Phononic Band Gaps Research Articles

Phonon dispersion of buckled two-dimensional GaN

Group-III nitride semiconductors such as GaN have various important applications based on their three-dimensional form. Previous work has demonstrated the realization of buckled two-dimensional GaN, which can be used in GaN-based nanodevices. However, the understanding of buckled two-dimensional GaN remains limited due to the difficulties in experimental characterization. Here, for the first time, we have experimentally determined the phonon dispersion of buckled two-dimensional GaN by using monochromatic electron energy loss spectroscopy in conjunction with scanning transmission electron microscopy. A phonon band gap of ~40 meV between the acoustic and optical phonon branches is identified for buckled two-dimensional GaN. This phonon band gap is significantly larger than that of ~20 meV for the tetrahedral-coordinated three-dimensional GaN. Our theoretical calculations confirm this larger phonon band gap. Our findings provide critical insights into the phonon behavior of buckled two-dimensional GaN, which can be used to guide high-performance thermal management in GaN-based high-power devices.

Monolayer and bilayer BP as efficient optoelectronic materials in visible and ultraviolet regions

Hexagonal boron phosphide (BP) shows significant promise for optoelectronic applications due to its high carrier mobility and moderate band gap. Strain inevitably occurs during the synthesis of two-dimensional (2D) nanomaterials. In this work, a detailed study on the strain-dependent phonon dispersion and optical properties of monolayer and bilayer BP was performed. The calculated phonon dispersion curves demonstrate that both monolayer and bilayer BP systems remain dynamically stable under tensile strain. By increasing tensile strain, the LO and TO modes soften and the phonon band gap between optical and acoustic modes becomes narrower. The LO and TO modes display expanded phonon spectra under large tensile strains in contrast to the ZA mode. The absorption edge of bilayer BP is located around 0.6 eV, lower in energy with respect to the monolayer BP at ∼ 0.8 eV. The results indicate that the optical absorption may be enhanced by applying the compressive strain. With their broad absorption range and strain-tunable absorption strength and phononic properties, monolayer and bilayer BP are highly promising for next-generation nanodevices.

Collaborative actuation of liquid crystal elastomer unit cells as a function design platform

AbstractAs future soft robotic devices necessitate a level of complexity surpassing current standards, a new design approach is needed that integrates multiple systems necessary to synchronize the motions of soft actuators and the response of signals, thereby enhancing the intelligence of flexible devices. Herein, we propose a liquid crystal elastomer unit cell-based platform that organizes the cells in a group to create expandable functions. One unit cell behaves like a flexible module that can expand biaxially into a specific, stable, and controllable pattern. Collaborating the unit cells in different manners results in an adaptable soft grasper, a half-adder for information processing, and a tunable phononic bandgap. This implies a high level of reconfigurability and scalability in both structures and functions by elegantly reassembling the unit cells. This design strategy has the potential to integrate multiple functions that traditional soft actuators cannot accommodate, providing a platform for developing intelligent soft robotics.

Improving the functionality of biosensors through the use of periodic and quasi-periodic one-dimensional phononic crystals

Abstract Resonant acoustic band gap materials have steered a new sensing technology era. This study is presented to investigate of the one-dimensional (1D) phononic crystals (PnCs), involving periodic, as well as quasi-periodic 1D layered PnCs represented as a highly sensitive biosensor to detect and monitor the quality of milk. In this regard, the numerical findings show that the examined periodic PnCs structure outperformed the quasi-periodic structure. In particular, it provides a wider phononic band gap and greater sensitivity as well. In addition, the quasi-periodic design (especially Fibonacci sequence S4) introduces multiple resonance peaks via transmission spectra, which may lead to some conflicts during the detection process. The findings reveal that the frequency of the resonant peak can effectively change with varied milk solution concentrations and temperatures. The optimized sensor is capable of differentiating between concentrations ranging between 0 and 50 % with a 10 % step, and it can also differentiate between temperatures, which range between 5 °C and 50 °C. This makes it ideal for precise detection of other liquids and solutions. The sensor performs efficiently for all milk solution concentrations. Here, the findings demonstrated that the examined defective PnC structure exhibited the most favorable sensitivity of the value of 94.34 MHz, so it showed the highest sensitivity when varying milk concentrations. In addition, the configurated sensor provided high QF and FOM values of 3,853.645161 and 157.42, respectively. On the other hand, the sensor performs very well for all temperatures of the milk solution. As such, the S 4 quasi-periodic structure is characterized as the optimal sensor structure when varying temperatures, introducing a sensitivity of 4.78 MHz/°C, QF of 4,278.521, and FOM of 7.48 °C−1.

Ultracompact multiway ultrasonic power splitters based on phononic crystal with a triangular lattice

We report the ultracompact multiway power splitters based on the phononic crystal with a triangular lattice. Such power splitters can effectively divide ultrasonic energy into multiple channels (n≥2) and output them. The arrow-shaped and star-shaped power splitters were separately discussed in detail based on the finite element method (FEM) as examples. The phononic bandgap in the triangular lattice arrangement and dispersive curves of a single phononic waveguide were analyzed, respectively. Also, the displacement field distribution and transmission efficiency of these outputs were calculated to evaluate the efficiency of the splitters. The results indicate that these splitters possess novel and promising properties, including ultracompact, high-efficiency, and large bandwidth. The perturbations analysis of the power splitter proves that it has good mechanical stability. It is to be expected that these ultracompact splitters will present practical applications in future acoustic wave circuits.

Design optimization of phononic-fluidic resonator systems

Phononic-fluidic resonators utilize an acoustic fluid domain as a defect inside a solid metamaterial lattice, which can be used used to precisely measure acoustic properties of liquids. The design goal is to offer ideal boundary conditions for the acoustic resonator by matching defect resonance with phononic band gap. The design space of metamaterial or phononic crystal and fluidic resonator is nearly unlimited, especially when utilizing fully three-dimensional structures. In this work, we explore numerical shape and topology optimization to focus acoustic energy into the fluid domain and maximize the quality factor of the defect resonance. This requires the use of complex multi-frequency objective functions, while taking into account practical limits such as finite size and losses in the fluid and solid domains. Results highlight notable but limited improvements of quality factor with shape optimization starting from an initial design constrained by the maximum deformation possible. On the other hand, topology optimization results offer unique and unexpected ideas, and thus a deeper dive into the design space.

Role of finite-temperature dynamics and dispersion interactions on the phonon bandgap in thermoelectric SnSe

Role of finite-temperature dynamics and dispersion interactions on the phonon bandgap in thermoelectric SnSe

Ab-Initio calculations on physical properties of Dirac semimetal AMgBi (A=K, Rb, Cs)

This study presents a comprehensive first-principles investigation of the structural, mechanical, vibrational, thermodynamic and electronic properties of AMgBi (A = K, Rb, Cs) compounds using Density Functional Theory. Also, the effect of substituting alkali atoms on the physical properties has been discussed. The tetragonal PbClF-type structure has been confirmed by the analysis and the results revealed good agreement between calculated and experimental lattice parameters for KMgBi. The mechanical properties have been investigated for the first time for RbMgBi and CsMgBi. The mechanical stability of the materials in the ground state has been confirmed through the use of obtained elastic constants. Furthermore, derived parameters from elastic constants such as bulk modulus, shear modulus, and Poisson's ratio indicated that the materials are brittle and exhibited anisotropic mechanical behavior due to their layered structure. This study conducts a detailed analysis of phonon modes, explores their connections to thermal and elastic properties, visualizes the movements of phonon modes at the gamma point, determines Born effective charges, and discusses LO/TO splitting, which is for the first time for RbMgBi and CsMgBi. Phonon dispersion calculations confirmed the dynamical stability of the compounds and revealed the presence of phonon band gaps, supporting their quasi-two-dimensional nature. Investigation of thermodynamic properties using the quasi-harmonic approximation has shown the temperature dependence of internal energy, Helmholtz free energy, specific heat, and entropy for the first time for all compounds. The materials exhibited relatively low thermal conductivity, following the order KMgBi > RbMgBi > CsMgBi. The calculated Grüneisen parameter values were found to be 1.42, 1.44, and 1.53 for KMgBi, RbMgBi, and CsMgBi, respectively, suggesting relatively weak anharmonicity within the materials.

Efficient phononic band gap optimization in two-dimensional lattice structures using extended multiscale finite element method

Efficient phononic band gap optimization in two-dimensional lattice structures using extended multiscale finite element method

Multistep and Elastically Stable Mechanical Metamaterials

Abstract Materials and structures with tunable mechanical properties are essential for numerous applications. However, constructing such structures poses a great challenge since it is normally very complicated to change the properties of a material after its fabrication, particularly in pure force fields. Herein, we propose a multistep and elastically stable 3D mechanical metamaterial having simultaneously tunable effective Young's modulus and auxeticity controlled by the applied compressive strain. Metamaterial samples are fabricated by 3D printing at the centimetric scale, with selective laser sintering, and at the micrometric scale, with two-photon lithography. Experimental results indicate an elementary auxeticity for small compressive strains but superior auxeticity for large strains. Significantly, the effective Young's modulus follows a parallel trend, becoming larger with increasing compressive strain. A theoretical model explains the variations of the elastic constants of the proposed metamaterials as a function of geometry parameters and provides a basic explanation for the appearance of the multistep behavior. Furthermore, simulation results demonstrate that the proposed metamaterial has the potential for designing metamaterials exhibiting tunable phononic band gaps. The design of reusable elastically stable multistep metamaterials, with tunable mechanical performances supporting large compression, is made possible thanks to their delocalized deformation mode.

Optical properties of popular dielectric substrate materials in a wide spectral range from far-infrared to ultraviolet

We investigated the optical properties of 13 different dielectric materials (slide glass, quartz, Al2O3 (c-cut), DyScO3 (110), KTaO3 (001), LaAlO3 (001), (LaAlO3)0.3-(Sr2AlTaO6)0.7 (001) (LSAT), MgF2 (100), MgO (100), SiC, SrTiO3 (001), TbScO3 (110), and TiO2). The single-bounce reflectance spectra of the bulk samples were measured using Fourier transform infrared (FTIR) and monochromatic spectrometers across a wide spectral range, from far infrared to ultraviolet (80–50,000 cm−1). Using the Kramers–Kronig analysis, we obtained the optical conductivity and dielectric function of the dielectric materials from their measured reflectance spectra. Moreover, we measured the transmittance spectra of the materials to obtain their bandgaps. We fitted the measured reflectance spectra using the Lorentz model to obtain phononic structures. Each dielectric material exhibits unique phononic structures and optical bandgaps, associated with the composition and crystal structure of the material. The observed optical properties of these dielectric materials provide valuable information for the optical analysis of thin films grown on them.

Reconfigurable frequency demultiplexer using coupled-resonator elastic waveguides

Reconfigurable coupled-resonator elastic waveguides are formed using defects composed of threaded rods, fixed with nuts and attached to a perforated two-dimensional phononic crystal slab. The resonant frequency of the defect can be tuned continuously within a complete phononic bandgap by adjusting the length of the threaded rod. Straight waveguides are formed from a line of defects. Phononic circuits are created by coupling three parallel straight waveguides. Through precise manipulation of the length of the threaded rod assembly, frequency demultiplexing of Lamb waves is achieved. Numerical and experimental results are found to be in good agreement. This work is of significance for the practical design of phononic devices including reconfigurable circuits.

Anomalous Electron–Phonon Coupling in Cubic Be–X (X = Co, Ni, Rh, Hf) Crystals and Insight from Fermi Surface Nesting and Phonon Bandgap

Anomalous Electron–Phonon Coupling in Cubic Be–X (X = Co, Ni, Rh, Hf) Crystals and Insight from Fermi Surface Nesting and Phonon Bandgap

Uncovering Pattern-Transformable Soft Granular Crystals Induced by Microscopic Instability

Abstract Upon compression, some soft granular crystals undergo pattern transformation. Recent studies have unveiled that the underlying mechanism of this transformation is closely tied to microscopic instability, resulting in symmetry breaking. This intriguing phenomenon gives rise to unconventional mechanical properties in the granular crystals, paving the way for potential metamaterial application. However, no consistent approach has been reported for studying other unexplored transformable granular crystals. In this study, we present a systematic approach to identify a new set of pattern-transformable diatomic granular crystals induced by microscopic instability. After identifying the kinematic constraints for diatomic soft granular crystals, we have generated a list of feasible particle arrangements for instability-induced pattern transformation under compression. Instead of computationally intensive finite element models (FEMs) with continuum elements, we adopt a simplified mass-spring model derived from granular contact networks to efficiently evaluate these feasible particle arrangements for pattern transformation. Our numerical analysis encompasses quasi-static analysis and microscopic/macroscopic instability analyses within the framework of linear perturbation. Subsequently, the pattern transformation of the identified particle arrangements is confirmed through quasi-static analyses employing detailed finite element (FE) simulations with continuum elements. Additional numerical simulations with continuum elements reveal that the pattern transformations of particle arrangements are significantly influenced by the initial void volume and some transformed granular crystals may exhibit strong low-frequency directional phononic band-gaps, which were not observed in the initial granular crystals.

Slow sound mode prediction and band structure calculation in 1D phononic crystal nanobeams using an artificial neural network.

Phononic crystals, which are artificial crystals formed by the periodic arrangement of materials with different elastic coefficients in space, can display modulated sound waves propagating within them. Similar to the natural crystals used in semiconductor research with electronic bandgaps, phononic crystals exhibit the characteristics of phononic bandgaps. A gap design can be utilized to create various resonant cavities, confining specific resonance modes within the defects of the structure. In studies on phononic crystals, phononic band structure diagrams are often used to investigate the variations in phononic bandgaps and elastic resonance modes. As the phononic band frequencies vary nonlinearly with the structural parameters, numerous calculations are required to analyze the gap or mode frequency shifts in phononic band structure diagrams. However, traditional calculation methods are time-consuming. Therefore, this study proposes the use of neural networks to replace the time-consuming calculation processes of traditional methods. Numerous band structure diagrams are initially obtained through the finite-element method and serve as the raw dataset, and a certain proportion of the data is randomly extracted from the dataset for neural network training. By treating each mode point in the band structure diagram as an independent data point, the training dataset for neural networks can be expanded from a small number to a large number of band structure diagrams. This study also introduces another network that effectively improves mode prediction accuracy by training neural networks to focus on specific modes. The proposed method effectively reduces the cost of repetitive calculations.

Maximizing band gaps of single-phase phononic plates: Isogeometric optimal approach and 3D printing experimental validation

This work presents an effective isogeometric shape optimization approach for finding and widening the phononic band gaps of single-phase Mindlin plate structures. As the single-phase material phononic plate is easy to be manufactured by additive manufacturing, it has been investigated here by optimized its thickness profile to find and widen the band gaps. The proposed method utilizes a coarse B-spline surface to model the thickness profile of periodic plate and a fine B-spline surface to model the mid-surface of plate structure for simulation. The optimal design variables are the thickness variables, i.e., the z-components of the control points of the coarse B-spline surface. To avoid specifying the initial control point locations manually, the constrained dynamic maximization problem is solved by a particle swarm optimization (PSO) algorithm here. Various numerical examples demonstrate the effectiveness and reliability of the proposed method in finding optimal phononic band gaps of periodic plates. And the numerical results show that there is no band gap for hmax = 3 hmin, and the band gaps can be found and widen for hmax ≥ 5 hmin. The obtained band range is 638.9–823.6 Hz with a decreased central frequency of 731.25 Hz for hmax = 5 hmin and the width and the number of band gaps are increased as the maximum allowable thickness increases. Finally, one optimized design is fabricated through additive manufacturing, and the experimental frequency response is consistent with the results based on isogeometric analysis.

Using Optimization Algorithms to Design Phononic Barriers Protecting Monuments or Building Facades

The work compares the design of phononic structures using two types of optimization algorithms. Using the genetic algorithm and the simulated annealing algorithm, optimal layer distributions were obtained in which the phononic band gap phenomenon occurs. The mechanical wave propagating in the obtained structure, for the given frequency ranges, significantly reduces the transmitted energy, thanks to which the building facade or monument located behind the obtained barrier is exposed to much smaller vibrations, which significantly reduces damage related to long-term fatigue load. The mechanical wave propagation was modeled using the Transfer Matrix Method algorithm and the proprietary objective function allows for the reduction of wave transmission with the simultaneous reduction of high transmission peaks with small half-widths.

Exploring regenerative coupling in phononic crystals for room temperature quantum optomechanics

Quantum technologies play a pivotal role in driving transformative advancements across diverse fields, surpassing classical approaches and empowering us to address complex challenges more effectively; however, the need for ultra-low temperatures limits the use of these technologies to particular fields. This work comes to alleviate this problem. We present a way of phononic bandgap engineering using FEM by which the radiative mechanical energy dissipation of a nanomechanical oscillator can be significantly suppressed through coupling with a complementary oscillating mode of a defect of the surrounding phononic crystal (PnC). Applied to an optomechanically coupled nanobeam resonator in the megahertz regime, we find a mechanical quality factor improvement of up to four orders of magnitude compared to conventional PnC designs. As this method is based on geometrical optimization of the PnC and frequency matching of the resonator and defect mode, it is applicable to a wide range of resonator types and frequency ranges. Taking advantage of the, hereinafter referred to as, “regenerative coupling” in phononic crystals, the presented device is capable of reaching f × Q products exceeding 10E16 Hz with only two rows of PnC shield. Thus, stable quantum states with mechanical decoherence times up to 700 μs at room temperature can be obtained, offering new opportunities for the optimization of mechanical resonator performance and advancing the room temperature quantum field across diverse applications.

Design of second-order phoxonic topological insulators with customized bandgaps

Second-order phononic and photonic topological insulators hosting topologically protected edge and corner states provide opportunities for the robust manipulation of elastic/acoustic and electromagnetic (EM) waves, respectively. Despite their potential, the development of second-order phoxonic topological insulators, which combine functionalities of second-order phononic and photonic topological insulators, remains largely unexplored. Herein, we design second-order phoxonic topological insulators (SPTI) with customized bandgaps. An inverse design approach is proposed to engineer phoxonic crystals (PCs) featuring customized odd-order phononic and photonic bandgaps simultaneously. Topological phase transition is induced by translating the primitive unit cell (UC) of the inverse-designed PC with half of the lattice constant horizontally and vertically. Thereafter, the SPTI is constructed by juxtaposing the primitive and translated UCs to form a corner between them. Multiple SPTIs, capable of manipulating both acoustic and EM waves, as well as those governing elastic and EM waves, are created. Our work paves the way for customized SPTIs with tailored bandgaps to support diverse phononic and photonic corner states. Meanwhile, the designed SPTIs also provide a platform to design the higher-order topological optomechanical devices.

First-principles calculations to investigate optical, phonon and electronic properties of quaternary sulfides SrRECuS3 (RE = La, Nd, Tm)

The structure and properties of three layered heterometallic quaternary sulfides SrLaCuS3, SrNdCuS3 and SrTmCuS3 were studied for the first time using first-principles calculations in the stoichiometric and nonstoichiometric approximations. The applied DFT-based computations were performed using a hybrid functional with the contribution of nonlocal exchange in the Hartree-Fock formalism. It was revealed that the nonstoichiometry of SrLaCuS3 and SrNdCuS3 must be considered for modeling phonon spectra, elastic properties and band gaps. The wavenumbers and types of the Raman and “silent” modes at the Г-point were determined. From the analysis of displacement vectors, the degree of participation of ions in each mode was determined. The elastic constants and elastic moduli of the reported sulfides were calculated.