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Metamaterials are engineered materials with unusual, unique properties and advanced functionalities that are a direct consequence of their microarchitecture. While initial properties and functionalities were limited to optics and electromagnetism, many novel categories of metamaterials that have applications in many different areas of research and practice, including acoustic, mechanics, biomaterials, and thermal engineering, have appeared in the last decade. This editorial serves as a prelude to the special issue with the same title that presents a number of selected studies in these directions. In particular, we review some of the most important developments in the design and fabrication of metamaterials with an emphasis on the more recent categories. We also suggest some directions for future research.

Architected metals and ceramics with nanoscale cellular designs, e.g., nanolattices, are currently subject of extensive investigation. By harnessing extreme material size effects, nanolattices demonstrated classically inaccessible properties at low density, with exceptional potential for superior lightweight materials. This study expands the concept of nanoarchitecture to dense metal/ceramic composites, presenting co-continuous architectures of three-dimensional printed pyrolytic carbon shell reinforcements and electrodeposited nickel matrices. We demonstrate ductile compressive deformability with elongated ultrahigh strength plateaus, resulting in an extremely high combination of compressive strength and strain energy absorption. Simultaneously, property-to-weight ratios outperform those of lightweight nanolattices. Superior to cellular nanoarchitectures, interpenetrating nanocomposites may combine multiple size-dependent characteristics, whether mechanical or functional, which are radically antagonistic in existing materials. This provides a pathway toward previously unobtainable multifunctionality, extending far beyond lightweight structure applications.

Widespread industrial adoption of metal additive manufacturing (AM) requires an in-depth understanding of microstructural evolution during AM. In this study, the effect of process parameters and feature thickness on the microstructures of 316L stainless steel components fabricated by laser powder bed fusion (LPBF) was examined. A standard benchmark geometry developed by the National Institute of Standards and Technology, which contained walls of 0.5, 2.5 and 5.0 mm in thickness, was used. Optical microscopy, finite element analysis, scanning electron microscopy and electron backscatter diffraction revealed dramatic microstructural differences in features of different thickness within the same component. The feature thickness influenced the cooling rate, which in turn impacted the melt pool size, solidification microstructure, grain morphology and density of geometrically necessary dislocations. The relationship between feature size and grain morphology was dependent on the energy input used during LPBF. Such behavior suggested that local manipulation of LPBF process parameters can be employed to achieve microstructural homogeneity within the as-printed stainless steel components.

Oxides, hydroxides, and other surface films act as impediments to metallurgical bonding during cold spray impact adhesion, raising the critical adhesion velocity and reducing the quality of the deposited coating. Using a single-particle impact imaging approach we study how altering the passivating surface oxides with exposures to various levels of heat and humidity affect the cold spray critical adhesion velocity in the case of aluminum. We analyze the thickness, composition and microstructure of the passivation layers with transmission electron microscopy (TEM), X-ray photoelectron spectroscopy (XPS), and Fourier-transform infrared spectroscopy (FTIR), and correlate our observations with a direct measurement of the critical adhesion velocity for each surface treatment. We conclude that exposures to temperatures as high as 300 °C for up to 240 min in dry air, or to room-temperature with humidity levels as high as 50% for 4 days, have negligible effect on the surface oxide layers, and by extension do not affect the critical adhesion velocity. In contrast, ambient-temperature exposure to 95% relative humidity levels for 4 days increases the critical adhesion velocity by more than 125 m/s, approximately a 14% percent increase. We observe that this distinct change in critical adhesion velocity is correlated with unique changes in the passivating layer thickness, thickness uniformity, crystallinity and composition resulting from exposure to high humidity. These results speak to particle surface treatments to improve the cold spray process.

Summary Ceramics would be ideal engineering materials if their brittleness and scattered fracture strength could be overcome. While ductility and extraordinary strength have been reported at the nanoscale, they both rapidly disappear when samples reach micrometer dimensions; furthermore, manufacturing is limited to elaborate approaches, which are purely scientific in nature. Here, we present a robust route to additively manufacture ductile, ultrastrong silicon oxycarbide (SiOC) via two-photon polymerization direct laser writing (TPP-DLW) of a preceramic resin and subsequent pyrolysis. We 3D-print micrometer-size pillars and architected materials with feature sizes down to ∼200 nm and characterize them under uniaxial compression. Independent of size, SiOC micropillars consistently deform plastically with strains up to 25% and strengths >7 GPa, across the entire range of examined diameters (1–20 μm). Our findings demonstrate straightforward fabrication of ductile, ultrastrong ceramics at previously unprecedented scales, potentially enabling manufacturing of engineering systems up to tens of millimeters in size.

Author(s): Zhang, Yunfei; Hsieh, Meng-Ting; Valdevit, Lorenzo | Abstract: The mechanical response of interpenetrating phase composites (IPCs) with stochastic spinodal topologies is investigated experimentally and numerically. Model polymeric systems are fabricated by Polyjet multi-material printing, with the reinforcing phase taking the topology of a spinodal shell, and the remaining volume filled by a softer matrix. We show that spinodal shell IPCs have comparable compressive strength and stiffness to IPCs with two well-established periodic reinforcements, the Schwarz P triply periodic minimal surface (TPMS) and the octet truss-lattice, while exhibiting far less catastrophic failure and greater damage resistance, particularly at high volume fraction of reinforcing phase. The combination of high stiffness and strength and a long flat plateau after yielding makes spinodal shell IPCs a promising candidate for energy absorption and impact protection applications, where the lack of material softening upon large compressive strains can prevent sudden collapse. Importantly, in contrast with all IPCs with periodic reinforcements, spinodal shell IPCs are amenable to scalable manufacturing via self-assembly techniques.

Author(s): Hsieh, Meng-Ting; Valdevit, Lorenzo | Abstract: This is an update to PII: S2665963820300178.We present an updated version v2.0 of our minimal surface generator MiniSurf v1.0, that creates triply periodic minimal surface (TPMS) computer-aided design (CAD) files for both finite element modeling and additive manufacturing. Besides making the GUI more user-friendly, in this new version we significantly improve the mesh quality of the generated CAD files by incorporating a mesh smoothing feature. With this new smoothing feature, MiniSurf v2.0 can now produce high quality CAD files for more accurate finite element modeling and more precise additive manufacturing.

Two-photon polymerization direct laser writing (TPP-DLW) is one of the most versatile technologies to additively manufacture complex parts with nanoscale resolution. However, the wide range of mechanical properties that results from the chosen combination of multiple process parameters imposes an obstacle to its widespread use. Here we introduce a thermal post-curing route as an effective and simple method to increase the mechanical properties of acrylate-based TPP-DLW-derived parts by 20-250% and to largely eliminate the characteristic coupling of processing parameters, material properties and part functionality. We identify the underlying mechanism of the property enhancement as a self-initiated thermal curing reaction, which robustly facilitates the high property reproducibility that is essential for any application of TPP-DLW.

In this article, we study the computational design of multiphase architected materials comprising a stiff phase, a dissipative phase, and void space, with enhanced vibration damping characteristics under wave propagation. We develop a topology optimization framework that maximizes a figure of merit comprising of effective stiffness, density and effective damping. We also propose novel material interpolation strategies to avoid the blending of different phases at any given point in the design domain. This is achieved by carefully defining different penalization schemes for different components of the merit function. The effective stiffness of the periodic multiphase material is calculated using homogenization theory and the Bloch–Floquet theorem is used to obtain its damping capacity, allowing for the investigation of the effect of wave directionality, material microarchitecture and intrinsic material properties on the wave attenuation characteristics. It is shown that the proposed topology optimization framework allows for systematic tailoring of microstructure of the multiphase materials for wide ranges of frequencies and densities and results in the identification of optimized multiphase cellular designs with void space that are superior to fully dense topologies.

Though beam-based lattices have dominated mechanical metamaterials for the past two decades, low structural efficiency limits their performance to fractions of the Hashin-Shtrikman and Suquet upper bounds, i.e. the theoretical stiffness and strength limits of any isotropic cellular topology, respectively. While plate-based designs are predicted to reach the upper bounds, experimental verification has remained elusive due to significant manufacturing challenges. Here, we present a new class of nanolattices, constructed from closed-cell plate-architectures. Carbon plate-nanolattices are fabricated via two-photon lithography and pyrolysis and shown to reach the Hashin-Shtrikman and Suquet upper bounds, via in situ mechanical compression, nano-computed tomography and micro-Raman spectroscopy. Demonstrating specific strengths surpassing those of bulk diamond and average performance improvements up to 639% over the best beam-nanolattices, this study provides detailed experimental evidence of plate architectures as a superior mechanical metamaterial topology., Plate-lattices are predicted to reach the upper bounds of strength and stiffness compared to traditional beam-lattices, but they are difficult to manufacture. Here, the authors use two-photon polymerization 3D-printing and pyrolysis to make carbon plate-nanolattices which reach those theoretical bounds, making them up to 639% stronger than beam-nanolattices.

Three-dimensional porous architectures of graphene are desirable for energy storage, catalysis, and sensing applications. Yet it has proven challenging to devise scalable methods capable of producing co-continuous architectures and well-defined, uniform pore and ligament sizes at length scales relevant to applications. This is further complicated by processing temperatures necessary for high quality graphene. Here, bicontinuous interfacially jammed emulsion gels (bijels) are formed and processed into sacrificial porous Ni scaffolds for chemical vapor deposition to produce freestanding three-dimensional turbostratic graphene (bi-3DG) monoliths with high specific surface area. Scanning electron microscopy (SEM) images show that the bi-3DG monoliths inherit the unique microstructural characteristics of their bijel parents. Processing of the Ni templates strongly influences the resultant bi-3DG structures, enabling the formation of stacked graphene flakes or fewer-layer continuous films. Despite the multilayer nature, Raman spectra exhibit no discernable defect peak and large relative intensity for the Raman 2D mode, which is a characteristic of turbostratic graphene. Moire patterns, observed in scanning tunneling microscopy images, further confirm the presence of turbostratic graphene. Nanoindentation of macroscopic pillars reveals a Young's modulus of 30 MPa, one of the highest recorded for sp2 carbon in a porous structure. Overall, this work highlights the utility of a scalable self-assembly method towards porous high quality graphene constructs with tunable, uniform, and co-continuous microstructure.

Tunable phononic metamaterials, which change their response to elastic wave propagation upon actuation, have important applications in cloaking, wave guiding, active noise reduction, superlensing, and acoustic mirrors. Most systems either require substantial morphological changes for actuation, or exhibit only high-frequency band gaps. The authors present a framework for developing tunable phononic metamaterials with low-frequency band gaps, using negative-stiffness inclusions in an elastic matrix, and demonstrate two implementations of this concept. The designs are robust and achieve substantial band-gap manipulation, without elastic instability or significant structural changes.

The mechanical response of cellular materials with spinodal topologies is numerically and experimentally investigated. Spinodal microstructures are generated by the numerical solution of the Cahn-Hilliard equation. Two different topologies are investigated: ‘solid models,’ where one of the two phases is modeled as a solid material and the remaining volume is void space; and ‘shell models,’ where the interface between the two phases is assumed to be a solid shell, with the rest of the volume modeled as void space. In both cases, a wide range of relative densities and spinodal characteristic feature sizes are investigated. The topology and morphology of all the numerically generated models are carefully characterized to extract key geometrical features and ensure that the distribution of curvatures and the aging law are consistent with the physics of spinodal decomposition. Finite element meshes are generated for each model, and the uniaxial compressive stiffness and strength are extracted. We show that while solid spinodal models in the density range of 30–70% are relatively inefficient (i.e., their strength and stiffness exhibit a high-power scaling with relative density), shell spinodal models in the density range of 0.01–1% are exceptionally stiff and strong. Spinodal shell materials are also shown to be remarkably imperfection insensitive. These findings are verified experimentally by in-situ uniaxial compression of polymeric samples printed at the microscale by Direct Laser Writing (DLW). At low relative densities, the strength and stiffness of shell spinodal models outperform those of most lattice materials and approach theoretical bounds for isotropic cellular materials. Most importantly, these materials can be produced by self-assembly techniques over a range of length scales, providing unique scalability.

We demonstrate the use of tip-enhanced Raman spectroscopy (TERS) on polymeric microstructures fabricated by two-photon polymerization direct laser writing (TPP-DLW). Compared to the signal intensity obtained in confocal Raman microscopy, a linear enhancement of almost two times is measured when using TERS. Because the probing volume is much smaller in TERS than in confocal Raman microscopy, the effective signal enhancement is estimated to be ca. 104. We obtain chemical maps of TPP microstructures using TERS with relatively short acquisition times and with high spatial resolution as defined by the metallic tip apex radius of curvature. We take advantage of this high resolution to study the homogeneity of the polymer network in TPP microstructures printed in an acrylic-based resin. We find that the polymer degree of conversion varies by about 30% within a distance of only 100 nm. The combination of high resolution topographical and chemical data delivered by TERS provides an effective analytical tool for studying TPP-DLW materials in a non-destructive way.

The epidemiology of valvular heart disease has significantly changed in the past few decades with aging as one of the main contributing factors. The available options for replacement of diseased valves are currently limited to mechanical and bioprosthetic valves, while the tissue engineered ones that are under study are currently far from clinical approval. The main problem with the tissue engineered heart valves is their progressive deterioration that leads to regurgitation and/or leaflet thickening a few months after implantation. The use of bioresorbable scaffolds is speculated to be one factor affecting these valves' failure. We have previously developed a non-degradable superelastic nitinol mesh scaffold concept that can be used for heart valve tissue engineering applications. It is hypothesized that the use of a non-degradable superelastic nitinol mesh may increase the durability of tissue engineered heart valves, avoid their shrinkage, and accordingly prevent regurgitation. The current work aims to study the effects of the design features on mechanical characteristics of this valve scaffold to attain proper function prior to in vivo implantation.

Author(s): Hsieh, Meng-Ting; Valdevit, Lorenzo | Abstract: Triply periodic minimal surfaces (TPMSs) have long been studied by mathematicians but have recently garnered significant interest from the engineering community as ideal topologies for shell-based architected materials with both mechanical and functional applications. Here, we present a TPMS generator, MiniSurf. It combines surface visualization and CAD file generation (for both finite element modeling and additive manufacturing) within one single GUI. MiniSurf presently can generate 19 built-in and one user-defined triply periodic minimal surfaces based on their level-set surface approximations. Users can fully control the periodicity and precision of the generated surfaces. We show that MiniSurf can potentially be a very useful tool in designing and fabricating architected materials.

An amendment to this paper has been published and can be accessed via a link at the top of the paper.

We have quantified the adhesion forces between two-photon polymerization direct laser writing (TPP-DLW) microstructures and glass surfaces with and without an adhesion promoter. Glass surfaces treated with an acryloxy-silane agent produce adhesion forces that are almost three times larger than the forces observed with pristine glass surfaces. Determination of the substrates’ surface free energies suggests that the observed adhesion enhancement is chemical in its nature, implying that covalent bonds are formed between the polymer and the glass by means of the silane agent. The importance of this finding is demonstrated in the successful production of glassy carbon microstructures using TPP-DLW, followed by pyrolysis.

The objective of this paper is to unveil a novel damping mechanism exhibited by 3D woven lattice materials (3DW), with emphasis on response to high-frequency excitations. Conventional bulk damping materials, such as rubber, exhibit relatively low stiffness, while stiff metals and ceramics typically have negligible damping. Here we demonstrate that high damping and structural stiffness can be simultaneously achieved in 3D woven lattice materials by brazing only select lattice joints, resulting in a load-bearing lattice frame intertwined with free, ‘floating’ lattice members to generate damping. The produced material samples are comparable to polymers in terms of damping coefficient, but are porous and have much higher maximum use temperature. We shed light on a novel damping mechanism enabled by an interplay between the forcing frequency imposed onto a load-bearing lattice frame and the motion of the embedded, free-moving lattice members. This novel class of damping metamaterials has potential use in a broad range of weight sensitive applications that require vibration attenuation at high frequencies.

This paper investigates the optimal architecture of planar micro lattice materials for minimum weight under simultaneous axial and shear stiffness constraints. A well-established structural topology optimization approach is used, where the unit cell is composed of a network of beam elements (Timoshenko beams are used instead of truss elements to allow modeling of bending-dominated architectures); starting from a dense unit cell initial mesh, the algorithm progressively eliminates inefficient elements and resizes the essential load-bearing elements, finally converging to an optimal unit cell architecture. This architecture is repeated in both directions to generate the infinite lattice. Hollow circular cross-sections are assumed for all elements, although the shape of the cross-section has minimal effect on most optimal topologies under the linear elasticity assumption made throughout this work. As optimal designs identified by structural topology optimization algorithms are strongly dependent on initial conditions, a careful analysis of the effect of mesh connectivity, unit cell aspect ratio and mesh density is conducted. This study identifies hierarchical lattices that are significantly more efficient than any isotropic lattice (including the widely studied triangular, hexagonal and Kagome lattices) for a wide range of axial and shear stiffness combinations. As isotropy is not always a design requirement (particularly in the context of sandwich core design, where shear stiffness is generally more important than compressive stiffness), these optimal architectures can outperform any established topology. Extension to 3D lattices is straightforward.

Recent progress in advanced manufacturing enables fabrication of macro-scale hollow metallic lattices with unit cells in the millimeter range and sub-unit cell features at the submicron scale. If designed to minimize mass, these metallic microlattices can be manufactured with densities lower than 1 mg/cm3, making them the lightest metallic materials ever demonstrated. Measuring the compressive stiffness of these ultralight lattices with conventional contact techniques presents a major challenge, as the lattices buckle or locally fracture immediately after contact with the loading platens is established, with associated reduction in stiffness. Non-contact resonant approaches have been successfully used in the past for modulus measurements in solid materials, at both small and large scales. In this work we demonstrate that Laser Doppler Vibrometry coupled with Finite Elements Analysis is a suitable technique for the reliable extraction of the Young’s modulus in ultralight microlattices.

Nanolattices are promoted as next-generation multifunctional high-performance materials, but their mechanical response is limited to extreme strength yet brittleness, or extreme deformability but low strength and stiffness. Ideal impact protection systems require high-stress plateaus over long deformation ranges to maximize energy absorption. Here, glassy carbon nanospinodals, i.e., nanoarchitectures with spinodal shell topology, combining ultrahigh energy absorption and exceptional strength and stiffness at low weight are presented. Noncatastrophic deformation up to 80% strain, and energy absorption up to one order of magnitude higher than for other nano-, micro-, macro-architectures and solids, and state-of-the-art impact protection structures are shown. At the same time, the strength and stiffness are on par with the most advanced yet brittle nanolattices, demonstrating true multifunctionality. Finite element simulations show that optimized shell thickness-to-curvature-radius ratios suppress catastrophic failure by impeding propagation of dangerously oriented cracks. In contrast to most micro- and nano-architected materials, spinodal architectures may be easily manufacturable on an industrial scale, and may become the next generation of superior cellular materials for structural applications.

This paper presents a resonant double-ended tuning fork (DETF) force sensor with an experimentally demonstrated resolution of 7 nN and a compressive load range of 0.08 N, exceeding a dynamic range of 140 dB (100 parts per billion). The resonator has a scale factor of 216 kHz/N, a Q -factor exceeding 60 000 at 3-mtorr ambient pressure, and a zero-load resonant frequency of 47.6 kHz. The resonator is kept at resonance via a phase-locked loop composed of discrete elements. The sensor is implemented with a silicon-on-glass process with a 100-μm -thick ; silicon structural layer. The sensor and the complete readout circuit are fully embedded in a compact 65 mm × 52 mm printed circuit board (PCB). The out-of-plane parasitic modes of the DETF are also investigated with finite-element simulations and laser Doppler vibrometry experiments, and are verified to be outside of the device working range. The PCB is mounted on a microstage and coupled with an off-the-shelf displacement actuator to realize an economical, versatile, and robust micromechanical test frame with unprecedented combination of force and displacement resolution and range.

Novel nickel-based microlattice materials with structural hierarchy spanning three different length scales (nm, lm, mm) are characterized microstructurally and mechanically. These materials are produced by plating a sacrificial template obtained by self-propagating photopolymer waveguide prototyping. Ni–P films with a thickness of 120 nm to 3 lm are deposited by electroless plating, whereas thicker films (5–26 lm) are obtained by subsequent electrodeposition of a pure Ni layer. This results in cellular materials spanning three orders of magnitude in relative density, from 0.01% to 8.5%. The thin electroless Ni–P films have ultra-fine grain size (7 nm) and a yield strength of � 2.5 GPa, whereas the thicker electrodeposited Ni films exhibit a much broader distribution with average grain size of 116 nm and strong (1 0 0) texture in the plating direction, resulting in a yield strength of � 1 GPa. Uniaxial compression experiments reveal two distinct mechanical responses. At ultra-low densities (

Cellular materials with periodic architectures have been extensively investigated over the past decade for their potential to provide multifunctional solutions for a variety of applications, including lightweight thermo-structural panels, blast resistant structures, and high-authority morphing components. Stiffer and stronger than stochastic foams, periodic cellular materials lend themselves well to geometry optimization, enabling a high degree of tailorability and superior performance benefits. This article reviews a commonly established optimal design protocol, extensively adopted at the macro-scale for both single and multifunctional structures. Two prototypical examples are discussed: the design of strong and lightweight sandwich beams subject to mechanical loads and the combined material/geometry optimization of actively cooled combustors for hypersonic vehicles. With this body of literature in mind, we present a motivation for the development of micro-architected materials, namely periodic multiscale cellular materials with overall macroscopic dimensions yet with features (such as the unit cell or subunit cell constituents) at the micro- or nano-scale. We review a suite of viable manufacturing approaches and discuss the need for advanced experimental tools, numerical models, and optimization strategies. In analyzing challenges and opportunities, we conclude that the technology is approaching maturity for the development of micro-architected materials with unprecedented combinations of properties (e.g., specific stiffness and strength), with tremendous potential impact on a number of fields.

3D tissue culture models are utilized to study breast cancer and other pathologies because they better capture the complexity of in vivo tissue architecture compared to 2D models. However, to mimic the in vivo environment, the mechanics and geometry of the ECM must also be considered. Here, we studied the mechanical environment created in two 3D models, the overlay protocol (OP) and embedded protocol (EP). Mammary epithelial acini features were compared using OP or EP under conditions known to alter acinus organization, i.e. collagen crosslinking and/or ErbB2 receptor activation. Finite element analysis and active microrheology demonstrated that OP creates a physically asymmetric environment with non-uniform mechanical stresses in radial and circumferential directions. Further contrasting with EP, acini in OP displayed cooperation between ErbB2 signalling and matrix crosslinking. These differences in acini phenotype observed between OP and EP highlight the functional impact of physical symmetry in 3D tissue culture models.

All-metallic sandwich panels with prismatic cores are being currently investigated for combined structural and active cooling performance. We present a new approach to active cooling performance, and use it to optimize the panel geometry for four different systems: aluminum-air, aluminum-water, aluminum-gasoline and titanium-gasoline. The results show that some geometric parameters can be fixed without much detriment in thermal performance. Moreover, while optimal core densities are typically 25–50%, near-optimal results can be obtained with densities as low as 10%. These findings provide considerable geometric flexibility when attempting combined thermal and structural optimization.

An experimental and computational study of the bending response of steel sandwich panels with corrugated cores in both transverse and longitudinal loading orientations has been performed. Panel designs were chosen on the basis of failure mechanism maps, constructed using analytic models for failure initiation. The assessment affirms that the analytic models provide accurate predictions when failure initiation is controlled by yielding. However, discrepancies arise when failure initiation is governed by other mechanisms. One difficulty is related to the sensitivity of the buckling loads to the rotational constraints of the nodes, as well as to fabrication imperfections. The second relates to the compressive stresses beneath the loading platen. To address these deficiencies, existing models for core failure have been expanded. The new results have been validated by experimental measurements and finite element simulations. Limit loads have also been examined and found to be sensitive to the failure mechanism. When face yielding predominates, appreciable hardening follows the initial non-linearity, rendering robustness. Conversely, for designs controlled by buckling (either elastic or plastic) failure initiation is immediately followed by softening. The implication is that, when robustness is a key requirement, designs within the face failure domain are preferred.

This paper demonstrates that the Thermal Coefficient of resonant Frequency (TCF) of a micro glass-blown Pyrex spherical resonator can be substantially reduced by the application of a titanium (Ti) coating. Finite Elements Analysis (FEA) is used to demonstrate that the temperature dependence of the Young's modulus of the shell material is the dominant parameter affecting the TCF of the resonator, clearly suggesting the use of a metallic compensating layer. Experimental characterization demonstrates that the TCF of a Pyrex glass-blown resonator is reduced by 70% (from 73 ppm/°C to 24 ppm/°C) by the application of a 1.33 μm thick layer of Ti. It is predicted by FEM that for a Ti layer thickness on the order of 2.5 μm the TCF will fall below 10 ppm an acceptable value for high performance resonators. This investigation is a step forward in the quest to employ the desirable properties of micro-blown resonators, such as high symmetry, manufacturing tolerances and environmental robustness.

Molecular dynamics simulations of nanocrystalline Ni revealed that the in-plane Young’s modulus of 2.2 nm grained Ni film with ∼10 grains across its thickness was only 0.64% smaller than that of bulk, while it dropped to 24.1% below bulk value for ∼1 grain across film. This size dependence arises from the increased number of more compliant grains adjacent to the free surface. Simulations of nanocrystalline diamond revealed that the anharmonicity of the potential curve determined the sensitivity of the Young’s modulus to variations in the sample size.