PHYSICAL REVIEW MATERIALS
7
, 073601 (2023)
Real-time characterization of dislocation slip and twinning of shock-compressed
molybdenum single crystals
Vatsa Gandhi
,
1
,
*
Suraj Ravindran
,
2
Akshay Joshi
,
3
and Guruswami Ravichandran
1
,
4
1
Division of Engineering and Applied Science, California Institute of Technology, Pasadena, California 91125, USA
2
Department of Aerospace Engineering and Mechanics, University of Minnesota, Minneapolis, Minnesota 55455, USA
3
Engineering Department, Cambridge University, Cambridge CB2 1PZ, United Kingdom
4
Jio Institute, Ulwe, Navi Mumbai, Maharashtra 410206, India
(Received 24 January 2023; revised 12 May 2023; accepted 12 June 2023; published 6 July 2023)
Characterizing the fundamental micromechanisms activated during plastic deformation is critical to explain
the macroscopic shock response of materials and develop accurate material models. In this paper, we investigate
the orientation dependence, and the mediated slip and twin systems on [1 0 0] and [1 1 1] bcc molybdenum
single crystals shock compressed up to 18 GPa with real-time Laue x-ray diffraction measurements. We report
that dislocation slip along the
{
110
}
111
and
{
112
}
111
systems is the governing deformation mechanism
during compression with negligible anisotropy observed at the Hugoniot state. We provide real-time evidence
that molybdenum undergoes deformation twinning along
{
11
2
}
111
during shock release.
DOI:
10.1103/PhysRevMaterials.7.073601
I. INTRODUCTION
When a metal undergoes shock compression beyond its
Hugoniot elastic limit (HEL), the plastic deformation is typi-
cally governed by generation and motion of dislocations [
1
].
Generally, establishing the active atomistic mechanisms dur-
ing inelastic loading is difficult but is critical to explain the
macroscopic response of materials for shock applications in-
volving high-velocity impacts such as planetary impacts [
2
],
aircraft collisions [
3
], spacecraft shielding [
4
], and even ar-
mor and antiarmor applications [
5
]. The high strain rates,
temperatures, and pressures experienced under shock com-
pression may activate different slip or twin systems than under
quasistatic loading and thus require real-time characterization
of the atomistics. However, most studies to date focus on
postmortem analysis of recovered samples which may not
reflect the material behavior during the passage of the shock
wave. To that end, recent efforts at the Dynamic Compression
Sector (DCS) at the Advanced Photon Source (APS) [
6
]have
enabled real-time x-ray diffraction (XRD) measurements in
shock compression experiments and have been critical in un-
derstanding phenomena such as phase transformations [
7
,
8
]
and equations of state [
9
–
11
].
Because of its high-temperature specific strength, creep
resistance, and ductility [
12
], body-centered cubic (bcc) re-
fractory metals, such as molybdenum (Mo), and their alloys
have significant technological implications motivating study-
ing their high-strain-rate material response. Plasticity in bcc
metals is governed by dislocation slip along the [1 1 1] di-
rection [
13
] and is mediated by various factors such as
interactions of defects with grain boundaries, the influence of
preexisting defects, and crystal structure [
14
]. Here, we focus
*
vgandhi@caltech.edu
on molybdenum single crystals as a representative refractory
bcc metal since single crystals help preclude the effect of
grain boundaries on the deformation response and provide key
insights concerning the role of crystal orientation.
Considerable work has been conducted to understand the
fundamental deformation mechanisms of molybdenum in the
quasistatic regime and it has been shown that its deforma-
tion is governed by the mobility of screw dislocations along
the
{
110
}
111
and
{
112
}
111
slip systems. At low tem-
peratures, the deformation of molybdenum is governed by
thermally activated kink pairs and kink pair migration of
screw dislocations along
{
110
}
slip planes [
15
–
17
] while at
higher temperatures, the deformation is governed by cross
slip along
{
112
}
planes [
15
]. Molybdenum also displays slip
and yield tension-compression asymmetry due to the differ-
ent Peirels stress in the twinning and antitwinning [
16
,
18
–
21
] direction, where the twinning is more prevalent at lower
temperatures [
18
,
22
]. In addition to slip, deformation twin-
ning in the
{
112
}
planes along the
111
direction [
23
,
24
]
has been observed from postmortem analysis of molybde-
num undergoing shock compression (high strain rate) or
low-temperature deformation. It was shown that the volume
fraction of twinning increases with pressure [
24
] while homo-
geneous distribution of initial dislocations from pre-straining
prior to shock compression suppressed twin formation [
23
].
Regardless, further experiments are required to understand
these deformation mechanisms.
Polycrystalline Mo has been studied over a wide range
of high pressures (up to 1 TPa) using diamond anvil cell
(DAC) [
25
], plate impact [
26
,
27
], and laser ramp com-
pression [
28
] experiments. However, limited plate impact
experimental studies have been performed on Mo single crys-
tals [
29
–
33
]. Studies by Mandal
et al.
[
30
,
31
] at low normal
stresses (12.5 GPa) and Oniyama
etal.
[
32
] at higher pressures
(up to 110 GPa) both report strong orientation dependence
2475-9953/2023/7(7)/073601(7)
073601-1
©2023 American Physical Society
VATSA GANDHI
et al.
PHYSICAL REVIEW MATERIALS
7
, 073601 (2023)
TABLE I. Material properties of single-crystal molybdenum [
32
].
Orientation
ρ
(kg
/
m
3
)
C
L
(m
/
s)
C
s
(m
/
s)
a
0
(Å)
V
c
(Å
3
)
[1 0 0]
6836
±
44
3300
±
14
[1 1 0]
10220
±
60
6432
±
3
3264
±
4
3.147
31.1616
[1 1 1]
6319
±
8
3666
±
5
on the Hugoniot elastic limit (HEL) [
30
–
32
]. The [111]
orientation was shown to exhibit the highest elastic ampli-
tude which increases proportionally to the impact stress [
32
]
while the behaviors along [1 0 0] and [1 1 0] were compa-
rable. Additionally, the authors observed attenuation of the
elastic precursor as a function of time and propagation dis-
tance hypothesizing a change in active slip systems during
this transition [
31
]. To explore the fundamental mechanisms
governing this observed anisotropy, Mandal
et al.
[
30
,
31
]
performed complementary crystal plasticity simulations but
suggested that
in situ
experiments be performed.
In this paper, we explore the underlying microstructural
reasons for the anisotropy of HEL, and the governing plastic
deformation mechanisms at the Hugoniot (steady) shock state
and during release using plate impact experiments coupled
with dynamic
in situ
x-ray diffraction (XRD). The experi-
mental observations are quantified using complimentary XRD
simulations for extracting the lattice strains and stresses using
which the active slip and twin deformation mechanisms are
characterized.
II. MATERIALS AND METHODS
Plate impact experiments were conducted on high-purity
(99.99%) molybdenum single crystals oriented along the
[1 0 0] and [1 1 1] directions at DCS. The ambient properties
of the single crystals are displayed in Table
I
. The material was
procured from Accumet Materials Co. (Ossining, New York)
as a 20 mm diameter cylindrical stock and powder diffraction
was conducted at Caltech to quantify the misalignment of
the crystallographic orientation. If the misalignment exceeded
2
◦
, the stock was cut into cylindrical disks at an angle to
correct the misorientation. The Mo stock was cut to disks after
which they were lapped flat on both sides and polished on
one surface for
in situ
XRD measurements. Because the sam-
ples underwent this additional processing, powder diffraction
was once again conducted on the [1 0 0] and [1 1 1] crystals
which confirmed that the samples remained as an ideal single
crystal. The diffraction data are presented in the Supplemental
Material (SM) [
34
].
A front surface impact configuration with reflection geom-
etry XRD was implemented for the plate impact experiments
at DCS [Fig.
1(a)
]. Here, a 2.5–4 mm thick molybdenum
single crystal is impacted onto a
∼
1
.
5 mm polycarbonate
window target at velocities ranging from 1800–2800 m
/
s
corresponding to elastic normal stresses of 8–19 GPa. The
polycarbonate window limits the achievable stresses in the
experiment to below 22 GPa due to the x-ray transparency
issues at higher pressures. Regardless, this configuration was
implemented rather than using the molybdenum as a target
with a window attached to its rear because the high impedance
of molybdenum requires a high impedance window such as
c-cut sapphire. In addition, the thickness of the sapphire win-
dow required to hold the pressure would result in x-rays being
fully absorbed at the experimental incidence angle. The exper-
iments were conducted using the powder and two-stage light
gas guns in Sector 35-Hutch E of the DCS using the 24-bunch
mode with 153.4 ns x-ray interspacing and
∼
100 ps expo-
sure time [
6
]. The white x-ray beam was generated using an
FIG. 1. (a) Schematic of the front surface plate impact and re-
flection geometry XRD configuration and (b) distance-time (
x-t
)
diagram indicating the designed XRD frame capture times. Here,
time
t
=
0 corresponds to the impact time and the first XRD
frame, not illustrated, is designed to be obtained prior to impact at
t
=−
100 ns.
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PHYSICAL REVIEW MATERIALS
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undulator with a 17.2 mm period (24 keV, 1st harmonic) and
focused to a beam size of 100
×
800 μm. The reflection ge-
ometry was conducted at an x-ray-to-gun angle of
θ
g
=
10–11
degrees using a four-camera detector array with 120 mm fiber
taper. These four charge-coupled device (CCD) cameras were
perfectly synchronized with the synchrotron x-ray bunches
using a delay generator and each camera was gated to capture
one frame during the experiment [
6
,
35
]. A polychromatic
x-ray spectrum is necessary since the dynamic experiments
were conducted at a constant inclination angle (
θ
g
); thus, to
obtain diffraction spots for varying
d
spacings, the wavelength
must vary according to Bragg’s law. The spectral scans of the
x-rays of the 24-bunch mode for the different APS cycles are
displayed in the SM.
The polycarbonate targets are attached to an aluminum tar-
get holder which houses a target optical beam block (TOBB)
system. Here, a laser is illuminated from one end of the target
holder using a fiber optic probe and is captured by a receiver
probe on the other end. Due to the impact event and the
x-ray event being completely independent, the events must be
synchronized to ensure the proper frames are captured during
an experiment. Given a desired projectile velocity, desired
first-frame time with respect to impact, and known distance
between the TOBB laser and impact surface, the necessary
delays are calculated and applied to synchronize first-frame
capture. Once the projectile crosses the TOBB laser, a series
of oscilloscopes and delay generators are triggered and initiate
diagnostics. Note that perfect synchronization between the
impact event and APS electron bunch structure is impossible;
thus, the actual first-frame capture can vary up to 153.4 ns.
This means if the desired first frame is
−
100 ns prior to
impact, even with the exact desired impact velocity, the first-
frame capture will occur between
t
=−
100 and 53.4 ns. As
a result, any fluctuation from the desired impact velocity can
affect the frame capture sequence [
36
].
As stated earlier, four XRD frames were obtained in each
experiment spaced 153.4 ns apart. The front surface impact
experiments were designed such that the first frame was ob-
tained before impact (
t
=−
100 ns) to calibrate the Laue
diffraction spots due to potential rotation of the projectile as
it traverses the barrel. The last three frames are obtained at
the Hugoniot state to understand the time-dependent response
of the material from the movement of diffraction spots. At the
pressures of interest (8–19 GPa), an overdriven wave traverses
the polycarbonate sample and thus, with the current design for
frame capture times, for the higher velocity experiments, only
frames 2 and 3 capture the Hugoniot state. The 4th frame cap-
tures the release behavior of the molybdenum which provides
important information on the elastic unloading behavior of
the crystals. Additionally, due to uncertainties in gun powder
explosion, the actual impact velocities deviated slightly from
the desired values and thus, in some experiments, the first
frame was captured immediately after impact resulting in the
4th frame capturing the release behavior even for lower pres-
sure experiments. This late impact complicates the analysis of
the diffraction spots and introduces uncertainties in the lattice
strain calculations. The experimental design is illustrated in
the time-distance (
x-t
) diagram in Fig.
1(b)
. Here, time
t
=
0
corresponds to the impact time and the first XRD frame, not il-
lustrated, is designed to be obtained at
t
=−
100 ns. Evolution
of the Laue spots from the XRD measurements were analyzed
by simulating the experimental conditions in MATLAB [
37
]
to extract the lattice strains and stresses for both single-crystal
orientations. This requires knowledge of the detector dis-
tances which were obtained using a polycrystalline silicon
standard prior to every shot and the diffraction pattern was
analyzed using a combination of Dioptas software [
38
] and
in-house polycrystalline XRD simulations. The full details of
the silicon calibration is described in the SM.
In addition to the x-rays, macroscopic laser interfer-
ometry measurements, using photonic Doppler velocimetry
(PDV) [
39
], were conducted simultaneously to link the micro-
scopic and continuum response of the single crystals. Because
the polycarbonate is transparent, an aluminum mirror, in the
shape of a semicircle, was vapor deposited (150 nm thickness)
onto the impact surface of the window as shown in Fig.
1(a)
and in-material measurements were conducted through the
polycarbonate. A total of three PDV probes were utilized in
each experiment where one probe was placed in the trans-
parent region looking down the barrel to measure the impact
velocity while the other two probes were placed on the de-
posited region. Here, one probe was placed at the center of
the sample to measure the in-material particle velocity and
the other probe was slightly offset from the center. The repre-
sentative velocity profiles are illustrated in Figs.
2(i)
and
2(j)
.
The velocity profiles of all experiments are plotted in the
Supplemental Material.
III. SIMULATION
As stated earlier, four XRD frames were captured during
each experiment which contain information on the atomistic
deformation of Mo single crystals. The representative diffrac-
tion spots for molybdenum shocked at
∼
10 GPa and
∼
20 GPa
on are shown in Fig.
2
. During the shocked state, since the ma-
terial undergoes compression, the crystallographic
d
spacing
tends to decrease resulting in the spots shifting to higher az-
imuthal angles based on Bragg’s law. This is illustrated in the
diffraction data in Fig.
2(b)
. The radial and azimuthal shifts of
the Laue spots contain information on the elastic lattice strains
and rotations in the material. However, to quantify the atom-
istic deformation, the diffraction spots must first be indexed.
This is done using Laue simulations in MATLAB [
37
].
Prior to indexing the spots, the x-ray and detector geometry
were determined using silicon calibration discussed earlier.
This provides information on the detector distance from the
sample, the location on the detector at which the x-ray beam is
incident, and the detector center. Using these parameters, the
x-ray wavelength spectrum, and the known orientation of the
sample (another axis beyond the sample normal) from powder
diffraction conducted during sample preparation, the allow-
able x-ray diffracted wave vectors
k
are determined using the
methodology outlined in Sec. III of the SM. These vectors are
projected onto a simulated detector screen and compared to
the experimental diffraction spots. Note that the direction of
the alternate axis is marked on the sample and the projectile
is placed in the barrel along this orientation. However, since
the projectile is allowed to rotate as it traverses the barrel, the
actual crystal orientation is unknown during the experiment.
Thus, if the simulation and experimental spots do not match,
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PHYSICAL REVIEW MATERIALS
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, 073601 (2023)
FIG. 2. (a)–(d) Experimentally obtained XRD frames which show both spots shifting due to compression and deformation twinning at
higher pressure during the unloading. The diffraction spots are labeled using (e)–(h) for the respective XRD simulations incorporating both
compression and twinning behavior. (i)–(j) The interferometry data are also shown indicating the time instances of XRD frame captures.
the sample is rotated in simulation along its outward normal
and the procedure is repeated until the diffraction spots match
experimental results.
Once these spots have been indexed, the lattice strains
and stresses can be determined from the observed shifts in
experimental diffraction spots. It can be shown that the am-
bient scattering vector
g
hkl
in the reciprocal space is related
to the scattering vector of the deformed lattices,
g
d
hkl
, through
the deformation gradient (
F
),
g
d
hkl
=
F
−
T
g
hkl
[
40
]. However,
the deformation gradient has nine unknowns but each ex-
periment does not contain enough information to resolve all
nine components. Since each experiment typically contains
two to four diffraction spots and plate impact experiments are
conducted under uniaxial strain conditions, an infinitesimal
strain (
ε
) linearization (
F
=
I
+
ε
) and plane strain assump-
tion was employed to uniquely determine the elastic strain
tensor. This was done through an optimization problem where
the objective function was
O
=
min
F
−
T
(
M
∑
i
=
1
N
∑
n
=
1
∥
∥
F
−
T
k
n
−
ˆ
k
n
∥
∥
F
−
T
k
n
+
k
n
0
(
λ
n
i
)
∥
∥
+
k
n
0
(
λ
n
i
)
∥
∥
)
.
(1)
Here, the incident vector
k
0
for a given wavelength
λ
i
is
known. Additionally, the scattering vector,
k
=
g
hkl
, and the
direction of the diffracted vectors
ˆ
k
from back projecting each
indexed diffraction spot to the sample location are known.
Thus, the goal is to determine the deformation gradient
F
that
minimizes the objective function from Eq. (
1
). Details of the
XRD simulation methodology and validation can be found in
Secs. III and IV of the SM, respectively.
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FIG. 3. Resolved shear stress (
τ
rss
) along the 12 different
{
110
}
111
and
{
112
}
111
slip systems of bcc single crystal for orientations
[1 0 0] and [1 1 1] molybdenum crystals at pressures ranging from 10–20 GPa. Only the data above the critical resolved shear stresses (dashed
lines) are shown.
IV. RESULTS
XRD simulations were conducted for all experiments from
which we propose that the shock compression behavior of
molybdenum single crystals is governed by dislocation slip
regardless of crystal orientation and impact stress. To fur-
ther investigate this observation, the resolved shear stresses
along the
{
110
}
111
and
{
112
}
111
slip systems were
calculated and plotted in Fig.
3
. It is apparent that both
these systems are active at the Hugoniot state for the two
orientations where the
{
110
}
111
contributes to slip in the
antitwinning sense and
{
112
}
111
in the twinning. Addi-
tionally, the resolved shear stress magnitudes are similar for
both orientations with the
{
11
2
}
111
system being the most
active. This explains the consistent peak Hugoniot velocity
observed from the continuum measurements for both orien-
tations for the same impact velocity and matches previous
work by Oniyama
et al.
[
33
]. They reported that the shock
velocity–particle velocity (
U
s
-
u
p
) equations of state for the
different molybdenum crystal orientations were very similar
to within experimental uncertainty, similarly to previous liter-
ature on fcc metals such as copper [
41
] and aluminum [
42
].
This implies that while single crystals exhibit orientation de-
pendence at the elastic limit, no anisotropy may be present for
the Hugoniot response of cubic crystals.
While the experiments in this study probed the diffrac-
tion spot evolution at the Hugoniot state, using the resolved
stresses in Fig.
3
, we anticipate the anisotropy at the elas-
tic limit could stem from the larger number of slip systems
activated for [1 0 0] orientation seen for the lowest stress ex-
periment (
∼
9 GPa) which are the closest to the elastic limit of
the two orientations. An alternate possibility is related to the
cubic symmetry of the stiffness tensor. For example, consider
a uniaxial elastic strain of 1% for both the [1 0 0] and [1 1 1]
single crystals. The maximum and minimum principal stress
for the [1 0 0] is 466 MPa and 163 MPa respectively whereas
for [1 1 1] it is 410 MPa and 191 MPa. This clearly implies
that the shear stresses along the [1 0 0] orientation will be
larger due to the anisotropy in the stiffness tensor and thus
justifies the observed lower elastic limit than for the [1 1 1]
orientation. Using this argument, the previous anisotropy in
the elastic limit is justified as the lattice strains obtained for
these experiments on [1 0 0] and [1 1 1] molybdenum were
comparable at similar pressures. Thus, larger shear strains
were present for the [1 0 0] crystals than the [1 1 1] and this
is illustrated in Fig.
3
.
At the highest pressures (
>
16 GPa), during unloading, new
diffraction spots were observed along with preexisting spots
splitting up. An example of this is shown in Fig.
2(d)
.This
indicates that deformation twinning, which has been previ-
ously observed for shock-compressed molybdenum [
23
,
24
],
possibly governs the unloading behavior of Mo single crystals
similar to what was observed for magnesium [
43
]. To deter-
mine the relevant twin systems, an additional contribution to
the deformation gradient from twinning,
F
t
, was incorporated
in the simulations such that
F
t
=
I
+
γ
ˆ
b
⊗
ˆ
n
. Here,
I
is the
identity tensor,
γ
=
1
√
2
is the twinning shear magnitude [
44
],
and
ˆ
n
and
ˆ
b
are the twin plane normal and the twinning
shear direction, respectively. The simulated diffraction with
twinning is shown in Fig.
2(h)
. By iterating through all the
possible
{
112
}
111
systems from Fig.
3
, it was determined
that twinning in both [1 0 0] and [1 1 1] molybdenum always
occurred along the
{
11
2
}
111
system. This is consistent
with the largest resolved shear stress observed along this sys-
tem for all crystal orientations (Fig.
3
).
073601-5
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PHYSICAL REVIEW MATERIALS
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Before discussing the possible mechanisms contributing to
deformation twinning, it is important to note that the inten-
sities of these new spots are weak but still easily discernible
from ambient noise. This is expected because a partial con-
structive interference could still occur if atomic locations
deviate slightly from their exact crystal structure, which satis-
fies the Laue condition. Furthermore, due to the abrupt nature
of a shock wave and the isentropic release, the atomic arrange-
ment undergoes a possible rearrangement across coherently
diffracting domains. This affects the observed diffraction in-
tensities and results in a mosaic spread that matches the
smearing of the diffraction spots observed in the experiments.
These weak intensity diffraction spots were also present in the
work by Turneaure
et al.
[
43
], who also observed deformation
twinning upon release in hexagonal close-packed magnesium.
Additionally, while twinning is rather complex and results in
multiple twin systems being activated, it is possible that these
multiple systems are present in our experiments but at a very
low volume fraction such that they get masked by ambient
noise and cannot be distinguished. Nonetheless, the data pro-
vide strong evidence regarding possible twinning occurring
during the release.
Multiple factors contribute to the nucleation and prop-
agation of deformation twinning in bcc crystals such as
pressure, strain rate, pre-straining, and grain size. Here, the
Mo are single crystals and hence the grain size
d
can be
assumed to be infinite. Thus, by the Hall-Petch scaling relation
d
−
1
/
2
[
14
,
44
,
45
], larger grain sizes correspond to lower twin-
ning shear stress. It was previously determined, using DFT
calculations [
46
,
47
], that a shear stress of 1.4 GPa is sufficient
to nucleate twins. While the magnitude of resolved shear
stress along the
{
11
2
}
111
system is beyond this critical
value during compression, here, twinning only occurs dur-
ing shock release. During unloading, the macroscopic normal
stress decreases faster than the lateral stresses which results
in a reverse yielding. Additionally, during release, the shear
stress along the
{
11
2
}
111
system reverses in direction.
Since twinning is polarized [
44
] unlike slip, the reversal in
direction due to unloading is critical to induce the nucleation
of twins.
The passage of the compressive shock wave contributes to
pre-straining and produces homogeneous nucleation of dislo-
cations [
44
,
45
]. Earlier work on shock-compressed molybde-
num and postmortem TEM analysis by Mahajan
et al.
[
23
]
demonstrated that homogeneous dislocation field and pre-
straining suppresses the formation of twins. However, during
unloading, dislocation annihilation tends to occur [
14
,
45
] po-
tentially generating a heterogeneous distribution similar to
what Mahajan
et al.
[
23
] observed in their shock-recovered
samples. With regard to pre-straining, Christian
et al.
[
44
]
claim that the amount of pre-straining required to suppress
twinning depends on the strain rate. Since the strain rates
during release in our experiments are lower than during com-
pression but still beyond 10
5
s
−
1
, this may be sufficient to
reduce the effect of pre-compression due to the shock wave.
Additionally, based on the experiments conducted here, both
shock and release behaviors of molybdenum at lower pressure
are primarily governed by dislocation slip; however, the criti-
cal pressure describing the slip-to-twin transition [
45
] occurs
around 16 GPa. This is much lower than the transition pres-
sure for [0 0 1] copper [
45
] possibly due to the higher stacking
fault energies in fcc metals. On the contrary, previous work
by Wongwiwat
et al.
[
24
] and Mahajan
et al.
[
23
] observed
twinning at lower pressures for polycrystalline Mo based on
recovered samples possibly due to higher deviatoric stresses
from grain-boundary interactions. This is consistent with what
is observed for iron single crystals where the critical stress
to induce phase transformation was lower for polycrystalline
iron due to generally higher deviatoric stresses present than
[1 0 0] iron [
48
].
V. CONCLUSION
In summary, plate impact experiments with real-time x-ray
diffraction were conducted to characterize the deformation
mechanisms governing the elastic-plastic compression of
molybdenum single crystals. We observe that the shock com-
pression and release behavior is dominated by dislocation slip
along
{
110
}
111
and
{
112
}
111
slip systems for both
[1 0 0] and [1 1 1] crystal orientations. However, at normal
stresses beyond 16 GPa,
{
11
2
}
111
twins are nucleated
during unloading. This explains why the loading orientation
does not effect the Hugoniot response and the anisotropy
only affects the elastic-plastic transition. Future works will
aim to explore the shock-and-release behaviors at higher
stress, at varying strain rates, and at varying pulse duration
to better characterize the mechanisms contributing to the on-
set of twinning and understand its role on material strength.
Additionally, exploring the role of grain boundaries on the
elastic-to-plastic transition and the shock-release behavior
would be an interesting next step.
ACKNOWLEDGMENTS
The authors gratefully acknowledge the support of
DOE
/
NNSA Award No. DE-NA0003957. The authors
also thank Zev Lovinger, James Hawreliak, Paulo Rigg,
Stefan Turneaure, Pritha Reganathan, Adam Schumann,
and the DCS staff for their help with designing, con-
ducting, and processing the experiments. This publi-
cation is based on work performed at the Dynamic
Compression Sector, which is operated by Washington
State University under the U.S. Department of Energy
(DOE)
/
National Nuclear Security Administration Award
No. DE-NA0003957. This research used resources of the
Advanced Photon Source, a DOE Office of Science User Fa-
cility operated for the DOE Office of Science by Argonne Na-
tional Laboratory under Contract No. DE-AC02-06CH11357.
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