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Cubic boron nitride as a primary calibrant for a high temperature pressure scale
Alexander F. Goncharov a; Stanislav Sinogeikin b; Jonathan C. Crowhurst c; Muhtar Ahart a; Dmitry Lakshtanov d; Vitali Prakapenka e; Jay Bass d; Pierre Beck a ; Sergei N. Tkachev a; Joseph M. Zaug c; Yingwei Fei a a Geophysical Laboratory, Carnegie Institution of Washington, Washington, DC, USA b HPCAT and Geophysical Laboratory, Carnegie Institution of Washington, Washington, DC, USA c Lawrence Livermore National Laboratory, University of California, Livermore, CA, USA d Geology Department, University of Illinois at Urbana-Champaign, Urbana, IL, USA e GeoSoilEnviroCARS, APS, ANL, USA Online Publication Date: 01 December 2007 To cite this Article: Goncharov, Alexander F., Sinogeikin, Stanislav, Crowhurst, Jonathan C., Ahart, Muhtar, Lakshtanov, Dmitry, Prakapenka, Vitali, Bass, Jay, Beck, Pierre, Tkachev, Sergei N., Zaug, Joseph M. and Fei, Yingwei (2007) 'Cubic boron nitride as a primary calibrant for a high temperature pressure scale', High Pressure Research, 27:4, 409 - 417 To link to this article: DOI: 10.1080/08957950701659726 URL: http://dx.doi.org/10.1080/08957950701659726
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High Pressure Research Vol. 27, No. 4, December 2007, 409–417
Cubic boron nitride as a primary calibrant for a high temperature pressure scale ALEXANDER F. GONCHAROV*†, STANISLAV SINOGEIKIN‡, JONATHAN C. CROWHURST§, MUHTAR AHART†, DMITRY LAKSHTANOV¶, VITALI PRAKAPENKA, JAY BASS¶, PIERRE BECK†, SERGEI N. TKACHEV†, JOSEPH M. ZAUG§ and YINGWEI FEI† †Geophysical Laboratory and ‡HPCAT and Geophysical Laboratory, Carnegie Institution of Washington, 5251 Broad Branch Road NW, Washington, DC 20015, USA §Lawrence Livermore National Laboratory, University of California, 7000 East Avenue, Livermore, CA 94551, USA ¶Geology Department, University of Illinois at Urbana-Champaign, 1301 W.Green street, Urbana, IL 61801, USA GeoSoilEnviroCARS, APS, ANL, USA (Received 6 June 2007; revised 15 August 2007; in final form 16 August 2007) We present results establishing a new high pressure scale at high temperature based on the thermal equation of state and elastic properties of cubic boron nitride (cBN). This scale is derived from simultaneous measurements of density and sound velocities at high pressure and temperature independent of any previous pressure scale. The present results obtained at room temperature to 27 GPa suggest the validity of the current ruby scale (within ±4% at 100 GPa). At high temperature, data obtained at 16 GPa to 723 K are in fair agreement with the thermal equation of state of cBN reported in our previous work. We have also shown that cBN can serve as a convenient pressure gauge in X-ray and optical studies using the laser heated diamond anvil cell. Keywords: Cubic BN; Brillouin spectroscopy; Equation of state; High-pressure scale
1.
Introduction
In recent years, the analytical techniques used in diamond anvil cell (DAC) research have greatly improved leading to higher precision of the data collected. Studies at simultaneous very high pressures and temperatures are also increasingly common. Therefore, there is an acute need for a pressure scale with a matching precision that can also operate at high temperature. The ruby pressure calibrations carried out at the Geophysical Laboratory in the 1970s and 1980s [1, 2] have served the high-pressure community for more than 20 years. The uncertainty of the former scale (so-called nonhydrostatic) is claimed to be better than ±6% at 100 GPa [1]. The quasi-hydrostatic scale [2] is believed to be more accurate (random scatter *Corresponding author. Email:
[email protected]
High Pressure Research ISSN 0895-7959 print/ISSN 1477-2299 online © 2007 Taylor & Francis http://www.tandf.co.uk/journals DOI: 10.1080/08957950701659726
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did not exceed 5%). These uncertainties were acceptable for the majority of DAC experiments, but the situation is more of a problem now when DAC work is routinely carried out at pressures above 200 GPa [3]. Furthermore, in this range of pressure, the extrapolations of different scales diverge. Accurate static high-pressure calibration is difficult because candidate material properties under high pressure and temperature conditions are not known with sufficient precision. However, pressure can be determined independently by performing additional experiments and/or theoretical calculations. Shock-wave experiments yield accurate pressure values (e.g., 3% as suggested in ref. [4]), and this procedure has been used for static calibration in the DAC in a number of works [1–2, 5–10]. This method requires reducing the shock compression curves to isotherms and also materials strength correction (see, e.g., ref. [4]). This naturally leads to uncertainties whose magnitudes are difficult to estimate. Alternatively, one can use theoretical calculations if the results are believed to be sufficiently accurate. Kunc et al. [11] constructed a high-pressure scale based on density functional theory calculations of the equation of state and Raman frequency of diamond. The uncertainties introduced by this procedure not only depend on the type of approximation used (local-density approximation (LDA) or generalised gradient approximation (GGA)), but also may be exacerbated depending on the material. Once again their magnitudes are difficult to estimate. An alternative way of constructing an accurate pressure scale is based on determination of pressure from simultaneous density and sound velocity measurements (e.g., ref. [12]) under static conditions using the so-called redundant scheme. This method requires only a relatively small correction from an adiabatic to an isothermal path at room or moderately elevated temperature, so from that point of view it is expected to be more accurate than shock-wave based calibrations. Here, we report preliminary data on the construction of the high-temperature pressure scale based on the use of cubic boron nitride (cBN) as a primary calibrant. We chose cBN because its pressure and temperature dependence is predictable, it is stable in a wide P –T range and has a number of other properties which make it convenient to use as a pressure sensor (see below). Room-temperature data agree with the current ruby calibration scale within the uncertainties. More data are, however, necessary to construct the high-temperature calibration, although Raman and X-ray diffraction measurements [13, 14] already performed may serve as an initial guide.
2.
Experiment
We performed our simultaneous measurements of elastic moduli and density of cBN at a new GSE CARS facility at Beamline 13 of the Advance Photon Source (Argonne National Laboratory). Technical details of this setup are presented in ref. [15]. Single crystal cBN samples were mechanically polished to the thickness of 15–20 μm. Our samples were annealed twice consecutively at 1 × 10−6 Torr and 1000 K for five hours. The temperature ramp rate was 21 K/min. Slow cooling of samples occurred after both heat treatments. Before loading in the DAC, several crystals were studied using Brillouin spectroscopy at the Geophysical laboratory. All Brillouin measurements were performed in a platelet or symmetric geometry (see, e.g., ref [15]) with 50◦ or 80◦ scattering angle. Brillouin scattering measurements in both laboratories were performed using a six-pass tandem Fabry–Perot interferometer. A single frequency argon ion laser (λexc = 514.5 nm) and Coherent Verdi V2 solid-state doubled frequency Nd:YVO4 lasers (λexc = 532 nm) were used as a light sources at Geophysical laboratory and GSE CARS, respectively.
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Figure 1. Left panel: microphotograph of cBN single crystal in the DAC cavity loaded in an argon medium to 16 GPa. Sample dimensions are 80 μm along the edges and 18 μm thick. Right panel: X-ray diffraction pattern of cBN of the sample shown in the left panel at 16 GPa. Rings correspond to diffraction from the argon medium; a dot marked by the red arrow corresponds to the (111) reflection of cBN. A bigger spot below is a diamond reflection. The pattern has been collected on a MAR image reader using a monochromatic radiation with wavelength of 0.3344 Å.
The angular dependences of sound velocities show a 60◦ periodicity, which is consistent with a (111) platelet orientation (see below). Moreover, the crystal habitus (figure 1a) also suggests this orientation. Samples of 50–80 μm linear dimensions were loaded in the DAC along with ruby spheres for additional fluorescence measurements and in one experiment with small pieces of gold and platinum to allow additional determinations of pressure using X-ray diffraction. Solid argon was used as a medium in a majority of the experiments. Use of neon (which is expected to serve as more hydrostatic medium) did not alter the results within the error bars. Our previous X-ray diffraction and Raman experiments with cBN using argon as a medium [13, 14] did not show any substantial difference compared to the results of experiments with He medium [16], so we believe that the use of argon is justified in case of such hard materials as cBN. Symmetrical DACs of different designs, but all with large optical angular openings (up to 90◦ ), were used. These designs include a Mao–Bell piston–cylinder cell with tungsten carbide (WC) Boehler–Almax (BA) seats [17], a Mao–Bell short piston–cylinder cell with stainless steel seats, and a Merrill–Bassett cell with three guiding pins and WC seats of standard design. The BA seats in a combination with the symmetric Mao–Bell cell allowed Brillouin measurements in a 50◦ scattering geometry, whereas the other two cells provided sufficient optical access to allow an 80◦ scattering geometry. The use of this latter geometry was crucial for determining an accurate elastic moduli of cBN due to increased accuracy of the sound velocity determination, which is adversely affected by the close proximity of diamond and cBN Brillouin peaks. To further mitigate the problem associated with the overlap of the Brillouin peaks of diamond and CBN, the diamond anvils (usually cut along [100] axis) were oriented with respect to each other in such a way that the fastest and slowest directions (determined in a separate Brillouin study) of the anvils would coincide.
3.
Results
The Brillouin spectra of cBN collected in the DAC are shown in figure 2. Most of the spectra show two shear (S1 and S2) modes and one compressional (P ) acoustic mode, but at some sample orientations only one S mode could be observed because of the close proximity in frequency and substantial difference in intensity of the shear modes. Moreover, Brillouin peaks of diamond tend to mask the S2 and P modes depending on the relative angular orientation of the sample with respect to the diamond anvils. Because of the different periodicity (90◦ for diamond and 60◦ for cBN), this could be avoided at some orientations. The highest pressure measurements increasingly suffered from the proximity of the sample peaks to those of
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Figure 2. Brillouin spectra of cBN single crystals in the DAC under pressures up to 27 GPa (room temperature). The crystal plane orientation was close to (111). Upper panel: 50◦ scattering geometry. Lower panel: 80◦ scattering geometry; VP , VS1 , and VS2 indicate compressional, shear 1, and shear 2 acoustic modes, accordingly. D and Ar indicate peaks due to diamond and argon, respectively. The spectra are shown in the directions where both shear waves and also a compressional wave could be observed. The spectra are plotted as a function of acoustic velocity (Vi = ωi λexc /(2 sin(θ/2))), which is proportional to the Brillouin shift ω.
diamond, the necessity of a thinner sample and also a smaller angle scattering geometry. Nevertheless, data obtained at all pressures and temperatures are of sufficient quality to determine the angular dispersion of the acoustic velocities in the (111) crystal plane. Figure 3 shows such dependence at 13 GPa and room temperature. Although small deviations of the crystal orientation from the ideal (111) are possible (we are planning to determine an orientation matrix of our crystals in future studies), we believe that this has little effect on the results obtained. Fitting of the experimental data to the calculated data, the angular dispersion of the acoustic velocities which include the crystal orientation as free parameters was also tried. The results were not sufficiently stable probably because of insufficient number of observations. The RMS deviation of the measured sound velocities was 50–90 m/s or less than 1% nominal error. For each Brillouin measurement, we determined the density of cBN by analyzing the X-ray diffraction patterns (figure 1b) collected on a position sensitive detector while the sample was rotated through ±15◦ with respect to the axis perpendicular to the X-ray beam (ω). We find an excellent agreement between the results obtained at room temperature in this study and in previous studies [14, 16]. Using the velocity and density data, we determined all three independent elastic moduli at each pressure and temperature by a linearized inversion procedure [18]. These results will be presented elsewhere. Here, we report pressure and temperature dependences of the bulk modulus KS = (C11 + C12 )/3.
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Figure 3. Compressional and shear acoustic velocities of cBN as a function of direction in the (111) crystallographic plane at 13 GPa. Points with error bars-experiment. Lines are calculated from the best-fitted elastic moduli. Multiple points at some angles correspond to data obtained at angular positions, which differ by ±n∗ 60◦ . Table 1. Comparison of the experimental and theoretical bulk modulus and its pressure derivative of cBN at ambient conditions. EOS parameters at 300 K X-ray [14] Theory [14] Brillouin (this work) Brillouin [20] Ultrasonic [21]
Bulk modulus K300,0 (GPa)
Pressure derivative of K300,0 –K300,0
387(4) 395.9 386(4) 400(20) 372 (4)
3.06(15) 3.58 2.85(0.31) Undetermined 3.5(0.4)
No distinction is made for the isothermal, KT and adiabatic, KS moduli since the correction factor (KT = KS /(1 + αγ T ), where α is the thermal expansivity, γ the Grüneisen parameter, T the temperature) is negligible (αγ T ≈ 10−3 at room temperature) compared to the experimental uncertainties. The results quoted as ‘this work’ were obtained from the best linear fit to the experimental pressure dependence of KS to 27 GPa.
In table 1, we compare the results of different determinations of the bulk elastic modulus of cBN and its pressure derivative at ambient conditions. The results of this work are in good agreement with our recent synchrotron X-ray diffraction study [14] (which, in turn, is in a good agreement with previous works [16, 19]). The results of theoretical studies vary (see refs. [13, 14] for references) between 363 and 400 GPa, the most recent results are in the range 390–400 GPa. An earlier Brillouin study by Grimsditch et al. [20] agrees with ours within the experimental uncertainty, where as the ultrasonic study of Manghnani [21] shows somewhat lower bulk modulus possibly because of the use of polycrystalline samples and the presence of Co binder. The dependence on density of the KS bulk modulus at room temperature is shown in figure 4a. Within the experimental uncertainty, it can be represented as a linear function of density. Under this assumption, we determined pressure at each pressure point by using
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Figure 4. Bulk modulus of cBN determined experimentally. (a) Density dependence of the adiabatic bulk modulus, KS . (b) A difference of pressure determined by direct integration of the experimentally determined bulk modulus (Equation (1)) and pressure determined by the ruby fluorescence technique [2].
the following equation
P (ρ) =
ρ ρ0
KT ρ
δρ
(1)
The results are presented in figure 4b, where we plot the deviation of pressure (1) from that determined by the conventional ruby scale [2]. As one can see, this present determination of pressure without use of an independent pressure scale agrees very closely (∼1% at the highest pressure) with that given by the ruby scale. Figures 5 and 6 show the results of the temperature scan to 727 K at 16 GPa. As seen from figure 6a, KS is almost temperature independent, while KT shows a decrease with temperature
Figure 5. Brillouin spectra of cBN single crystals in the externally heated DAC at high temperatures to 723 K at the nominal pressure of 16 GPa . Peaks are marked as in figure 2.
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Figure 6. Bulk modulus and lattice parameter at a pressure of 16 GPa at various temperatures. (a) Temperature dependence of the bulk modulus. Open circles – adiabatic bulk modulus KS determined from the Brillouin data. Solid circles – isothermal bulk modulus, KT = KS /(1 + αγ T ), where the Gruneisen parameter γ is equal to 1.05 [14, 16]; the thermal expansivity α is assumed to be the same as at ambient pressure ref. [27]. Use of a pressure dependent thermal expansivity would affect the results negligibly compared to the experimental uncertainties. Gray solid line, KT as determined from our thermal EOS [14], black solid and dashed lines best linear fits to KT and KS , respectively. (b) Lattice parameters determined in this study in comparison with the at 16 GPa isobar calculated from the thermal EOS [14].
comparable to that determined from our laser heating X-ray diffraction study [14]. A small difference in absolute values is within the mutual uncertainties. Moreover, the lattice constants (figure 6b) are in a good agreement with the 16-GPa isobar calculated from the same data [14]. Data obtained from a simultaneous powder diffraction study of Pt and Au show consistency with the previously determined thermal EOSs of these materials [22].
4.
Discussion
The simultaneous measurements of the bulk modulus and density of cBN lead to a cBN pressure scale that is consistent with the conventional ruby scale [2] up to 27 GPa (figure 4b). It is important to assess the sources of uncertainties and provide guidance for further study that aims to improve pressure scales. The uncertainties in pressure determination come from the following potential errors in measurements of the density and bulk modulus. The accuracy of determination of the lattice constant is approximately 10−4 , which leads to better than 0.1% accuracy in density determination. The precision of the bulk modulus (KS = VB2 ρ, VB is the bulk sound velocity) is limited mainly by that of the sound velocities. The sound velocity determination has an estimated precision of approximately 0.5% (see, e.g., [23]), which leads to an uncertainty of approximately 1–2% in the bulk modulus. Because the maximum change associated with the conversion of the adiabatic to the isothermal bulk modulus does not exceed 1% (T < 1000 K) this procedure would not reduce the accuracy considerably even at high temperature. Because of the limited pressure range studied (
