Mechanical response of SiC sheet under strain [616957]

Materials Chemistry and Physics
Manuscript Draft

Manuscript Number: MATCHEMPHYS -D-17-01577

Title: Mechanical response of SiC sheet under strain

Article Type: Full Length Ar ticle

Keywords: SiC hybrid; non linear elastic constants; strain effects; Debye
temperature; piezoelectric coefficients

Abstract: The effect of biaxial strain on crystallographic structure,
band gap, polarization, linear and non linear elastic prop erties of 2D
SiC hybrid are studied using ab -initio calculations. The determination of
the two critical strain points reveals an elastic region just a little
smaller than that of graphene. With load, charge distributions vary and
electronic states CBM and VBM undergo a location change. Consequently,
enlarging strain reduces the band gap monotonically leading to a
semiconductor –metal transition. Debye temperature 407.81K intermediates
between the ones of silicene and germanene. Planar SiC shows a
piezoelect ric response comparable to 2D buckled compounds materials. The
negative sign of the effective non linear modulus reveals an hyperelastic
softening behavior of SiC. Under pressure, second order elastic
constants show a small anisotropie. The results show t hat tailoring
physical properties of SiC under strain reveals its great potential in
the electronic and mechanical devices.

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65 Mechanical response of SiC sheet under strain
Lalla Btissam Drissi1,2,∗, Kawtar Sadki1, Mohammed-Hamza Kourra1
1-LPHE, Modeling & Simulations, Faculty of Science,
Mohammed V University in Rabat, Morocco and
2- CPM, Centre of Physics and Mathematics,
Faculty of Science, Mohammed V University in Rabat, Morocco
Abstract
The effect of biaxial strain on crystallographic structure, b and gap, polarization, linear and non
linear elastic properties of 2D SiC hybrid are studied using ab-initio calculations. The determi-
nation of the two critical strain points reveals an elastic r egion just a little smaller than that of
graphene. With load, charge distributions vary and electro nic states CBM and VBM undergo a
location change. Consequently, enlarging strain reduces t he band gap monotonically leading to
a semiconductor–metal transition. Debye temperature 407 .81Kintermediates between the ones
of silicene and germanene. Planar SiC shows a piezoelectric response comparable to 2D buckled
compounds materials. The negative sign of the effective non li near modulus reveals an hyperelastic
softening behavior of SiC. Under pressure, second order ela stic constants show a small anisotropie.
The results show that tailoring physical properties of SiC u nder strain reveals its great potential
in the electronic and mechanical devices.
Keywords: SiC hybrid; non linear elastic constants; strain effects; Debye temperature; piezoelectric coeffi-
cients
1*Manuscript
Click here to view linked References

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65 I. INTRODUCTION
Recently, SiC hybrid analog of graphene, has been a subject of inte nse fundamental
research investigations as promising candidate for nanotechnolog ical applications requiring
hydrogen storage and catalyst for reduction and oxidation [1, 2]. S iC is also considered
as potential material for electronics and optics and is suitable for n anodevices with , high-
power, high-frequency and high pressure [3]. Bidimentional SiC is a ho neycomb sheet that
is stable in planar geometry [1, 4]. This non magnetic semiconductor ha s more surface
charge polarization compared to graphene which makes possible rem arkable interactions
with adsorbed atoms and molecules [1, 5]. Moreover, SiC hybrid is char acterized with a
high excitonic binding energy [6] and is a rigid material with an important value of stiffness
[7]. SiC based p–n junctions display diode behavior with a high rectificat ion performance
that can be optimized when designing the device along zigzag direction [8].
Interestingly, completehydrogenation ofSiCleadstostablestruc tures withsp3hybridiza-
tion. Therefore, the synthesis of graphane-like SiC sheet should b e feasible. Hydrogenation
increases the gap and affects also the elastic properties by decrea sing the value of Young
modulus and increasing the Poisson ratio. Partial and half hydrogen ation seem to be better
choice in engineering band gap and inducing magnetism. Elastic behavio r of SiC hybrid
versus the hydrogen coverage shows reduced values of Young mo dulus upon hydrogenation
particularly along zigzag direction [9]. Partial fluorination presents a lso a good alternative
to engineer the gap and magnetism in SiC depending on which atoms (ca rbone or silicone)
the F atoms are adsorbed [10]. Magnetic comportment is observed in SiC monolayer ad-
sorbed with series TM dopants with different magnetic moments and b inding energies in Si
and C sites [11].
In SiC nanoribbon (NR) with armchair edges, the wide gap increases w ith increasing the
width [12]. However, with zigzag shaped edges, SiC-NR is magnetic and presents a half
metallic behavior for narrow width less than 4 nm. By applying uniaxial e lastic strain, the
bandenergies ofthetwotypesofgraphanelikeSiC-NRdecrease un der bothcompression and
tension. A direct-to-indirect band gap transition is observed only f or tensed zigzag ribbons
[13]. SiC nanotube (SiCNT) is another derivative of SiC material that is useful to store
hydrogen because of its higher polarity compared to CNT [14]. An incr easing transverse
electric field decreases the band of SiCNT changing it from semicondu ctor to conductor [15].
2

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65 Mechanically, experimental and numerical research show that gra phene is the strongest
material ever measured, with Young’s modulus of 340 ±40N.m−1and Poisson ratio υ= 0.16
[16]. Moreover, nanoindentation experiment shows that graphene remains elastic until the
fracture. The investigation of nonlinear elastic properties of grap hene calculates a negative
valueof−690±120N.m−1fornonlineareffectifmodulus Drevealinganhyperelasticsoftening
behavior of this material [17]. To open and tune the band energy in ga pless graphene and
to observe spin polarization, applying strain is a good alternative [18]. Strain strength
control also efficiently properties of spin transport such as angula r range of spin-inversion
and spin-dependent conductivity [19]. The application of tensile hard ens the role of flexural
acousticphononsresponsibleforthermaltransportduetothec ompetitionbetweenboundary
scattering and intrinsic phonon–phonon scattering [20].
Low buckled silicene presents also remarkable values of Young modulu s, ultimate stress
and strain that are lower than those of graphene values [21]. This diff erence can be inter-
preted by the low strength of the bond between atoms ESi−Si= 256kj.mol−1compared to
EC−C= 346kj.mol−1. Like graphene, nonlinear mechanical properties deal with a negat ive
sign of all third order elastics constants in silicene [21]. Small mechanic al strain influences
buckling constants, electronic band structures and dielectric pro perties of silicene. At a
critical strain of 0 .20, silicene changes from buckled to a completely planar structure [2 2].
Moreover, the application of asymmetric strains causes the disapp earance of πplasmons and
linear red-shift in π+σones [23]. Tensile strain larger than 7% destroys Dirac cone located
at the Fermi level changing silicene into a conventional metal [24]. Bia xial strain tunes also
ferromagnetic order to antiferromagnetic state in Mn-silicene [25].
To achieve dynamic control of materials, nano-piezoelectric mater ial constitute a first
choice. Graphene and silicene are not piezoelectric due to their cent rosymmetric crystal
structure. However, piezoelectric effects is observed in single laye r materials such as boron
nitride, group-III monochalcogenides, transition metal dichalcog enides and dioxides [26].
Accordingtotheirsymmetry, thesematerialsshoweitherin-planeo r/andout-of-planedipole
moments. Moreover, the small thickness of these materials makes possible the feature to
apply experimentally large transverse electric fields in contrast to t heir bulk counterparts
[27]. The experimental measure of piezoelectricity in a free-standin gMoS2monolayer shows
ae11= 2.9×10−10Cm−1[28].
Seeking mechanical response of 2D materials is a compelling necessity to model and
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65 engineer new based-devices, reinforce material in nanocomposite s or determine the nature
of waves motion. So, aware of the importance of mechanical prope rties for characterizing
the behavior of nanomaterials, we study the effect of strain in regu lating key quantities of
SiC hybrid for potential mechanical applications. Load engineering b uckling parameter and
band gap, determination of nonlinear elastic constants, piezoelect ric coefficient and Debye
temperature are all reported in this work. It is found that metast able region, occurring
between the two critical strain points, is large compared to silicene. Charge distribution of
electronic states near CBM and VBM displays significant change in ter m of applied load
which decrease band energy. At high values of strain, SiC sheet sho ws a semiconductor-to-
metal transition. Piezoelectric response and Debye temperature of SiC are comparable to
some potential 2D materials. This study goes beyond linear elasticity that becomes invalid
forlargedeformation. Thirdorderelasticconstants arecalculate d, nonlinear elasticmodulus
is given and pressure dependence of second order elastic constan ts are plotted.
Thispaperisorganizedasfollows. Section2reportsgeneralcompu tationalsetupadopted.
Section 3 presents the obtained results and the corresponding dis cussion. Finally we give
the conclusion.
II. COMPUTATIONAL DETAILS
All calculations to study electronic, piezoelectric and elastic proper ties in linear regime,
are performed using generalized gradient approximation (GGA) for exchange-correlation
potential with Perdew-Burke-Ernzerhof (PBE) functional within the frame of density func-
tional theory (DFT). The code is executed in the Quantum Espress o Package (QE) [29]. An
ultra-soft pseudo-potential description of the electron-electr on is used. A cutoff energy of 40
Ry and 400 Ry is employed for the plane wave expansion of the wave fu nction. In the (6 ×8)
supercell used, a large interlayer distance of 20 ˚Ais considered to eliminate interactions be-
tween adjacent layers. The Brillouin zone is sampled with 8 ×8×1 Monkhorst–Pack k-point
mesh. Equilibrium geometries were obtained by minimum energy and ionic forces are set
to be 10−5eVand 0.01eV/A. For any deformation, the magnitude of the strain parameter
is increased in steps of 0 .001 up to a maximum strain of 0 .05 to warrant that the linear
elastic regime is carefully explored. The strain parameter ε= ((a′−a)/a) wherea′anda
present the lattice constant under strain and without strain resp ectively. The piezoelectric
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65 elements eijanddijare calculated from Berry’s Phase approximation, with applied strain
ranging from 0 to 0 .015 and increasing in steps of 0 .0025. On the other hand, atomic charge
distributions are obtained using Bader analysis [30].
Second and third order elastic constants (SOECs and TOECs) are c alculated with Ex-
citing code [31] based on full-potential augmented plane wave and loc al-orbitals method
and using GGA approach for exchange-correlation function. All th e results were executed
relaxing the atomic positions down to a residual force lower than 0 .0005Ha/bohr acting on
each atom. A mesh of k-points 8 ×8×1 in reciprocal space were considered.
For each type of deformation, the magnitude of Lagrange strain ηis increased from −0.7
to 0.7 in steps of 0 .02. In this case, the elastic energy of strained SiC is expressed by:
U(η) =U0+1
2U2+1
6U3
whereU0is strain energy of non-deformed system and U2andU3are combination of SOECs
and TOECs depending on deformation respectively. The fit of energ y-deformation curves
gives all independent elastic constants and then all key quantities d escribing the elastic
properties.
III. RESULTS AND DISCUSSION
Pure silicene-graphene hybrid is a planar hexagonal lattice where C a toms occupy the
sites of sub-lattice A remaining the B-sites to Si atoms as plotted in F ig.1-a. The atoms Si
and C form mainly a sp2hybridization with a bond length dC-Siof 1.78˚A[1].
A. Yielding points
Fig.1-b presents the strain energy ESand its derivative the stressdES
dεwith respect to the
applied biaxial strain. In term of linear elastic constants C11,C22,C12andC44,we have:
Es=1
2C11ǫ2
xx+1
2C22ǫ2
yy+C12ǫxxǫyy+2C44ǫ2
xy, (1)
whereǫxx,ǫyyandǫxyare the elements of the infinitesimal strain tensor. The strain ener gy
density is defined as Es= (Etot−E0) whereEtotis the total energy of the strained system
andE0is the total energy of the strain-free system. For pure SiC, the c onstants Cijsatisfy
the isotropy condition C11=C22and the Cauchy relation 2 C44=C11−C12.
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FIG. 1: Pure SiC sheet (a) supercell (6×8) with blue-large an d yellow-small balls corresponding to
Si and C atoms, respectively. (b) Variation of the strain ene rgyESand its derivative dES/dεof
pristine SiC with the applied biaxial strain.
The in-plane hydrostatic deformation εapplied to the equilibrium honeycomb structure
of pure SiC leads to a harmonic region for εranging from -0.02 to 0.02 followed by an
anharmonic region for higher values of strain 0 .02< ε≤εC2. The two critical strain points
εC1andεC2, describing the instability of the system, are presented in Fig.1-b. εC1= 0.18 is
the point at which the curve of stress with respect to strain reach es its maximum and then
starts to decrease for ε > εC1indicating the beginning of phonon instability under certain
acoustic waves. The yielding point εC2, that corresponds to the maxima of the ES(ε) curve,
isaround0 .23. This critical point isthe limit ofthe elasticregionwhere the system preserves
its honeycomb-like structure. Up to εC2, the strain energy decreases leading to the set up
of the plastic region. For εC1< ε < εC2pure SiC is in a meta-stable range and its structure
can be easily damaged.
Compared to εC1= 0.19 andεC2= 0.26 obtained in pure graphene [32] and εC1= 0.18
andεC2= 0.20 found in pure silicene [24], we deduce that the critical strain points εC1and
εC2of SiC intermediates between the ones of graphene and silicene.
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65 B. Debye temperature
At low temperatures, Debye temperature Θ Dcalculated using elastic constants is the
same as that determined from specific heat measurements. Moreo ver, it is associated to
some physical properties such as specific heat and melting tempera ture. In Debye theory
based on wave mechanics, in particular on standing waves that corr espond to normal modes
of elastic vibration, the parameter Θ Dis related to a maximum phonon frequency. The
temperature Θ Dis proportional to the atomic area of the unit cell and the average s ound
velocityVmthat is expressed as follows:
Vm=/bracketleftbigg1
3/parenleftbigg1
V3
P+2
V3
S/parenrightbigg/bracketrightbigg−1
3
whereVpis the longitudinal speed of waves vibrating in parallel direction to the polarization
andVscorresponds to transverse elastic wave velocity [7]. The coefficient of proportionality
between Θ DandVmis in term of the reduced Planck’s constant, the Boltzmann’s consta nt
and the number of atoms in the considered cell.
For pure SiC, it is found that Vp= 31.19Km/sandVs= 16.88Km/s[7]. Consequently,
Debye temperature Θ D= 407.81Kin all directions of isotropic SiC hybrid. This calculated
value intermediates between the ones 748 .5Kand 423.4Kfound for silicene and arsenene
respectively and the ones 387 .1Kand 258.0Kobtained for germanene and antimonene re-
spectively [33]. It is around 2 times bigger than stanene that shows t he smallest Debye
temperature in 2D materials and it is around 7 times lower than Θ D= 2751.4Kcalculated
for graphene that shows very robust rigidity in its planar structur e. Higher Debye tem-
perature exhibits higher lattice thermal conductivity which makes t he material suitable for
thermal application such as cooling microelectronics for passive hea t spreading [34]. How-
ever, materials with strongly suppressed thermal conductivity (lo w value of Θ D) are required
in thermoelectric devices for energy conversion.
C. Piezoelectric response
In contrast to graphene and silicene, pristine SiC is intrinsically piezoe lectric due to
the lowering of point group rotation symmetry from hexagonal C6to trigonal C3.Mir-
ror symmetry, included in this point group symmetry, nullifies e31coefficients. There-
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FIG. 2: The absolute value of 2D polarization change with res pect to uniaxial strains.
fore, pure SiC exhibits only the coefficient e11.Using “Berry phase” technique, the piezo-
electric coefficient e11is expressed in term of the surface polarizations P1as follows:
P1(ε11)−P1(0) =e11ε11[35].Therefore, linear fitting of the polarization P1change-vs-
strain curve ε11plotted in Fig.2 gives e11= 37.08pC/m. The corresponding piezoelectric
strain components d11= 0.29pmV−1is calculated using the relation d11=e11
C11−C12. This
calculated strain coefficient d11is comparable to hexagonal buckled hybrids (GaP, GaAs,
GaSb, InP, InAs and InSb) with values ranging between 0 .02 and 5.5pmV−1[36]. Similarly,
e11is also comparable to relaxed-ion piezoelectric coefficients e11of the same pre-cited group
In-V and Ga-V compounds that order in the interval between 24 pC/mand 44pC/m[27].
However, it is lower than e11= 371pC/mcalculated for BN sheet [26] and e11= 290pC/m
measured in single-layer MoS 2through nanoindentation and electromechanical actuation
[28].
D. Crystal structure under strain
Fig.3,thatpresentstheeffectofbiaxialstrainonSiCcrystalstru cture, showsaprogressive
increase in the lattice parameter with increasing strain. Moreover, the interatomic length
dSi−Cstretchesfrom1 .78˚Ato2.16˚Awhenstrainincreasesintherange[0 ,0.26]. Inparticular,
the system conserves its honeycomb structure with a bond length of 2.03˚Aatε= 0.08. The
first break of atomic bonds accompanied by formation of pentagon s starts at ε= 0.14. For
ε≥0.16, bonds continue breaking and multiple atomic chains Si−CandC−Cappear. For
these values of biaxial strain, the system breaks into two parts alo ng zigzag direction. For
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65
FIG. 3: A 6 ×4 SiC-supercell under strain 0.14, 0.16 and 0.22.
ε= 0.22,SiC is completely broken along both zigzag and armchair directions. We deduce
that under biaxial strain, chemical bonds weaken giving rise to a red uction of their stiffness.
FIG. 4: Charge densities in (x,y) plane of SiC sheet under str ain 0, 0.08, 0.14, 0.16, 0.22 and 0.26.
To get more information on the variation of the symmetry connectin g Si and C atoms,
Fig.4 plots distributions of charge of SiC sheet under biaxial strains v arying between 0
and 0.26.The highest charge is around C atoms and the lowest one is around Si atoms
whatever ε. Structures under strain show smaller charge concentrations co mpared to SiC
without strain where the charges are distributed in a symmetric man ner and with the same
magnitude. Moreover, the magnitude of charge distributions decr ease when biaxial strain
increases as it is clear when comparing 0 .22 and 0.26. The change in charge distribution is
mainly attributed to the redistribution of atomic orbitals under stra in.
Bader charge distributions for SiandCatoms in free SiC hybrid are 0 eand 7.95e
respectively in good agreement with [4]. Under biaxial strain, the par tial charge of C atom
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65 increases from 7 .95eto 8.04eand 8.14efor strains of 14% and 18% respectively. The partial
charge of Si atoms increases also from 0 eat 0% to 2 .53eobtained at 16%, then it decreases
forε≥0.22. It follows that thecharge transfer fromSi to Catoms increas e until theyielding
point then reduce with increasing strain. This result is confirmed by t he increase in Si-C
bond length that occurs until a strain value of 16% that is followed by the rupture of system.
E. Electronic properties
FIG. 5: Band structures of SiC sheet at different strains ε=0, 0.04, 0.08, 0.14, 0.16 and 0.22. The
K-points are located at Γ=0.0, K=0.47 and M= 0.84
The analysis of band structure under strain effect shows a reduct ion of the energy level
of CBM and an increase of the energy level at VBM state as shown in F ig.5. A band gap of
2.16eVis obtained for strained structure 0.04. It is smallest than Eg= 2.5eVcorresponding
to free strained SiC. The band gap continues to decrease progres sively with biaxial strain to
reach 1.86eVat 8%. Notice that with increasing biaxial strain, all the band gaps ar e direct.
For higher strains, ε≥0.14, the band gaps between CBM and VBM cross at the Fermi
level indicating a metallic character of SiC hybrid. This semiconductor -to-metal transition
induced by strain effect is in good agreement with results obtained fo r planar CdS[37]
and monolayer MoS2[38] that become also metallic at maximum strain of 20% and 10%
respectively.
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65 Furthermore, charge distribution of electronic states CBMandVBMunder strain in
Fig.6 shows that at 0%; charges in CBM and VBM are located only on C at oms. Then, the
chargedistributionconnectsatomsalongarmchairdirectioninasym metric wayfor ε= 0.14.
This behavior is also observed for higher values of biaxial strain with h igher magnitude of
charge distributions connecting atoms and also hexagons. Thus, t he variation of the gap
energy under biaxial strain (0 to 26%) is a direct consequence of th e location change of the
conduction band minimum and valence band maximum.
FIG. 6: Partial charge densities corresponding to CBM and VB M in SiC sheet at different values
of strain 0, 0.04, 0.08, 0.14, 0.16, and 0.22.
F. Nonlinear behavior
The nonlinear elastic behavior of SiC can be expressed as a function o f the direction
of stretching /vector nthrough the effective nonlinear modulus D/vector n. In the basis (− →ex,− →ey),the
arbitrary direction takes the form− →n= cosθ− →ex+ sinθ− →eywhereθis the angle between
zigzag direction and /vector n−direction.
For a hexagonal symmetry, D/vector nis given by the following equation:
D/vector n=3
2(1−ν)3Λ3+3
2(1−ν)(1+ν)2Λ2+3(2c2−1)(16c4−16c2+1)(1+ ν)3Λ1,
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FIG.7: Polar plotofabsolutevalueofeffective nonlinearmod ulusD/vector nwithazoom ontheboundary.
wherec=cosθandνis the Poisson ratio defined as C11/C12and Λ i(i=1,2,3)are expressed in
term of the third-order elastic constants Cijkas follows:
Λ1=1
12(C111−C222),
Λ2=1
4(C222−C112),
Λ3=1
12(2C111−C222+3C112), (2)
Notice that C111=−1853.59N.m−1is a little bit different from C222=−1866.95N.m−1
which means that SiC presents a very small anisotropy in the nonlinea r regime. As expected
C112=−309.58N.m−1has the lowest absolute value of nonlinear constants. The negative
sign of all independent third-order elastic constants signifies that SiC is an hyperelastic
softening system. Compared to its counterparts, low-buckled silic ene [21] has the smallest
third-order elastic constants followed by SiC then graphene [39].
Fig.7 displays polar plot of effective non linear modulus that has the ave rage value of
−796.17N.m−1. The negative sign of < D/vector n>indicates a softening behavior of SiC for large
deformations whatever the direction of the traction. The zoom on the boundary shows a non
circular form of D/vector nrevealing a small anisotropic behavior of SiC in the non linear regime.
Remark also that D/vector nhas a minimum value of −789.81 atθ=kπ/3 (k∈Z) and a maximum
of−805.41 atθ=π/6 +kπ/3. This nonlinear modulus is around six times higher than
silicene [21] and around 1.3 lower than graphene [39].
In hexagonal structures, the dependence of the second order elastic constants to the
pressure applied in the in-plane is expressed in term of both second a nd third order elastic
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65 constants, Poisson ratio ν,Young modulus Υ and the pressure Pas follows:
/tildewideC11=C11−(C111+C112)1−ν
ΥP
/tildewideC22=C11−C2221−ν
ΥP
/tildewideC12=C12−C1121−ν
ΥP. (3)
FIG. 8: Second-order elastic constants as a function of the p ressure.
Fig.8 shows that second-order elastic moduli /tildewideCijincrease linearly with applied pressure.
Unlike the zero pressure case where /tildewideC11=/tildewideC22,the line presenting /tildewideC11is asymmetrical to
/tildewideC22for pressure different than zero. This small anisotropy results fr om the little difference
between C111andC222.This could be the outcome of anharmonicity that is a direct conse-
quence of large vibrational amplitudes of atoms in the solid. With incre asing pressure, the
slope of /tildewideC11and/tildewideC22increase much more than /tildewideC12.Moreover, /tildewideC11is the most increasing
with pressure which means that zigzag direction represents the mo st stiffer directions in SiC
sheet and hence the anharmonicity along this direction is more marke d.
Under isotropic pressure, the elastic stability is expressed by ˜CP
11>|˜CP
12|where˜CP
11=
/tildewideC11−Pand˜CP
12=/tildewideC12+P. This condition is satisfied for SiC sheet indicating that this
hybrid stills always stable until the failed is achieved.
Stress-strain
The nonlinear elastic response /tildewideσis a function expressed in term of Young and effective
nonlinear moduli as follows:
/tildewideσ= Υη+Dη2(4)
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65 whereηis the Lagrangien strain that is gives the variation between the scala r product
(dX.dY) before strain and (dx.dy) after strain. In term of strain ε,it takes the following
form:η=ε+1
2ε2. At small stain values, we have η=ε.However, for large deformation,
ε2becomes non negligible, therefore the negative sign of Din Eq(4) renders SiC monolayer
less rigid with increasing traction.
The corresponding plot of nonlinear stress-strain response is disp layed in Fig.9. The
FIG. 9: Stress-strain elastic response for SiC
ultimate stress /tildewideσultim= 10.86N.m−1.It is the maximal stress value in stress-strain plot
corresponding to−Υ2
4Ddeduced from the relation:d/tildewideσ
dη= 0.The corresponding ultimate strain
ηultim= 0.116 satisfies the relation ηultim=−Υ
2D. Beyond ηultim,SiC becomes unstable and
the interatomic bonds break. Compared to its counterparts, the ultimate stress of SiC
is smaller than 32 .1N.m−1and 20.8N.m−1calculated for graphene and graphane [39] and
bigger than 6 .2N.m−1and 5.7N.m−1reported for silicene and silicane [21].
IV. CONCLUSION
Inconclusion, the modulationofstructural, electronic, elastic and piezoelectric properties
as well as Debye temperature of SiC monolayer under biaxial strain is reported. It is shown
that the hybrid is mechanically stable with a metastable region ranging in the interval
0.18< ε <0.23.Consequently, its large elastic region is comparable to graphene. Bo th
band gap and charge distributions present a significant variation wit h respect to stain and
a metallic character appears for high values of ε. Debye temperature of SiC sheet indicates
a robust rigidity in its planar structure and a possible higher lattice th ermal conductivity.
A small anisotropy is observed in polar plot of non linear modulus and se cond order elastic
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65 constants are pressure-dependent. Piezoelectric response of SiC is comparable to hexagonal
buckled compounds. All the reported features show that SiC is a ve ry suitable materiel for
nano-devices.
Acknowledgement 1 The authors would like to acknowledge financial support from the
Centre National pour la Recherche Scientifique et Technique (CNRST)-Morocco.
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