Effect of Tensile Strain on Thermal Properties of Graphene
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Effect of Tensile Strain on Thermal Properties of Graphene
Ayman Salman Alofi, Gyaneshwar P. Srivastava School of Physics, University of Exeter, Stocker Road, Exeter, EX4 4QL, UK
ABSTRACT We have employed a semicontinuum model to investigate the effect of tensile strain on thermal properties of graphene. Analytical expressions derived by Nihira and Iwata for phonon dispersion relations and vibrational density of states are employed, based on the semicontinuum model proposed by Komatsu and Nagamiya. The thermal conductivity is computed within the framework of Callaway’s effective relaxation time theory. It is found that thermal properties of graphene are quite sensitive to tensile strain. In the presence of tensile strain, the specific heat increases but the thermal conductivity decreases. INTRODUCTION Graphene, a single layer of two-dimensional carbon atoms, has attracted intensive research efforts due to its outstanding electronic and thermal properties [1, 2, 3, 4, 5]. The reported values for the thermal conductivity of graphene at room temperature are in the range 2000–6000 Wm−1 K−1 [6, 7, 8], being higher than the results measured for graphite [9] and diamond [10], suggesting potential applications in thermal management devices. The presence of strain, applied intentionally or unintentionally, can affect the thermal properties of graphene. It has been suggested [11, 12] that stress/strain effects can be used to tune the thermal conductivity of nanostructures, including graphene. In particular, it has been revealed that the thermal conductivities of graphene and carbon nanotubes decrease monotonically as the tensile stress increases [11]. Stress related change in the thermal conductivity of graphene can largely be related to changes in the phonon dispersion relation, velocity, and density of states. Therefore, any estimate of changes in the conductivity of graphene must be made with due consideration of these features. In this work, we elucidate the effect of tensile strain on the specific heat and thermal conductivity of graphene. We apply Callaway’s theory in its full form [13] to study the thermal conductivity. Our calculations employ the analytical expressions for the phonon dispersion relations and the vibrational density of states based on the work by Nihira and Iwata [14] within the semicontinuum model developed by Komatsu and Nagamiya [15].
THEORY We use the phonon dispersion relations adopted by Nihira and Iwata [14], based on the semicontinuum model proposed by Komatsu and Nagamiya [15] : 4ζ sin2 (cqz /2), 2 c 4ζ 2 2 2 = vt (qx + qy ) + 2 sin2 (cqz /2), c = b2 (qx2 + qy2 )2 + 4µ2 sin2 (cqz /2) + ζ(qx2 + qy2 ).
ωl2 = vl2 (qx2 + qy2 ) + ωt2 ωc2
(1)
Here the subscripts l and t refer to the in-plane modes longitudinal acoustic LA and transverse acoustic TA, respectively, and the subscript c refers to vibrations of atoms perpendicular to the layer plane (out-of-plane or flextural mode ZA). In these equations, υl and υt are the wave velocities, c is the interlayer spacing in graphite, b is the bending
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