In this paper, a class of plane homogeneous fifth system with six special direction is studied, and the global topological classification and coefficient conditions is discussed.
Based on the reported physical parameters for hexagonal system solids,we have calculated the effects of anisotropy on polarization of plane P-wave propagation.Herein we report the results of calculations and the newly...Based on the reported physical parameters for hexagonal system solids,we have calculated the effects of anisotropy on polarization of plane P-wave propagation.Herein we report the results of calculations and the newly observed physical phenomena.It is found that,for a given propagation,if the polarization is parallel to the wave vector,so also to the Poynting vector.In such a case,the phase velocity is identical to the energy velocity;the quasi P-wave degenerates to a pure P-wave along the propagation.It is also noted that if the polarization is parallel to the Poynting vector but not to the wave vector,the propagating wave cannot be a pure P-wave.Furthermore,the polarization in a quasi P-wave may deviate from the wave vector for more than 45°,but the deviation from the Poynting vector is always less than 45°.The energy velocity of a quasi SV-wave can be larger than that of the quasi P-wave in some propagation directions,even though the phase velocity of a quasi SV-wave may never be larger than either the phase velocity or energy velocity of the quasi P-wave.Finally,in case of parameters ε=0 and δ*≠0,the polarization of a quasi P-wave has an observed symmetry at a 45°phase angle.The anisotropy of a hexagonal system solid determines if a pure P-wave can be created and what the propagation direction is for a plane wave propagating inside such a hexagonal system solid.展开更多
We analyze thickness-stretch vibrations of a plate of hexagonal crystal carrying an array of micro-rods with their bottoms fixed to the top surface of the plate.The rods undergo longitudinal vibrations when the crysta...We analyze thickness-stretch vibrations of a plate of hexagonal crystal carrying an array of micro-rods with their bottoms fixed to the top surface of the plate.The rods undergo longitudinal vibrations when the crystal plate is in thickness-stretch motion.The plate is modeled by the theory of anisotropic elasticity.The rods are modeled by the one-dimensional structural theory for extensional vibration of rods.A frequency equation is obtained and solved using perturbation method.The effect of the rod array on the resonant frequencies of the crystal plate is examined.The results are potentially useful for using thickness-stretch modes of crystal plates to measure the mechanical properties of microrod arrays.展开更多
The thermal expansion coefficient(TEC)and thermal conductivity(k)of thermal fillers are key factors for designing thermal management and thermal protection composite materials.Due to its unique advantages,hexagonal bo...The thermal expansion coefficient(TEC)and thermal conductivity(k)of thermal fillers are key factors for designing thermal management and thermal protection composite materials.Due to its unique advantages,hexagonal boron nitride(h-BN)is one of the most commonly used thermal fillers.However,its TEC and k values are still unclear due to the inconsistency of characterization techniques and sample preparations.In this work,these disputes were addressed using the quasi-harmonic approximation(QHA)method and phonon Boltzmann transport equation(BTE)theory based on the density functional theory(DFT),respectively.The accuracy of our calculated TEC and k values was confirmed by previously reported experimental results,and the underlying physical principles were analyzed from the phonon behaviors.Our TEC results show that the h-BN has small in-plane negative value and large cross-plane positive value,which are-2.4×10^(-6) and 36.4×10^(-6) K^(-1) at 300 K,respectively.And the anisotropic TEC is mainly determined by the anisotropic isothermal bulk modulus and the low-frequency out-of-plane longitudinal phonon modes.We found that the convergence of cutoff radius and q-grid size have significant effect on the accuracy of k of h-BN.Our results show that the in-plane k is much higher than the cross-plane k,and the values at 300 K are 286.6 and 2.7 W m^(-1) K^(-1),respectively.The anisotropic phonon group velocity arising from the vibration behaviors of acoustic phonon modes should be primarily responsible for the anisotropic k.Our calculated TEC and k values will provide important references for the design of h-BN composite materials.展开更多
文摘In this paper, a class of plane homogeneous fifth system with six special direction is studied, and the global topological classification and coefficient conditions is discussed.
基金supported by the National Natural Science Foundation of China(Grant No.40974078)the Physical Sciences Division at University of Chicago
文摘Based on the reported physical parameters for hexagonal system solids,we have calculated the effects of anisotropy on polarization of plane P-wave propagation.Herein we report the results of calculations and the newly observed physical phenomena.It is found that,for a given propagation,if the polarization is parallel to the wave vector,so also to the Poynting vector.In such a case,the phase velocity is identical to the energy velocity;the quasi P-wave degenerates to a pure P-wave along the propagation.It is also noted that if the polarization is parallel to the Poynting vector but not to the wave vector,the propagating wave cannot be a pure P-wave.Furthermore,the polarization in a quasi P-wave may deviate from the wave vector for more than 45°,but the deviation from the Poynting vector is always less than 45°.The energy velocity of a quasi SV-wave can be larger than that of the quasi P-wave in some propagation directions,even though the phase velocity of a quasi SV-wave may never be larger than either the phase velocity or energy velocity of the quasi P-wave.Finally,in case of parameters ε=0 and δ*≠0,the polarization of a quasi P-wave has an observed symmetry at a 45°phase angle.The anisotropy of a hexagonal system solid determines if a pure P-wave can be created and what the propagation direction is for a plane wave propagating inside such a hexagonal system solid.
基金supported by the National Natural Science Foundation of China (Grant No. 10932004)the Industrial Technology Research Program of the City of Ningbo (Grant No. 2007B10052)the WONG K C Magna Fund of Ningbo University
文摘We analyze thickness-stretch vibrations of a plate of hexagonal crystal carrying an array of micro-rods with their bottoms fixed to the top surface of the plate.The rods undergo longitudinal vibrations when the crystal plate is in thickness-stretch motion.The plate is modeled by the theory of anisotropic elasticity.The rods are modeled by the one-dimensional structural theory for extensional vibration of rods.A frequency equation is obtained and solved using perturbation method.The effect of the rod array on the resonant frequencies of the crystal plate is examined.The results are potentially useful for using thickness-stretch modes of crystal plates to measure the mechanical properties of microrod arrays.
基金the National Natural Science Foundation of China(51621091,51225203,and 51672060)the National Key Research and Development Program of China(2017YFB0310400)。
文摘The thermal expansion coefficient(TEC)and thermal conductivity(k)of thermal fillers are key factors for designing thermal management and thermal protection composite materials.Due to its unique advantages,hexagonal boron nitride(h-BN)is one of the most commonly used thermal fillers.However,its TEC and k values are still unclear due to the inconsistency of characterization techniques and sample preparations.In this work,these disputes were addressed using the quasi-harmonic approximation(QHA)method and phonon Boltzmann transport equation(BTE)theory based on the density functional theory(DFT),respectively.The accuracy of our calculated TEC and k values was confirmed by previously reported experimental results,and the underlying physical principles were analyzed from the phonon behaviors.Our TEC results show that the h-BN has small in-plane negative value and large cross-plane positive value,which are-2.4×10^(-6) and 36.4×10^(-6) K^(-1) at 300 K,respectively.And the anisotropic TEC is mainly determined by the anisotropic isothermal bulk modulus and the low-frequency out-of-plane longitudinal phonon modes.We found that the convergence of cutoff radius and q-grid size have significant effect on the accuracy of k of h-BN.Our results show that the in-plane k is much higher than the cross-plane k,and the values at 300 K are 286.6 and 2.7 W m^(-1) K^(-1),respectively.The anisotropic phonon group velocity arising from the vibration behaviors of acoustic phonon modes should be primarily responsible for the anisotropic k.Our calculated TEC and k values will provide important references for the design of h-BN composite materials.
