Mechanical properties of stanene under uniaxial and biaxial loading: A moleculardynamics studySatyajit Mojumder, Abdullah Al Amin, and Md Mahbubul Islam Citation: Journal of Applied Physics 118, 124305 (2015); doi: 10.1063/1.4931572 View online: http://dx.doi.org/10.1063/1.4931572 View Table of Contents: http://scitation.aip.org/content/aip/journal/jap/118/12?ver=pdfcov Published by the AIP Publishing Articles you may be interested in Effects of temperature and strain rate on the mechanical properties of silicene J. Appl. Phys. 115, 023519 (2014); 10.1063/1.4861736 Molecular dynamics study on the failure modes of aluminium under decaying shock loading J. Appl. Phys. 113, 163507 (2013); 10.1063/1.4802671 Dynamic mechanical response of magnesium single crystal under compression loading: Experiments, model,and simulations J. Appl. Phys. 109, 103514 (2011); 10.1063/1.3585870 Deformation mechanisms and damage in α -alumina under hypervelocity impact loading J. Appl. Phys. 103, 083508 (2008); 10.1063/1.2891797 Fracture initiation mechanisms in α -alumina under hypervelocity impact Appl. Phys. Lett. 91, 121911 (2007); 10.1063/1.2786865

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Mechanical properties of stanene under uniaxial and biaxial loading:A molecular dynamics study

Satyajit Mojumder,1 Abdullah Al Amin,2 and Md Mahbubul Islam3,a)

1Department of Mechanical Engineering, Bangladesh University of Engineering and Technology, Dhaka 1000,Bangladesh2Department of Mechanical and Aerospace Engineering, Case western Reverse University, Cleveland,Ohio 44106, USA3Department of Mechanical and Nuclear Engineering, The Pennsylvania State University, University Park,Pennsylvania 16802, USA

(Received 14 May 2015; accepted 10 September 2015; published online 23 September 2015)

Stanene, a graphene like two dimensional honeycomb structure of tin has attractive features in

electronics application. In this study, we performed molecular dynamics simulations using

modified embedded atom method potential to investigate mechanical properties of stanene. We

studied the effect of temperature and strain rate on mechanical properties of a-stanene for both uni-

axial and biaxial loading conditions. Our study suggests that with the increasing temperature, both

the fracture strength and strain of the stanene decrease. Uniaxial loading in zigzag direction shows

higher fracture strength and strain compared to the armchair direction, while no noticeable varia-

tion in the mechanical properties is observed for biaxial loading. We also found at a higher loading

rate, material exhibits higher fracture strength and strain. These results will aid further investigation

of stanene as a potential nano-electronics substitute. VC 2015 AIP Publishing LLC.

[http://dx.doi.org/10.1063/1.4931572]

I. INTRODUCTION

Two dimensional (2D) hexagonal array (honeycomb

structure) of carbon, namely, graphene, exhibits numerous

interesting electronic properties, making it promising to be

considered widely in future electronics applications1,2 and bat-

tery electrode materials.3,4 However, the semiconductor appli-

cation becomes limited because of the zero energy gap that

indicates semi-metallic nature of the graphene. Moreover, the

chemical inertness has led the researchers to investigate further

in an attempt to modify the properties by manipulating the

structure of graphene, such as cutting, rolling, forming nano

ribbons, and nano tubes.5–7 Further investigations led the

researchers to experiment with silicene8–12 and germanene13—

2D analogues of silicon and germanium.14–17 Extensive studies

in these materials established their potential to be used in elec-

tronic applications9,12,18–23 as their electrical properties are

possible to alter by electrically and thermally tuning the band

gap.8 In search of a better substitute, researchers continued

their search through other group IV elements24 in the periodic

table, where tin has been reported as one of the promising ele-

ment for electronics applications.25

The 2D structure of the tin layer, called stanene, has been

theoretically predicted as quantum hall insulator26,27 and topo-

logical insulator.28 Also, by incorporating the effective spin-

orbit coupling (SOC),29 an energy gap at Dirac point for free

standing stanene is observed. Analogous to other 2D topologi-

cal insulators that display helical edge states, stanene is good

giant magneto-resistance28 and behaves as a perfect spin fil-

ter.30 The reported 0.10 eV band gap of stanene makes it a

promising alternative to the silicone for electronic

applications.15,27 The other interesting phenomenon includes

the tuning of quantum spin hall (QSH) insulator properties by

chemical functionalization.27 Novel 2D structure of stanene

with dumbbell units also showed QSH insulator properties.25,28

With all these favorable electrical properties, the major chal-

lenge posed is the scalable production of stanene. Researchers

have studied the stability of high buckled 2D tin; however,

fullerene type spherical structures were not observed.31 The

stability of stanene is challenged by the fact that it is compara-

tively heavier than other elements in the group, i.e., carbon, sil-

icon, and germanium. It was reported that sp2 hybridization is

preferred for lighter elements of group IV and sp3 hybridiza-

tion is favorable for the heavier elements like tin.32 In the free-

standing stanene monolayer—sp3 hybridization is observed—

where a weak overlap between neighboring pz orbital resulting

in buckled shape in contrast to sp2 hybridization in graphene-

like planer structure. However, to form a planer structure with

larger pz orbital overlap, charge transfer from the Sn to a sup-

port is necessary to form sp2 hybridization.32 Using first princi-

ples calculations, Nigam et al.32 predicted the growth and

stability of 2D tin structure in presence of Au (111).

Electronic properties of QSH insulator change under de-

formation and mechanical loading. Previously, it was

reported that GaAs films exhibit QSH insulation property

variation under applied tensile strain.33 Also, Modarresi

et al.34 demonstrated that the electronic properties of stanene

are tunable under applied strain. Therefore, the study of me-

chanical properties of stanene under various loading condi-

tions is critical in order to utilize this material in electronic

component design.

Molecular dynamics (MD) has been extensively used to

explore the mechanical properties of various materials.26,34–37

This work aims to investigate mechanical properties of

a)Author to whom correspondence should be addressed. Electronic mail:

mmi122@psu.edu

0021-8979/2015/118(12)/124305/8/$30.00 VC 2015 AIP Publishing LLC118, 124305-1

JOURNAL OF APPLIED PHYSICS 118, 124305 (2015)

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stanene using Modified Embedded Atom Method (MEAM)

potential. Over the last decades, MEAM potential has been

well established in studying material properties.38–40 In this

study, uniaxial and biaxial loadings in both armchair and zig-

zag directions of stanene are investigated at various loading

conditions. We also report the effect of strain rate on the mate-

rial strength, and failure behavior as well as loading rate sensi-

tivity at different temperatures.

II. METHODOLOGY

To perform molecular dynamics simulations, we

employed MEAM potential.41 MEAM potential is a modifi-

cation of embedded atom method, where system energy is a

summation of direct contribution from all atoms. There are

two major energy components in this force field. One is

embedding energy potential and another is pair potential.

The energy terms are expressed as

E ¼X

i

Fi �qið Þ þ1

2

Xi 6¼j

/ij rijð Þ( )

: (1)

Again, the embedding function has the form

Fið�qiÞ ¼ AiE0i �qiln�qi; (2)

where E0i is the sublimation energy, Ai is a parameter that

depends on the element type of atom i, and �qi is the back-

ground electron density.

The pair potential includes the screening effect and

expressed by

/ijðrijÞ ¼ �/ijðrijÞSij; (3)

�/ij rijð Þ ¼1

Zij02E0

i rijð Þ � Fi �qi rijð Þ� �� Fj �qi rijð Þ

� �h i; (4)

where E0i , rij are parameters that depend on element i and j

and Zij0 depends on the structure of reference system. Sij is

the screening function between atom i and j. MEAM

potential parameters used for current simulation are listed in

Table I.

MD simulations for characterizing mechanical behavior

of stanene were carried out using LAMMPS42 software

package. The stanene sheet used for the simulations has a

dimension of 20.50 nm� 20.50 nm and contains 4032 Sn

atoms. Armchair direction of the sheet is along the X axis,

while zigzag direction is in Y axis (Fig. 1). Periodic bound-

ary conditions were considered for the X and Y directions,

while Z direction was set as non-periodic.

Geometries were relaxed using conjugate gradient mini-

mization scheme. Optimized stanene sheet shows out-of-

plane buckling as shown in Fig. 1(c) where the buckling

height is �1.02 A, in excellent agreement with the study per-

formed by Zhu et al.43 Previously, Pei et al.36 utilized

MEAM potential to capture the buckling phenomenon for

silicene. The sp3 hybridization is observed for the stanene

and bond angle between Sn atoms is calculated as 109�.After geometry relaxation, we performed equilibration

simulations at NVE ensemble for 10 ps. NVE simulations

were followed by a pressure equilibration for 50 ps using

NPT ensemble at atmospheric pressure and prescribed tem-

peratures. NPT simulation resulted in reconfiguration in the

stanene sheet. An MD time step of 1.0 fs was used for all the

simulations considered in this study. Under uniform uniaxial

tensile loading condition, simulations were performed at var-

ious strain rates and temperatures. We considered loading

rate of 106, 107, 108, 109 (s�1) and temperature of 100, 150,

200, and 250 K. Each deformation simulations were run until

the failure of stanene sheet. To obtain direction dependent

stress strain curve, uniaxial loading was applied in both arm-

chair and zigzag directions. Atomic stress was calculated

based on the definition of virial stress, which is expressed

as35

rvirial rð Þ ¼ 1

X

Xi

�mi _ui � _ui þ1

2

Xj6¼i

rij � fij

!" #; (5)

TABLE I. MEAM potential parameter used for stanene.41

Ec (eV) r0 (A) a A b (0) b (1) b (2) b (3) t(0) t(1) t(2) t(3)

3.14 1.0 5.09 1.12 5.42 8.0 5.0 6.0 1.0 3.0 5.707 þ0.30

FIG. 1. (a) A typical stanene sheet is

shown along with its loading direction.

(b) A zoom in view of the hexagonal

honeycomb structure of stanene. (c)

Buckle shape of the stanene sheet.

Armchair and zigzag directions of sta-

nene sheet are shown by arrow.

124305-2 Mojumder, Amin, and Islam J. Appl. Phys. 118, 124305 (2015)

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where the summation is over all the atoms occupying the

total volume, mi is the mass of atom i, _ui is the time deriva-

tive which indicates the displacement of atom with respect to

a reference position, rij is the position vector of atom, � is

the cross product, and fij is the interatomic force applied on

atom i by atom j.The atomic stresses are averaged at every 100 time

steps. For uniaxial zigzag loading, the simulation box is

deformed along the Y axis with the prescribed strain rate. In

case of biaxial loading, load was applied both in X and Y

directions simultaneously at a constant strain rate. A thick-

ness of 5.32 A (van der Waals radiusþ buckling height) is

used for volume calculation. The strain rate and temperature

were varied to understand the effect of temperature and load-

ing rate on fracture pattern and strength. It was reported that

phase transition of tin from a- phase to b-phase happens at

286 K.44,45 However, in this manuscript, we limited our

study to a-phase only, while leaving the phase transition and

mechanical characterization of b-phase as a future study.46

III. RESULT AND DISCUSSION

A. Validation of bulk properties

In order to validate the MEAM potential employed in

this study, we calculated bulk modulus and lattice constants

of bulk tin. In this calculation, we considered a 4� 4� 4

unit cell of tin (symmetry group Fd�3m). We applied both

compression and expansion with respect to the equilibrium

volume of the crystal and corresponding strain energies were

calculated at different volume states. Murnaghan equation of

state47,48 is employed to fit the data (Fig. 2) for bulk modulus

and equilibrium lattice parameter calculation.

Data obtained from our calculation and comparisons

with the available literatures are presented in Table II. It is

found that the calculated lattice constants and bulk modulus

agree well with other numerical and experimental studies.

In order to calculate Young’s modulus (YM), we per-

formed deformation simulations for circular and square cross

section of Sn-nanowire. In this simulation, boundary condi-

tion at [1 0 0] direction was set as periodic to mimic

infinitely long nanowire, while other two directions were set

as non-periodic. The stress-strain diagram for the circular

cross section nanowire is presented in Fig. 3. The linear

region of the uniaxial stress-strain curve corresponds to elas-

tic deformation and the gradient of this part is defined as

YM. In this study, YM was calculated using linear regression

on the initial linear portion of the stress-strain curve. Our cal-

culated YM for circular and square cross section nanowire is

39 GPa and 51 GPa which is in good agreement with experi-

mental value of 50 GPa.57

B. Effect of temperature on uniaxial loading

The effect of temperature on the stress strain diagram

for uniaxial loading is represented in Figs. 4 and 5 for the

strain rate of 107 (s�1). Uniaxial loading was applied in arm-

chair (Fig. 4(a)) and zigzag directions (Fig. 4(b)). Figure 4

reveals that temperature has a significant effect in the mate-

rial properties. We found that with the increment of the tem-

perature for both armchair and zigzag directional loadings of

stanene sheet, the ultimate fracture stress reduces. For lower

temperature (100 K), the fracture occurs at about 22% of

strain for zigzag direction. At the same temperature in arm-

chair directional loading, the fracture strain is about 18%.

The zigzag direction of stanene is more resilient to the

applied strain. This can be attributed to the bond orientation

along the loading direction. When strain is applied along the

zigzag direction, the chemical bonds of this direction are not

FIG. 2. Equation of state (EOS) calculation for bulk Sn and fitted data by

Murnaghan equation.

TABLE II. Comparison of the lattice constant and bulk modulus with litera-

ture data.

Lattice constants (A) Bulk modulus (GPa)

Our calculation 6.57 39.0

Other calculation 6.38 (Ref. 45), 6.48,

6.55, 6.40 (Ref. 49),

6.47 (Ref. 50),

6.64 (Ref. 49)

47 (Ref. 45),

42.1 (Ref. 51),

44.7 (Ref. 52),

51.2 (Ref. 53),

45.6 (Ref. 50),

47 (Ref. 54)

Experiment 6.491 (Ref. 55) 53 (Ref. 56)

FIG. 3. Stress-strain behavior of Sn nanowire of round cross section. The

loading is applied in the [1 0 0] direction of the nanowire.

124305-3 Mojumder, Amin, and Islam J. Appl. Phys. 118, 124305 (2015)

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parallel to the loading direction. Hence, the relative increase

in the global strain is not same as the relative increase in the

bond stretch. However, in case of armchair directional load-

ing, some of the bonds are parallel to the loading direction

that contributes to the larger local strain. Therefore, for a

similar amount of applied global strain, bond stretches are

smaller in the zigzag direction than the armchair counterpart.

This allows the zigzag directional loading to withstand more

strain before fracture, resulting in a higher ultimate strain.

For both armchair and zigzag directions at 100 K, the frac-

ture pattern is brittle in nature and no plastic deformation

region was observed when uniaxial tensile load was applied.

Sudden drops in the stress profile can be attributed to the

major atomic rearrangement past the yield point of the sta-

nene sheet.

For higher temperature, the stress strain pattern

remained similar. Higher temperature reduces both the frac-

ture strength and strain. With the temperature rise, the frac-

ture strength and strain in armchair directional loading

reduce significantly compared to the zigzag loading.

At a temperature of 250 K, fracture strain reduces to

12% for armchair direction, while it is about 18% for zigzag

direction. The toughness of the material also decreases with

temperature. Fracture behavior of stanene at 100 K is quite

analogous to its silicon counterparts. For silicene, higher

fracture strain was observed for the zigzag direction.36 For

armchair direction, silicene fails at a strain rate of 25%, cor-

responding fracture strength of 15 GPa, whereas stanene fails

at around 3.30 GPa with a strain of 18%. Therefore, it is evi-

dent that stanene is relatively weaker in terms of mechanical

properties as compared to silicene.36

C. Effect of temperature on biaxial loading

Uniform bi-axial tensile loading was applied on both the

armchair and zigzag directions at various temperatures and

strain rates. Figs. 5(a) and 5(b) represent stress-strain diagram

for armchair and zigzag directions, respectively, at a strain rate

of 107 (s�1). The stress-strain pattern is significantly different

than uniaxial loading. We found a yielding region in case of

biaxial loading. With the increment in temperature, both frac-

ture strength and strain reduce. However, the properties of arm-

chair and zigzag directions are comparable and show minimal

variation. As the loading surpasses 15% of the strain, the stress

increases significantly and shows yielding. When the load is

applied in both directions, it causes two simultaneous forces

working on a bond from two different directions. These acting

forces facilitate bond orientation and causes stress concentra-

tion. As a result, stress increases suddenly and leads to failure

of the material. At higher temperature, bond strength reduces

and the effect is translated into relatively lower fracture strain.

It is observed that stanene exhibits a lower fracture

strength for biaxial loading compared to the uniaxial loading.

The fracture strength for biaxial loading is about 3.0 GPa,

whereas for uniaxial loading, this was found up to 3.5 GPa.

This trend of reduction in materials strength under biaxial

loading is consistent with other 2D material, such as the study

performed on graphene sheet by Song et al.58 A comparison

of Young’s modulus for different temperatures and loadings is

presented in Table III for the strain rate of 107 (s�1). One can

observe that in case of uniaxial loading, stanene mechanical

properties show strong directional dependency, i.e., the prop-

erties in armchair and zigzag directions are noticeably differ-

ent. However, interestingly, under biaxial loading, these

FIG. 4. Stress strain diagram at differ-

ent temperatures for (a) uniaxial arm-

chair and (b) uniaxial zigzag loading at

a strain rate of 107 (s�1). Legend

shows the temperature in Kelvin.

FIG. 5. Stress strain plot for different

temperatures and biaxial loadings at

(a) armchair direction and (b) zigzag

direction at a strain rate of 107 (s�1).

Legend shows the temperature in

Kelvin.

124305-4 Mojumder, Amin, and Islam J. Appl. Phys. 118, 124305 (2015)

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properties become independent of the direction and stanene

possesses more isotropic behavior. Young’s modulus for arm-

chair and zigzag directions is comparable under biaxial load-

ing. The Young’s modulus decreases with temperature for all

loading cases. Similar behavior for YM is noticed in silicene,

however, its YM is higher than stanene.36

D. Effect of loading direction on fracture stress andstrain

In Fig. 6(a), effect of temperature and different loading

conditions on fracture strength is presented. It can be seen

that the fracture strength reduces with the temperature and

follows a general trend for all the loading conditions. The

armchair and zigzag loading directions do not have signifi-

cant effect on fracture strength at low temperature for both

uniaxial and biaxial cases. However, for biaxial loading,

lower fracture strength is always observed. For uniaxial load-

ing at higher temperature, zigzag direction shows higher

fracture strength compared to armchair direction. Stanene

exhibits a noticeable variation in ultimate strain for uniaxial

and zigzag loading. Apparently, stanene fails at a relatively

lower strain under uniaxial loading than the biaxial in the

armchair direction. We observed that the ultimate strains are

comparable for biaxial loading in both armchair and zigzag

directions. However, in case of uniaxial loading, zigzag

direction exhibits higher fracture strain.

In Fig. 7, fracture behavior for uniaxial zigzag loading

at temperature 150 K and strain rate 108 (s�1) is shown. One

can see that atomic stress is distributed over the entire sta-

nene sheet due to the thermal effect caused by the applied

temperature. The fracture pattern is observed to follow typi-

cal failure behavior of 2D materials.36 Fracture initiates via

formation of small fissure in the structure due to the stress

FIG. 7. Fracture behavior for uniaxial

zigzag loading at temperature 150 K

and strain rate 108 (s�1). Color bar

shows atomic stress in GPa. Arrows

indicate loading direction.

FIG. 8. Variation of strain rate on

stress strain curve for (a) uniaxial arm-

chair and (b) uniaxial zigzag loading at

temperature 100 K.

TABLE III. Young’s modulus of stanene at different temperatures and load-

ing conditions for strain rate 107 (s�1).

Temperature (K) 100 K 150 K 200 K 250 K

Uniaxial armchair (GPa) 24.20 23.20 22.20 20.30

Uniaxial zigzag (GPa) 23.80 22.80 21.90 21.70

Biaxial (GPa) 28.10 27.10 26.30 25.30

FIG. 6. (a) Variation of ultimate stress

at different temperatures with different

loading conditions and (b) variation of

ultimate strain at different tempera-

tures with different loading conditions

at a strain rate of 107 (s�1).

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concentration through breaking of Sn-Sn bonds. This nuclea-

tion of crack starts to develop at a strain value of 21%. With

the increasing strain, crack continues to propagate and even-

tually leads to the rupture of the stanene sheet.

E. Effect of strain rate on mechanical properties ofstanene

Finally, we investigated the effect of strain rate on the

strength of the stanene sheet at different temperatures. We

varied the strain rates from 106 to109 (s�1). The influence of

different strain rates on stress strain curve is shown in Fig. 8

for uniaxial loading and in Fig. 9 for biaxial loading at tem-

perature 100 K. For uniaxial zigzag loading, both fracture

stress and strain reduce with the strain rate. At the strain rate

of 109 (s�1), the fracture strain is reduced by �5% as the

strain rate is lowered to 106 (s�1) for both loading directions.

The Young’s modulus is unaffected by the strain rate varia-

tion in the range of 106–109 (s�1).

However, a significant effect of strain rate is observed

for biaxial loading. For biaxial loading at a higher strain rate,

stanene shows double yielding point similar to steel, how-

ever, at lower strain rate, single yielding is observed as

explained before in Section III C. Under biaxial loading, we

observed that both armchair and zigzag directional fracture

stresses stay similar although the value is much less than the

uniaxial loading at different strain rates. For biaxial loading,

YM of stanene is insensitive to varying stain rate.

In Fig. 10(a), variation of fracture strength with strain

rate is presented for uniaxial armchair loading at different

temperatures. It can be seen that fracture stress reduces with

the reduction of strain rate. This phenomenon is obvious due

to the fact that at a slower strain rate, the atoms get sufficient

time to respond with the thermal fluctuation and stress relax-

ation.35 This causes the atoms to overcome the energy barrier

to break bonds at a lower strength. With the increasing strain

rate, materials exhibit higher strength. This behavior is con-

sistent with previous studies.35,36

The effect of strain rate on the mechanical properties is

also contingent on the temperature. The effect of tempera-

ture, strain rate, and fracture strength is visible and it is

found that at low temperature (100 K), there are no signifi-

cant effects on fracture strength due to the variation in strain

rate. For uniaxial armchair directional loading (see Fig.

10(a)), it is found that the slope of the line is higher at ele-

vated temperature (250 K).

The effect of biaxial loading rate on fracture strength is

represented in Fig. 11. At low temperature, slope of the line

(see Table IV) is almost constant and increases with the tem-

perature. The relation between the fracture stress and strain

can be expressed36 by

r ¼ C�ef; (6)

where r is the fracture stress, �e is the strain rate, and f is

called the strain rate sensitivity. Equation (6) can be written as

FIG. 9. Variation of strain rate on stress strain curve for biaxial loading at

temperature 100 K.

FIG. 10. Effect of strain rate on the

fracture strength in uniaxial (a) arm-

chair loading and (b) zigzag loading of

stanene at different temperature results

are shown in logarithmic scale.

FIG. 11. Effect of strain rate on the fracture strength in biaxial loading of

stanene at different temperatures. Results are shown in logarithmic scale.

124305-6 Mojumder, Amin, and Islam J. Appl. Phys. 118, 124305 (2015)

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lnr ¼ lnCþ fln�e: (7)

In Table III, parameters of the fitted data are presented for

strain rate sensitivity for different loadings. As we can see,

the value of f increases as the temperature increases, there-

fore, at a low temperature, thermal vibration of Sn atoms is

weak and that is observed in the stanene sheet.

IV. CONCLUSIONS

In conclusion, we investigated mechanical properties of

stanene by molecular dynamics simulations using MEAM

potential. From the investigation, we find that the fracture

strength of stanene is sensitive to the loading direction, load-

ing type, applied strain rate, and temperature. Our findings

are listed as follows:

• In case of biaxial loading, stanene exhibits isotropic mate-

rial properties. The fracture stress is less variant of loading

direction (armchair or zigzag) for biaxial loading, how-

ever, under uniaxial loading, fracture stresses are contin-

gent on the direction of loading. Under uniaxial loading in

the armchair direction, stanene fails at lower strain value

than the zigzag direction.• For uniaxial loading, the fracture pattern is brittle in na-

ture, while biaxial loading shows sign of yielding.• As the temperature rises, fracture strength of stanene

decreases for both loading direction and loading type. This

is attributed by the significant reduction in the fracture

stress and strain with the increase in temperature.• With the increase in loading rate, stanene seems resilient

to failure. At low temperature, strain rate sensitivity is in-

significant but as the temperature rises, sensitivity

becomes obvious.

Our results provide useful information about tempera-

ture dependent uniaxial and biaxial loading fractures of sta-

nene sheet which can be effective for nano-electronics

application.

ACKNOWLEDGMENTS

Authors would like to acknowledge mMAS (Multiscale

Modeling and Simulation Group) for providing necessary

supports to carry out this research. Authors would also like

to express their gratitude to anonymous reviewer for their

suggestion for the improvement of present paper.

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TABLE IV. Fitted data parameter (intercepts and strain rate sensitivity) for different loading conditions and temperatures.

100 K 150 K 200 K 250 K

Temperature (K) lnC f lnC f lnC f lnC f

Uniaxial armchair 1.15 0.003 0.96 0.011 0.49 0.034 1.20 0.114

Uniaxial zigzag 1.12 0.005 1.08 0.005 1.02 0.006 0.79 0.016

Biaxial 0.87 0.011 0.87 0.009 0.60 0.020 0.12 0.043

124305-7 Mojumder, Amin, and Islam J. Appl. Phys. 118, 124305 (2015)

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