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It is demonstrated through the nonequilibrium Greens function method that the Kapitza resistance(Ω)of graphite can be modulated by loading pressure in x direction,x and y directions and all three directions respectively in this paper.For graphite without pressure,the Kapitza resistance is about 8×10-9 m2K/W.The pressure in the z direction from tensile-1GPa to compressive 10GPa can reduce the Ω by one order of magnitude,which is caused by the increase in the phonon transmission possibility resulting from the increase in the interlayer interaction strength and weaker interface scattering.And the phonon transmission function has the phenomenon of blue shift in the low-frequency range during the process.The pressure in the x-y plane changes from-10GPa to 0GPa (tensile)has little effect on the phonon transmission and Kapitza resistance Ω while there has no pressure or a small pressure in the z direction.So pressure in the basal plane has little effect on the interfacial thermal conductance and phonon transmission in the graphite.Furthermore,the discrete layer in the graphite separates mutually when the pressure in the x and y directions reaches to the critical value 1~2GPa or to-2~-1GPa in the z direction.It is worth noted that low-frequency phonons have larger phonon transmission due to longer mean free path and the soft Van der Waals interaction between the neighboring layers.Our results suggest that the Kapitza resistance of graphite or few-layer graphene can be modulated in a large scope and then can be applied for both heat dissipation and insulation through the pressure engineering.