Identifying Intersections of Dispersion Curves for Phononic Crystals

2013 ◽  
Author(s):  
Kuo-Chung Liu ◽  
Yuan-Fang Chou
Keyword(s):  
Band Structure ◽  
Plane Waves ◽  
Computation Time ◽  
Expansion Method ◽  
Dispersion Curves ◽  
Phononic Crystals ◽  
Alloy Matrix ◽  
Finite Group Theory ◽  
Secular Equations ◽  
Square Array

Many methods have been developed to obtain the band structure of crystals. Generally, they all require numerical computation to construct the spectrum. Therefore, only discrete points instead of continuous lines provided for dispersion relations. This makes it difficult to distinguish the modes of nearby discrete points without calculating mode profiles. That is, more effort is required to determine whether two dispersion curves intersect each other or not. A new method of investigation for phononic crystals is proposed which takes advantage of finite group theory and symmetrized plane waves that can block-diagonalize secular equations. A system consisting of a periodic square array of nickel alloy cylinders and an aluminum alloy matrix is studied. Intersections between dispersion curves of different modes can be identified directly. The result contradicts that presented by Kushwaha in 1993. The method can not only distinguish different modes directly from the computed band structure but also saves computation time. Compared to plane wave expansion method, only one quarter of computation time is required for calculating the spectrum. The higher symmetry a group has, the shorter the computation time expected.

Study on band gap properties of two-dimensional phononic crystals based on generalized viscoelastic modeling

2019 ◽  
Vol 33 (32) ◽  
pp. 1950403
Author(s):  
Fengxiang Guo ◽  
Hui Guo ◽  
Pei Sun ◽  
Tao Yuan ◽  
Yansong Wang
Keyword(s):  
Plane Waves ◽  
Single Mode ◽  
Expansion Method ◽  
Maxwell Model ◽  
Phononic Crystals ◽  
Band Gaps ◽  
Two Dimensional ◽  
Band Structures ◽  
Material Parameters ◽  
Multi Mode

Viscoelastic materials can dissipate energy and hinder propagation for plane waves, which can adjust the band structures of phononic crystals (PCs). In this study, the wave propagation in a two-dimensional PC with a viscoelastic matrix is investigated. The Maxwell model is utilized to analyze the effect of material parameters on the frequency dependence of viscoelasticity. Material parameters include the relaxation time, the initial value and the final value of the shear modulus. Band structures of viscoelastic phononic crystals (VPCs) are solved by combining the plane wave expansion method and iterative algorithm based on Bloch theory. The effects of the viscoelasticity on the band structures are studied using the single-mode and multi-mode Maxwell models. Results reveal that the viscoelasticity of the materials not only extends the band gaps but also shifts the band gaps to lower frequencies. Furthermore, the viscoelasticity simulated by the multi-mode model can precisely adjust anyone of the band gaps of VPCs separately. Results provide insights into the design and applications of VPCs.

Thermal Design of Highly-Efficient Thermoelectric Materials With Atomic-Scale Three-Dimensional Phononic Crystals

2007 ◽  
Author(s):  
Jean-Numa Gillet ◽  
Yann Chalopin ◽  
Sebastian Volz
Keyword(s):  
Thermal Conductivity ◽  
Bulk Material ◽  
Phononic Crystal ◽  
Three Dimensional ◽  
Mean Free Path ◽  
Dispersion Curves ◽  
Phononic Crystals ◽  
Thermal Design ◽  
Atomic Scale ◽  
Thermal Insulating

Owing to their thermal insulating properties, superlattices have been extensively studied. A breakthrough in the performance of thermoelectric devices was achieved by using superlattice materials. The problem of those nanostructured materials is that they mainly affect heat transfer in only one direction. In this paper, the concept of canceling heat conduction in the three spatial directions by using atomic-scale three-dimensional (3D) phononic crystals is explored. A period of our atomic-scale 3D phononic crystal is made up of a large number of diamond-like cells of silicon atoms, which form a square supercell. At the center of each supercell, we substitute a smaller number of Si diamond-like cells by other diamond-like cells, which are composed of germanium atoms. This elementary heterostructure is periodically repeated to form a Si/Ge 3D nanostructure. To obtain different atomic configurations of the phononic crystal, the number of Ge diamond-like cells at the center of each supercell can be varied by substitution of Si diamond-like cells. The dispersion curves of those atomic configurations can be computed by lattice dynamics. With a general equation, the thermal conductivity of our atomic-scale 3D phononic crystal can be derived from the dispersion curves. The thermal conductivity can be reduced by at least one order of magnitude in an atomic-scale 3D phononic crystal compared to a bulk material. This reduction is due to the decrease of the phonon group velocities without taking into account that of the phonon average mean free path.

Optimization of Phononic Crystals for the Simultaneous Attenuation of Out-of-Plane and In-Plane Waves

2011 ◽  
Author(s):  
Osama R. Bilal ◽  
Mahmoud I. Hussein
Keyword(s):  
Genetic Algorithm ◽  
Phononic Crystal ◽  
Plane Waves ◽  
Phononic Crystals ◽  
Gap Size ◽  
Two Dimensional ◽  
Dispersion Characteristics ◽  
Out Of Plane ◽  
Optimization Methodology ◽  
Application Specific

The topological distribution of the material phases inside the unit cell composing a phononic crystal has a significant effect on its dispersion characteristics. This topology can be engineered to produce application-specific requirements. In this paper, a specialized genetic-algorithm-based topology optimization methodology for the design of two-dimensional phononic crystals is presented. Specifically the target is the opening and maximization of band gap size for (i) out-of-plane waves, (ii) in-plane waves and (iii) both out-of-plane and in-plane waves simultaneously. The methodology as well as the resulting designs are presented.

Evanescent Bloch waves and the complex band structure of phononic crystals

2009 ◽  
Vol 80 (9) ◽  
Author(s):  
Vincent Laude ◽  
Younes Achaoui ◽  
Sarah Benchabane ◽  
Abdelkrim Khelif
Keyword(s):  
Band Structure ◽  
Phononic Crystals ◽  
Bloch Waves

Band structure of evanescent waves in phononic crystals

2008 ◽  
Author(s):  
Vincent Laude ◽  
Boujemaa Aoubiza ◽  
Younes Achaoui ◽  
Sarah Benchabane ◽  
Abdelkrim Khelif
Keyword(s):  
Band Structure ◽  
Evanescent Waves ◽  
Phononic Crystals

Synthesis, XRD analysis and electronic structure of InGaTe2 chain semiconductor

2020 ◽  
pp. 2150029
Author(s):  
E. M. Gojayev ◽  
S. S. Osmanova ◽  
S. I. Safarova ◽  
D. M. Gafarova
Keyword(s):  
Band Structure ◽  
Density Functional ◽  
Plane Waves ◽  
Density Functional Method ◽  
Xrd Analysis ◽  
Unit Cell ◽  
Lattice Parameters ◽  
Tetragonal Symmetry ◽  
Diagonal Form ◽  
Surface Microrelief

In this work, we developed a technology for growing a single crystal of a ternary compound, using the Atomic Force Microscope (AFM), we studied the surface microrelief in 2D and 3D modes, using X-ray diffraction (XRD) analysis, determined the parameters of the unit cell of this phase and revealed that it crystallizes in tetragonal symmetry with lattice parameters [Formula: see text] Å and [Formula: see text] Å, space group I4/mcm. Using the density functional method, using the ABINIT software package, using the Troiller–Martins pseudopotentials in the basis of plane waves, the band structure was calculated, the origin of the valence and conduction bands was determined. It was revealed that this phase is a direct-gap semiconductor with a bandgap of 0.56 eV. The parameters of the InGaTe2 unit cell were calculated by the pseudopotential and linearized attached plane wave (LAPW) methods, the theoretical and experimental values of the lattice parameters are in good agreement. Based on the band structure, the effective masses of electrons and holes are determined. It is shown that the tensors of the inverse effective mass for both extreme have a diagonal form.

Band structure in two-dimensional fiber–air phononic crystals

2011 ◽  
Vol 406 (4) ◽  
pp. 963-966 ◽  
Author(s):  
Shu Yang ◽  
Wei-Dong Yu ◽  
Ning Pan
Keyword(s):  
Band Structure ◽  
Phononic Crystals ◽  
Two Dimensional
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