Neighboring Unit Cells Research Articles

FR2/mmWave, N258 and N261 Bands, 5G Frequency‐Compatible Ultra‐Thin Metamaterial Absorber with Polarization Insensitivity for EMI shielding Applications

AbstractSince adopting 5G technology, a notable rise in the prevalence of electromagnetic (EM) waves in the environment has become a significant concern. To reduce EM interference, broadband metamaterial absorbers offer an alternative solution for protecting devices in defense, communication, and healthcare applications, unlike their narrowband counterparts. This article presents a numerical investigation of an ultra‐thin, polarization‐insensitive metamaterial absorber (MMA) that uses metasurfaces and provides electromagnetic interference (EMI) reduction, covering the FR2/mmWave licensed N258 and N261 bands with an oblique incidence angle of up to 15 degrees. Comprehensive simulations are performed within the CST Studio Suite S2 2023 to examine the absorber's performance. Under normal incidence, the proposed MMA exhibits a wideband absorbency response exceeding 90% within the frequency range of 24.30–28.12 GHz. Moreover, the physical absorption mechanism is explained with electric and magnetic field distributions, including surface current distributions. Confirmation of the lack of mutual interaction among neighboring unit cells is established through testing with 1 × 2 and 2 × 2 arrays. An equivalent circuit model is also developed to confirm the EM simulation findings. The notable features of the proposed MMA make it an exceptional candidate for EM shielding applications, providing EMI reduction and covering the N258 and N261 bands.

Anisotropy and dispersion of elastic waves in periodically multilayered anisotropic media

The propagation characteristics of elastic waves in general periodically multilayered media formed by alternate arrangement of two or more arbitrarily-anisotropic materials are comprehensively studied. Combining with the state-space formalism for obtaining the wave solutions to the constituent layers, the Floquet-Bloch theorem for providing the periodic relations between neighboring unit cells, the method of reverberation-ray matrix (MRRM) is employed to derive the general dispersion equations of the periodically multilayered anisotropic media. By solving the dispersion equations in cases of all possible sorts of wavenumber components, the complete anisotropic and dispersion characteristics of elastic waves can be provided. By numerical examples, the slowness and the phase velocity curves are provided to summarize the innovative anisotropic characteristics of elastic waves in three coordinate planes. The effects of the anisotropic parameters on the slowness/phase velocity curves have also been discussed. Moreover, all kinds of dispersion curves including the frequency-related and phase velocity-related curves along the directions perpendicular, parallel, and oblique to the layering are provided to reflect the general dispersion characteristics of elastic waves from various viewpoints. It is found that the innovative anisotropy characteristics of elastic waves in the periodically multilayered anisotropic media include that the slowness curves have periodicity in the thickness direction and the least positive period decreases with the increasing of frequency. As the frequency becomes big enough, the slowness/phase velocity curves show interactions between the modes within the overlapping neighboring periods. The common dispersion characteristics of elastic waves along various directions include the symmetry of wavenumber, the asymptotic of the wavelength and the phase velocity curves to the frequency lines corresponding to zero wavenumber, as well as the cutoff property of the phase velocities of the lowest three basis modes. The waves in oblique directions are special in that the mode transition and repulsion due to the zone folding effect of periodicity along thickness as well as the cutoff property of higher-than-third-order overtones along layering are simultaneously in effective.

Observation of Electronic and Structural Interaction between Small Polaron and Host Material Using Femtosecond XUV Reflection Spectroscopy

Small polaron formation in transition metal oxides is believed to be a reaction bottleneck in many solar energy conversion applications. While polaron formation has been previously confirmed, the microscopic interaction between a small polaron and its host material is largely unexplored. Here, using femtosecond XUV reflection spectroscopy, we report the evidence of electronic and structural interaction between the small polaron and its host material in CuFeO2, a photoelectrode material for CO2 reduction. Initial small polaron formation is observed as a spectral blue shift occurring within the first 100 fs. After polaron formation, we observe an increased coherent oscillation signal around the polaron sites, which is attributed to polaron-induced optical phonons. This observation suggests that the polaron-associated local lattice distortion can launch optical phonons in neighboring unit cells. In addition to structural coupling, the electronic states in the host materials can also be modified during polaron formation. As an example, we report an increase of Fe oxidation states after photoexcitation. The population of these highly oxidized Fe atoms strongly correlates with polaron dynamics, suggesting that polaron can alter its surrounding electronic states in host materials.

A bilayer array metamaterial based on silicon carbon foam/FeSiAl for broadband electromagnetic absorption

In this paper, a bilayer array metamaterial (BAMM) based on silicon carbon (SiC) foam/FeSiAl composite was proposed and the electromagnetic (EM) absorption performance of the BAMM was enhanced by regulating the material composition and geometrical parameters. The introduction of magnetic FeSiAl particles contributed to the reinforced low-frequency absorption of the BAMM. The geometrical parameter design resulted in the broadened effective absorption bandwidth (EAB, reflection loss value≤−10 dB) by improving the impedance matching between the BAMM and the free space. At the same time, it was found that the tuning of the geometrical parameters has a more crucial effect on the absorption properties than the regulation of material composition. Moreover, the EM absorption mechanism was investigated by analyzing the distribution of the EM field and the power loss. In addition to the polarization and magnetic losses in the BAMM, the EM energy is mainly dissipated by the scattering effects concentrated at the outer edge of the unit cell and by the EM resonances between neighboring unit cells. The optimized SiC foam/FeSiAl-1based BAMM exhibits an effective absorption in the frequency range of 2–18 GHz by calculation, and then the corresponding experimental BAMM sample is prepared and measured. The experimental results are in good agreement with the simulations and demonstrate an EAB of 15.77 GHz, indicating that the geometrical parameters design based on high-loss materials is an attractive and efficient strategy to obtain broadband absorbers.

Pair distribution function analysis of discrete nanomaterials in PDFgui

Pair distribution functions (PDFs) are a leading tool for atomic structure analysis of nanomaterials. However, the most widely used programs for refining atomic structure against PDF data are based on extended crystallographic models, which cannot be applied to discrete, whole nanoparticles. This work describes a straightforward approach to simulate and refine atomistic models of discrete clusters and nanoparticles employing widely used PDF modelling programs such as PDFgui [Farrow et al. (2007). J. Phys. Condens. Matter, 19, 335219] that utilize extended crystallographic models. In this approach, the whole particle to be modelled is contained within an expanded, and otherwise empty, unit cell that is sufficiently large to avoid correlations between atoms in neighbouring unit cells over the r range analysed. The PDF of the particle is simulated as a composite using two conventional `phases': one that calculates the atom–atom correlations and one that approximates the local number density. This approach is first validated for large nanoparticles that are well modelled by a conventional shape factor model, and then applied to simulate the PDF of discrete particles and low-dimensional materials (graphene and MXene) and to model the experimental PDF data for single-layer FeS nanosheets. A comparison of this approach with the DiffPy-CMI program [Juhás et al. (2015). Acta Cryst. A71, 562–568], which calculates the PDF of discrete species, shows that the composite modelling approach is equally or more accurate. Example input files for implementing this approach within PDFgui and TOPAS [Coelho (2018). J. Appl. Cryst. 51, 210–218], and recommendations for selecting model parameters for reliable application of this refinement strategy, are provided.

Simultaneous Manipulation of Line‐Gap and Point‐Gap Topologies in Non‐Hermitian Lattices

AbstractNon‐Hermiticity may significantly influence the topology of a photonic/electronic lattice, giving rise to point gaps, which have attracted much attention in recent years. While the influences of the point‐gap topology on the bulk‐boundary correspondence for the line gap have been widely studied, the topological lattice that simultaneously processes the line‐gap and point‐gap topological transitions has not been reported. Here, a strategy to simultaneously manipulate the line‐gap and point‐gap topologies in non‐Hermitian lattices is proposed. By introducing the asymmetric intercell coupling, the line‐gap topological transition process is demonstrated. By further considering the nonreciprocal coupling between the nearest neighboring unit cells, the point‐gap and line‐gap topological transitions can be simultaneously realized. Finally, the influence of the next nearest coupling on non‐Hermitian line‐gap and point‐gap topologies is also discussed.

Design and analysis of Matts-shaped perfect metamaterial absorber using equivalent circuit model

A mid-infrared perfect metamaterial absorber (PMA) consisting of well-engineered unit cells, composed of metallic backed layer (Cu), dielectric layer (Al2O3), matts-shaped meta cell (Cu), and an anti-oxidation layer from bottom to top, is proposed in this paper. The electromagnetic response of the designed PMA is analyzed using 3D full-wave computational model. Our analysis demonstrates that the maximum absorption is enhanced to 99.9% at the resonance wavelength of 7.35 µm, which is caused by magnetic polaritons (MPs) resonance between the incident beam and magnetic polaritons formed by three fluxing currents. Specially, a three-circulation equivalent circuit model is proposed to predict the resonant wavelength of the designed PMA, which comprehensively considers the influence of coupling capacitance not only between neighboring unit cells, but also between the metal lines inside the top metal pattern for the first time. The influence of geometrical parameters on resonant wavelength is predicted by the equivalent circuit model proposed in this paper, and the prediction error is less than 5% as compared with that of computational analysis. With well-engineered plasmonic meta-atoms, the designed PMA presents the characteristics of angle and polarization- independent with a smaller relative size (0.245λ) and a thinner relative thickness (0.053λ). Besides, an obvious red-shift of the resonance frequency of PMA is observed as the permittivity of dielectric layers is increased. The approach of establishing equivalent circuit model will provide methods for the analysis of PMA based on MPs with complex electromagnetic behavior.

Characterization and design of two-dimensional multi-morphology cellular structures for desired deformation

AbstractMulti-morphology cellular structures have recently gained increased attention in many areas owing to their capability to adjust their geometric and mechanical properties spatially. These cellular structures hence deform differently from conventional uniform cellular structures. However, the relationship between their geometric and the manner of their deformation has not been extensively investigated. In this study, the deformation of multi-morphology cellular structures was characterized, and a deformation prediction method was proposed. More closely, the effects of multi-morphology cellular structures’ design variables on their deformation were measured, and the effect of neighbouring unit cells at a given local area on deformation was evaluated. Based on the observations, a deformation prediction model considering the neighbouring effect was developed, and used in an optimization process for achieving the desired deformation. A numerical study was conducted to validate the proposed method, and the deformation of optimized multi-morphology cellular structures showed good agreement with the desired deformation.

Multicomponent induced localized coupling in Penrose tiling for electromagnetic wave absorption and multiband compatibility

• Design quasiperiodic absorbers with long-range order but no periodicity. • Explored the relationship between electromagnetic parameters and frequency by structural design and component selection in depth. • The effective absorption bandwidth of Penrose absorber can realize 9.32 GHz in 2 mm thickness. • The multilayer metamaterials perfectly unify radar-infrared compatible capability. In the electronic information and intelligent era, microwave absorption materials have been focused on the issue of electromagnetic (EM) pollution, but high-performance absorbers with thin thickness are highly desirable. The positive action between structural design and component selection can be regarded as a function to optimize the microwave loss capacity, which contributes to understanding the response mechanisms from the micro and macro. Therefore, we designed the absorber with quasiperiodic structures of Penrose tiling that has finely engineered the location of maximum absorption peak, the spherical carbonyl iron in thin rhombus, and flakey carbonyl iron in fat rhombus, the effective absorption bandwidth (Reflection Loss ≤ –10 dB) was realized from 6.46 GHz to 15.78 GHz in the 2 mm thickness. The unique arrangement of Penrose tiling can respond alternatingly to EM waves at large scales, and multicomponent coupling is distinctly in the neighboring unit cells. In addition, spraying aluminum pigment as the upper layer, the infrared emissivity is less than 0.35 to meet the complex application environment. This work opens up novel ideas on quasiperiodic structure combined multicomponent and injects infinite vitality to provide prospects for broadband responsive and high-efficiency EM absorbers.

A fast method for imposing periodic boundary conditions on arbitrarily-shaped lattices in two dimensions

A new scheme is presented for imposing periodic boundary conditions on unit cells with arbitrary source distributions. We restrict our attention here to the Poisson, modified Helmholtz, Stokes and modified Stokes equations. The approach extends to the oscillatory equations of mathematical physics, including the Helmholtz and Maxwell equations, but we will address these in a companion paper, since the nature of the problem is somewhat different and includes the consideration of quasiperiodic boundary conditions and resonances. Unlike lattice sum-based methods, the scheme is insensitive to the unit cell's aspect ratio and is easily coupled to adaptive fast multipole methods (FMMs). Our analysis relies on classical “plane-wave” representations of the fundamental solution, and yields an explicit low-rank representation of the field due to all image sources beyond the first layer of neighboring unit cells. When the aspect ratio of the unit cell is large, our scheme can be coupled with the nonuniform fast Fourier transform (NUFFT) to accelerate the evaluation of the induced field. Its performance is illustrated with several numerical examples.

Variable-thickness sheet lattices with controlled fracture performances

This work aims to make an initial attempt to the controllable fracture performances of sheet lattices. Four types of variable-thickness sheet lattices (VTSLs) are designed using the Schwarz-P type triply periodic minimal surface, taking into account the manufacturability of the laser powder bed fusion technique. Three-point bending tests are conducted to investigate the fracture performance of VTSLs. Using ductile damage simulations, the fracture evolution process is analyzed, and mechanisms of fracture initiation and crack interaction are described. Experimental and numerical studies have established that distributions of local materials have a significant impact on fracture patterns, including intracellular and intercellular fractures. Under the same condition, the flexural strength, energy absorption capability, and fracture force can be improved for VTSLs with smooth transitions of neighboring unit cells. Specifically, the strength of VTSLs can be further enhanced when the homogenized material model is used. This work establishes a link between the controllable fracture performance and the additive manufacturing design of VTSLs.

MEMS Tunable Metasurfaces Based on Gap Plasmon or Fabry–Pérot Resonances

Tunable metasurfaces promise to enable adaptive optical systems with complex functionalities. Among possible realizations, a recent platform combining microelectromechanical systems (MEMS) with gap-surface plasmon (GSP) metasurfaces offers high modulation efficiency, broadband operation, and fast response. We compare tunable metasurfaces operating in GSP and Fabry–Pérot (FP) regions by investigating polarization-independent blazed gratings both numerically and experimentally. Peak efficiency is calculated to be ∼75% in both cases (∼40% in measurements), while the operation bandwidth is found larger when operating in the GSP region. Advantages of operating in the FP region include relaxed assembly requirements and operation tolerances. Additionally, simulation and experimental results show that coupling between neighboring unit cells increases for larger air gaps, resulting in deteriorated efficiency. We believe the presented analysis provides important guidelines for designing tunable metasurfaces for diverse applications in miniaturized adaptive optical systems.

A Hybrid Level Set Method for the Topology Optimization of Functionally Graded Structures

This paper presents a hybrid level set method (HLSM) to design novelty functionally graded structures (FGSs) with complex macroscopic graded patterns. The hybrid level set function (HLSF) is constructed to parametrically model the macro unit cells by introducing the affine concept of convex optimization theory. The global weight coefficients on macro unit cell nodes and the local weight coefficients within the macro unit cell are defined as master and slave design variables, respectively. The local design variables are interpolated by the global design variables to guarantee the C0 continuity of neighboring unit cells. A HLSM-based topology optimization model for the FGSs is established to maximize structural stiffness. The optimization model is solved by the optimality criteria (OC) algorithm. Two typical FGSs design problems are investigated, including thin-walled stiffened structures (TWSSs) and functionally graded cellular structures (FGCSs). In addition, additively manufactured FGCSs with different core layers are tested for bending performance. Numerical examples show that the HLSM is effective for designing FGSs like TWSSs and FGCSs. The bending tests prove that FGSs designed using HLSM are have a high performance.

High-efficiency wavefront manipulation in thin plates using elastic metasurfaces beyond the generalized Snell’s law

Elastic metasurfaces have shown immense potential in exotic wavefront manipulations based on the generalized Snell’s law (GSL), stimulating applications in various engineering fields such as vibration and noise reduction, structural health monitoring and signal processing. One recognized bottleneck is that the GSL can lead to limited efficiencies of metasurfaces at steep deflection angles, which thereby arouses intense efforts in realizing perfect efficiencies, however, mainly in acoustics and electromagnetics. In this paper, we propose a paradigm to design high-efficiency elastic metasurfaces beyond the GSL efficiency limit, for the refraction manipulations of flexural waves in thin plates. We first find that the theoretical efficiency limits of anomalous refractions of flexural waves approach to zero at large deflection angles, but are higher than those of acoustic and electromagnetic waves due to the inherent evanescent mode contributing to a better impedance matching. A genetic algorithm-based inverse method is then proposed to design metasurfaces with almost perfect efficiencies (>95%), by engineering the nonlocal coupling between neighboring unit cells, which works well for the coarse assembly of only two unit cells in one period. Furthermore, by introducing bianisotropy, we demonstrate advanced high-efficiency functions such as the asymmetric transmission and spatial filtering. This work may offer insights towards the design of high-efficiency and structurally simplified wave-based devices.

Suppressing high-dimensional crystallographic defects for ultra-scaled DNA arrays

While DNA-directed nano-fabrication enables the high-resolution patterning for conventional electronic materials and devices, the intrinsic self-assembly defects of DNA structures present challenges for further scaling into sub-1 nm technology nodes. The high-dimensional crystallographic defects, including line dislocations and grain boundaries, typically lead to the pattern defects of the DNA lattices. Using periodic line arrays as model systems, we discover that the sequence periodicity mainly determines the formation of line defects, and the defect rate reaches 74% at 8.2-nm line pitch. To suppress high-dimensional defects rate, we develop an effective approach by assigning the orthogonal sequence sets into neighboring unit cells, reducing line defect rate by two orders of magnitude at 7.5-nm line pitch. We further demonstrate densely aligned metal nano-line arrays by depositing metal layers onto the assembled DNA templates. The ultra-scaled critical pitches in the defect-free DNA arrays may further promote the dimension-dependent properties of DNA-templated materials.

Adjustable Resolution for Localized FSS-Based Sensing by Synthetic Beamforming

Recently, frequency-selective surface (FSS)-based sensors have shown potential for structural health monitoring due to their sensitivity to changes in element geometry, interelement spacing, substrate properties, and local environment. In addition, these sensors are remotely interrogated and are planar in design, thereby providing a wireless sensing solution that can cover large areas. Traditionally, FSS sensors are analyzed assuming a uniform (plane wave) illumination. However, practically speaking, the sensor will be illuminated with a nonuniform excitation. In this way, the resolution of the sensor is limited to the illumination pattern (footprint) on the sensor. As such, an adjustable illumination pattern is advantageous as it relates to the ability to interrogate the sensor on a localized or comprehensive basis. To this end, this article considers a synthetic beamforming approach to adjust the beamwidth of the focused illumination beam on the sensor as a solution for localized sensing applications. This approach is proposed to generate an arbitrary beam shape with a desired footprint. Moreover, the illumination and spillover efficiencies of the synthetic beam (SB) are defined, simulated, and discussed. The results show that a minimum focal area of <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$1\lambda _{0} \times 1\lambda _{0}$ </tex-math></inline-formula> ( <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$3\times3$ </tex-math></inline-formula> unit cells for the FSS sensors considered here) is essential to achieve a spillover efficiency of greater than 80%, thereby reducing the contribution of other neighboring unit cells on the sensor response. In addition, the illumination efficiency when an SB is utilized for illumination is greater than 80% due to the uniformity of the SB. Representative measurements were also performed on a sensor with a simulated strain profile.

A Predictive Theory for Domain Walls in Oxide Ferroelectrics Based on Interatomic Interactions and its Implications for Collective Material Properties.

Domain walls separating regions of ferroelectric material with polarization oriented in different directions are crucial for applications of ferroelectrics. Rational design of ferroelectric materials requires the development of a theory describing how compositional and environmental changes affect domain walls. To model domain wall systems, a discrete microscopic Landau-Ginzburg-Devonshire (dmLGD) approach with A- and B-site cation displacements serving as order parameters is developed. Application of dmLGD to the classic BaTiO3 , KNbO3, and PbTiO3 ferroelectrics shows that A-B cation repulsion is the key interaction that couples the polarization in neighboring unit cells of the material. dmLGD decomposition of the total energy of the system into the contributions of the individual cations and their interactions enables the prediction of different properties for a wide range of ferroelectric perovskites based on the results obtained for BaTiO3 , KNbO3, and PbTiO3 only. It is found that the information necessary to estimate the structure and energy of domain-wall "defects" can be extracted from single-domain 5-atom first-principles calculations, and that "defect-like" domain walls offer a simple model system that sheds light on the relative stabilities of the ferroelectric, antiferroelectric, and paraelectric bulk phases. The dmLGD approach provides a general theoretical framework for understanding and designing ferroelectric perovskite oxides.

3D networks of nanopores in alumina: Structural and optical properties

The production of spatially ordered arrays of nanopores in alumina is attracting considerable attention due to their valuable filtering and sensing applications. Here we investigate the production conditions of thin films consisting of a continuous 3D network of nanopores in alumina, with the network nodes arranged in a body-centered tetragonal lattice, and the pore size about 1 nm. The emphasis is on controlling the nanopores length, radius, and geometry of their network by the preparation parameters. The material is produced from 3D network of 1D Ge nanowires in alumina by a dedicated annealing treatment that causes Ge to evaporate. We show that the main limiting factors for the production of the nanopore networks are the fraction of Ge nanowires before annealing combined with the unit cell parameters of their network. The 3D networks of nanopores form easily when the Ge atomic fraction in the film is less than 40 %. For larger Ge percentages, the alumina matrix collapses because the interconnection to the neighbouring unit cells in the vertical direction is lost. The refractive index of the materials can be tuned in a wide range by varying the porosity, i.e. the parameters of the Ge nanowire network.

Crushing of additively manufactured thin-walled metallic lattices: Two-scale strain localization analysis

The response of architectured structures is characterized by multi-scale kinematics, which complex relation and effect on the engineering load response is still not completely understood and therefore needs further investigations. More precisely, the lack of experimental methods enabling to provide multi-scale data remains a key issue. The paper presents an experimental and numerical analysis of crushing tests performed on thin-walled auxetic metallic lattices manufactured by Directed Energy Deposition. The work is focused on the two-scale strain localization occurring (a) at the microscopic scale of the unit cell and (b) at the macroscopic scale corresponding to the homogenized continuum. The structures of interest are defined as the extrusion of a 2D auxetic wireframe and allow the application of an adapted digital image correlation scheme dedicated to the identification of the kinematics at the two considered scales. In particular, the microscopic kinematics are studied by following the deformation of lattice crossings, while the macroscopic strains are deduced from the motion of virtual unit cell corners. The results show that the global elastic-plastic response of the lattices is completely driven by the formation of plastic hinges at specific locations, leading to characteristic deformation patterns and eventually a collective behavior of neighboring unit cells. Companion finite element computations show an excellent match with experiments and thus enable to assess the effect of modeling assumptions, unit cell geometry, strain rate and geometrical imperfections in the global response of the architecture material.

Evolution of high-pressure metastable phase Si-XIII during silicon nanoindentation: A molecular dynamics study

Berkovich indenters are widely employed in nanoindentation experiments of single-crystal silicon, in molecular dynamic simulations of silicon nanoindentation, however, spherical indenters are generally employed. To close this gap, in this paper, a series of molecular dynamic simulations are conducted on (001), (101), and (111) silicon surfaces to explore the evolution of high-pressure phases. Several possible silicon phases are tracked by coordination number (CN), radial distribution function (RDF), and angular distribution function (ADF). Results show that the metastable phases and the high-pressure phases present different symmetrical patterns along different crystallographic orientations. A large amount of high-pressure phase Si-XIII, which is seldomly observed in nanoindentation using a spherical indenter, is first discovered under the Berkovich indenter, and the evolution mechanism is characterized by tracking the position transition of labeled silicon atoms. As a transition phase for high-pressure phase Si-II and Si-XIII, bct5 phase is found in the {111} [110] slip systems, which is related with slipping flatten lattice structures. Different from the phase transformation criterion for Si-II, the transformation from Si-I to Si-XIII companies with the local elastic deformation of (001) surface. The atoms in the three neighboring unit cells are compressed into a uniform long-distance ordered crystal structure. Upon indenter extraction and rapid stress releasing, the elastic deformation of the crystal surface resumes incompletely. A part of Si-XIII recovers to pristine Si-I and the rest changes into amorphous phase. The distribution of local hydrostatic pressure and von Mises stress in the phase transformation regions indicates that the concentrated hydrostatic pressure and specific stress induce this high-pressure silicon phase. This research clarifies the evolutionary process of Si-XIII phase generation and enriches fundamental understanding on the mechanisms of silicon phase transformations in nanoindentation.