- Email: [email protected]
Laser-shock compression experiment on magnesium hydride
High Energy Density Physics 33 (2019) 100703
Contents lists available at ScienceDirect
High Energy Density Physics journal homepage: www.elsevier.com/locate/hedp
Laser-shock compression experiment on magnesium hydride ⁎,a
a,b
a
a
c
S. Morioka , N. Ozaki , M. Hosomi , K. Katagiri , T. Matsuoka , K. Miyanishi T. Sanob, Y. Umedaa, R. Kodamaa,b
a,b
d
, T. Okuchi ,
T
a
Graduate School of Engineering, Osaka University, Suita, Osaka 565-0871, Japan Institute of Laser Engineering, Osaka University, Suita, Osaka 565-0871, Japan Open and Transdisciplinary Research Initiatives, Suita, Osaka 565-0871, Japan d Institute for Planetary Materials, Okayama University, Misasa, Tottori 682-0193, Japan b c
ARTICLE INFO
ABSTRACT
Keywords: Magnesium hydride Shock compression Laser-driven shock Hugoniot measurement Velocity interferometer
A dynamic high-pressure experiment was performed on magnesium hydride to measure the Hugoniot equationof-state point using laser-driven shock waves. By measuring the mean shock velocity of MgH2 and the timeresolved shock velocity of the quartz reference, the Hugoniot state of MgH2 at 150 GPa was determined. The reliability of the data is ensured by using another reference material, polystyrene, which is next to the sample and is compressed by the same. This work validates the experimental methodology to obtain further highpressure data of MgH2 with high accuracy.
1. Introduction
2. Experimental descriptions
Hydrogen is the most abundant chemical substance in the universe. It is also one of the most important elements in material science because it is the lightest and smallest element. The unique features of hydrogen provide many possible origins for unusual properties such as hightemperature superconductivity expected in the solid metallic hydrogen [1]. Hydrides also often show interesting properties reflecting the features of hydrogen [2]. It was reported that hydrogen sulfide (H2S) undergoes a structural change to a superconducting phase under static high pressures ( ∼ 150 GPa) and shows an extremely high critical temperature (203 K) [3]. The high-pressure superconducting phase was recently confirmed to be H3S [4]. Ab-initio calculations also predict such phase transformation in many other hydrides under high pressures [5–10]. Therefore, better data on the equation-of-state (EOS) of hydrides at high pressures are necessary for comprehensively understanding the phase transition and the phase diagram. In this paper, we present the first high-pressure experiment on magnesium hydride (MgH2) using laser-driven shock waves. The development of the MgH2 samples and the target design are described. The shock velocities of the MgH2 sample and quartz reference for the impedance mismatching analysis were measured with line-imaging velocity interferometry. This work validates the experimental methodology to obtain further MgH2 equation-of state data for MgH2 and other similar materials.
2.1. MgH2 samples
⁎
Planar MgH2 samples were made by pressing MgH2 powder using a compaction molding container and hydraulic press device. The particle size of the powder was ∼ 3 µm. The shape of the MgH2 samples was an approximately elliptical disk with a longer diameter of approximately ∼ 3 mm, as shown in Fig. 1(a). The thickness (d) and area (S) of the samples were measured with a confocal laser microscope with typical uncertainties of 1.5% and 0.8%, respectively. The sample mass (M) was measured with 0.1 mg resolution. We measured each sample five times and used the average value as the sample mass. The uncertainty of the measured sample mass was typically 10%. The porosity (Φ) of samples was obtained by
=1
0
,
(1)
s M
where ρs and ρ0 (= dS ) were the mass densities of bulk single crystal MgH2 [13] and our samples, respectively. Typical porosity of the samples was ∼ 12%. The metrological data of the samples are summarized in Table 1, although shock data was only taken for sample #1. 2.2. Target Fig. 1 (b) shows the target assembly and experimental setup. The
Corresponding author. E-mail address: [email protected] (S. Morioka).
https://doi.org/10.1016/j.hedp.2019.100703 Received 15 October 2018; Received in revised form 11 July 2019; Accepted 23 July 2019 Available online 23 July 2019 1574-1818/ © 2019 Published by Elsevier B.V.
High Energy Density Physics 33 (2019) 100703
S. Morioka, et al.
Fig. 2. Diagram of the impedance mismatching analysis. The solid and dashed curves represent the Hugoniot of quartz [19] and CH (SESAME 7952) [25], respectively. The dotted curve represents the quartz release model [18,19]. The impedance mismatching for MgH2 occurs at the intersection of a MgH2 Rayleigh line (thin straight line) and the quartz release adiabat from the inferred quartz Hugoniot point (solid triangle). The solid circle and square are the measured Hugoniot points of MgH2 and CH witness, respectively. Open triangles [21], squares [22], diamond [23], and circles [24] are the available experimental data of CH [26].
respectively, and the time-resolved quartz and CH shock velocities. The top half of the target provides the arrival time (t3) to the MgH2/Qz rear interface. The rear-Qz has an anti-reflection coating layer on the VISAR side with reflectivity of less than 0.5%. The shock transit time of MgH2 is obtained from the t2 and t3. The role of the rear CH and Qz is to facilitate visualization of the shock arrival to the Qz/MgH2 and MgH2/ Qz interfaces, respectively. The rear CH also works as a reference for validating this impedance mismatching experiment, because the CH Hugoniot is well known[21–25]. The target baseplate consists of a 15 µm-thick polypropylene (CH2) layer, 40 µm aluminum, and 50 µm z-cut α-quartz from the drive laser side. The CH2 was used as an ablator for absorbing the shock-driving laser light, Al as a pusher, and Qz as an EOS reference for the impedance mismatching analysis. The drive laser first hits the CH2 ablator to prevent radiation preheating of the sample and references by minimizing the photon energies of X-rays generated from the coronal plasma.
Fig. 1. (a) Photograph of the MgH2 sample fabricated by pressing MgH2 powder. (b) Target assembly and experimental setup. The target baseplate consists of CH2, Al, and Qz from the drive laser side. The MgH2 sample and CH witness are attached onto the top and bottom half of the baseplate, respectively. (c) Raw VISAR image. Time proceeds from the left to the right. The times t1, t2, and t3 represent the arrival times of shock wave to the Al/Qz, Qz/MgH2 (= Qz/ CH), and MgH2/Qz interfaces, respectively. (d) Velocity history extracted from the bottom half of the VISAR image (corresponding to the target bottom half). Table 1 MgH2 sample metrological data. Sample No. 1 2 3 4
Thickness, d (µm)
Volume, V
52.7 40.9 56.2 65.3
3.42 3.05 3.21 3.37
± ± ± ±
0.8 0.6 0.8 0.9
(10
4
cm3)
Density, ρ0 (g/cm3)
Porosity, Φ (%)
± ± ± ±
1.24 1.27 1.25 1.19
12.4 10.3 12.1 16.5
0.06 0.05 0.03 0.03
± ± ± ±
0.16 0.14 0.16 0.14
2.3. Laser-shock experiment The laser-shock experiment was conducted on the GEKKO XII laser facility at the Institute of Laser Engineering, Osaka University [15,16]. The experiment used three of the twelve beams at a wavelength of 527 nm, which was the second harmonics of the neodymium-doped glass laser. The temporal shape of the laser pulse was approximately a square with the full width at half maximum (FWHM) of 2.5 ns and the rise and fall times of 100 ps each. The experiment used the target described above, with the MgH2 sample #1 in Table 1. The focal-spot diameter of the shock driving laser was ∼ 1 mm with a flat top distribution made by Kinoform phase plates, resulting in a planar shock front of more than 400 µm in diameter [16,17]. Both the time-resolved and mean shock velocities were measured using the two line-imaging VISARs. The VISAR probe laser operated at 532 nm was incident on the rear of the target. The velocity sensitivities (velocity-per-fringe, VPF) of the VISARs were 6.377 and 15.121 km/s/ fringe under vacuum, respectively. The typical uncertainty of the measured time-resolved shock velocity was ∼ 1.5–2%. The shock arrival (t2) and breakout (t3) times of MgH2 were obtained from the VISAR velocity and intensity profiles of the bottom and
MgH2 Hugoniot is measured using α-quartz (Qz) for reference with the impedance mismatching technique [11]. Time-resolved shock velocity (Us) of quartz are measured using line-imaging velocity interferometers (line VISARs) [12], because quartz is transparent to the VISAR probe light (532 nm) at ambient pressure but shocked quartz becomes reflective at pressures of interest in this work; i.e., above 100 GPa [14]. On the other hand, for MgH2 only the time-integrated (mean) shock velocity is measured, because the MgH2 samples are not transparent to the probe light. The mean velocity is obtained from the measurements of sample initial thickness and shock transit time. The bottom half of the target shown in Fig. 1(b) provides the arrival times (t1 and t2) of shock wave to the Al/Qz and Qz/CH (= Qz/MgH2) interfaces, 2
High Energy Density Physics 33 (2019) 100703
S. Morioka, et al.
Table 2 Shock compression experiment results. The Us, up, P, and ρ are shock velocity, particle velocity, pressure, and density, respectively. The superscripts denote the sample and reference materials. UsQz
Us
UsCH
up
upCH
P MgH2
PCH
(km/s)
(km/s)
(km/s)
(km/s)
(km/s)
(GPa)
(GPa)
(g/cm3)
13.30 ± 0.22
14.37 ± 0.45
14.10 ± 0.21
8.48 ± 0.09
8.86 ± 0.09
150 ± 19
130 ± 2
3.03 ± 0.44
MgH2
MgH2
top half of the target, respectively. The shock breakout time as a function of position at the target were found by looking for 50% point of the VISAR intensity change on the leading edge.
MgH2
shock velocity of the MgH2 sample and the time-resolved shock velocity of the quartz reference were measured within uncertainties of a few percent, resulting in the measured Hugoniot data of 150 GPa and 2.5fold density compression (i.e., 3.1 g/cm3). In future experiments, we expect to improve the precision of the shock pressure and density (currently 12.7% and 14.3% uncertainties, respectively) by improving the initial density measurements of the MgH2 samples. This work demonstrates the possibility of Hugoniot measurements toward the understanding of the equation-of-state and phase diagram of MgH2 and other similar materials.
3. Results and discussion Fig. 1 (c) shows a raw VISAR image. Time proceeds from the left to the right. The shock arrival times t1 to t3 are denoted by arrows. The shock transit time for the MgH2 layer (Δt = t3 − t2) was determined after accounting for the calibration data of sweep nonlinearity of the streak camera. Here, Δt was 3.83 ± 0.07 ns, and consequently the mean shock velocity UsMgH2 was 13.83 ± 0.32 km/s. Using this mean velocity, a time-resolved velocity at the t2 was estimated considering the unsteadiness of the shock in the MgH2, because correct application of the impedance-mismatching condition requires that UsQz (t2 ) and MgH Us 2 (t2 ) be determined at breakout from the quartz-MgH2 interface. MgH MgH Determining Us 2 (t2 ) requires estimation of the time history, Us 2 (t). This can be achieved using the UsCH (t) measured directly by the VISAR measurement, given that the same pressure source drives both materials in parallel. Since MgH2 and CH have such similar impedances, to a good MgH approximation Us 2 (t) âUsMgH2 = UsCH (t)ãâ aUsCH , provided the average for both materials is taken over the same time period the step MgH transit time in this case [20]. Finally, the corrected Us 2 (t2 ) was 14.37 ± 0.32 km/s. Fig. 1 (d) shows the velocity record extracted from the bottom half of the VISAR image (corresponding to the target bottom half). From the velocity record, the time-resolved quartz shock velocity at t2, just before the shock arrival to the Qz/MgH2 interface, was determined to be UsQz = 13.30 ± 0.22 km/s. The impedance mismatching analysis was performed using these MgH time-resolved shock velocities, Us 2 and UsQz . The states of quartz was inferred from the measured quartz shock velocity and a quartz Hugoniot and release model established by Knudson et al., [18,19]. MgH Finally, the obtained particle velocity and pressure of MgH2 were up 2 MgH 2 = 8.48 ± 0.09 km/s and P = 150 ± 19 GPa, respectively. Fig. 2 shows the diagram of the impedance mismatching analysis for determining the MgH2 Hugoniot. The impedance mismatching occurs at the intersection of a MgH2 Rayleigh line (solid straight line with the MgH slope, 0 Us 2 ) and the release adiabat of quartz (dotted line) from the inferred quartz Hugoniot point (solid triangle). The measured MgH2 Hugoniot is represented by the solid circle with the uncertainty. The solid square represents the Hugoniot of CH witness determined from the impedance mismatching analysis in the same shot. Table 2 summarized the experimental data of quartz, polystyrene, and MgH2. Our CH data is in very good agreement with the available experimental data [21–24] and the well-known EOS model (SESAME 7952) [25]. Although this method is already able to produce good data for the MgH2 Hugoniot, we expect that the precision can be improved in future experiments. The uncertainty in the condition reached is mainly due to that of the sample initial density, and so by fabricating larger samples, the uncertainty of the initial density could be improved by a factor of two or more.
Acknowledgment The laser-shock experiments were conducted under the joint research project of the Institute of Laser Engineering, Osaka University. The authors would like to thank Y. Kimura and H. Hosokawa at the Osaka University for the sample preparation, S. Kubo for the sample metrological characterization, Y. Seto at the Kobe Univerisity for fruitful comments on the sample fabrication, N. J. Hartley for help preparing the manuscript, and all of the technical staffs of the GXII laser facility for their support for the experiments. This work was supported in part by KAKENHI (grant nos. 16H02246) from Japan Society for the Promotion of Science (JSPS), and by the Genesis Research Institute, Inc. (Konpon-ken, TOYOTA). References [1] W.J. Nellis, Rep. Prog. Phys. 69 (2006) 1479. [2] N.W. Ashcroft, Phys. Rev. Lett. 92 (2004) 187002. [3] A.P. Drozdov, M.I. Eremets, I.A. Troyan, V. Ksenofontov, S.I. Shylin, Nature 525 (2015) 73. [4] M. Einaga, M. Sakata, T. Ishikawa, K. Shimizu, M.I. Eremets, A.P. Drozdov, I.A. Troyan, N. Hirao, Y. Ohishi, Nat. Phys. 12 (2016) 835. [5] L. Zhang, Y. Wang, T. Cui, Y. Li, Y. Li, Z. He, Y. Ma, G. Zou, Phys. Rev. B 75 (2007) 144109. [6] S. Cui, W. Feng, H. Hu, Z. Feng, Y. Wang, Solid State Commun. 148 (2008) 403. [7] D.Y. Kim, R.H. Scheicher, R. Ahuja, Phys. Rev. Lett. 103 (2009) 077002. [8] C. Zhang, X.J. Chen, R.Q. Zhang, H.Q. Lin, J. Phys. Chem. C 114 (2010) 14614. [9] E.L.P. y Blanca and R. del P.N. Maldonado, Eur. Phys. J. B 87, 2014, 110. [10] M. Durandurdu, EPL 105 (2014) 46001. [11] Y.B. Zeldovich, Y.P. Raizer, Physics of Shock Waves and High-Temperature Hydrodynamic Phenomena, Academic Press, 1966. [12] P.M. Celliers, Rev. Sci. Instrum. 75 (2004) 4916. [13] U. Wietelmann, Hydride, in: B. Elvers, et al. (Ed.), Encyclopedia of Industrial Chemistry, 2016. [14] P.M. Celliers, et al., Phys. Rev. Lett. 104 (2010) 184503. [15] N. Ozaki, Phys. Plasmas 11 (2004) 1600. [16] N. Ozaki, Phys. Plasmas 16 (2009) 062702. [17] N. Ozaki, Sci. Rep. 6 (2016) 26000. [18] M.D. Knudson, M.P. Desjarlais, Phys. Rev. Lett. 118 (2017) 035501. [19] M.P. Desjarlais, M.D. Knudson, K.R. Cochrane, J. Appl. Phys. 122 (2017) 035903. [20] D.G. Hicks, T.R. Boehly, P.M. Celliers, J.H. Eggert, E. Vianello, D.D. Meyerhofer, G.W. Collins, Phys. Plasmas 12 (2005) 082702. [21] I.P. Dudoladov, V.I. Rakitin, Y.N. Sutulov, G.S. Telegin, Prikl. Mekh. Tekh. Fiz. 4 (1969) 148. [22] R.G. McQueen, S.P. Marsh, J.W. Taylor, J.N. Fritz, W.J. Carter, The equation of state of solids from shock wave studies, in: R. Kinslow (Ed.), High Velocity Impact Phenomena, Academic Press, 1970, pp. 293–417. [23] A.V. Bushman, M.V. Zhernokletov, I.V. Lomonosov, Y.N. Sutulov, V.E. Fortov, K.V. Khishchenko, JETP 82 (1996) 895. [24] M.A. Barrios, D.G. Hicks, T.R. Boehly, D.E. Fratanduono, J.H. Eggert, P.M. Celliers, G.W. Collins, D.D. Meyerhofer, Phys. Plasmas 17 (2010) 056307. [25] S.P. Lyon, J.D. Johnson, Los Alamos National Laboratory report no. LA-CP-98-100, 1998. [26] The original CH data from the different papers are plotted. if the data are reanalyzed using the latest EOS model of quartz[18,19], the plots move slightly and systematically to the lower left of the diagram.
4. Summary In summary, we have presented the first EOS measurement for magnesium hydride under laser-driven shock compression. The mean 3
Contents lists available at ScienceDirect
High Energy Density Physics journal homepage: www.elsevier.com/locate/hedp
Laser-shock compression experiment on magnesium hydride ⁎,a
a,b
a
a
c
S. Morioka , N. Ozaki , M. Hosomi , K. Katagiri , T. Matsuoka , K. Miyanishi T. Sanob, Y. Umedaa, R. Kodamaa,b
a,b
d
, T. Okuchi ,
T
a
Graduate School of Engineering, Osaka University, Suita, Osaka 565-0871, Japan Institute of Laser Engineering, Osaka University, Suita, Osaka 565-0871, Japan Open and Transdisciplinary Research Initiatives, Suita, Osaka 565-0871, Japan d Institute for Planetary Materials, Okayama University, Misasa, Tottori 682-0193, Japan b c
ARTICLE INFO
ABSTRACT
Keywords: Magnesium hydride Shock compression Laser-driven shock Hugoniot measurement Velocity interferometer
A dynamic high-pressure experiment was performed on magnesium hydride to measure the Hugoniot equationof-state point using laser-driven shock waves. By measuring the mean shock velocity of MgH2 and the timeresolved shock velocity of the quartz reference, the Hugoniot state of MgH2 at 150 GPa was determined. The reliability of the data is ensured by using another reference material, polystyrene, which is next to the sample and is compressed by the same. This work validates the experimental methodology to obtain further highpressure data of MgH2 with high accuracy.
1. Introduction
2. Experimental descriptions
Hydrogen is the most abundant chemical substance in the universe. It is also one of the most important elements in material science because it is the lightest and smallest element. The unique features of hydrogen provide many possible origins for unusual properties such as hightemperature superconductivity expected in the solid metallic hydrogen [1]. Hydrides also often show interesting properties reflecting the features of hydrogen [2]. It was reported that hydrogen sulfide (H2S) undergoes a structural change to a superconducting phase under static high pressures ( ∼ 150 GPa) and shows an extremely high critical temperature (203 K) [3]. The high-pressure superconducting phase was recently confirmed to be H3S [4]. Ab-initio calculations also predict such phase transformation in many other hydrides under high pressures [5–10]. Therefore, better data on the equation-of-state (EOS) of hydrides at high pressures are necessary for comprehensively understanding the phase transition and the phase diagram. In this paper, we present the first high-pressure experiment on magnesium hydride (MgH2) using laser-driven shock waves. The development of the MgH2 samples and the target design are described. The shock velocities of the MgH2 sample and quartz reference for the impedance mismatching analysis were measured with line-imaging velocity interferometry. This work validates the experimental methodology to obtain further MgH2 equation-of state data for MgH2 and other similar materials.
2.1. MgH2 samples
⁎
Planar MgH2 samples were made by pressing MgH2 powder using a compaction molding container and hydraulic press device. The particle size of the powder was ∼ 3 µm. The shape of the MgH2 samples was an approximately elliptical disk with a longer diameter of approximately ∼ 3 mm, as shown in Fig. 1(a). The thickness (d) and area (S) of the samples were measured with a confocal laser microscope with typical uncertainties of 1.5% and 0.8%, respectively. The sample mass (M) was measured with 0.1 mg resolution. We measured each sample five times and used the average value as the sample mass. The uncertainty of the measured sample mass was typically 10%. The porosity (Φ) of samples was obtained by
=1
0
,
(1)
s M
where ρs and ρ0 (= dS ) were the mass densities of bulk single crystal MgH2 [13] and our samples, respectively. Typical porosity of the samples was ∼ 12%. The metrological data of the samples are summarized in Table 1, although shock data was only taken for sample #1. 2.2. Target Fig. 1 (b) shows the target assembly and experimental setup. The
Corresponding author. E-mail address: [email protected] (S. Morioka).
https://doi.org/10.1016/j.hedp.2019.100703 Received 15 October 2018; Received in revised form 11 July 2019; Accepted 23 July 2019 Available online 23 July 2019 1574-1818/ © 2019 Published by Elsevier B.V.
High Energy Density Physics 33 (2019) 100703
S. Morioka, et al.
Fig. 2. Diagram of the impedance mismatching analysis. The solid and dashed curves represent the Hugoniot of quartz [19] and CH (SESAME 7952) [25], respectively. The dotted curve represents the quartz release model [18,19]. The impedance mismatching for MgH2 occurs at the intersection of a MgH2 Rayleigh line (thin straight line) and the quartz release adiabat from the inferred quartz Hugoniot point (solid triangle). The solid circle and square are the measured Hugoniot points of MgH2 and CH witness, respectively. Open triangles [21], squares [22], diamond [23], and circles [24] are the available experimental data of CH [26].
respectively, and the time-resolved quartz and CH shock velocities. The top half of the target provides the arrival time (t3) to the MgH2/Qz rear interface. The rear-Qz has an anti-reflection coating layer on the VISAR side with reflectivity of less than 0.5%. The shock transit time of MgH2 is obtained from the t2 and t3. The role of the rear CH and Qz is to facilitate visualization of the shock arrival to the Qz/MgH2 and MgH2/ Qz interfaces, respectively. The rear CH also works as a reference for validating this impedance mismatching experiment, because the CH Hugoniot is well known[21–25]. The target baseplate consists of a 15 µm-thick polypropylene (CH2) layer, 40 µm aluminum, and 50 µm z-cut α-quartz from the drive laser side. The CH2 was used as an ablator for absorbing the shock-driving laser light, Al as a pusher, and Qz as an EOS reference for the impedance mismatching analysis. The drive laser first hits the CH2 ablator to prevent radiation preheating of the sample and references by minimizing the photon energies of X-rays generated from the coronal plasma.
Fig. 1. (a) Photograph of the MgH2 sample fabricated by pressing MgH2 powder. (b) Target assembly and experimental setup. The target baseplate consists of CH2, Al, and Qz from the drive laser side. The MgH2 sample and CH witness are attached onto the top and bottom half of the baseplate, respectively. (c) Raw VISAR image. Time proceeds from the left to the right. The times t1, t2, and t3 represent the arrival times of shock wave to the Al/Qz, Qz/MgH2 (= Qz/ CH), and MgH2/Qz interfaces, respectively. (d) Velocity history extracted from the bottom half of the VISAR image (corresponding to the target bottom half). Table 1 MgH2 sample metrological data. Sample No. 1 2 3 4
Thickness, d (µm)
Volume, V
52.7 40.9 56.2 65.3
3.42 3.05 3.21 3.37
± ± ± ±
0.8 0.6 0.8 0.9
(10
4
cm3)
Density, ρ0 (g/cm3)
Porosity, Φ (%)
± ± ± ±
1.24 1.27 1.25 1.19
12.4 10.3 12.1 16.5
0.06 0.05 0.03 0.03
± ± ± ±
0.16 0.14 0.16 0.14
2.3. Laser-shock experiment The laser-shock experiment was conducted on the GEKKO XII laser facility at the Institute of Laser Engineering, Osaka University [15,16]. The experiment used three of the twelve beams at a wavelength of 527 nm, which was the second harmonics of the neodymium-doped glass laser. The temporal shape of the laser pulse was approximately a square with the full width at half maximum (FWHM) of 2.5 ns and the rise and fall times of 100 ps each. The experiment used the target described above, with the MgH2 sample #1 in Table 1. The focal-spot diameter of the shock driving laser was ∼ 1 mm with a flat top distribution made by Kinoform phase plates, resulting in a planar shock front of more than 400 µm in diameter [16,17]. Both the time-resolved and mean shock velocities were measured using the two line-imaging VISARs. The VISAR probe laser operated at 532 nm was incident on the rear of the target. The velocity sensitivities (velocity-per-fringe, VPF) of the VISARs were 6.377 and 15.121 km/s/ fringe under vacuum, respectively. The typical uncertainty of the measured time-resolved shock velocity was ∼ 1.5–2%. The shock arrival (t2) and breakout (t3) times of MgH2 were obtained from the VISAR velocity and intensity profiles of the bottom and
MgH2 Hugoniot is measured using α-quartz (Qz) for reference with the impedance mismatching technique [11]. Time-resolved shock velocity (Us) of quartz are measured using line-imaging velocity interferometers (line VISARs) [12], because quartz is transparent to the VISAR probe light (532 nm) at ambient pressure but shocked quartz becomes reflective at pressures of interest in this work; i.e., above 100 GPa [14]. On the other hand, for MgH2 only the time-integrated (mean) shock velocity is measured, because the MgH2 samples are not transparent to the probe light. The mean velocity is obtained from the measurements of sample initial thickness and shock transit time. The bottom half of the target shown in Fig. 1(b) provides the arrival times (t1 and t2) of shock wave to the Al/Qz and Qz/CH (= Qz/MgH2) interfaces, 2
High Energy Density Physics 33 (2019) 100703
S. Morioka, et al.
Table 2 Shock compression experiment results. The Us, up, P, and ρ are shock velocity, particle velocity, pressure, and density, respectively. The superscripts denote the sample and reference materials. UsQz
Us
UsCH
up
upCH
P MgH2
PCH
(km/s)
(km/s)
(km/s)
(km/s)
(km/s)
(GPa)
(GPa)
(g/cm3)
13.30 ± 0.22
14.37 ± 0.45
14.10 ± 0.21
8.48 ± 0.09
8.86 ± 0.09
150 ± 19
130 ± 2
3.03 ± 0.44
MgH2
MgH2
top half of the target, respectively. The shock breakout time as a function of position at the target were found by looking for 50% point of the VISAR intensity change on the leading edge.
MgH2
shock velocity of the MgH2 sample and the time-resolved shock velocity of the quartz reference were measured within uncertainties of a few percent, resulting in the measured Hugoniot data of 150 GPa and 2.5fold density compression (i.e., 3.1 g/cm3). In future experiments, we expect to improve the precision of the shock pressure and density (currently 12.7% and 14.3% uncertainties, respectively) by improving the initial density measurements of the MgH2 samples. This work demonstrates the possibility of Hugoniot measurements toward the understanding of the equation-of-state and phase diagram of MgH2 and other similar materials.
3. Results and discussion Fig. 1 (c) shows a raw VISAR image. Time proceeds from the left to the right. The shock arrival times t1 to t3 are denoted by arrows. The shock transit time for the MgH2 layer (Δt = t3 − t2) was determined after accounting for the calibration data of sweep nonlinearity of the streak camera. Here, Δt was 3.83 ± 0.07 ns, and consequently the mean shock velocity UsMgH2 was 13.83 ± 0.32 km/s. Using this mean velocity, a time-resolved velocity at the t2 was estimated considering the unsteadiness of the shock in the MgH2, because correct application of the impedance-mismatching condition requires that UsQz (t2 ) and MgH Us 2 (t2 ) be determined at breakout from the quartz-MgH2 interface. MgH MgH Determining Us 2 (t2 ) requires estimation of the time history, Us 2 (t). This can be achieved using the UsCH (t) measured directly by the VISAR measurement, given that the same pressure source drives both materials in parallel. Since MgH2 and CH have such similar impedances, to a good MgH approximation Us 2 (t) âUsMgH2 = UsCH (t)ãâ aUsCH , provided the average for both materials is taken over the same time period the step MgH transit time in this case [20]. Finally, the corrected Us 2 (t2 ) was 14.37 ± 0.32 km/s. Fig. 1 (d) shows the velocity record extracted from the bottom half of the VISAR image (corresponding to the target bottom half). From the velocity record, the time-resolved quartz shock velocity at t2, just before the shock arrival to the Qz/MgH2 interface, was determined to be UsQz = 13.30 ± 0.22 km/s. The impedance mismatching analysis was performed using these MgH time-resolved shock velocities, Us 2 and UsQz . The states of quartz was inferred from the measured quartz shock velocity and a quartz Hugoniot and release model established by Knudson et al., [18,19]. MgH Finally, the obtained particle velocity and pressure of MgH2 were up 2 MgH 2 = 8.48 ± 0.09 km/s and P = 150 ± 19 GPa, respectively. Fig. 2 shows the diagram of the impedance mismatching analysis for determining the MgH2 Hugoniot. The impedance mismatching occurs at the intersection of a MgH2 Rayleigh line (solid straight line with the MgH slope, 0 Us 2 ) and the release adiabat of quartz (dotted line) from the inferred quartz Hugoniot point (solid triangle). The measured MgH2 Hugoniot is represented by the solid circle with the uncertainty. The solid square represents the Hugoniot of CH witness determined from the impedance mismatching analysis in the same shot. Table 2 summarized the experimental data of quartz, polystyrene, and MgH2. Our CH data is in very good agreement with the available experimental data [21–24] and the well-known EOS model (SESAME 7952) [25]. Although this method is already able to produce good data for the MgH2 Hugoniot, we expect that the precision can be improved in future experiments. The uncertainty in the condition reached is mainly due to that of the sample initial density, and so by fabricating larger samples, the uncertainty of the initial density could be improved by a factor of two or more.
Acknowledgment The laser-shock experiments were conducted under the joint research project of the Institute of Laser Engineering, Osaka University. The authors would like to thank Y. Kimura and H. Hosokawa at the Osaka University for the sample preparation, S. Kubo for the sample metrological characterization, Y. Seto at the Kobe Univerisity for fruitful comments on the sample fabrication, N. J. Hartley for help preparing the manuscript, and all of the technical staffs of the GXII laser facility for their support for the experiments. This work was supported in part by KAKENHI (grant nos. 16H02246) from Japan Society for the Promotion of Science (JSPS), and by the Genesis Research Institute, Inc. (Konpon-ken, TOYOTA). References [1] W.J. Nellis, Rep. Prog. Phys. 69 (2006) 1479. [2] N.W. Ashcroft, Phys. Rev. Lett. 92 (2004) 187002. [3] A.P. Drozdov, M.I. Eremets, I.A. Troyan, V. Ksenofontov, S.I. Shylin, Nature 525 (2015) 73. [4] M. Einaga, M. Sakata, T. Ishikawa, K. Shimizu, M.I. Eremets, A.P. Drozdov, I.A. Troyan, N. Hirao, Y. Ohishi, Nat. Phys. 12 (2016) 835. [5] L. Zhang, Y. Wang, T. Cui, Y. Li, Y. Li, Z. He, Y. Ma, G. Zou, Phys. Rev. B 75 (2007) 144109. [6] S. Cui, W. Feng, H. Hu, Z. Feng, Y. Wang, Solid State Commun. 148 (2008) 403. [7] D.Y. Kim, R.H. Scheicher, R. Ahuja, Phys. Rev. Lett. 103 (2009) 077002. [8] C. Zhang, X.J. Chen, R.Q. Zhang, H.Q. Lin, J. Phys. Chem. C 114 (2010) 14614. [9] E.L.P. y Blanca and R. del P.N. Maldonado, Eur. Phys. J. B 87, 2014, 110. [10] M. Durandurdu, EPL 105 (2014) 46001. [11] Y.B. Zeldovich, Y.P. Raizer, Physics of Shock Waves and High-Temperature Hydrodynamic Phenomena, Academic Press, 1966. [12] P.M. Celliers, Rev. Sci. Instrum. 75 (2004) 4916. [13] U. Wietelmann, Hydride, in: B. Elvers, et al. (Ed.), Encyclopedia of Industrial Chemistry, 2016. [14] P.M. Celliers, et al., Phys. Rev. Lett. 104 (2010) 184503. [15] N. Ozaki, Phys. Plasmas 11 (2004) 1600. [16] N. Ozaki, Phys. Plasmas 16 (2009) 062702. [17] N. Ozaki, Sci. Rep. 6 (2016) 26000. [18] M.D. Knudson, M.P. Desjarlais, Phys. Rev. Lett. 118 (2017) 035501. [19] M.P. Desjarlais, M.D. Knudson, K.R. Cochrane, J. Appl. Phys. 122 (2017) 035903. [20] D.G. Hicks, T.R. Boehly, P.M. Celliers, J.H. Eggert, E. Vianello, D.D. Meyerhofer, G.W. Collins, Phys. Plasmas 12 (2005) 082702. [21] I.P. Dudoladov, V.I. Rakitin, Y.N. Sutulov, G.S. Telegin, Prikl. Mekh. Tekh. Fiz. 4 (1969) 148. [22] R.G. McQueen, S.P. Marsh, J.W. Taylor, J.N. Fritz, W.J. Carter, The equation of state of solids from shock wave studies, in: R. Kinslow (Ed.), High Velocity Impact Phenomena, Academic Press, 1970, pp. 293–417. [23] A.V. Bushman, M.V. Zhernokletov, I.V. Lomonosov, Y.N. Sutulov, V.E. Fortov, K.V. Khishchenko, JETP 82 (1996) 895. [24] M.A. Barrios, D.G. Hicks, T.R. Boehly, D.E. Fratanduono, J.H. Eggert, P.M. Celliers, G.W. Collins, D.D. Meyerhofer, Phys. Plasmas 17 (2010) 056307. [25] S.P. Lyon, J.D. Johnson, Los Alamos National Laboratory report no. LA-CP-98-100, 1998. [26] The original CH data from the different papers are plotted. if the data are reanalyzed using the latest EOS model of quartz[18,19], the plots move slightly and systematically to the lower left of the diagram.
4. Summary In summary, we have presented the first EOS measurement for magnesium hydride under laser-driven shock compression. The mean 3