We determine the strength of laser shock-compressed polycrystalline diamond at stresses above the Hugoniot elastic limit using a technique combining x-ray diffraction from the Linac Coherent Light Source with velocity interferometry. X-ray diffraction is used to measure lattice strains, and velocity interferometry is used to infer shock and particle velocities. These measurements, combined with density-dependent elastic constants calculated using density functional theory, enable determination of material strength above the Hugoniot elastic limit. Our results indicate that diamond retains approximately 20 GPa of strength at longitudinal stresses of 150–300 GPa under shock compression.

Diamond is a remarkable material with many unique properties including high strength and high thermal conductivity. The behavior of diamond under extreme conditions is an important topic for understanding the structure and properties of planetary bodies,1–5 static high-pressure materials science,6,7 and shock design for inertial confinement fusion experiments.8,9 For example, diamond's high strength, high mechanical impedance, and broad optical transparency make it an ideal window in shock and ramp compression experiments10 and for pre-compression and reverberating shock wave compression platforms11,12 to study material properties. However, its behavior above the elastic limit is largely unknown, and its observed elastic–inelastic response under shock compression13 makes it unique among brittle materials, which typically exhibit a significant loss of strength above the elastic limit.14 The dynamic response of diamond has been studied under both ramp compression15,16 and shock compression at17,18 and above13 the Hugoniot elastic limit (HEL) using wave profile analysis to measure the equation of state (EOS) and infer dynamic strength.

Shear strength provides a fundamental description of a material's mechanical behavior during dynamic compression, and it plays an essential role in the material's equation of state (EOS). There are several techniques from which strength or flow stress can be inferred from dynamically compressed materials. These methods include x-ray diffraction (XRD),19–21 radiography of Rayleigh Taylor growth in ramp compression,22,23 ramp release,24 and extended x-ray absorption fine structure.10 Besides XRD, all these approaches have a significant dependence on physical models and often also rely on hydrodynamic simulations. X-ray diffraction is unique among these approaches in that the strain anisotropy induced in the crystal lattice by strength is directly measured.

Under shock compression, the HEL is the applied stress at which failure begins. For applied stresses below the HEL, the material compresses uniaxially and no permanent deformation occurs. Applied stresses above the HEL result in material failure, where the stress state relaxes toward hydrostatic compression. This relaxation is typically either ductile-like, where uniaxial stress is dissipated by plastic flow, brittle, where stress is dissipated by fracture, or results in a phase transformation where stress dissipation occurs by atomic rearrangement.25 The stress profile of materials exhibiting strength above the HEL is a mixture of hydrostatic (isotropic) and deviatoric (anisotropic) stresses, where the deviatoric component is a function of the strength of the material. Diamond, like many other materials with large initial strength, exhibits a brittle response at ambient conditions; however, a plastic response has also been observed under shock compression.13 Characterizing the dynamic strength is important for accurate determination of the high-pressure stress state and density but is experimentally challenging. While efforts have been made to develop strength models for diamond,26 progress has been limited by uncertainty in the nature of failure in shocked diamond.

In this Letter, we demonstrate a technique to determine the material strength of diamond under laser shock compression up to stresses of 300 GPa. We calculate dynamic material strength by combining direct lattice strain measurements from XRD, wave profile measurements from velocity interferometry (VISAR), and ab initio calculations of elastic constants using density functional theory (DFT). While each individual measurement cannot rule out complete loss of strength, our collection of data consistently shows a residual strength of approximately 20 GPa at longitudinal stresses of 150–300 GPa. Furthermore, future experiments using this method could significantly reduce the uncertainty in these measurements by probing more crystallites to improve diffraction statistics by increasing the probe volume using a larger drive laser and x-ray probe spot sizes or using a sample with a smaller average initial grain size.

The experiments were conducted at the Matter in Extreme Conditions (MEC) end-station of the Linac Coherent Light Source (LCLS).27,28Figure 1 shows a schematic of the experimental setup. Two Nd:glass lasers, frequency-doubled to a wavelength of 527 nm, were overlapped on the target using 150 μm phase plates to drive a locally planar shock into the sample. The combined beams delivered a laser energy of up to 25 J in a 10 ns square pulse, producing a maximum intensity of 1.5×1013 W/cm2. To ensure the spatial overlap of the drive beams with respect to the x-ray free electron laser (XFEL) on each shot, we utilized line imaging VISAR to measure the position, spatial extent, and planarity of the two wave fronts (elastic and plastic) entering and exiting the diamond layer.

FIG. 1.

Experimental geometry showing the orientation of the three CSPAD detectors and the VISAR beam. The upper left inset shows the target specification and beam diameters drawn to scale. An example VISAR image is shown in the bottom-right inset with the free-surface velocities inferred from the two VISAR cameras with clear signatures of the elastic and plastic waves.

FIG. 1.

Experimental geometry showing the orientation of the three CSPAD detectors and the VISAR beam. The upper left inset shows the target specification and beam diameters drawn to scale. An example VISAR image is shown in the bottom-right inset with the free-surface velocities inferred from the two VISAR cameras with clear signatures of the elastic and plastic waves.

Close modal

The nominal target design is shown in the upper-left inset of Fig. 1, consisting of 40-μm-thick polycrystalline diamond foils, a 100 nm Al layer to provide a reflecting surface for the VISAR probe, and a 25-μm-thick Mylar ablator. The polycrystalline diamond samples were optical grade, synthetic type IIa diamond foils obtained from Applied Diamond Inc. prepared via chemical vapor deposition (CVD) with an initial density of 3.5 g/cm3. Electron backscatter diffraction measurements of the diamond foils showed no preferred texture in the samples with observed grain sizes of 1–10 μm. The Mylar ablator reduced the high-frequency spatial structure in the laser drive created by the phase plates before the shock entered the diamond sample, improving drive uniformity.

The compressed sample was probed using the LCLS XFEL operating in self-amplified spontaneous emission (SASE) mode to provide ∼2 mJ of 10 keV x-rays in 50 fs pulses with a full width at half maximum spectral bandwidth of 50 eV (0.5%). Compound refractive lenses focused the x-rays to a 10 μm diameter at the sample plane. Cornell-SLAC Pixel Array Detectors (CSPADs)29,30 detected scattered x-rays over the range 2θ = 25° to 100° in a transmission geometry at azimuthal angles of ϕ=60° to ϕ=170°, where θ is the Bragg angle and ϕ is the azimuthal angle around the diffraction ring with ϕ=0 in the horizontal plane. The CSPADs recorded XRD from the {111}, {220}, and {311} planes in diamond, as shown in Fig. 1. Background emission produced by the ablation plasma was attenuated by 100 μm of Al filtering on each CSPAD.

Line-imaging VISAR measured shock timing and free-surface velocity profiles on each shot. The bottom-right inset of Fig. 1 shows example VISAR data and calculated free-surface velocity profiles from each VISAR streak camera and the three timing measurements (t0, t1, and t2). At t0, the shock enters the diamond layer, changing the dominant reflecting surface from the first Al layer to the rear surface of the diamond. The diamond has a lower reflectivity than Al, reducing the contrast of the interference fringes observed at t0. The elastic wave reaches the rear surface at t1, accelerating the surface and causing a fringe shift. Finally, the plastic wave reaches the rear surface at t2, creating a release wave resulting in a reduction in reflectivity of the free surface. From each VISAR image, we measure t0, t1, and t2, and the free surface velocities after the elastic and plastic waves break out of the rear surface (ufs1 and ufs2, respectively).

Following the Rankine–Hugoniot shock relations, the conditions across a shock front are related by

σz,f=σz,i+ρi(Dui)(ufui),
(1)
ρf=ρiDuiDuf,
(2)

where σz is the stress in the shock direction, ρ is the density, D is the shock velocity, u is the particle velocity, and the subscripts i and f denote the initial and final states. Here, the subscript 0 refers to the unshocked state, 1 refers to the conditions in the elastic phase, and 2 refers to the plastic phase.

The elastic shock velocity is measured directly using the shock transit time (t1t0). The particle velocity in the elastic wave is assumed to be equal to half the free surface velocity, u1=uf1/2.13,31,32 To account for the reflection of the elastic wave at the rear surface of the diamond, corrections were applied to the plastic wave velocity measurements following the treatment of Ahrens et al.33 The thickness of the diamond layer was thin to minimize the uncertainty created by shock reverberations at the rear surface. The uncertainty resulting from wave interactions with the rear surface in VISAR measurements becomes large for shocks just above the HEL, where the plastic wave velocity is significantly slower than that of the elastic precursor.

Previous studies have reported ufs2/u2 between 1.2 and 1.7 for single crystal diamond samples,13,34 while the reported values for the two studies do not agree for the same orientation. In these experiments, we did not have impedance matching standards to measure this quantity directly, so we use ufs2/u2=1.45±0.25 to include the full range of reported values for diamond in our error analysis.

For XRD analysis, we work in the Voigt (iso-strain) limit, which assumes that all crystallites in the material are subjected to a single strain tensor in the laboratory frame. In a previous study,35 we showed that diffraction from polycrystalline diamond in the Voigt and Reuss (iso-stress) limits gives nearly identical results at these conditions. In the case of uniaxial compression with the probe at angle χ=30° with respect to the target normal, the diffraction condition is given by36 

λ2d02=23(αx2αz2)cosϕsin3θcosθ+(αx2+3αz2)sin4θ+[14(3αx2+αz2)cos2ϕ+αx2sin2ϕ]sin22θ,
(3)

where αi=1εii is the deformation in the i direction, εij is a component of the applied strain tensor, λ is the x-ray probe wavelength, and d0 is the uncompressed plane spacing. For χ>0, the strength of the material results in variations in 2θ with the azimuthal position due to the anisotropic strain in the sample. In order to measure diffraction from both shocked diamond and uncompressed diamond, the FEL pulse delay was set to be at least 0.5 ns before the elastic wave reached the rear surface of the diamond.

We observe diffraction from both uncompressed crystallites in the unshocked material and larger diffraction spots at increased 2θ from the plastically deformed region, as shown in Fig. 2. A small number of diffraction spots from the aluminum target mount are also present and are treated as the background. For each shot, the locations of diffraction spots in 2θ-ϕ space from {111}, {220}, and {311} were measured by fitting the centroid of each spot. Figure 2 shows XRD data from a single shot with the measured XRD peak locations marked in red. The diffraction spots from the plastic phase are significantly brighter than the unshocked diffraction spots due to the disorder in the crystallites introduced by deformation and heating. The increased disorder broadens the rocking curve of the crystallites, resulting in diffraction from a much larger fraction of the probe spectrum. Two diffraction spots in the {111} data had to be excluded from the fitting due to detector saturation, as noted in Fig. 2.

FIG. 2.

Single shot XRD data in 2θ-ϕ space with measured diffraction spot locations (red crosses), the best Voigt fit (solid blue line), uncertainty bounds (shaded), and the diffraction angle for uncompressed planes (dashed). Two diffraction spots in the {111} data were excluded from the fit due to detector saturation.

FIG. 2.

Single shot XRD data in 2θ-ϕ space with measured diffraction spot locations (red crosses), the best Voigt fit (solid blue line), uncertainty bounds (shaded), and the diffraction angle for uncompressed planes (dashed). Two diffraction spots in the {111} data were excluded from the fit due to detector saturation.

Close modal

Longitudinal and transverse strains were varied to find the best fit value using diffraction peaks from all three lattice planes simultaneously, and the error was determined using least squares fitting analysis. The best fit diffraction line and error bound for the fit in Fig. 2 are shown in blue, corresponding to εzz=0.123±0.046 and εxx=0.085±0.004. To further constrain the strain data, we restrict the reported strains to values that are consistent with the measurement of longitudinal stress, σzz, from the VISAR diagnostic. The resulting strains are shown in Fig. 3 with the shaded regions corresponding to the uncertainty in the combined XRD and VISAR measurements. The measurement in orange is highlighted to show the strains calculated from XRD only and the reduced region of strain space consistent with both XRD and VISAR measurements. As expected, the constraint on longitudinal strain provided by VISAR is limited at lower compression where wave interactions between the reflected elastic precursor and the plastic wave become significant.

FIG. 3.

Calculated strains for shock-compressed diamond. The shaded regions for each data point correspond to the strains satisfying both the XRD fit and the longitudinal stress measured by VISAR. The measurement in orange shows the improvement provided by including VISAR to constrain the possible states.

FIG. 3.

Calculated strains for shock-compressed diamond. The shaded regions for each data point correspond to the strains satisfying both the XRD fit and the longitudinal stress measured by VISAR. The measurement in orange shows the improvement provided by including VISAR to constrain the possible states.

Close modal

The stress tensor in the laboratory frame can be decomposed into a hydrostatic term (mean pressure, σh) and a traceless term, known as the deviatoric stress tensor,

σ=(σxx000σxx000σzz)=σh+(t/3000t/30002t/3),
(4)

where the parameter t is the uniaxial stress component.37 Above the HEL, the residual strength in the material is given by t, the difference in stress between the longitudinal and transverse directions. The strain tensor is defined in a similar way, separating the tensor into hydrostatic and deviatoric terms and replacing σh and t with hydrostatic and deviatoric strains, εh and εd, respectively.

The strength is calculated directly from the measured strains, ϵxx and εzz, and elastic constants calculated using DFT. The elastic constants were calculated as a function of material density to account for nonlinear effects due to stiffening of the lattice under compression. This allows the deviatoric perturbations about the hydrostatic compression state to be calculated using the generalized form of Hooke's law: σd=C(ρ)εd, where C(ρ) is the elastic stiffness tensor calculated as a function of material density. The details and results of the DFT calculations are published in Ref. 35. For diamond (cubic crystal structure), the deviatoric stresses and strains are related by

(t/3t/32t/3)=(C11C12C12C12C11C12C12C12C11)(εd/3εd/32εd/3),
(5)

where εd=εzzεxx is the deviatoric strain; we have assumed that shear terms are zero. The strength is thus given in terms of the calculated elastic constants and the measured strains by

t=[C11(ρ)C12(ρ)](εzzεxx),
(6)

where the density of the compressed material is calculated using ρ0/ρ=(1εzz)(1εxx)2. Our calculated strength values are shown in Fig. 4(a), applying Eq. (6) to the strain measurements from Fig. 3.

FIG. 4.

(a) Strength, t, calculated using Eq. (6) and the strains reported in Fig. 3. (b) EOS data for diamond from this experiment (blue) and previously reported data, showing the significant improvement in density resolution by combining XRD and VISAR. The shaded regions denote the uncertainty region for each measurement.

FIG. 4.

(a) Strength, t, calculated using Eq. (6) and the strains reported in Fig. 3. (b) EOS data for diamond from this experiment (blue) and previously reported data, showing the significant improvement in density resolution by combining XRD and VISAR. The shaded regions denote the uncertainty region for each measurement.

Close modal

We compare the EOS of diamond calculated from these results to previously reported data in Fig. 4(b) along with the cold curve and Hugoniot for diamond using the Mie–Grüneisen fits as described in Ref. 16. The Hugoniot is fit to data at much higher pressures and does not include strength effects present at these conditions. We therefore use the Hugoniot for the hydrostatic stress component to account for the additional internal energy created by shock compression and calculate the longitudinal stress using σzz=σh+2t/3. We note that the uncertainty in the EOS data using this technique is significantly lower than previous VISAR-only studies due to the added constraint provided by in situ XRD.

In conclusion, the results from this experiment demonstrate a significant improvement in strength determination and EOS measurement resolution that is made possible by combining XRD and VISAR. We demonstrated a method to study the strength of materials above the HEL, which can be applied to other initially transparent materials. Our results consistently show that diamond retains approximately 20 GPa of strength at longitudinal stresses of 150–300 GPa, although individual measurements cannot exclude complete loss of strength. These results provide valuable experimental data to develop improved material strength models for diamond. The accuracy of the strength data can be improved by increased statistical sampling in the diffraction measurements. This can be accomplished by either increasing the probed volume or reducing the grain size in the material, although the latter may affect the strength of the bulk material. Such models will lead to more reliable simulations of inertial confinement fusion implosions and reduced uncertainties in EOS experiments using diamond as ablators and VISAR windows.

This work was supported by DOE Office of Science, Fusion Energy Science, under No. FWP 100182, and is based upon work supported by the National Science Foundation Graduate Research Fellowship Program under Grant No. 2013155705. Use of the Linac Coherent Light Source (LCLS), SLAC National Accelerator Laboratory, is supported by the U.S. Department of Energy (DOE), Office of Science, Office of Basic Energy Sciences under Contract No. DE AC02-76SF00515. The Matter in Extreme Conditions (MEC) instrument of LCLS has additional support from the DOE, Office of Science, Office of Fusion Energy Sciences under Contract No. DE-AC02-76SF00515. This research used resources of the National Energy Research Scientific Computing Center, a DOE Office of Science User Facility supported by the Office of Science of the U.S. Department of Energy under Contract No. DE-AC02-05CH11231. This work was supported by the U.S. DOE under Grant Nos. DE-NA0001859 and DE-NA0002956 and performed under the auspices of the U.S. DOE by the Lawrence Livermore National Laboratory under Contract No. DE-AC52-07NA27344. E. E. McBride acknowledges funding from the Volkswagen Foundation.

The data that support the findings of this study are available from the corresponding author upon reasonable request. Document released as LLNL-JRNL-809384.

1.
M.
Ross
,
Nature
292
,
435
436
(
1981
).
2.
W. B.
Hubbard
,
Science
214
,
145
149
(
1981
).
3.
L. R.
Benedetti
,
J. H.
Nguyen
,
W. A.
Caldwell
,
H.
Liu
,
M.
Kruger
, and
R.
Jeanloz
,
Science
286
,
100
102
(
1999
).
4.
A.
Roberge
,
P. D.
Feldman
,
A. J.
Weinberger
,
M.
Deleuil
, and
J. C.
Bouret
,
Nature
441
,
724
726
(
2006
).
5.
D.
Kraus
,
J.
Vorberger
,
A.
Pak
,
N.
Hartley
,
L.
Fletcher
,
S.
Frydrych
,
E.
Galtier
,
E.
Gamboa
,
D. O.
Gericke
,
S.
Glenzer
,
E.
Granados
,
M.
MacDonald
,
A.
MacKinnon
,
E.
McBride
,
I.
Nam
,
P.
Neumayer
,
M.
Roth
,
A. M.
Saunders
,
A.
Schuster
,
P.
Sun
,
T.
van Driel
,
T.
Döppner
, and
R.
Falcone
,
Nat. Astron.
1
,
606
611
(
2017
).
6.
J. J.
Zhao
,
S.
Scandolo
,
J.
Kohanoff
,
G. L.
Chiarotti
, and
E.
Tosatti
,
Appl. Phys. Lett.
75
,
487
488
(
1999
).
7.
H.
Chacham
and
L.
Kleinman
,
Phys. Rev. Lett.
85
,
4904
4907
(
2000
).
8.
A. J.
Mackinnon
,
N. B.
Meezan
,
J. S.
Ross
,
S. L.
Pape
,
L.
Berzak Hopkins
,
L.
Divol
,
D.
Ho
,
J.
Milovich
,
A.
Pak
,
J.
Ralph
,
T.
Döppner
,
P. K.
Patel
,
C.
Thomas
,
R.
Tommasini
,
S.
Haan
,
A. G.
Macphee
,
J.
McNaney
,
J.
Caggiano
,
R.
Hatarik
,
R.
Bionta
,
T.
Ma
,
B.
Spears
,
J. R.
Rygg
,
L. R.
Benedetti
,
R. P.
Town
,
D. K.
Bradley
,
E. L.
Dewald
,
D.
Fittinghoff
,
O. S.
Jones
,
H. R.
Robey
,
J. D.
Moody
,
S.
Khan
,
D. A.
Callahan
,
A.
Hamza
,
J.
Biener
,
P. M.
Celliers
,
D. G.
Braun
,
D. J.
Erskine
,
S. T.
Prisbrey
,
R. J.
Wallace
,
B.
Kozioziemski
,
R.
Dylla-Spears
,
J.
Sater
,
G.
Collins
,
E.
Storm
,
W.
Hsing
,
O.
Landen
,
J. L.
Atherton
,
J. D.
Lindl
,
M. J.
Edwards
,
J. A.
Frenje
,
M.
Gatu-Johnson
,
C. K.
Li
,
R.
Petrasso
,
H.
Rinderknecht
,
M.
Rosenberg
,
F. H.
Séguin
,
A.
Zylstra
,
J. P.
Knauer
,
G.
Grim
,
N.
Guler
,
F.
Merrill
,
R.
Olson
,
G. A.
Kyrala
,
J. D.
Kilkenny
,
A.
Nikroo
,
K.
Moreno
,
D. E.
Hoover
,
C.
Wild
, and
E.
Werner
,
Phys. Plasmas
21
,
056318
(
2014
).
9.
S. L.
Pape
,
L. F.
Berzak Hopkins
,
L.
Divol
,
A.
Pak
,
E. L.
Dewald
,
S.
Bhandarkar
,
L. R.
Bennedetti
,
T.
Bunn
,
J.
Biener
,
J.
Crippen
,
D.
Casey
,
D.
Edgell
,
D. N.
Fittinghoff
,
M.
Gatu-Johnson
,
C.
Goyon
,
S.
Haan
,
R.
Hatarik
,
M.
Havre
,
D. D.
Ho
,
N.
Izumi
,
J.
Jaquez
,
S. F.
Khan
,
G. A.
Kyrala
,
T.
Ma
,
A. J.
Mackinnon
,
A. G.
Macphee
,
B. J.
Macgowan
,
N. B.
Meezan
,
J.
Milovich
,
M.
Millot
,
P.
Michel
,
S. R.
Nagel
,
A.
Nikroo
,
P.
Patel
,
J.
Ralph
,
J. S.
Ross
,
N. G.
Rice
,
D.
Strozzi
,
M.
Stadermann
,
P.
Volegov
,
C.
Yeamans
,
C.
Weber
,
C.
Wild
,
D.
Callahan
, and
O. A.
Hurricane
,
Phys. Rev. Lett.
120
,
245003
(
2018
).
10.
Y.
Ping
,
F.
Coppari
,
D. G.
Hicks
,
B.
Yaakobi
,
D. E.
Fratanduono
,
S.
Hamel
,
J. H.
Eggert
,
J. R.
Rygg
,
R. F.
Smith
,
D. C.
Swift
,
D. G.
Braun
,
T. R.
Boehly
, and
G. W.
Collins
,
Phys. Rev. Lett.
111
,
065501
(
2013
).
11.
P.
Loubeyre
,
P. M.
Celliers
,
D. G.
Hicks
,
E.
Henry
,
A.
Dewaele
,
J.
Pasley
,
J.
Eggert
,
M.
Koenig
,
F.
Occelli
,
K. M.
Lee
,
R.
Jeanloz
,
D.
Neely
,
A.
Benuzzi-Mounaix
,
D.
Bradley
,
M.
Bastea
,
S.
Moon
, and
G. W.
Collins
,
High Pressure Res.
24
,
25
31
(
2004
).
12.
R.
Jeanloz
,
P. M.
Celliers
,
G. W.
Collins
,
J. H.
Eggert
,
K. K. M.
Lee
,
R. S.
McWilliams
,
S.
Brygoo
, and
P.
Loubeyre
,
Proc. Natl. Acad. Sci. U. S. A.
104
,
9172
9177
(
2007
).
13.
R. S.
McWilliams
,
J. H.
Eggert
,
D. G.
Hicks
,
D. K.
Bradley
,
P. M.
Celliers
,
D. K.
Spaulding
,
T. R.
Boehly
,
G. W.
Collins
, and
R.
Jeanloz
,
Phys. Rev. B
81
,
014111
(
2010
).
14.
D. E.
Grady
,
J. Geophys. Res.
85
,
913
, (
1980
).
15.
D. K.
Bradley
,
J. H.
Eggert
,
R. F.
Smith
,
S. T.
Prisbrey
,
D. G.
Hicks
,
D. G.
Braun
,
J.
Biener
,
A. V.
Hamza
,
R. E.
Rudd
, and
G. W.
Collins
,
Phys. Rev. Lett.
102
,
075503
(
2009
).
16.
R. F.
Smith
,
J. H.
Eggert
,
R.
Jeanloz
,
T. S.
Duffy
,
D. G.
Braun
,
J. R.
Patterson
,
R. E.
Rudd
,
J.
Biener
,
A. E.
Lazicki
,
A. V.
Hamza
,
J.
Wang
,
T.
Braun
,
L. X.
Benedict
,
P. M.
Celliers
, and
G. W.
Collins
,
Nature
511
,
330
333
(
2014
).
17.
J. M.
Lang
and
Y. M.
Gupta
,
J. Appl. Phys.
107
,
113538
(
2010
).
18.
J. M.
Lang
,
J. M.
Winey
, and
Y. M.
Gupta
,
Phys. Rev. B
97
,
104106
(
2018
).
19.
A. K.
Singh
,
C.
Balasingh
,
H-K
Mao
,
R. J.
Hemley
, and
J.
Shu
,
J. Appl. Phys.
83
,
7567
7575
(
1998
).
20.
S.
Merkel
,
J. Phys.: Condens. Matter
18
,
S949
S962
(
2006
).
21.
A. J.
Comley
,
B. R.
Maddox
,
R. E.
Rudd
,
S. T.
Prisbrey
,
J. A.
Hawreliak
,
D. A.
Orlikowski
,
S. C.
Peterson
,
J. H.
Satcher
,
A. J.
Elsholz
,
H.-S.
Park
,
B. A.
Remington
,
N.
Bazin
,
J. M.
Foster
,
P.
Graham
,
N.
Park
,
P. A.
Rosen
,
S. R.
Rothman
,
A.
Higginbotham
,
M.
Suggit
, and
J. S.
Wark
,
Phys. Rev. Lett.
113
,
115501
(
2014
).
22.
H.-S.
Park
,
R. E.
Rudd
,
R. M.
Cavallo
,
N. R.
Barton
,
A.
Arsenlis
,
J. L.
Belof
,
K. J. M.
Blobaum
,
B. S.
El-dasher
,
J. N.
Florando
,
C. M.
Huntington
,
B. R.
Maddox
,
M. J.
May
,
C.
Plechaty
,
S. T.
Prisbrey
,
B. A.
Remington
,
R. J.
Wallace
,
C. E.
Wehrenberg
,
M. J.
Wilson
,
A. J.
Comley
,
E.
Giraldez
,
A.
Nikroo
,
M.
Farrell
,
G.
Randall
, and
G. T.
Gray
,
Phys. Rev. Lett.
114
,
065502
(
2015
).
23.
A.
Krygier
,
P. D.
Powell
,
J. M.
McNaney
,
C. M.
Huntington
,
S. T.
Prisbrey
,
B. A.
Remington
,
R. E.
Rudd
,
D. C.
Swift
,
C. E.
Wehrenberg
,
A.
Arsenlis
,
H.-S.
Park
,
P.
Graham
,
E.
Gumbrell
,
M. P.
Hill
,
A. J.
Comley
, and
S. D.
Rothman
,
Phys. Rev. Lett.
123
,
205701
(
2019
).
24.
J. L.
Brown
,
C. S.
Alexander
,
J. R.
Asay
,
T. J.
Vogler
, and
J. L.
Ding
,
J. Appl. Phys.
114
,
223518
(
2013
).
25.
E. E.
McBride
,
A.
Krygier
,
A.
Ehnes
,
E.
Galtier
,
M.
Harmand
,
Z.
Zonopkova
,
H. J.
Lee
,
H.-P.
Liermann
,
B.
Nagler
,
A.
Pelka
,
M.
Röedl
,
A.
Schropp
,
R. F.
Smith
,
C.
Spindloe
,
D.
Swift
,
F.
Tavella
,
S.
Toleikis
,
T.
Tschentscher
,
J. S.
Wark
, and
A.
Higginbotham
,
Nat. Phys.
15
,
89
(
2019
).
26.
D.
Orlikowski
,
A. A.
Correa
,
E.
Schwegler
, and
J. E.
Klepeis
,
AIP Conf. Proc.
955
,
247
250
(
2007
).
27.
B.
Nagler
,
B.
Arnold
,
G.
Bouchard
,
R. F.
Boyce
,
R. M.
Boyce
,
A.
Callen
,
M.
Campell
,
R.
Curiel
,
E.
Galtier
,
J.
Garofoli
,
E.
Granados
,
J.
Hastings
,
G.
Hays
,
P.
Heimann
,
R. W.
Lee
,
D.
Milathianaki
,
L.
Plummer
,
A.
Schropp
,
A.
Wallace
,
M.
Welch
,
W.
White
,
Z.
Xing
,
J.
Yin
,
J.
Young
,
U.
Zastrau
, and
H. J.
Lee
,
J. Synchrotron Radiat.
22
,
520
525
(
2015
).
28.
S. H.
Glenzer
,
L. B.
Fletcher
,
E.
Galtier
,
B.
Nagler
,
R.
Alonso-Mori
,
B.
Barbrel
,
S. B.
Brown
,
D. A.
Chapman
,
Z.
Chen
,
C. B.
Curry
,
F.
Fiuza
,
E.
Gamboa
,
M.
Gauthier
,
D. O.
Gericke
,
A.
Gleason
,
S.
Goede
,
E.
Granados
,
P.
Heimann
,
J.
Kim
,
D.
Kraus
,
M. J.
MacDonald
,
A. J.
Mackinnon
,
R.
Mishra
,
A.
Ravasio
,
C.
Roedel
,
P.
Sperling
,
W.
Schumaker
,
Y. Y.
Tsui
,
J.
Vorberger
,
U.
Zastrau
,
A.
Fry
,
W. E.
White
,
J. B.
Hasting
, and
H. J.
Lee
,
J. Phys. B
49
,
092001
(
2016
).
29.
P.
Hart
,
S.
Boutet
,
G.
Carini
,
M.
Dubrovin
,
B.
Duda
,
D.
Fritz
,
G.
Haller
,
R.
Herbst
,
S.
Herrmann
,
C.
Kenney
,
N.
Kurita
,
H.
Lemke
,
M.
Messerschmidt
,
M.
Nordby
,
J.
Pines
,
D.
Schafer
,
M.
Swift
,
M.
Weaver
,
G.
Williams
,
D.
Zhu
,
N.
van Bakel
, and
J.
Morse
,
Proc. SPIE
8504
,
85040C
(
2012
).
30.
S.
Herrmann
,
S.
Boutet
,
B.
Duda
,
D.
Fritz
,
G.
Haller
,
P.
Hart
,
R.
Herbst
,
C.
Kenney
,
H.
Lemke
,
M.
Messerschmidt
,
J.
Pines
,
A.
Robert
,
M.
Sikorski
, and
G.
Williams
,
Nucl. Instrum. Methods Phys. Res., Sect. A
718
,
550
553
(
2013
).
31.
J. M.
Walsh
and
R. H.
Christian
,
Phys. Rev.
97
,
1544
1556
(
1955
).
32.
J.
Wackerle
, “
Shock-wave compression of quartz
,”
J. Appl. Phys.
33
,
922
937
(
1962
).
33.
T. J.
Ahrens
,
W. H.
Gust
, and
E. B.
Royce
,
J. Appl. Phys.
39
,
4610
4616
(
1968
).
34.
K.-I.
Kondo
and
T. J.
Ahrens
,
Geophys. Res. Lett.
10
,
281
284
, (
1983
).
35.
M. J.
MacDonald
,
J.
Vorberger
,
E. J.
Gamboa
,
R. P.
Drake
,
S. H.
Glenzer
, and
L. B.
Fletcher
,
J. Appl. Phys.
119
,
215902
(
2016
).
36.
A.
Higginbotham
and
D.
McGonegle
,
J. Appl. Phys.
115
,
174906
(
2014
).
37.
A. K.
Singh
,
J. Appl. Phys.
73
,
4278
4286
(
1993
).