Acoustic Gaps Research Articles

Symmetry breaking and gap opening in two-dimensional hexagonal lattices

The inhibition in wave propagation at band gap energies plays a central role in many areas of technology such as electronics (electron gaps), nanophotonics (light gaps) and phononics (acoustic gaps), among others. Here we demonstrate that metal surfaces featuring free-electron-like bands may become semiconducting by periodic nanostructuration. We combine scanning tunneling spectroscopy and angle-resolved photoemisssion to accurately determine the energy-dependent local density of states and band structure of the Ag/Cu(111) noble metal interface patterned with an array of triangular dislocations, demonstrating the existence of a 25 meV band gap that extends over the entire surface Brillouin zone. We prove that this gap is a general consequence of symmetry reduction in close-packed metallic overlayers; in particular, we show that the gap opening is due to the symmetry lowering of the wave vector group at the K point from C3v to C3.

Acoustic gaps in a chain of magnetic spheres

Acoustic gaps are normally observed in granular inhomogeneous structures made of composite materials. The modulation of the elastic properties in such media creates the coherent effects of scattering and interference that ultimately lead to frequency intervals where sound propagation is forbidden. Contrastingly, we report here an experimental observation of acoustic gaps in homogeneous media; specifically, in granular chains. The beads used in our study are magnetic. Therefore, instead of modulating the elastic properties of the chain, we modulate the magnetization (i.e., the contact forces). We also observe that the propagation speed of acoustic signals through the magnetic chains used in this study is at odds with the speed predicted by Hertz's law.

気柱共鳴現象に及ぼす格子配列円管群内のキャビティの影響(流体工学,流体機械)

In the present paper the attention is focused on the effect of small cavities inside in-line tube banks on acoustic resonance which occurred in the two-dimensional model of boiler. We measured sound pressure level (SPL), amplitude and phase delay of acoustic pressures and gap velocity. As a result, we found many peak frequencies of sound pressure level with different Strouhal numbers, mainly about S_t=0.15, 0.26 and 0.52. The variation of SPL for S_t=0.26, 0.52 components in tube banks with cavities were the same as the result of no cavities. The existence of cavities inside in-line tube banks caused the resonance of S_t=0.15. And the acoustic resonance of first mode in the transverse direction was generated if the small cavities existed inside tube banks. This resonance was not generated from tube banks of no cavities. The resonance onset velocity in the transverse mode was fairly slower than that of no cavities. It was easy to generate acoustic resonance when there were small cavities inside in-line tube banks. And we have examined the effect of baffle plates for controlling acoustic resonance generated from tube banks with cavities.

Effects of morphology on phonons in nanoscopic silver grains

The morphology of nanoscopic Ag grains significantly affects the phonons. Atomistic simulations show that realistic nanograin models display complex vibrational properties. (1) Single-crystalline grains. Nearly pure torsional and radial phonons appear at low frequencies. For low-energy, faceted models, the breathing mode and acoustic gap (lowest frequency) are about 10% lower than predicted by elasticity theory (ET) for a continuum sphere of the same volume. The sharp edges and the atomic lattice split the ET-acoustic-gap quintet into a doublet and triplet. The surface protrusions associated with nearly spherical, high-energy models produce a smaller acoustic gap and a higher vibrational density of states (DOS) at frequencies $\ensuremath{\nu}<2\phantom{\rule{0.3em}{0ex}}\mathrm{THz}$. (2) Twined icosahedra. In contrast to the single-crystal case, the inherent strain produce a larger acoustic gap, while the core atoms yield a DOS tail extending beyond the highest frequency of single-crystalline grains. (3) Mark's decahedra, in contrast to (1) and (2), do not have a breathing mode; although twined and strained, do not exhibit a high-frequency tail in the DOS. (4) Irregular nanograins. Grain boundaries and surface disorder yield nondegenerate phonon frequencies, and significantly smaller acoustic gap. Only these nanograins exhibit a low-frequency ${\ensuremath{\nu}\phantom{\rule{0.1em}{0ex}}}^{2}$ DOS in the interval 1--2 THz.

Evidence of the existence of phononic band gaps: A practical example of a tunable sound insulation by a periodic device of rods

Based on the principle of phononic band gap materials, the control of acoustic frequency gaps by altering the geometry of the system is analyzed in the particular case of a set of parallel solid square-section columns distributed in air on a square lattice. This system is shown to be sensitive enough to the rotation of the columns to be considered for a practical sonic band gap width engineering. For different geometric configurations, experimental and theoretical results are presented and a discussion about the application of such structures as sound insulators is discussed. We acknowledge the use of the Namur Scientific Computing Facility (Namur-SCF), a common project between FNRS, IBM Belgium, and the Facultés Universitaires Notre-Dame de la Paix (FUNDP). [C. Goffaux acknowledges the financial support of the FIRST program of the Walloon Region Government and the Research and Development Centre of Cockerill-Sambre (ARCELOR Group).]

Recent observations with air-coupled NDE in the frequency range of 650 kHz to 1.2 MHz

An air-coupled NDE-system has been used for the inspection and imaging of discontinuities and inhomogenities in different kinds of materials, such as coating variations on tissue, spot welds on steel, and air inclusions in metal plates and welds. The measurement system operates in either continuous or pulse mode at sound frequencies between 0.65 and 1.2 MHz. Air-coupled piezo-based transducers with matching layers are used to overcome the acoustic impedance gap with air.

Surface Acoustic Wave Pressure Sensor

A sensitive sensor for measurement of pressure and strain is created by fabricating a surface acoustic wave (SAW) delay line on a quartz substrate. The SAW device which acts as a band pass filter has a central frequency of 98MHz. When an external force, strain, pressure is applied to the acoustic gap, then the gap length and IDT finger spacing will change and thus cause a shift of the central frequency and of the phase. Our approach was first to generate a 98MHz signal at the input transducer and to evaluate the relative phase shift due to the pressure or the strain. The second approach was to introduce the SAW device in an oscillator loop to measure the relative variations of the central frequency. A simulation based on finite elements was carried out to compare the length variations and an experimental study of the IDTs position, substrate thickness and orientation on the sensor response.

Acoustic band gaps in 2D liquid phononic crystals of rectangular structure

We present band structure results for a new two dimensional(2D) rectangular array geometry of water (mercury) cylindersof square cross section in a mercury (water) host. The resultsshow that the water/mercury system, consisting of low-densitycylinders in a high-density host, is the most favourable configurationfor obtaining large acoustic gaps. Otherwise, only very smallstop gaps can be found for the mercury/water systems. For a givencylinder width value, the lowest band gap may not always havethe maximum width, but at some value in both systems the lowestband gap will always have the largest width. The differencesin the case of circular cylinders are also discussed.

Tunability of acoustic spectral gaps and transmission in periodically stubbed waveguides

A theoretical investigation is made of acoustic wave propagation in a periodically stubbed waveguide. In general the waveguide segments and stubs are made of different materials. The acoustic wave in such a system has two independent polarizations: out-of-plane and in-plane modes. The band structure and transmission spectrum is studied for diverse geometries using a simple and efficient version of the transfer-matrix method. For the same material between the waveguide and symmetric stubs the width of some gaps can change, upon varying the stub length or width, by more than one order of magnitude. A further modulation can be achieved for different material between the stubs and the main waveguide or if the stubs are asymmetric. The gaps in the band structure of an infinitely long system correspond to those in the transmission spectrum of the same system but with finite number n of units. For n finite (i) there exist pseudogaps that gradually turn into complete gaps with increasing n and (ii) the introduction of defects gives rise to states in the gaps and leads to transmission resonances.

Acoustic stop bands for two-dimensional periodic arrays of metallic rods: Square geometry

Extensive band structures have been performed for two-dimensional periodic arrays of rigid stainless steel cylinders in air, with Bloch vector being perpendicular to the cylinders. For cylinders 2.9 cm in diameter and period of 10 cm (i.e., the filling fraction f=0.066) there is no acoustic gap for frequencies below 6.4 kHz. However, the density of states reveals prominent minima at 1.7 and 2.4 kHz. These frequencies do agree with those of the first two attenuation maxima observed in the experiment [Nature 378, 241 (1995)] and are indeed related to diffraction from the [100] and [110] planes. Thus even with idealization, Sempere’s sculpture exhibits pseudogaps—not full gaps. It is stressed that, for any value of the period of the system, there is no acoustic gap for f≤30%; magnitude of the gap, for f≥30%, is inversely proportional to the period of the system. Moreover, if the filling fraction exceeds 40%, a second gap, higher in frequency, opens up. In addition, the fabrication of a multiperiodic system in tandem that could create a huge hole in sound within the human audible range of frequencies is proposed. [Work partially supported by CONCyT Grant No. 28110E.]

One-phonon relaxation of localized electronic states inanharmonic nanoparticles

There is currently great interest in the dynamics ofelectrons and phonons in low-dimensional systems, where the effectsof quantum confinement cause a dramatic difference in their behaviouras compared with bulk systems. In this paper we consider a localizedelectronic impurity state (an electronic two-level system) linearlycoupled to the vibrational modes of an isolated nanometre-scaleinsulating crystal, and study the phonon emission rate atfrequencies less than that of the lowest internal vibrational mode,i.e., in the acoustic `gap'. We show that, at finite temperature,electronic energy relaxation below the acoustic gap can occur as aresult of anharmonic broadening of vibrational modes, and wecalculate the frequency and temperature dependence of the relaxationprovided by this mechanism.

Direct observation of the acoustic gaps in Ge/GexSi1−x superlattices

Direct observation of the acoustic gaps in Ge/GexSi1−x superlattices

The existence of full gaps and deaf bands in two-dimensional sonic crystals

Theoretical and experimental determination of sonic band structures of two-dimensional (2-D) arrays of rigid cylinders in air is reported. We present measurements for square and triangular lattices. A variational method is employed to calculate the acoustic dispersion relation. Experimentally, a transmission technique and the analysis of the phase delay between the incident and scattered waves by the structure are used to construct the acoustic bands. The comparison between theory and experiments allows to fully characterize the band gaps and it has also demonstrated the existence of deaf bands; i.e., bands which cannot be excited due to symmetry reasons. For the case of square lattice we show that the structure with a filling fraction of 0.41 has a full acoustic gap.

Acoustic spectral gaps and discrete transmission in slender tubes

This work reports on the band structure and transmission spectrum for the longitudinal (acoustic) wave propagation in a system made up of N′ dangling side branches (DSB) periodically grafted at each of the N equidistant sites on a slender tube. A periodic pattern of large stop bands is obtained for the airy DSB on the slender water tube. The emphasis is laid on the interesting result of huge gaps and discrete transmission spectrum due only to the DSB grafted at a single site (N=1) on the slender tube. Designing the system with open tubes allows achievement of the lowest gap below a threshold frequency and extending up to zero—thereby providing an entirely discrete band structure and transmission spectrum. This should have important consequences for the suppression of low-frequency noise and for designing filters and transducers.

Sound attenuation by a two dimensional array of cylinders

Here, it is shown, for the first time, a systematic analysis (experiment and theory) of the acoustic transmission of a two-dimensional periodic array of rigid cylinders with two different configurations: square and triangular. The influence of the filling fractions, ranging from 0.06 up to 0.41, on the appearance of the pseudogaps and full band gaps is studied. Above a certain filling fraction, an overlap is observed between the attenuation peaks measured along the two high symmetry directions of the Brillouin zone. This effect is considered as the fingerprint of the existence of a full acoustic gap. Nevertheless, the comparison with our calculation of band structures shows that the lattice has band states in that frequency range. These bands are called deaf bands (i.e., they cannot be excited by experiments of sound transmission) [Sanchez-Perez et al., Phys. Rev. Lett. (to be published)].

Sound Attenuation by a Two-Dimensional Array of Rigid Cylinders

In this Letter we present an experimental analysis of the acoustic transmission of a two-dimensional periodic array of rigid cylinders in air with two different geometrical configurations: square and triangular. In both configurations, and above a certain filling fraction, we observe an overlap, in the range of the audible frequencies, between the attenuation peaks measured along the two high-symmetry directions of the Brillouin zone. This effect is considered as the fingerprint of the existence of a full acoustic gap. Nevertheless, the comparison with our calculation of band structures shows that the triangular lattice has band states in that frequency range. We call them deaf bands. This contradictory result is explained by looking at the symmetry of the deaf bands; they cannot be excited by experiments of sound transmission.

Acoustic spectral gaps and discrete transmisson in slender tubes

We report the band structure and transmission spectrum for the longitudinal (acoustic) wave propagation in a system made up of N′ dangling side branches (DSB) periodically grafted at each of the N equidistant sites on a slender tube. A periodic pattern of large stop bands is obtained for the airy DSB on a slender water tube. We emphasize the interesting result of huge gaps and the discrete transmission spectrum due only to the DSB grafted at a single site ( N=1) on the slender tube. Designing the system with open tubes allows achievement of the lowest gap below a threshold frequency and extending up to zero — thereby providing an entirely discrete band structure and transmission spectrum. This should have important consequences for the suppression of low-frequency noise and for designing filters and transducers.

Stop-bands for periodic metallic rods: Sculptures that can filter the noise

We perform extensive band structure computation for two-dimensional (2D) periodic arrays of rigid stainless steel cylinders in air, with Bloch vector being perpendicular to the cylinders. For cylinders 2.9 cm in diameter and period of 10 cm (i.e., filling fraction f=0.066) there is no acoustic gap for frequencies below 6.4 kHz. However, the density of states reveals prominent minima at 1.7 and 2.4 kHz. These frequencies do agree with those of the first two attenuation maxima observed in the experiment [Nature 378, 241 (1995)] and are indeed related to diffraction from the [100] and [110] planes. Thus, even with idealization, Sempere’s sculpture exhibits pseudogaps—not full gaps. We stress that, for any value of the period, there is no acoustic gap for f⩽30%; magnitude of the gap, for f>30%, is inversely proportional to the period of the system. Moreover, if the filling fraction exceeds 40%, a second gap, higher in frequency, opens up. In addition, we propose the fabrication of a multiperiodic system in tandem that could create a huge hole in sound within the human audible range of frequencies.

Acoustic stop bands for periodic arrays of metallic rods

Extensive band structure computations are performed for two-dimensional periodic arrays of rigid cylinders in air, with the Bloch vector being perpendicular to the cylinders. It is found that for any value of the period (of the square lattice), there is no acoustic gap for filling fraction f<30%; the magnitude of the gap, for f >30%, is inversely proportional to the period. Moreover, if the filling fraction exceeds 40%, a second gap, higher in frequency, opens up. Within these gaps (or stop bands) sound and vibrations are forbidden, irrespective of the direction of propagation. It is noted that for cylinders 2.9 cm in diameter and period of 10 cm (i.e., f=0.066), there is no acoustic gap for frequencies below 6.4 kHz. However, the density of states reveals prominent minima at 1.7 and 2.4 kHz. These frequencies do agree with those of the first two attenuation maxima observed in a recent experiment [Nature 378, 241 (1995)] and are indeed related to diffraction from the [100] and [110] planes. Thus, even with idealization, Sempere’s sculpture (investigated in the above reference) exhibits pseudogaps—not full gaps. A proposed application of the above-mentioned band structure calculations is presented in the following abstract.

Spin-wave study of the magnetic excitations in a layered structure with bilinear and biquadratic interlayer exchange

Using a microscopic and quantum approach, we study the ground state configuration and the spin-wave excitations of a model of two ferromagnetic monolayers, interacting via both bilinear and biquadratic exchange, and subject to an easy-plane anisotropy, a quartic in-plane anisotropy, and an external field. Peculiar features are found in the field dependence of the acoustic and optical frequency gaps in correspondence to the critical fields for which the canting angle between the magnetizations of the two coupled layers presents discontinuities. In particular, we suggest that a minimum in the optical gap at the saturation field could be experimentally observed by Brillouin light scattering in real systems, like Fe/Cr/Fe trilayers.