Calculations of properties of materials require performing numerical integrals over the Brillouin zone(BZ).Integration points in density functional theory codes are uniformly spread over the BZ(despite integration err...Calculations of properties of materials require performing numerical integrals over the Brillouin zone(BZ).Integration points in density functional theory codes are uniformly spread over the BZ(despite integration error being concentrated in small regions of the BZ)and preserve symmetry to improve computational efficiency.Integration points over an irreducible Brillouin zone(IBZ),a rotationally distinct region of the BZ,do not have to preserve crystal symmetry for greater efficiency.This freedom allows the use of adaptive meshes with higher concentrations of points at locations of large error,resulting in improved algorithmic efficiency.We have created an algorithm for constructing an IBZ of any crystal structure in 2D and 3D.The algorithmuses convex hull and half-space representations for the BZ and IBZ to make many aspects of construction and symmetry reduction of the BZ trivial.The algorithm is simple,general,and available as open-source software.展开更多
Rotating elliptical nanowire arrays as two-dimensional photonic crystals has been proposed and studied in this Letter.The analysis of the four lowest energy bands and the first bandgap width of some examples illustrat...Rotating elliptical nanowire arrays as two-dimensional photonic crystals has been proposed and studied in this Letter.The analysis of the four lowest energy bands and the first bandgap width of some examples illustrates that the rotation and configuration of the primitive cell can have effects on the reducibility of the Brillouin zone.As the central element’s orientation changes,the irreducible Brillouin zone could be expanded to the whole first Brillouin zone.Special attention has been paid to the nanowire arrays with adjacent elements perpendicular to each other,and the irreducible Brillouin zone unexpectedly retracted back to the 1/8 of the first Brillouin zone though the symmetry of elements is lower than that of the square lattice.Meanwhile,the first bandgap width of the perpendicular array can be adjusted by the rotation of each primitive element.展开更多
We have proposed an"exact"strain gradient(SG)continuum model to properly predict the dispersive characteristics of diatomic lattice metamaterials with local and nonlocal interactions.The key enhancement is p...We have proposed an"exact"strain gradient(SG)continuum model to properly predict the dispersive characteristics of diatomic lattice metamaterials with local and nonlocal interactions.The key enhancement is proposing a wavelength-dependent Taylor expansion to obtain a satisfactory accuracy when the wavelength gets close to the lattice spacing.Such a wavelength-dependent Taylor expansion is applied to the displacement field of the diatomic lattice,resulting in a novel SG model.For various kinds of diatomic lattices,the dispersion diagrams given by the proposed SG model always agree well with those given by the discrete model throughout the first Brillouin zone,manifesting the robustness of the present model.Based on this SG model,we have conducted the following discussions.(Ⅰ)Both mass and stiffness ratios affect the band gap structures of diatomic lattice metamaterials,which is very helpful for the design of metamaterials.(Ⅱ)The increase in the SG order can enhance the model performance if the modified Taylor expansion is adopted.Without doing so,the higher-order continuum model can suffer from a stronger instability issue and does not necessarily have a better accuracy.The proposed SG continuum model with the eighth-order truncation is found to be enough to capture the dispersion behaviors all over the first Brillouin zone.(Ⅲ)The effects of the nonlocal interactions are analyzed.The nonlocal interactions reduce the workable range of the well-known long-wave approximation,causing more local extrema in the dispersive diagrams.The present model can serve as a satisfactory continuum theory when the wavelength gets close to the lattice spacing,i.e.,when the long-wave approximation is no longer valid.For the convenience of band gap designs,we have also provided the design space from which one can easily obtain the proper mass and stiffness ratios corresponding to a requested band gap width.展开更多
The high-frequency edge of the first-order Raman mode of diamond reflects the stress state at the culet of anvil, and is often used for the pressure calibration in diamond anvil cell(DAC) experiments. Here we point ou...The high-frequency edge of the first-order Raman mode of diamond reflects the stress state at the culet of anvil, and is often used for the pressure calibration in diamond anvil cell(DAC) experiments. Here we point out that the high-frequency edge of the diamond Raman phonon corresponds to the Brillouin zone(BZ) center Γ point as a function of pressure. The diamond Raman pressure gauge relies on the stability of crystal lattice of diamond under high stress. Upon the diamond anvil occurs failure under the uniaxial stress(197 GPa), the loss of intensity of the first-order Raman phonon and a stressdependent broad Raman band centered at 600 cm^(-1) are observed, which is associated with a strain-induced local mode corresponding to the BZ edge phonon of the L1 transverse acoustic phonon branch.展开更多
文摘Calculations of properties of materials require performing numerical integrals over the Brillouin zone(BZ).Integration points in density functional theory codes are uniformly spread over the BZ(despite integration error being concentrated in small regions of the BZ)and preserve symmetry to improve computational efficiency.Integration points over an irreducible Brillouin zone(IBZ),a rotationally distinct region of the BZ,do not have to preserve crystal symmetry for greater efficiency.This freedom allows the use of adaptive meshes with higher concentrations of points at locations of large error,resulting in improved algorithmic efficiency.We have created an algorithm for constructing an IBZ of any crystal structure in 2D and 3D.The algorithmuses convex hull and half-space representations for the BZ and IBZ to make many aspects of construction and symmetry reduction of the BZ trivial.The algorithm is simple,general,and available as open-source software.
基金This work was supported by the National Natural Science Foundation of China(No.61875153).
文摘Rotating elliptical nanowire arrays as two-dimensional photonic crystals has been proposed and studied in this Letter.The analysis of the four lowest energy bands and the first bandgap width of some examples illustrates that the rotation and configuration of the primitive cell can have effects on the reducibility of the Brillouin zone.As the central element’s orientation changes,the irreducible Brillouin zone could be expanded to the whole first Brillouin zone.Special attention has been paid to the nanowire arrays with adjacent elements perpendicular to each other,and the irreducible Brillouin zone unexpectedly retracted back to the 1/8 of the first Brillouin zone though the symmetry of elements is lower than that of the square lattice.Meanwhile,the first bandgap width of the perpendicular array can be adjusted by the rotation of each primitive element.
基金Project supported by the National Natural Science Foundation of China(Nos.11972174 and 11672119)。
文摘We have proposed an"exact"strain gradient(SG)continuum model to properly predict the dispersive characteristics of diatomic lattice metamaterials with local and nonlocal interactions.The key enhancement is proposing a wavelength-dependent Taylor expansion to obtain a satisfactory accuracy when the wavelength gets close to the lattice spacing.Such a wavelength-dependent Taylor expansion is applied to the displacement field of the diatomic lattice,resulting in a novel SG model.For various kinds of diatomic lattices,the dispersion diagrams given by the proposed SG model always agree well with those given by the discrete model throughout the first Brillouin zone,manifesting the robustness of the present model.Based on this SG model,we have conducted the following discussions.(Ⅰ)Both mass and stiffness ratios affect the band gap structures of diatomic lattice metamaterials,which is very helpful for the design of metamaterials.(Ⅱ)The increase in the SG order can enhance the model performance if the modified Taylor expansion is adopted.Without doing so,the higher-order continuum model can suffer from a stronger instability issue and does not necessarily have a better accuracy.The proposed SG continuum model with the eighth-order truncation is found to be enough to capture the dispersion behaviors all over the first Brillouin zone.(Ⅲ)The effects of the nonlocal interactions are analyzed.The nonlocal interactions reduce the workable range of the well-known long-wave approximation,causing more local extrema in the dispersive diagrams.The present model can serve as a satisfactory continuum theory when the wavelength gets close to the lattice spacing,i.e.,when the long-wave approximation is no longer valid.For the convenience of band gap designs,we have also provided the design space from which one can easily obtain the proper mass and stiffness ratios corresponding to a requested band gap width.
基金Project support by the National Natural Science Foundation of China(Grant No.11774247)。
文摘The high-frequency edge of the first-order Raman mode of diamond reflects the stress state at the culet of anvil, and is often used for the pressure calibration in diamond anvil cell(DAC) experiments. Here we point out that the high-frequency edge of the diamond Raman phonon corresponds to the Brillouin zone(BZ) center Γ point as a function of pressure. The diamond Raman pressure gauge relies on the stability of crystal lattice of diamond under high stress. Upon the diamond anvil occurs failure under the uniaxial stress(197 GPa), the loss of intensity of the first-order Raman phonon and a stressdependent broad Raman band centered at 600 cm^(-1) are observed, which is associated with a strain-induced local mode corresponding to the BZ edge phonon of the L1 transverse acoustic phonon branch.
