of 10
Article
https://doi.org/10.1038/s41467-022-35647-x
Deformation characteristics of solid-state
benzeneasasteptowardsunderstanding
planetary geology
Wenxin Zhang
1,8
, Xuan Zhang
2,8
, Bryce W. Edwards
1
, Lei Zhong
3
,
Huajian Gao
3,4,5
, Michael J. Malaska
6
, Robert Hodyss
6
& Julia R. Greer
1,7
Small organic molecules, like ethane and benzene, are ubiquitous in the
atmosphere and surface of Saturn
s largest moon Titan, forming plains, dunes,
canyons, and other surface features. Understanding Titan
s dynamic geology
and designing future landing missions requires suf
fi
cient knowledge of the
mechanical characteristics of these soli
d-state organic minerals, which is cur-
rently lacking. To understand the defor
mation and mechanical properties of a
representative solid organic material
at space-relevant temperatures, we
freeze liquid micro-droplets of benzene to form ~10
μ
m-tall single-crystalline
pyramids and uniaxially compress t
hem in situ. These micromechanical
experiments reveal contact pressures decaying from ~2 to ~0.5 GPa after ~1
μ
m-
reduction in pyramid height. The deformation occurs via a series of stochastic
(~5-30 nm) displacement bursts, corresponding to densi
fi
cation and stiffening
of the compressed material during cyc
lic loading to progressively higher
loads. Molecular dynamics simulations
reveal predominantly plastic defor-
mation and densi
fi
ed region formation by the re-o
rientation and interplanar
shear of benzene rings, providing a two-
step stiffening mechanism. This work
demonstrates the feasibili
ty of in-situ cryogenic nanomechanical character-
ization of solid organics as a pathway to
gain insights into the geophysics of
planetary bodies.
Simple organic molecules
e.g., ethane
1
and benzene
2
exist in gas and
liquid phases in Earth
s atmosphere and surface. These molecules are
also found to be ubiquitous on another planetary body in the solar
system,Titan,thelargestmoonofSaturn
3
.TheCassini
Huygens
mission
two spacecrafts, one for orbiting Saturn, the other for landing
on Titan
has revealed that Titan
s thick nitrogen and methane-rich
atmosphere enabled dynamic weather, precipitation, and surface
liquids. Many eolian, pluvial, and
fl
uvial geological processes, similar to
Earth
s, have been observed on Titan to produce rivers, canyons, lakes,
and dunes
4
. At the average temperature of ~94 K, Titan
s
hydrology
and landforms consist not of liquid water and silicates, but pre-
dominantly liquid methane and a mixture of water ice and solid
organics that originated through complex photochemical processes in
the upper atmosphere
5
.
Equipped with instruments including the radio detection and
ranging instrument (RADAR) and visual and infrared mapping
Received: 22 February 2022
Accepted: 15 December 2022
Check for updates
1
Division of Engineering and Applied Sciences, California Institute of Technology, 1200 E. California Blvd, Pasadena, CA 91125, USA.
2
INM
Leibniz Institute for
New Materials, Campus D2 2, 66123 Saarbrücken, Germany.
3
School of Engineering, Brown University, Providence, RI 02912, USA.
4
School of Mechanical and
Aerospace Engineering, College of Engineering, Nanyang Technological University, 70 Nanyang Drive, 639798 Singapore, Singapore.
5
Institute of High
Performance Computing, A*STAR, 138632 Singapore, Singapore.
6
Jet Propulsion Laboratory, California Institute of Technology, 4800 Oak Grove Drive,
Pasadena, CA 91109, USA.
7
Kavli Nanoscience Institute, California Institute of Technology, 1200 E. California Blvd, Pasadena, CA 91125, USA.
8
These authors
contributed equally Wenxin Zhang, Xuan Zhang.
e-mail:
wzhang2@caltech.edu
Nature Communications
| (2022) 13:7949
1
1234567890():,;
1234567890():,;
spectrometer (VIMS), Cassini
Huygens mapped the surface mor-
phology of Titan, whose hazy organic atmosphere hinders visual-based
observation of the surface. Titan
ssurfacewasidenti
fi
ed as being
composed of multiple components, including 14% of hummocky/
mountainous terrains, which are the oldest on Titan, and 17% of dunes
which are relatively young
6
8
. Infrared spectral analysis
9
and micro-
wave radiometry
10
reveal the dunes to be comprised of organic
materials. Limited data has led to the formulation of multiple com-
peting theories to explain the fundamental mineralogy and geology of
Titan. From dune sand transport distances
11
,
12
, eolian
13
and
fl
uvial
14
erosion, karst
15
and yardang
16
formation, to putative cryovolcanic
processes
17
, many distinguishing mechanisms of these processes are
dictated by the largely unexplored fundamental mechanical properties
of the frozen organic minerals.
Photochemical models have predicted the formation of benzene
in Titan atmosphere
18
and through a chemical transformation from
acetylene in dunes
19
. Single-crystalline benzene (as well as its co-
crystals with ethane
3
, acetonitrile
20
, and acetylene
21
, etc.) has been
proposed as a potential proxy candidate of the Titan surface
mineralogy
5
. Various solid benzene derivatives have demonstrated
intriguing mechanical properties. For example, tens-of-micron-wide
crystalline hexachlorobenzene exhibits ~360° bending with a local
radius of curvature comparable to the width while retaining its mac-
roscopic integrity, presumably enabled by anisotropic supramolecular
interactions
22
. Existing studies on solid benzene include high-pressure
solid phases of benzene
23
25
, high-pressure high-temperature equation
of state calculations
26
and phase diagram maps
27
, superconductivity of
solid benzene under high pressure
28
, stress-induced amorphization
29
,
and polymerization of benzene into carbon nanothreads
30
. However,
the basic mechanical properties and deformation mechanism of ben-
zene (and of other molecular proxies) in the solid state and at space-
relevant temperatures remain open questions and hinder further
understanding of the geophysics and surface topographies of Titan
and other cold Solar System bodies.
In this work, we freeze liquid micro-droplets of benzene into
micro-pyramids, perform uniaxial compression in situ, and corrobo-
rate with molecular dynamics simulations, unveiling that crystalline
benzene plastically deforms via benzene rings densi
fi
cation, collective
reorientation, and gliding according to the local shear direction. We
demonstrate the signi
fi
cance of in situ cryogenic nanomechanical
characterizations of solid organics towards insights into planetary
geophysical studies.
Results
Mechanical response of benze
ne microcrystal under in situ
compression
We performed in situ nanomechanical experiments and atomistic
simulations on solid-state benzene microcrystals, as the repre-
sentative solid organic material. To create solid-state samples,
liquid benzene droplets were
fi
rst dispensed from a pipette onto a
standard SEM stub mounted on a liquid nitrogen-cooled cryogenic
sample stage in a scanning electron microscope (SEM) chamber
within a custom-built nanomechanical instrument connected to a
nitrogen-purged glove-bag (Fig.
1
a). The chamber was then imme-
diately closed and pumped to ~10
5
mbar, while the droplets were
fl
ash-frozen on contact with a stage held at ~125 K to form multiple
~10-
μ
m-tall cuboid pyramids (Fig.
1
b
e). The sample stage was then
tilted to align the micro-pyramids to be amenable to uniaxial com-
pression with initial contact at the apex, deforming uniformly
towards the base (Fig.
2
a and Supplementary Movie 1). The pyr-
amidal shape of the benzene crystals is practically a nonstandard
geometry for mechanical measurements (Supplementary Note 8). It
was dif
fi
cult to reshape or control the geometry as it was formed
naturally when the droplets freely fell on the cryogenic stage; still,
we need always keep in mind that the plots of posterior force-
displacement curves and the way for extracting the modulus are not
standard.
Monotonic and cyclical in situ quasi-static micro-compressions on
the individual benzene pyramids were performed at a constant loading
rate of ~50
μ
Ns
1
at ~125
145 K. We prescribed two distinct four-step
loading schedules to each sample: (i) loading to a maximum load of
~1.0
1.2 mN, unloading to ~10% of the maximum load, followed by
reloading to ~90% the maximum load for three cycles (Same-Reload
test, Fig.
2
b and Supplementary Fig. 1) and (ii) loading to an initial load
~25% the same maximum load, unloading, and reloading to ~50, 75, and
100% of the maximum load in the three subsequent cycles (Higher-
Reload test, Fig.
2
c and Supplementary Fig. 1).
Figure
2
a shows that the compressed pyramid was
fl
attened from
the apex, consistent with a maximum displacement of ~1
μ
m, with no
observable deformation in its volume below the deformation front.
The
fl
attened top layer appears brighter in the SEM secondary-electron
contrast, which is consistent with a localized densi
fi
cation-type of
deformation observed in open-pore foams
31
. Figure
2
b, c contains two
representative load/contact pressure versus displacement data of
Same-Reload and Higher-Reload tests, where contact pressure is cal-
culated by dividing the applied load by the contact area (Supplemen-
tary Note 1). Figure
2
b and Supplementary Fig. 2 demonstrate that
during the initial compression on pristine benzene in the Same-Reload
test, the compressive load increased linearly with displacement, and
most of the deformation was permanent, with marginal elastic recov-
ery (~15%) after unloading. The deformation behavior in the three
subsequent cycles were consistent, exhibiting a common stiffness
during reloading and unloading, which suggests that the sequent
deformation within the historical maximum was highly repeatable and
predominantly elastic in both loading and unloading directions. The
contact pressure peaked at ~2 GPa after establishing incipient contact
and then monotonically decayed to ~0.4
0.6 GPa at ~1000-nm dis-
placement with the continuously increasing contact area of the
pyramid.
Another characteristic of the Same-Reload experiments is the
presence of ubiquitous, stochastically distributed, 5
30 nm displace-
ment bursts, marked by arrows over the
fi
rst loading cycle in Fig.
2
b.
Despite the noises from cryogenic system vibrations, the displacement
bursts could be distinguished through multiple thresholds for the
displacement increment between adjacent data points collected at
100 Hz (Supplementary Note 3). In contrast, the displacement bursts
are absent in the second-fourth reloading cycles in the Same-Reload
test, where the deformation was mainly elastic with negligible hyster-
esis over a ~85% lower displacement than that in the
fi
rst cycle. These
observations indicate that the permanent densi
fi
cation-induced
microstructural deformation occurs nearly entirely during the
fi
rst
cycle, with the deformation in subsequent loading cycles restricted to
the previously densi
fi
ed region. Stochastic displacement bursts have
indeed been widely observed in nanomechanical studies of metal,
especially in single-crystalline metallic nano-pillar compression
experiments, where displacement bursts correspond to dislocation
avalanches
32
35
. Post-mortem observations always show well-resolved
slip lines on the pillar surface
as direct evidence of the deformation
mechanism of crystallographic slip via dislocation avalanches. Differ-
ently, we did not observe any slip lines in the deformed solid benzene
pyramids; instead, the pyramids
top was
fl
attened in a continuous
manner, and the side slopes remained mostly unchanged throughout
(Fig.
2
a and Supplementary Movie 1), suggesting densi
fi
cation that is
distinct from the volume-preserving dislocation plasticity in metallic
systems.
Our experiments can be viewed as a reversed classical inden-
tation contact problem where a
fl
at, stiff indenter tip is used to
compress the compliant and deformable benzene pyramids. In the
mechanical model for indentation, a parameter called the reduced
modulus,
E
r
, is used to describe the stiffness contribution from
Article
https://doi.org/10.1038/s41467-022-35647-x
Nature Communications
| (2022) 13:7949
2
both bodies through
1
E
r
=
1

υ
2
1
E
1
+
1

υ
2
2
E
2
ð
1
Þ
where
ν
and
E
represent Poisson
s ratio and Young
s modulus, and
1
and
2
refer to the two bodies. The expression is symmetric
with respect to
1
and
2,
suggesting that
E
r
is insensitive to
which body is more compliant and that classical nanoindentation
theories are appliable to our reversed scenario
36
.Theelastic
indentation mechanics theory predicts a nonlinear load-
displacement relation
36
, while the plasticity events (e.g., the
successive discrete displacement excursions, indicated by the
pop-ins or displacement bursts) interrupt the nonlinear elastic
solution and may explain the linear-like load-displacement rela-
tion in the Same-Reload test. Similar linear loading curves were
widely observed in single-crystalline nanoindentation tests in
metals and small molecules
37
41
.
As for the Higher-Reload tests, we adopt the nomenclature from
soil mechanics, where the preconsolidation (i.e., the historical max-
imum) stress dictates the transition from preceding (elastic) to virgin
(plastic) consolidation (i.e., removal of pore volume)
42
. The benzene
pyramids experienced such tangent stiffness enhancement during
each Higher-Reload reloading cycle (Fig.
2
b, Supplementary Note 2,
and Supplementary Figs. 3, 4) that the elastic compression from each
previous cycle transitions to the onset of plasticity with further load-
ing, and compression then progress into the deeper, undeformed
layers of benzene. This transition is also evident in the scarcity of
displacement bursts during preceding elastic compression and their
emergence during further virgin compression (Fig.
2
d and Supple-
mentary Fig. 5). We observed systematic stiffening in each consecutive
loading of the virgin material during Higher-Reload cycles, with the
average stiffness progressively increasing by half, one-third, and one-
eighth of the previous value, respectively. The increasing stiffness per
cycle
indicating overall nonlinear load-displacement relation
is
consistent with the elastic response of the densi
fi
ed region from
10 μm
200 μm
Nano-
indenter
Pyramidal
Benzene
microcrystals
B
Cu wires
Electron gun
Indenter tip
Transducer
Extension
arm
Nitrogen
environment
High
vacuum
Sample
stage
Benzene crystallites
Indenter tip
Transducer
Extension
arm
Electron gun
LN
2
Dewar
Transfer line
SEM column
Glove bag
Oxygen monitor
Indenter arm
a
b
c
d
e
Benzene
pyramid
Nanoindenter
flat punch
Fig. 1 | Cryogenic in situ nanomechanical experiment. a
Schematic of in situ
freezing of benzene droplet.
b
Schematic of the cryogenic in situ nanomechanical
compression of benzene solid.
c
Picture of the in situ SEM nanomechanics instru-
ment, attached to the glove-bag and connected to the liquid nitrogen cryogenic
cooling system.
d
,
e
SEM images of massive pyramidal benzene crystals and one
zoom-in benzene pyramid with the nanomechanical indenter
fl
at punch above (the
background is shaded, and the indenter and the crystallite are outlined for
eye guide).
Article
https://doi.org/10.1038/s41467-022-35647-x
Nature Communications
| (2022) 13:7949
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