- Email: [email protected]
rhodium alloy at high temperature by combined laser heating and laser ultrasonic techniques
Ultrasonics 54 (2014) 963–966
Contents lists available at ScienceDirect
Ultrasonics journal homepage: www.elsevier.com/locate/ultras
Short Communication
Elastic characterization of platinum/rhodium alloy at high temperature by combined laser heating and laser ultrasonic techniques K. Burgess a, V. Prakapenka b, E. Hellebrand c, P.V. Zinin a,⇑ a
Hawaii Institute of Geophysics and Planetology, University of Hawaii, Honolulu, HI, USA Center for Advanced Radiation Sources, University of Chicago, IL, USA c Department of Geology and Geophysics, University of Hawaii, Honolulu, HI, USA b
a r t i c l e
i n f o
Article history: Received 26 September 2013 Received in revised form 9 January 2014 Accepted 10 January 2014 Available online 22 January 2014
a b s t r a c t We demonstrate an innovative pump–probe technique combined with laser heating to determine the velocity of a surface Rayleigh wave at high temperature. Laser ultrasonics in a point-source–point-receiver configuration was combined with laser heating to evaluate the elastic properties of micron size specimens. The measurements of the velocity of the surface Rayleigh wave (SRW) were conducted at 1070 K. Ó 2014 Elsevier B.V. All rights reserved.
Keywords: Laser ultrasonics Surface acoustic waves High temperature
1. Introduction
2. Experiment
There is widespread interest in the elastic properties of solids at elevated temperatures [1]. Much of the impetus for current research in this area has arisen from geophysical and geochemical studies of the Earth’s mantle and core [2] and the need to understand the elastic properties of refractory materials and hard coatings [3]. Laser ultrasonics (LU) appears to be the most appropriate technique for determination of the acoustical properties of very small non-transparent solids and thin films at high temperatures [4,5]. Usually, these measurements are conducted inside a vacuum furnace [4,6], which makes it difficult to apply this technique to study the effect of high temperature on the elastic properties of small micron-sized specimens synthesized under high temperature. The most effective way to heat a small specimen is to use laser heating. In our study, we combined LU with advanced flat-top laser heating (LH) techniques [7,8] to study the behavior of the velocity of a Rayleigh wave (RW) in a PtRh alloy at high temperatures up to 1500 K. The choice of platinum based alloy was due to its very high chemical stability at high temperatures and its possible application as a transducer in laser ultrasonics measurements to study the acoustical properties of liquids and nanomaterials at high temperatures at ambient [9] and high pressures inside diamond anvil cells (DAC) [10,11].
A sketch of the laser ultrasonics-laser heating (LU-LH) system is shown in Fig. 1. The system consists of five major components: (1) the LU-DAC system (probe and pump lasers, photo detector, and oscilloscope); (2) the laser heating system: a fiber laser (1064 nm) and a p-shaper, which is designed to allow precise control of the laser heating spot shape (e.g., gauss, flat-top, donut [8]) and size from 8 lm to 100 lm, laser power is controlled by diode current remotely in the range from 2 to 100 W; (3) the spectrometer for measuring temperature of the sample (using a black-body radiation fit), Raman and fluorescence spectroscopy for pressure determination and sample characterization; (4) the motorized sample stage; (5) double side high magnification imaging based on two long working distance infinity corrected objectives. In our configuration, the laser heating is applied to one side of the specimen (plate) and the velocity of the RW is measured on the opposite side of the specimen (Fig. 2). The experimental LU set-up is typical of many all-optical pump–probe systems [9]. We used a Nd:YAG laser from TEEM Photonics™, with a pulse width of 0.5 ns at a repetition frequency of 20 kHz, and 100 mW power at k = 1064 nm as the pump laser for acoustic wave excitation and an oscilloscope (‘‘Le Croy’’ 7300A, 3 GHz frequency band) for recording signals. The pump laser beam is focused by a Mitutoyo 50 objective with a working distance of 20 mm to a size of 3 lm on the sample surface. We used a 532-nm, 150 mW Compass laser as a probe. The micro-mechanical system measuring the displacement d of the focal spot of the pump laser relative to that
⇑ Corresponding author. Tel.: +1 8089569960. E-mail address: [email protected] (P.V. Zinin). 0041-624X/$ - see front matter Ó 2014 Elsevier B.V. All rights reserved. http://dx.doi.org/10.1016/j.ultras.2014.01.011
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K. Burgess et al. / Ultrasonics 54 (2014) 963–966
Fig. 1. (a) A sketch of the LU-LH system.
Fig. 2. A sketch of the SRW excitation and detection in the laser heated foil. Here, d is the distance between the pump and the probe laser beams.
of probe laser on the sample surface had been calibrated using preliminary optical measurements. The elemental composition of the sample was determined using an electron microprobe analysis (EMPA) JEOL Hyperprobe JXA8500F at the School of Ocean and Earth Science and Technology, University of Hawaii. In order to ensure a reliable result, a pure platinum powder was used as the standard for calibration of boron and carbon in the sample. The result obtained from the EMP measurements gives 18% rhodium (Rh) and 82% platinum.
nated by pulses due to arrival of the surface Rayleigh wave (SRW) in the PtRh alloy, but the skimming longitudinal wave (SLW) was also detected (see insert in Fig. 3) up to d = 30 lm [12]. To measure the acoustic pulse arrival times, the positions of the peaks were determined as an average of the position of the maximum and minimum of the pulse. The velocities (VR) of these waves are determined by using the arrival time (s) and a simple equation (Fig. 3b): d = s VR. The velocity of the Rayleigh wave in the platinum alloy was found to be 2.111 ± 0.040 km/s, and for the longitudinal velocity VL = 4.252 ± 0.057 km/s. The longitudinal wave velocity in pure platinum is VL = 3.260 km/s, and the shear wave velocity is VS = 1.730 km/s [13,14]. The Victorov’s formula for the Rayleigh wave velocity can be used to estimate the value of the Rayleigh wave velocity in platinum, which is VR = 1.608 km/s. For rhodium, we can estimate velocity of the SRW using data for velocities in the [10 0] direction, VL = 5.81 km/s, and VS = 3.965 km/s [15]. This gives an estimate for the Rayleigh wave velocity of Rh as VR = 3.5177 km/s. If Pt and Rh contribute proportionally to the velocities of the SRW in Pt/Rh alloy then we would have VR = 0.82 ⁄ 1.608 + 0.18 ⁄ 3.51 = 1.988 km/s for an 18% Rh platinum alloy. This is close to the value of the SRW, 2.111 km/s, which was obtained experimentally. Fig. 4a shows signals detected by the probe laser in the PtRh alloy at different distances at 1070 ± 112 K. The main peak can be attributed to the SRW wave in the alloy. At high temperatures we were not able to determine pulses attributed to SLW (Fig. 4a). The velocities of SRWs are determined using arrival time s and a simple linear equation (Fig. 4b). The velocities of the SRWs in PtRh alloy at high temperature were found to be 1.751 ± 0.074 km/s at 1070 ± 112 K. 4. Discussion
3. Results Fig. 3a shows signals detected by the probe laser in platinum at different distances at ambient temperature. The signals are domi-
The penetration depth of the SRW at 2 GHz in the PtRh alloy, is around 1 lm. The temperature gradient, DT, over the thickness of h = 1 lm is equal to power per unit area transported by the alloy divided by the coefficient of the conductivity of the alloy. If the
965
K. Burgess et al. / Ultrasonics 54 (2014) 963–966
80
80
(a)
VL = 4.252 ± 0.057 km/s
60
(b)
60
d, μm
50 40 8.0
SLW
7.5
30
Reflectivity variation, au
Reflectivity variation, au
70
20
40
7.0 6.5 6.0 5.5
VR = 2.111 ± 0.007 km/s
20
5.0 4.5
SRW
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10
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t, ns
0
0 5
10
15
20
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35
40
45
50
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20
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40
50
τ, ns
time, ns
Fig. 3. (a) Raw data for the transient reflectivity change at different distances (d) at ambient temperature. The scales are common for all the curves, which are shifted vertically for clarity. The step of the scan is 5.6 lm. The bottom signal was measured at d = 5.6 lm. The longest distance signal was measured at d = 78.4 lm. The insert in Fig. 3 a shows the signal collected when d = 11.2 lm. (b) Graph showing experimentally measured distances (d) versus time of flight (s).
(a)
50
50
40
40
30
30
20
20
10
10
0
(b)
60
d, μm
Reflectivity variation, a.u.
60
VR = 1.751 ± 0.074 km/s
0 0
10
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10
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30
35
τ, ns
time, ns
Fig. 4. (a) Raw data for the transient reflectivity change at different distances (d) at 1100 K. The scales are common for all the curves, which are shifted vertically for clarity. The step of the scan is 5.6 lm. The first signal was measured when d = 5.6 lm. The longest distance signal was measured when d = 45.0 lm. (b) Graph showing experimentally measured distances (d) versus time of flight (s).
power P of the laser beam is 10 W, the area (S) of the laser spot is p (100 lm)2 and the conductivity kt of the alloy is close to that of Pt, which is 71.6 W m1 K1, then the gradient of temperature over 1 lm depth is equal to DT = h ⁄ P/(S ⁄ kt) ffi 5 K. This estimate is close to the gradient measured in the experiments. The measured temperature difference between the front and the back (hot) side at 39 W is 674 K, and at 42 W is 665 K. The foil is 125 lm, so the gradient is 5.3–5.4 K/lm. Therefore, the effect of the temperature variation over the depth of SRW penetration depth is small at temperatures near 1000 K. Further research is required to determine a temperature at which the radiation from the heated sample deteriorates the signal of the LU-LH system so much that the peak of the SRW becomes smaller due to noise from the black body radiation. We did not find such a temperature in this research. The highest temperature at which the signal of the SRW wave was detected was 1500 K. A further increase in laser power led to the melting of the specimen on the back side of the sample, making the signal unstable. To increase the temperature range and reduce axial and radial T gradient we plan to implement a double-sided laser heating technique.
5. Conclusions We demonstrate an innovative pump–probe technique combined with laser heating to determine the velocity of a surface
Rayleigh wave at high temperature. Laser ultrasonics in a pointsource–point-receiver configuration was combined with laser heating to evaluate the elastic properties of micron size specimens. The measurements of the velocity of the surface Rayleigh wave (SRW) were conducted at 1070 K. Acknowledgement The development of the LU-LH system was supported by U.S. Department of Energy Grant No. DE-FG02-07ER46408. KB was supported by NSF, Grant No. EAR-1215796. References [1] P.R. Stoddart, J.D. Comins, A.G. Every, Brillouin scattering measurements of surface acoustic wave velocities in silicon at high temperatures, Phys. Rev. B 51 (1995) 17574–17578. [2] A.P. Kantor, I.Y. Kantor, A.V. Kurnosov, A.Y. Kuznetsov, N.A. Dubrovinskaia, M. Krisch, A.A. Bossak, V.P. Dmitriev, V.S. Urusov, L.S. Dubrovinsky, Sound wave velocities of fcc Fe–Ni alloy at high pressure and temperature by mean of inelastic X-ray scattering, Phys. Earth Planet. Int. 164 (2007) 83–89. [3] X. Zhang, P.R. Stoddart, J.D. Comins, A.G. Every, High-temperature elastic properties of a nickel-based superalloy studied by surface Brillouin scattering, J. Phys.–Condes. Matter 13 (2001) 2281–2294. [4] R.J. Dewhurst, C. Edwards, A.D.W. McKie, S.B. Palmer, A remote laser system for ultrasonic velocity measurement at high temperatures, J. Appl. Phys. 63 (1988) 1225–1227. [5] M.H. Nadal, L. Bourgeois, A. Migliori, Analytical models for the shear modulus of alpha-Pu and Ga-stabilized delta-Pu versus temperature and pressure from measurements, J. Appl. Phys. 109 (2011).
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K. Burgess et al. / Ultrasonics 54 (2014) 963–966
[6] C. Hubert, M.H. Nadal, G. Ravel-Chapuis, R. Oltra, Contactless ultrasonic device to measure surface acoustic wave velocities versus temperature, Rev. Sci. Instrum. 78 (2007). [7] L.C. Ming, W.A. Bassett, Laser heating in the diamond anvil press up to 2000 °C sustained and 3000 °C pulsed at pressures up to 260 kilobars, Rev. Sci. Instrum. 45 (1974) 1115–1118. [8] V.B. Prakapenka, A. Kubo, A. Kuznetsov, A. Laskin, O. Shkurikhin, P. Dera, M.L. Rivers, S.R. Sutton, Advanced flat top laser heating system for high pressure research at GSECARS: application to the melting behavior of germanium, High Pressure Res. 28 (2008) 225–235. [9] N. Chigarev, V. Tournat, V. Gusev, All-optical monitoring of acoustic waves guided by confined micro-fluidic layers, Appl. Phys. Lett. 100 (2012) 144102. [10] N. Chigarev, P. Zinin, L.C. Ming, G. Amulele, A. Bulou, V. Gusev, Laser generation and detection of longitudinal and shear acoustic waves in a diamond anvil cell, Appl. Phys. Lett. 93 (2008) 181905.
[11] N. Chigarev, P. Zinin, D. Mounier, A. Bulou, L.C. Ming, T. Acosta, V. Gusev, Analysis of ultrasonic echoes induced by pulsed laser action on an iron film in a diamond anvil cell, High Pressure Res. 30 (2010) 78–82. [12] A. Zerr, N. Chigarev, R. Brenner, D.A. Dzivenko, V. Gusev, Elastic moduli of hard c-Zr(3)N(4) from laser ultrasonic measurements, Phys. Status Solidi–Rapid Res. Lett. 4 (2010) 353–355. [13] B.R. Tittmann, R. Crane, Ultrasonic inspection of composites, in: A. Kelly, C. Zweben (Eds.), Comprehensive Composite Materials, Elsevier, New York, 2002, pp. 259–320. [14] S.M. Collard, R.B. McLellan, High temperature elastic constants of platinum single crystals, Acta Metall. Mater. 40 (1992) 699–702. [15] D. Maurer, R. Heichele, N. Lingg, V. Muller, K.H. Rieder, Elastic properties of purified single-crystalline rhodium, Phys. Status Solidi A–Appl. Res. 160 (1997) 403–411.
Contents lists available at ScienceDirect
Ultrasonics journal homepage: www.elsevier.com/locate/ultras
Short Communication
Elastic characterization of platinum/rhodium alloy at high temperature by combined laser heating and laser ultrasonic techniques K. Burgess a, V. Prakapenka b, E. Hellebrand c, P.V. Zinin a,⇑ a
Hawaii Institute of Geophysics and Planetology, University of Hawaii, Honolulu, HI, USA Center for Advanced Radiation Sources, University of Chicago, IL, USA c Department of Geology and Geophysics, University of Hawaii, Honolulu, HI, USA b
a r t i c l e
i n f o
Article history: Received 26 September 2013 Received in revised form 9 January 2014 Accepted 10 January 2014 Available online 22 January 2014
a b s t r a c t We demonstrate an innovative pump–probe technique combined with laser heating to determine the velocity of a surface Rayleigh wave at high temperature. Laser ultrasonics in a point-source–point-receiver configuration was combined with laser heating to evaluate the elastic properties of micron size specimens. The measurements of the velocity of the surface Rayleigh wave (SRW) were conducted at 1070 K. Ó 2014 Elsevier B.V. All rights reserved.
Keywords: Laser ultrasonics Surface acoustic waves High temperature
1. Introduction
2. Experiment
There is widespread interest in the elastic properties of solids at elevated temperatures [1]. Much of the impetus for current research in this area has arisen from geophysical and geochemical studies of the Earth’s mantle and core [2] and the need to understand the elastic properties of refractory materials and hard coatings [3]. Laser ultrasonics (LU) appears to be the most appropriate technique for determination of the acoustical properties of very small non-transparent solids and thin films at high temperatures [4,5]. Usually, these measurements are conducted inside a vacuum furnace [4,6], which makes it difficult to apply this technique to study the effect of high temperature on the elastic properties of small micron-sized specimens synthesized under high temperature. The most effective way to heat a small specimen is to use laser heating. In our study, we combined LU with advanced flat-top laser heating (LH) techniques [7,8] to study the behavior of the velocity of a Rayleigh wave (RW) in a PtRh alloy at high temperatures up to 1500 K. The choice of platinum based alloy was due to its very high chemical stability at high temperatures and its possible application as a transducer in laser ultrasonics measurements to study the acoustical properties of liquids and nanomaterials at high temperatures at ambient [9] and high pressures inside diamond anvil cells (DAC) [10,11].
A sketch of the laser ultrasonics-laser heating (LU-LH) system is shown in Fig. 1. The system consists of five major components: (1) the LU-DAC system (probe and pump lasers, photo detector, and oscilloscope); (2) the laser heating system: a fiber laser (1064 nm) and a p-shaper, which is designed to allow precise control of the laser heating spot shape (e.g., gauss, flat-top, donut [8]) and size from 8 lm to 100 lm, laser power is controlled by diode current remotely in the range from 2 to 100 W; (3) the spectrometer for measuring temperature of the sample (using a black-body radiation fit), Raman and fluorescence spectroscopy for pressure determination and sample characterization; (4) the motorized sample stage; (5) double side high magnification imaging based on two long working distance infinity corrected objectives. In our configuration, the laser heating is applied to one side of the specimen (plate) and the velocity of the RW is measured on the opposite side of the specimen (Fig. 2). The experimental LU set-up is typical of many all-optical pump–probe systems [9]. We used a Nd:YAG laser from TEEM Photonics™, with a pulse width of 0.5 ns at a repetition frequency of 20 kHz, and 100 mW power at k = 1064 nm as the pump laser for acoustic wave excitation and an oscilloscope (‘‘Le Croy’’ 7300A, 3 GHz frequency band) for recording signals. The pump laser beam is focused by a Mitutoyo 50 objective with a working distance of 20 mm to a size of 3 lm on the sample surface. We used a 532-nm, 150 mW Compass laser as a probe. The micro-mechanical system measuring the displacement d of the focal spot of the pump laser relative to that
⇑ Corresponding author. Tel.: +1 8089569960. E-mail address: [email protected] (P.V. Zinin). 0041-624X/$ - see front matter Ó 2014 Elsevier B.V. All rights reserved. http://dx.doi.org/10.1016/j.ultras.2014.01.011
964
K. Burgess et al. / Ultrasonics 54 (2014) 963–966
Fig. 1. (a) A sketch of the LU-LH system.
Fig. 2. A sketch of the SRW excitation and detection in the laser heated foil. Here, d is the distance between the pump and the probe laser beams.
of probe laser on the sample surface had been calibrated using preliminary optical measurements. The elemental composition of the sample was determined using an electron microprobe analysis (EMPA) JEOL Hyperprobe JXA8500F at the School of Ocean and Earth Science and Technology, University of Hawaii. In order to ensure a reliable result, a pure platinum powder was used as the standard for calibration of boron and carbon in the sample. The result obtained from the EMP measurements gives 18% rhodium (Rh) and 82% platinum.
nated by pulses due to arrival of the surface Rayleigh wave (SRW) in the PtRh alloy, but the skimming longitudinal wave (SLW) was also detected (see insert in Fig. 3) up to d = 30 lm [12]. To measure the acoustic pulse arrival times, the positions of the peaks were determined as an average of the position of the maximum and minimum of the pulse. The velocities (VR) of these waves are determined by using the arrival time (s) and a simple equation (Fig. 3b): d = s VR. The velocity of the Rayleigh wave in the platinum alloy was found to be 2.111 ± 0.040 km/s, and for the longitudinal velocity VL = 4.252 ± 0.057 km/s. The longitudinal wave velocity in pure platinum is VL = 3.260 km/s, and the shear wave velocity is VS = 1.730 km/s [13,14]. The Victorov’s formula for the Rayleigh wave velocity can be used to estimate the value of the Rayleigh wave velocity in platinum, which is VR = 1.608 km/s. For rhodium, we can estimate velocity of the SRW using data for velocities in the [10 0] direction, VL = 5.81 km/s, and VS = 3.965 km/s [15]. This gives an estimate for the Rayleigh wave velocity of Rh as VR = 3.5177 km/s. If Pt and Rh contribute proportionally to the velocities of the SRW in Pt/Rh alloy then we would have VR = 0.82 ⁄ 1.608 + 0.18 ⁄ 3.51 = 1.988 km/s for an 18% Rh platinum alloy. This is close to the value of the SRW, 2.111 km/s, which was obtained experimentally. Fig. 4a shows signals detected by the probe laser in the PtRh alloy at different distances at 1070 ± 112 K. The main peak can be attributed to the SRW wave in the alloy. At high temperatures we were not able to determine pulses attributed to SLW (Fig. 4a). The velocities of SRWs are determined using arrival time s and a simple linear equation (Fig. 4b). The velocities of the SRWs in PtRh alloy at high temperature were found to be 1.751 ± 0.074 km/s at 1070 ± 112 K. 4. Discussion
3. Results Fig. 3a shows signals detected by the probe laser in platinum at different distances at ambient temperature. The signals are domi-
The penetration depth of the SRW at 2 GHz in the PtRh alloy, is around 1 lm. The temperature gradient, DT, over the thickness of h = 1 lm is equal to power per unit area transported by the alloy divided by the coefficient of the conductivity of the alloy. If the
965
K. Burgess et al. / Ultrasonics 54 (2014) 963–966
80
80
(a)
VL = 4.252 ± 0.057 km/s
60
(b)
60
d, μm
50 40 8.0
SLW
7.5
30
Reflectivity variation, au
Reflectivity variation, au
70
20
40
7.0 6.5 6.0 5.5
VR = 2.111 ± 0.007 km/s
20
5.0 4.5
SRW
4.0
10
10
20
30
40
50
60
70
t, ns
0
0 5
10
15
20
25
30
35
40
45
50
10
20
30
40
50
τ, ns
time, ns
Fig. 3. (a) Raw data for the transient reflectivity change at different distances (d) at ambient temperature. The scales are common for all the curves, which are shifted vertically for clarity. The step of the scan is 5.6 lm. The bottom signal was measured at d = 5.6 lm. The longest distance signal was measured at d = 78.4 lm. The insert in Fig. 3 a shows the signal collected when d = 11.2 lm. (b) Graph showing experimentally measured distances (d) versus time of flight (s).
(a)
50
50
40
40
30
30
20
20
10
10
0
(b)
60
d, μm
Reflectivity variation, a.u.
60
VR = 1.751 ± 0.074 km/s
0 0
10
20
30
40
50
5
10
15
20
25
30
35
τ, ns
time, ns
Fig. 4. (a) Raw data for the transient reflectivity change at different distances (d) at 1100 K. The scales are common for all the curves, which are shifted vertically for clarity. The step of the scan is 5.6 lm. The first signal was measured when d = 5.6 lm. The longest distance signal was measured when d = 45.0 lm. (b) Graph showing experimentally measured distances (d) versus time of flight (s).
power P of the laser beam is 10 W, the area (S) of the laser spot is p (100 lm)2 and the conductivity kt of the alloy is close to that of Pt, which is 71.6 W m1 K1, then the gradient of temperature over 1 lm depth is equal to DT = h ⁄ P/(S ⁄ kt) ffi 5 K. This estimate is close to the gradient measured in the experiments. The measured temperature difference between the front and the back (hot) side at 39 W is 674 K, and at 42 W is 665 K. The foil is 125 lm, so the gradient is 5.3–5.4 K/lm. Therefore, the effect of the temperature variation over the depth of SRW penetration depth is small at temperatures near 1000 K. Further research is required to determine a temperature at which the radiation from the heated sample deteriorates the signal of the LU-LH system so much that the peak of the SRW becomes smaller due to noise from the black body radiation. We did not find such a temperature in this research. The highest temperature at which the signal of the SRW wave was detected was 1500 K. A further increase in laser power led to the melting of the specimen on the back side of the sample, making the signal unstable. To increase the temperature range and reduce axial and radial T gradient we plan to implement a double-sided laser heating technique.
5. Conclusions We demonstrate an innovative pump–probe technique combined with laser heating to determine the velocity of a surface
Rayleigh wave at high temperature. Laser ultrasonics in a pointsource–point-receiver configuration was combined with laser heating to evaluate the elastic properties of micron size specimens. The measurements of the velocity of the surface Rayleigh wave (SRW) were conducted at 1070 K. Acknowledgement The development of the LU-LH system was supported by U.S. Department of Energy Grant No. DE-FG02-07ER46408. KB was supported by NSF, Grant No. EAR-1215796. References [1] P.R. Stoddart, J.D. Comins, A.G. Every, Brillouin scattering measurements of surface acoustic wave velocities in silicon at high temperatures, Phys. Rev. B 51 (1995) 17574–17578. [2] A.P. Kantor, I.Y. Kantor, A.V. Kurnosov, A.Y. Kuznetsov, N.A. Dubrovinskaia, M. Krisch, A.A. Bossak, V.P. Dmitriev, V.S. Urusov, L.S. Dubrovinsky, Sound wave velocities of fcc Fe–Ni alloy at high pressure and temperature by mean of inelastic X-ray scattering, Phys. Earth Planet. Int. 164 (2007) 83–89. [3] X. Zhang, P.R. Stoddart, J.D. Comins, A.G. Every, High-temperature elastic properties of a nickel-based superalloy studied by surface Brillouin scattering, J. Phys.–Condes. Matter 13 (2001) 2281–2294. [4] R.J. Dewhurst, C. Edwards, A.D.W. McKie, S.B. Palmer, A remote laser system for ultrasonic velocity measurement at high temperatures, J. Appl. Phys. 63 (1988) 1225–1227. [5] M.H. Nadal, L. Bourgeois, A. Migliori, Analytical models for the shear modulus of alpha-Pu and Ga-stabilized delta-Pu versus temperature and pressure from measurements, J. Appl. Phys. 109 (2011).
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K. Burgess et al. / Ultrasonics 54 (2014) 963–966
[6] C. Hubert, M.H. Nadal, G. Ravel-Chapuis, R. Oltra, Contactless ultrasonic device to measure surface acoustic wave velocities versus temperature, Rev. Sci. Instrum. 78 (2007). [7] L.C. Ming, W.A. Bassett, Laser heating in the diamond anvil press up to 2000 °C sustained and 3000 °C pulsed at pressures up to 260 kilobars, Rev. Sci. Instrum. 45 (1974) 1115–1118. [8] V.B. Prakapenka, A. Kubo, A. Kuznetsov, A. Laskin, O. Shkurikhin, P. Dera, M.L. Rivers, S.R. Sutton, Advanced flat top laser heating system for high pressure research at GSECARS: application to the melting behavior of germanium, High Pressure Res. 28 (2008) 225–235. [9] N. Chigarev, V. Tournat, V. Gusev, All-optical monitoring of acoustic waves guided by confined micro-fluidic layers, Appl. Phys. Lett. 100 (2012) 144102. [10] N. Chigarev, P. Zinin, L.C. Ming, G. Amulele, A. Bulou, V. Gusev, Laser generation and detection of longitudinal and shear acoustic waves in a diamond anvil cell, Appl. Phys. Lett. 93 (2008) 181905.
[11] N. Chigarev, P. Zinin, D. Mounier, A. Bulou, L.C. Ming, T. Acosta, V. Gusev, Analysis of ultrasonic echoes induced by pulsed laser action on an iron film in a diamond anvil cell, High Pressure Res. 30 (2010) 78–82. [12] A. Zerr, N. Chigarev, R. Brenner, D.A. Dzivenko, V. Gusev, Elastic moduli of hard c-Zr(3)N(4) from laser ultrasonic measurements, Phys. Status Solidi–Rapid Res. Lett. 4 (2010) 353–355. [13] B.R. Tittmann, R. Crane, Ultrasonic inspection of composites, in: A. Kelly, C. Zweben (Eds.), Comprehensive Composite Materials, Elsevier, New York, 2002, pp. 259–320. [14] S.M. Collard, R.B. McLellan, High temperature elastic constants of platinum single crystals, Acta Metall. Mater. 40 (1992) 699–702. [15] D. Maurer, R. Heichele, N. Lingg, V. Muller, K.H. Rieder, Elastic properties of purified single-crystalline rhodium, Phys. Status Solidi A–Appl. Res. 160 (1997) 403–411.