材料物理112161358

A study on phononic crystalsAbstract: As is known to all, phononic crystal is a new type of acoustic functional material, which is necessary to be used in some special occasions, the study of phononic crystals caused a great deal of attention in the national research institutes. This article introduces the concept and the basic characteristics of phononic crystals in detail, the phononic crystal defects state characteristics, the phononic crystals forbidden band mechanism and various potential application areas (noise and vibration reduction) in phononic crystals. Finally, we prospect the research and development of the phononic crystals.Keywords: phononic crystals noise and vibration reduction prospect 1 IntroductionThe potential field of semiconductor atoms arranges periodically. When the propagation of the electrons happen in the semiconductor, the interaction between electronics and atomic periodic potential makes semiconductor electronic occupy band gap, which is able to manipulate the flow of electrons. On behalf of the silicon crystal semiconductor has brought a revolution in science and technology. With the development of the transistors, integrated circuits, large-scale integrated circuits even ultra-large-scale integrated circuits, semiconductor technology has a profound impact on the progress of human civilization [1,2].More than ten years ago, people began to touch on the opticalproperties of the structure and function of materials research. Theory and experiments have proved that if the dielectric of the material is a constant, the structure and function in the periodic variation in the optical wavelength scale, the interaction of photons with periodic structure makes the material has a similar semiconductor electronic band-gap energy band structure, called photonic band gap (known as photonic band gap). Periodic dielectric photonic band gap structure and function of materials are called photonic crystal (photonic crystals). Photon energy falls on the light waves in the photonic band gap can not be in the photon propagation in the crystal. When the photonic crystal exists (or introduced) point defects or line defects, the forbidden band of light waves will be localized in the point defect or only along the defect propagation. The design of the periodic structure of the photonic crystal and its defects, can artificially regulate the flow of photons[3].In 1987, the concept of photonic crystals independently proposed by E. Yabionovithch and S. John two[4]. In 1991, Yabionovitch verified the exist of microwave photonic band gap by experimental. Photonic crystal then quickly became photoelectron and information technology research in the field hot spots. Subsequently, it is discovered that when the elastic wave propagation exists in periodic elastic composite medium, it will have a similar elastic wave band, therefore, putting forward the concept of phononic crystals. Phononic crystal has a wealth of physicalconnotation and potentially broad application prospects. Phononic crystals have caused great concern of national research institutions[5].2Phononic crystals2.1The concepts and basic characteristics of phononic crystalsThe Phononic crystal is the cyclical nature of the elastic wave band structure and function of materials[6]. Phononic crystal internal material component (called groups) of the elastic constants and mass density parameters cyclical changes. With the band gap of the material components with different periodic structures in the form of different phonon crystal elastic wave characteristics are different.Phononic crystals have similar basic characteristics: when the elastic wave frequency falls within the band gap range, the elastic wave is prohibition of the dissemination, when there exists a point defect or line defect, the elastic wave is localized at the point defects, or only along the defect propagation[7]. Similarly, the design of the the phononic crystal periodic structure defects can artificially regulate the flow of elastic waves.Elastic wave is coupled by longitudinal and transverse waves full vector wave, three independent elastic parameters are in each group, that the mass density P, the longitudinal wave velocity Ci and shear wave wave velocity Ct (in the fluid medium, Ct =0); light wave is a scalar wave, only one independent elastic parameter is the dielectric constant in eachelement. The phononic crystals, therefore, possessing a richer physical meaning[8]. The following lists the relevant characteristics of the (electronic) crystals, photonic crystals and phonon crystals compared with three striking similarities can be seen from the table, the (electronic) crystals, photonic crystal research methods phonon crystals have a guiding role.According to the crystal structure of the phonons in the Cartesian coordinate system, in three orthogonal directions in the circumferential, periodic phononic crystals can be divided into one-dimensional, two-dimensional, three-dimensional phononic crystals. Scholars research has been carried out on some of the specific structure of phononic crystals: a one-dimensional phononic crystals, general periodic layered structure consisting of two or more materials; dimensional phononic crystals. Usually a certain direction is parallel to the space for the center axis of the cylinder material[9], and the periodicity of the lattice structure are formed in the buried base material, the cylinder material can be hollow or solid, generally circular cross-section of the cylinder, can also be square. Cylinder arrangement form may be a square arrangement, delta arrangement, the hexagonal array like dimensional phonon crystals are generally buried in a base material formed of a spherical scattering body periodic lattice structure, periodic lattice structures can be in the form of a body-centered cubic structure, face-centered cubic structure, hexagonalclose-packed structure. Figure 1 shows a typical schematic block diagram of the various phonon crystals.Fig 1 Phononic crystals of different dimensions2.2 The research overview of phononic crystalThe propagation characteristics of elastic waves in layered media research has been for nearly 70 years’ history, while the phononic crystals proposal of the concept and the theory of phonon crystal was just nearly 10-year history[10]. Phononic crystal researches, due to the difficulties of theoretical research, as well as other factors, making relatively slow progress and the crystal literature of total are no more than 150, according to incomplete statistics. In 1992, MM Signal and EN Economou first confirmed in theory that a spherical scattering body embedded in a matrix material to form a three-dimensional periodic lattice structure having elastic wave band gap characteristics[11]. In 1993, M. S. Kushwaha et.al first clear phononic crystals and the concept, and nickel column aluminum alloy forming the composite dielectric matrix, calculated by the plane wave method can be obtained in shear polarization direction ofelastic wave band. In 1995, R. Martinez-Sala et.al in the West Spain Madrid 200 years ago, a sculpture made flowing melody acoustic properties research, first confirmed the presence of the elastic wave band from the experimental point of view from this phonon crystal caused great concern[12]. Phononic crystal research work focuses on the formation of the band gap of phononic crystals and phase should the theoretical calculations[13]. In addition, scholars are from various countries in crystal defects phonon state study, experimental research has also been made good progress in applications of explore infancy . Phononic crystal research areas are in the country, Wuhan University and Guandong University of Science and Technology has made some progress. National University of Defense Technology Photonic/phononic crystal research center is currently engaged in the study of phononic crystals[14].2.3 Research content of phonon crystalsPhononic crystal researches mainly includes three aspects: the band gap of the phononic crystal mechanism, characteristics of defect states and application researches.2.3.1 phononic crystal band gap mechanismA lot of theoretical and experimental studies have proved the existence of a phononic crystal elastic wave band, Figure 2 shows a typical phonon crystal band structure, shaded in Figure 2 is the elastic wave band gap.Fig 2 An elastic band gap of a typical phononic crystalThere are two more mature about the mechanism of elastic wave band formed, scattering mechanisms and locally resonant mechanism in Prague. Bragg scattering leaded by crystal band theory in solid state physics, photonic crystals comply with the Bragg scattering mechanism. Bragg scattering caused by the band gap is mainly due to[15]: the cycle changing in material properties with elastic wave interaction, such that certain frequencies of the wave does not correspond to the vibration mode in the periodic structure, which can not spread, resulting in the forbidden band. Large number of studies of elastic wave band gap formed literature focuses on the Bragg scattering mechanism, the study shows that the elastic wave band gap generates composite media related component of the elastic constants, density and speed of sound, and the filling ratio of the component; and lattice structure and size. In general, non-network type of the lattice structure than network-type lattice structure is easy to produce the band gap; elastic component in the composite dielectric constant, the greater the difference, the more prone the forbidden band [16]. In addition, the wavelength of the elastic wave band correspondingBragg scattering formes of the elastic wave is usually associated with periodic structure, the size parameter (i.e, the lattice size or lattice constant) equivalent to the forbidden band is consistent with the mechanism in concept with the photonic crystal periodic structure. Bragg scattering mechanism phononic crystals at low frequencies (especially below 1khz), the application causes some difficulties.Liu Zhengyou et.al did research on viscoelastic soft materials with shot simple cubic lattice structure buried in the epoxy resin to form the three-dimensional phononic crystals found the phononic crystal band gap is much larger than the wavelength corresponding to the size of the lattice, breaking through the limitations of the Bragg scattering mechanism, and not strictly in the scatterer cycle distribution, even random distribution, the composite structure also has a band gap, and thus raise locally resonant elastic wave band mechanism[17]. Localized resonance mechanism, under the excitation of an elastic wave of a specific frequency, the single scattering body resonance, and the interaction with the incident, so that it can not continue to spread. Band-gap generation mainly depends on the individual single scattering body itself, the structure and the interaction of the elastic wave. Local resonance mechanism, phononic crystals, the vibration inherent characteristics of the band gap and single scattering body is closely related to the cyclical nature of the scattering body and the lattice constant has nothing to dowith it, and this has opened up a broad road in the application of the low-frequency band for phononic crystals.In a word, Bragg scattering mechanism emphasizes the periodic structure of the wave, and how to design the periodic structure of the lattice constant and the material component of the mix is one of the critical factors of the design band gap; localized resonance mechanism to emphasize the role of the special structure of the single scattering body wave, how to design the resonance structure of the single scatterer and scattering body in the spread characteristics of the base body is a key issue[18].Phononic crystal band gap mechanism relies on the calculation of the elastic wave band, the mature elastic wave band gap calculation method transfers matrix method, plane wave expansion method, finite different time domain method, multiple scattering method.2.3.2 Transfer matrix methodThe method used for the band gap of the one-dimensional phononic crystal (layered medium) calculation are very simple tools. Basic side of the transfer matrix method parameters from the contact state (stress, particle velocity, etc.) process to start, drawing the transfer matrix of the solid plate medium, and then by the surrounding medium and intermediate dielectric interface characteristics given boundary conditions, the solution of the system can be finally obtained. Because the transfer ofthe matrix is generally smaller, and catalytical solutions, so the smaller is the amount of calculation.In a real crystal, various couplings exist between the motions of electrons, photons, and phonons. For example, infrared absorption and polariton excitation results from the coupling between lattice vibrations and electromagnetic (EM) waves in an ionic crystal[19]. If the ferroelectric domain or piezoelectric coefficient is modulated in a phononic crystal, the interaction between the super lattice vibrations and EM wave may be established. Similar effects can be expected in such an artificial medium. This kind of phononic crystal is termed an ionic-type phononic crystal (ITPC).2.3.3 Plane wave expansion methodThis method can be used for two-dimensional and three-dimensional phononic crystals band-gap calculation. Plane wave method by the displacement in the wave equation, elastic parameters and other physical quantities in the reciprocal lattice vector space in the form of a plane wave superposition of approximate expand, the wave equation into an intrinsic equation solving eigenvalue can get the frequencies and wave vector between the dispersion relation, namely the so-called band structure[20]. Phononic crystals forbidden band structure calculations, the plane wave expansion method has been widely used. It can transfer from solid-solid, liquid(gas)-liquid (gas) in the calculation of other componentsof the various structures of the phonon crystal has achieved considerable success. Plane wave expansion method for phononic crystal band gap calculated convergence is slow, and phononic crystals constituted by the solid-liquid (gas) can not be accurately calculated, so it has some limitations.2.3.4 FDTD methodThis method can be used for two-dimensional and three-dimensional phononic crystals band gap calculation. FDTD[21] method is a direct time-domain discrete wave equation method to solve the differential equations, a problem of numerical methods for solving the band gap of the phononic crystal. The method can simulate a variety of complex periodic structure, the non-uniformity of the medium, anisotropy, dispersion characteristics and nonlinear problems can be accurately simulated. FDTD method phonon band-gap calculated phonon band-gap calculated with the use of multiple scattering method are in good agreement. We should pay attention to the numerical stability and convergence the calculated phonon crystals instantaneous nonlinear response problems.2.3.5 Multiple scattering methodThis method is mainly used for three-dimensional phononic crystal band gap. Multiple scattering method can calculate the energy band structure of the crystal depends on each ball between the elastic scatteringby calculation incident since the sound waves of the other ball to the the single ball surface scattering, can solve the characteristic frequency equation can also calculate the reflection and transmission coefficients of the elastic wave scattered body periodic array of finite-layer structure. The theory of multiple scattering method cited in the electronic band structure calculations KKR (korringa-kohn-roskoker), is very suitable for the calculation of the special structure (such as solid spheres dispersed in the fluid) the phonon crystals[22]. Calculating the phonon energy band structure of the crystal, the usual plane wave method can not give the exact solution. Multiple scattering method is complex and difficult to use.2.4 phonon characteristics of crystal defect statesBragg scattering mechanism of phonon crystals have ideal periodic structure, the destruction of this ideal periodic structure is generally referred to as the defects(the concept follows the solid-state physics about defects in concept). The defects can be classified according to their dimension point defects, line defects and surface defects. When the existence of a crystal phonon in defects so-called defect states in the band-gap range, defect states in existence will phononic crystals forbidden band features a significant impact the phononic crystal defect states characteristics of great significance[23]. MM Signals et.al study two-dimensional lead/epoxy phononic crystals exist of elastic wave propagation, the point defects with changing the diameter of a leadcolumn to obtain, the calculations show that point defects on the elastic wave has a local role. Kafesaki et.al used the finite-difference time-domain (FDTD) method to study the elastic waves in a two-dimensional lead/epoxy phononic crystals spread in the presence of line defects, the line defect phononic crystals in the removal of a row or a lead bar, and studies have shown that the elastic wave propagation only along the defect[24]. Experimental defect states, Torres et.al studied the surface states in the two-dimensional mercury/aluminum phononic crystals, pointed out that the sound waves of acoustic waves in phononic crystal interface localized phenomenon. Also with experimental research by removing some of the water silver.The formation of the silver column formed L-shaped line defect and piezoelectric vibrator instead of a mercury column the acoustic wave propagation in the case of point defects, the experiments show that sound waves only along the defect. Propagation or localized at the point defects, the experimental results well validate the theoretical calculation results. Defects study three-dimensional phononic crystals, only a theoretical work. Psarobas et.al in this paper three-dimensional shot in the epoxy matrix face-centered cubic array in the presence of surface defects makes the band gap of the phononic crystal in transverse waves and longitudinal waves localized phenomenon[25]. Crystal defect states in phonon, most are just theoretical calculation work. Band-gap calculation method is alsoa major plane wave method, finite difference time domain method, multiple scattering method. Phononic crystals have only point defects, line defects, surface defects, three kinds of missing notch forms, but they can have the form of a variety of structures for each defective form. The sound photonic crystal defect states characteristics will phononic crystal engineering applications to provide a wide range of theoretical guidance.2.5 phononic crystals applicationsThe phononic crystals used largely in the prospect stage, phonon crystal characteristics of the body has a band gap, defect states features make it the vibration, noise, acoustic devices, so has a potentially broad application prospects. Phononic crystals in damping characteristics of the forbidden band, high precision machinery without vibration in the processing system provides a certain frequency range within the processing environment, thus ensuring plus machining accuracy level; certain sophisticated equipment can also provide a certain frequency range vibration-free work environment, and to improve the accuracy of operating parameters, improve reliability, extend life. Noise reduction, the band gap of the phononic crystal characteristics, possible to design a new noise reduction materials and manufacturing. This material may be in the noise propagation isolation of noise on the way, they can control the noise at the noise source. According to the local resonance machine reasonable, if you break through the low-frequency band gap of the phononic crystaldesign phononic crystals in the latent. Anechoic tiles boats, sonar has a broad application prospects[26]. When some defects in phononic crystals forbidden in periodic structures are within the so-called defect states. According to the Bureau defective sonic phononic crystal domain characteristics, you can design a new type of high-efficiency, low-power acoustic filter can also be designed with features highly focused, low-power acoustic lens. Very little about the the phononic crystals applied research literature. As far as we know, currently there are only two articles on the work in this area: A. Diez and other people through the fiber engraved the eclipse acoustic grating one-dimensional phononic crystal fiber anticous-optic modulation; F. Cervera et.al elastic material arranged in the air constitute dimensional phononic crystals real now a the acoustic lens function[27]. We have also noted that the U.S. Defense Advanced Research Projects Agency (DARPA) in 1999 phononic crystal financial support for sound filter, vibration and noise isolation. With Phononic crystal theory research being mature, the phononic crystals applied research will also arouse more and more attention. The phononic crystals research will involve phononic crystal preparation theory and technology surgery phononic crystal test characterization, they are also a phononic crystal research. Although there is no specialized literature work in this area, but with the sound sub-crystal applied research work commenced, this part of the research work will be paid attention to.3 ConclusionsThe phononic crystals theoretical studies have just has a certain basis, applied research begun. Research on a large number of domestic and foreign literatures and based on our current work situation conditions, we believe that further research work on phononic crystals will include the following several aspects.(1) On the basis of the theoretical calculation of the existing phononic crystals forbidden band fully studied various structural forms, material properties, lattice size phononic crystal band gap characteristics phononic crystals forbidden band characteristics, and strive to be drawn with each correspondence between a function of the parameters (structure, material properties, lattice size, etc.), so as to realize the band gap of the phononic crystal design. Phononic crystal band gap.(2) Studying the introduction of the damping effect theory, and striving to accurately describe phonon crystal energy distribution (phononic crystal elastic wave transmission, absorption, reflection), and thus further reveal the role of phononic crystals mechanism.(3) Further study on the phononic crystal defect states in the propagation of elastic waves in a forbidden band calculation theory. (4) On the basis of the above work, explore phononic crystals in vibration, noise reduction, sound waves change can applications such research.The phononic crystals with a new acoustic functional materials has rich connotation of physical and potentially broad application prospects. 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