temporal variation of the reflectance 共real part兲 due to the acoustic field. The experiments were conducted in a membrane diamond anvil cell. Ultrapure mercury 共99.99%兲 was loaded into the experimental volume. The gasket material was in rhenium, known to be chemically inert at high temperature with mercury.9 Two holes of about 30 m of diameters were drilled, closed one to the other but not connected. One was full of Hg, the other being loaded with a mixture of KCl and a small amount of SrB4O7 : Sm2+ used as a primarily pressure gauge. In such a way, we have prevented any chemical reaction between the pressure gauges and Hg, and avoid the samarium powder to be swallowed up in the mercury at high pressure. The absolute uncertainty on pressure was about 0.1 GPa at 700 K in the hole containing KCl. However, because of remaining stresses inside the rhenium gasket, a difference of pressure between the two holes may be present, which should lead to an effective pressure uncertainty higher than 0.1 GPa. The whole diamond anvil cell was heated by means of a ring-shaped resistive heater enveloping the cell: in that case, the cell is globally heated, which provides minimal temperature gradients across the cell. The temperature was regulated within 1 K using an electronic module and measured with an accuracy better than 5 K by a K-type thermocouple glued onto the side of one anvil. In this geometry, the sound velocity v can be deduced from the travel time t measurement through v = 2d / t, where d is the thickness of the gasket, unknown at high pressure. We thus have adapted the design of the diamond culet in such a manner that measurements of acoustic sound velocities in DAC be possible. A squared pit has been drilled in the center of the culet of one of the diamond anvils using a fast ion beam, with a side of about 23 m and a depth h = 1.443共3兲 m 共the error bar is mainly due to the roughness of the deep hole, see Fig. 1兲. This last value has been accurately determined by profilometry and a fine determination of the root mean square roughness have been performed by conventional atomic force microscopy technique. As can be seen in Fig. 2, this configuration enables the determination of the sound velocity through two consecutive travel time measurements between the diamonds anvils 共through and outside of the pit兲. Under extreme conditions, our technique obviously assumes that the dimensions of the diamond culet hole is not varying in the pressure and temperature range probe. Using SOLIDWORKS SIMULATION PROFESSIONAL, we performed a finite elements calculation which shows that the variation of the pit depth ␦h / h between 0 and 10 GPa at ambient temperature lies around 0.2%, say that on the order of the surface roughness of the deep pit, and much lower Rev. Sci. Instrum. 80, 073902 共2009兲 FIG. 1. 共Color online兲 Top-view pictures and profile of the pit drilled on the diamond culet. than the travel time absolute uncertainties 共1%兲. The results of the pressure dependence of the liquid mercury sound velocity along several isotherms is given in Fig. 3. At ambient temperature, our data are in a good agreement with Davis and Gordon10 共at high pressure and temperatures higher than 330 K, no data can be found in the literature兲. However, the relatively large dispersion of the data along the high temperature isotherms did not allowed to extract the liquid mercury equation of state with a good accuracy.11 It has been recently shown that the dispersion of the ultrasonic attenuation and sound velocity of Hg at ambient conditions can be derived from the analysis of the strain pulses shape.12 In our case, the pressure dependence of most of the input parameters is unknown which prevents any extraction of the relaxation processes at high density using this method. An alternative analysis relies on computing the relative attenuation variation with pressure from the Fourier amplitude ratio of two consecutive echoes.7 In the case of the present study where the liquid mercury has been clamped between the anvils, the surface roughness of the diamonds is not enough characterized, especially in the bottom of the pit. Since liquid Hg is known to not wet diamond at ambient conditions, it is likely that we mainly measured at high pres- FIG. 2. 共Color online兲 Principle of sound velocity measurements in a DAC using a time-resolved acoustics technique: v = h / ⌬t where h is the pit depth and ⌬t the travel time difference between a measurement through and out of the diamond pit. Author complimentary copy. Redistribution subject to AIP license or copyright, see http://rsi.aip.org/rsi/copyright.jsp 073902-3 Rev. Sci. Instrum. 80, 073902 共2009兲 Decremps et al. FIG. 3. 共Color online兲 Pressure dependence of the liquid mercury sound velocity along several isotherms. Inset: comparison between sound velocities at ambient temperature and high pressure from Ref. 10 共line兲 and the present work 共red crosses兲. The data dispersion for each isotherm is mainly due to the remaining stresses inside the rhenium gasket 共leading to a difference between the pressure measured inside the KCl hole and the Hg one兲. FIG. 4. 共Color online兲 Difference between the solid and the liquid phase reflectance of mercury at 567 K. The two spectra have been collected upon downloading pressure at 465 K, just above 共DAC membrane at 63.5 bars兲 and below 共DAC membrane at 63.1 bars兲 the melting pressure 共5.0 GPa兲. Inset: melting curve of mercury 共red crosses: present work and black circlesline: Ref. 13兲. sure the variation of Hg-diamond boundary as a function of the DAC membrane force. We thus did not pursue this part further. Finally, we also observed that the melting of mercury can easily be detected since the difference of reflectivity between the solid and the liquid phase is obvious 共see Fig. 4兲. Here again, a comparison with previously published data shows a good agreement, which proves that our technique is also well adapted to the determination of melting curve, and more generally of the phase diagram, for nontransparent materials. In summary, present efforts have led to the successful implementation of a laboratory tool that allow sound velocity and phase diagram investigation of opaque liquids up to several gigapascals and thousands of kelvins. Technical details on the high pressure and acoustics setups are presented and a way to measure the sound velocity in DAC is described. Special care has been taken to avoid any chemical reaction between mercury and the gasket of the pressure calibration gauge, using two different holes in a rhenium gasket. However the difference of pressure due to a possible remaining stress inside the rhenium gasket may be the source of a relatively large dispersion of our data along each high temperature isotherms. More works are needed to improve the metrology in order to be able to extract the equation of state of the liquid with a reasonable accuracy. This work has been supported by an ANR 共Contract No. ANR-08-BLAN-0109-01兲. 1 B. Li, I. Jackson, T. Gasparik, and R. C. 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