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DOE OSTI2025

Shock-induced chemistry and high strain-rate viscoelastic behavior of a phenolic polymer

We use impact experiments and a finite element model (up to 1.2 GPa), and molecular dynamics simulations (up to 60 GPa), to examine the behavior of a phenolic polymer under shock compression, spanning both nonreactive and reactive regimes. In the nonreactive regime, relaxation following compression at strain rates of ∼105 s−1 can be explained by viscoelasticity observed at ordinary laboratory rates (≲1 s−1) by accounting for the temperature dependence of the phenolic β-transition. Reasonable agreement is found between the measured shock Hugoniot up to 1.2 GPa and molecular dynamics simulation for cross-linked structures of comparable density. We also observed a first-order mechanical transition near 0.36 GPa shock stress and estimated a spall strength of 0.102 GPa and Hugoniot elastic limit of 1–2 GPa. The shock stress is found to vary up to 24% among phenolics made with different resin and/or cure processes. Finally, molecular dynamics simulations are used to identify a reactive regime at shock pressures ≳20 GPa that is characterized by chemically driven, rate-dependent relaxation processes, including dehydrogenation and dehydration reactions that promote the formation of a dense, highly cross-linked carbonaceous solid and the release of light volatiles.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

DOE OSTI2024

Dependence of Heat Removal Rate of Pebble-Based Rods on Inter-Pebble Matrix Fill Fraction

Carbon pebble rods are a promising candidate for use in high heat flux regions of magnetic fusion energy reactor walls. Under high (10 – 50 MW/m 2 ) heat loads, carbon pebble rods release hot pebbles from the exposed surface, carrying away heat as the pebble rod surface recedes. In this work, we show that the surface recession rate during heating can be adjusted by changing the mechanical strength of the extruded rods, modifying the heat removal rate; this is accomplished here by varying the fill fraction of the inter-pebble matrix. A three-dimensional finite element model is presented that captures many experimental observations, including the sphere temperature and the surface recession rate. The model predicts that pebble release is caused by thermally driven crack propagation through the matrix and that the matrix strength against breaking is the single most important material parameter setting the pebble release rate; this prediction is supported by experimental results.

36 MATERIALS SCIENCE↗

DOE OSTI2025

Thermal-Fluid and Thermal-Structural Response of the T-Tube Modular Divertor to Spatiotemporally Varying Heat Loads

Tungsten (W) is the leading candidate for divertor target plates because of its high melting point (>3000°C), thermal conductivity, and ultimate tensile stress. While W and its alloys are the only solid materials that can survive the high heat fluxes incident on the divertor, W’s low-ductility high ductile-to-brittle transition temperature of ~600°C and relatively low recrystallization temperature (RT) of ~1300°C pose structural (among other) challenges. The objective of this work is to estimate the thermal-fluid and thermal-structural performance of the helium (He)-cooled T-tube divertor, which was originally developed by the Advanced Reactor Innovation and Evaluation Study (ARIES) using numerical simulations. Here, predictions of temperature distributions across the plasma-facing structural component and surface pressures from computational fluid dynamics simulations are used to determine stress distributions using commercial structural finite element modeling software over a range of fusion-relevant conditions. The maximum allowable incident heat fluxes are determined based on the temperature limits imposed by the ITER elastic Structural Design Criteria for In-vessel Components (SDC-IC) and the maximum RT over a range of He mass flow rates and presented in the form of performance design charts. Our recent work found that thermal- structural criteria accounting for the low ductility of W in a finger-type modular divertor constrain the maximum incident heat fluxes to values well below the ITER specifications, and those based on considering only the RT demonstrate that integrated thermal-fluid and elastic structural performance evaluation are required for accurate assessment of divertor performance. This novel analysis of the T-tube considers how nonuniform and transient incident heat fluxes affect its thermal-fluid and thermal-structural performance, as well as the effect of volumetric heating, which can be as great as 27% of the power incident on the divertor surface. The W tile of the T-tube, with its relatively large plasma-facing area of ~15 cm 2 , will likely experience significant spatial variations in incident heat flux. This work therefore assesses whether steady-state incident heat flux profiles with a peak of 10 MW/m 2 and maximum heat flux gradients of 200 MW/m 2 per m exceed the structural limits imposed by the ITER elastic SDC-IC and the maximum RT over a range of fusion-relevant conditions. The effect of transient heat fluxes typical of plasma detachment and reattachment from the target plate due, for example, to gas injection are also evaluated

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

DOE OSTI2025

Electromagnetic coil optimization for reduced Lorentz forces

Abstract The reduction of magnetic forces on electromagnetic coils is an important consideration in the design of high-field devices such as the stellarator or tokamak. Unfortunately, these forces may be too time-consuming to evaluate by conventional finite element modeling within an optimization loop. Although mutual forces can be computed rapidly by approximating large-bore coils as infinitely thin, this approximation does not hold for self-forces as it leads to an unphysical divergence. Recently, a novel reduced model for the self-field, self-force, and self-inductance of electromagnetic coils based on filamentary models was rigorously derived and demonstrated to be highly accurate and numerically efficient to evaluate (Hurwitz et al 2024 IEEE Trans. Magn. 60 7001614). In this paper, we present an implementation of the reduced self-force model employing automatic differentiation within the simsopt stellarator design software and use it in derivative-based coil optimization for a quasi-axisymmetric stellarator. We show that it is possible to significantly reduce point-wise forces throughout the coils, though this comes with trade-offs to fast particle losses and the minimum distance between coils and the plasma surface. The trade-off between magnetic forces and coil-surface distance is mediated by the minimum coil–coil distance for coils near the inboard side of the ‘bean’ cross-section of the plasma. The relationship between forces and fast particle losses is mediated by the normal field error. Coil forces can be lowered to a threshold with minimal deterioration to losses. Importantly, the magnet optimization approach here can be used also for tokamaks, other fusion concepts, and applications outside of fusion.

Hurwitz, Siena (ORCID:0000000166599659)↗

DOE OSTI2026

Effect of deposition rate on microstructure and mechanical properties of 17-4 PH stainless steel fabricated by laser engineered net shaping

Laser engineered net shaping (LENS) is an additive manufacturing technique for fabricating and repairing metallic components. However, the relationships between its process parameters and the resulting mechanical properties of alloys such as 17-4 precipitation-hardening (PH) stainless steel require further investigation to enable reliable application. This study examines the specific effect of LENS deposition rate on the microstructure and mechanical properties of 17-4 PH stainless steel. Specimens were fabricated at two different deposition rates (8.47 and 9.31 mm s−1), subjected to subsequent solution and H900 aging treatment, and then evaluated via tensile testing, hardness measurements, and microscopy. A higher deposition rate results in a finer grain structure but increased porosity, leading to greater ultimate tensile strength (∼1294 MPa) yet lower ductility (strain at failure ∼5.8%) compared to the slower deposition rate (∼1266 MPa, ∼9.0% strain). Hardness follows the same trend as tensile strength. Tensile fracture surfaces for both conditions exhibited a mixed mode of ductile dimples and brittle quasi-cleavage regions, with chromium/silicon oxide particles identified within dimples. Complementary finite element modeling indicates that small void fractions primarily reduce ductility by enhancing localized plasticity, with only a marginal decrease in tensile strength. These integrated experimental and numerical results elucidate the mechanical properties linked to deposition rate, providing insight into tailoring LENS processes to achieve desired properties of 17-4 PH stainless steel.

17-4 PH stainlesssteel↗

DOE OSTI2021

Correlation Between Corrugation-Induced Flexoelectric Polarization and Conductivity of Low-Dimensional Transition Metal Dichalcogenides

The tunability of polar and semiconducting properties of low-dimensional transition metal dichalcogenides (TMDs) have propelled them to the forefront of fundamental and applied physical research. These materials can vary their electrophysical properties from nonpolar to ferroelectric, and from direct-band semiconducting to metallic. In addition to classical controlling factors, such as field effect, composition, and doping, new degrees of freedom emerge in TMDs due to the curvature-induced electron redistribution and the associated changes in electronic properties. Here we theoretically explore the elastic and electric fields, flexoelectric polarization and free charge density for a TMD nanoflake placed on a rough substrate with a sinusoidal corrugation profile. Finite element modelling results for different flake thickness and corrugation depth yield insights into the flexoelectric nature of the out-of-plane electric polarization and establish the unambiguous correlation between the polarization and static conductivity modulation. The modulation is caused by the coupling between the deformation potential and inhomogeneous elastic strains, which evolve in the TMD nanoflake due to the adhesion between the flake surface and corrugated substrate. We reveal a pronounced maximum in the thickness dependences of the electron and hole conductivity of MoS 2 and MoTe 2 nanoflakes placed on a corrugated substrate, which opens the way for the optimization of their geometry towards significant improvement in their polar and electronic properties, necessary for advanced applications in nanoelectronics and memory devices. Specifically, the obtained results can be useful for the development of nanoscale straintronic devices based on the bended MoS 2 , MoTe 2 , and MoSTe nanoflakes, such as diodes and bipolar transistors with a bending-controllable sharpness of p-n junctions.

42 ENGINEERING↗

DOE OSTI2024

Influence of chemical strains on the electrocaloric response, polarization morphology, tetragonality, and negative-capacitance effect of ferroelectric core-shell nanorods and nanowires

Using Landau-Ginzburg-Devonshire (LGD) approach, we proposed the analytical description of the influence of chemical strains on spontaneous polarization and the electrocaloric response in ferroelectric core-shell nanorods. We postulate that the nanorod core presents a defect-free single-crystalline ferroelectric material, and elastic defects are accumulated in the ultrathin shell, where they can induce tensile or compressive chemical strains. Finite-element modeling (FEM) based on the LGD approach reveals transitions of domain-structure morphology induced by chemical strains in the Ba Ti O 3 nanorods. Namely, tensile chemical strains induce and support the single-domain state in the central part of the nanorod, while the curled domain structures appear near the unscreened or partially screened ends of the rod. The vortexlike domains propagate toward the central part of the rod and fill it entirely, when the rod is covered by a shell with compressive chemical strains above some critical value. The critical value depends on the nanorod sizes, aspect ratio, and screening conditions at its ends. Both analytical theory and FEM predict that the tensile chemical strains in the shell increase the nanorod polarization, lattice tetragonality, and electrocaloric response well above the values corresponding to the bulk material. The physical reason for the increase is strong electrostriction coupling between the mismatch-type elastic strains induced in the core by chemical strains in the shell. Comparison with earlier XRD data confirmed an increase of the tetragonality ratio in tensile Ba Ti O 3 nanorods compared to the bulk material. Obtained analytical expressions, which are suitable for the description of strain-induced changes in a wide range of multiaxial ferroelectric core-shell nanorods and nanowires, can be useful for strain engineering of advanced ferroelectric nanomaterials for energy storage, harvesting, electrocaloric applications, and negative capacitance elements. Published by the American Physical Society 2024

36 MATERIALS SCIENCE↗

DOE OSTI2022

Observability of negative capacitance of a ferroelectric film: Theoretical predictions

Here, we theoretically explore mechanisms that can potentially give rise to the steady-state and transient negative capacitance in a uniaxial ferroelectric film stabilized by a dielectric layer. The analytical expressions for the steady-state capacitance of a single-domain and polydomain states are derived within the Landau-Ginzburg-Devonshire approach and used to study the state stability vs the domain splitting as a function of dielectric layer thickness. Analytical expressions for the critical thickness of the dielectric layer, polarization amplitude, equilibrium domain period, and susceptibility are obtained and corroborated by finite element modeling. Furthermore we explore the possible effects of nonlinear screening by two types of screening charges at the ferroelectric-dielectric interface and show that if at least one of the screening charges is very slow, the total polarization dynamics can exhibit complex time- and voltage-dependent behaviors that can be interpreted as an observable negative capacitance. In this setting, the transient negative capacitance effect is accompanied by almost zero dielectric susceptibility in a wide voltage range and low frequencies. These results may help to elucidate the observation of the transient negative capacitance in thin ferroelectric films, and identify materials systems that can give rise to the behavior.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗

DOE OSTI2020

Mesoscopic structure of mixed type domain walls in multiaxial ferroelectrics

The structure of a 180° uncharged rotational domain wall in a multiaxial ferroelectric film is studied in the framework of an analytical Landau-Ginzburg-Devonshire (LGD) approach. Finite element modeling (FEM) is used to solve numerically the system of the coupled nonlinear Euler-Lagrange (EL) second-order differential equations for two components of polarization. We show that the structure of the domain wall and corresponding metastable or stable phase of the film are controlled by a single parameter—the dimensionless ferroelectric anisotropy factor μ. We fitted the static profile of a solitary domain wall, calculated by FEM, with kinklike functions for polarization components, and extracted the five μ-dependent parameters from the fitting to FEM curves. The surprisingly high accuracy of the fitting results for two polarization components in the entire μ range allows us to conclude that the analytical functions, which are trial functions in the direct variational method, can be treated as a high-accuracy variational solution of the static EL equations. We further derive exact two-component analytical solutions of the static EL equations for a polydomain 180° domain structure in a multiaxial ferroelectric film. Using these, we derive analytical expressions for the system free energy and analyze its dependence on the film thickness and boundary conditions at the film surfaces. The single-domain state is ground for zero polarization derivative at the surfaces, while the polydomain states minimize the system energy for zero polarization at the surfaces. Counterintuitively, the energy of the polydomain states split into two levels, “0” and “1,” for zero polarization at the surfaces, and each of the levels contains a large number of close-energy sublevels, whose structure is characterized by a different number and type of domain walls. The analytical solutions can become a useful tool for Bayesian analysis of high-resolution scanning transmission electron microscopy images in ferroelectric films.

36 MATERIALS SCIENCE↗

DOE OSTI2025

Tip-based proximity ferroelectric switching and piezoelectric response in wurtzite multilayers

Proximity ferroelectricity is a paradigm for inducing ferroelectricity when a nonferroelectric polar material (such as Al⁢ N), which is unswitchable with an external field below the dielectric breakdown field, becomes a practically switchable ferroelectric in direct contact with a thin switchable ferroelectric layer (such as Al 1−𝑥 ⁢Sc 𝑥 ⁢N). Here, we develop a Landau-Ginzburg-Devonshire approach to study the proximity effect of local piezoelectric response and polarization reversal in wurtzite ferroelectric multilayers under a sharp electrically biased tip. Using finite-element modeling, we analyze the probe-induced nucleation of nanodomains, the features of local polarization hysteresis loops and coercive fields in the Al 1−𝑥 ⁢Sc 𝑥 ⁢N/Al⁢ N bilayers and three-layers. Similar to the wurtzite multilayers sandwiched between two parallel electrodes, the regimes of “proximity switching” (when all layers collectively switch) and the regime of “proximity suppression” (when they collectively do not switch) are the only two possible regimes in the probe-electrode geometry. However, the parameters and asymmetry of the local piezoresponse and polarization hysteresis loops depend significantly on the sequence of the layers with respect to the probe. The physical mechanism of proximity ferroelectricity in the local probe geometry is a depolarizing electric field determined by the polarization of the layers and their relative thickness. The field, whose direction is opposite to the polarization vector in the layer(s) with the larger spontaneous polarization (such as Al⁢ N), renormalizes the double-well ferroelectric potential to lower the steepness of the switching barrier in the “otherwise unswitchable” polar layers. Tip-based control of domains in otherwise nonferroelectric layers using proximity ferroelectricity can provide nanoscale control of domain reversal in memory, actuation, sensing, and optical applications. The ability of the tip-induced proximity switching to differentially switch multilayers, based on the order of the layers, provides a powerful tool for selective domain engineering.

36 MATERIALS SCIENCE↗

DOE OSTI2020

Versatile compact heater design for in situ nano-tomography by transmission X-ray microscopy

A versatile, compact heater designed at National Synchrotron Light Source-II for in situ X-ray nano-imaging in a full-field transmission X-ray microscope is presented. Heater design for nano-imaging is challenging, combining tight spatial constraints with stringent design requirements for the temperature range and stability. Finite-element modeling and analytical calculations were used to determine the heater design parameters. Performance tests demonstrated reliable and stable performance, including maintaining the exterior casing close to room temperature while the heater is operating at above 1100°C, a homogenous heating zone and small temperature fluctuations. Two scientific experiments are presented to demonstrate the heater capabilities: (i) in situ 3D nano-tomography including a study of metal dealloying in a liquid molten salt extreme environment, and (ii) a study of pore formation in icosahedral quasicrystals. The progression of structural changes in both studies were clearly resolved in 3D, showing that the new heater enables powerful capabilities to directly visualize and quantify 3D morphological evolution of materials under real conditions by X-ray nano-imaging at elevated temperature during synthesis, fabrication and operation processes. This heater design concept can be applied to other applications where a precise, compact heater design is required.

36 MATERIALS SCIENCE↗

DOE OSTI2020

Copper-Clad Aluminum Windings as an Alternative Conductor for High-Power Electric Vehicle Wireless Charging

In this paper, copper and copper-clad aluminum winding conductors were compared. The effective resistances as functions of frequency for the cored coils were compared using the 3D finite element model frequency sweep analysis for low, medium, and high frequencies. To compare equivalent designs, both coils were designed to have similar direct-current resistance. Benefits of the copper-clad aluminum over the copper coils are presented.

Wojda, Rafal↗

DOE OSTI2021

High Temperature Sodium Submersible Flowmeter Design and Analysis

This work details the design and analysis of a permanent magnet flowmeter designed to be submerged in a pool type sodium fast reactor environment. Recently developed Samarium Cobalt rare earth magnets were utilized that have demonstrated resilience to temperature and neutron flux up to 550 °C and 10 18 n/cm 2 , respectively. This paper will discuss the theory, design, calibration and uncertainty quantification of the flowmeter. The flowmeter was calibrated over a flowrate range of 11.4 - 90.9 LPM at temperatures of 220 and 400 °C, yielding an uncertainty in calibration of 2-3.6%. Here, a finite element model was developed and validated experimentally, yielding <; 3.2% error.

47 OTHER INSTRUMENTATION↗

DOE OSTI2025

Design and Analysis of a Mutual Inductance Level Sensor for Liquid Metals

Here, this article describes the design and analysis of an electromagnetic level sensor for use in high-temperature liquid metal systems. The mutual inductance level sensor (MILS) described in this work was fabricated using two single-conductor mineral insulated cables wrapped in a bifilar fashion around a stainless steel tube core and was housed in an isolating thimble that preserved the pressure boundary of the test vessel. Two sensor variations were fabricated that differ only in active length, 1016 and 1778 mm. Experimental data were collected using the 1016-mm sensor (MILS-MKII-040) that demonstrated a sensitivity of 9.2 μ V/mm in a room temperature testing stand that used solid aluminum as a surrogate for liquid metal. Experimental data were collected using the 1778-mm sensor (MILS-MKII-070) that demonstrated a sensitivity of 6.9 μ V/mm in the high-temperature (300 ° C) liquid sodium environment at the mechanisms engineering test loop (METL) of Argonne National Laboratory. The sensor performance was found to be repeatable over the course of several months, with roughly ±1% deviation from nominal output. Finite element models were developed in COMSOL Multiphysics that fully describe each test setup, and the models were validated using experimental data. The validated COMSOL models were used to perform an array of analyses that examined the performance of the sensor in differing environments. Maximizing the coil diameter inside the isolating thimble was found to maximize the signal and sensitivity of the sensor. An optimal operating frequency was found near 1000 Hz using both experimental data and COMSOL. The influence of a metallic thimble surrounding the sensor and a metallic sensor core was quantified and found to be negligible at the optimal operating frequency. The sensitivity of the sensor was quantified when monitoring the level of additional liquid metals. These include lead, lead-bismuth eutectic (LBE), sodium-potassium alloy (NaK), and lithium (in addition to sodium). The sensitivities were quantified using liquid metal properties at 350 ° C and 650 ° C. The geometry of the test stand model, all material properties used in the model, and the results are presented in a manner that allows the reader can replicate the model and perform additional analyses.

COMSOL↗

DOE OSTI2022

Towards 20 T Hybrid Accelerator Dipole Magnets

We report the most effective way to achieve very high collision energies in a circular particle accelerator is to maximize the field strength of the main bending dipoles. In dipole magnets using Nb-Ti superconductor the practical field limit is considered to be 8-9 T. When Nb 3 Sn superconductor material is utilized, a field level of 15-16 T can be achieved. To further push the magnetic field beyond the Nb 3 Sn limits, High Temperature Superconductors (HTS) need to be considered in the magnet design. The most promising HTS materials for particle accelerator magnets are Bi2212 and REBCO. However, their outstanding performance comes with a significantly higher cost. Therefore, an economically viable option towards 20 T dipole magnets could consist in an “hybrid” solution, where both HTS and Nb3Sn materials are used. We discuss in this paper preliminary conceptual designs of various 20 T hybrid magnet concepts. After the definition of the overall design criteria, the coil dimensions and parameters are investigated with finite element models based on simple sector coils. Preliminary 2D cross-section computation results are then presented and three main layouts compared: cos-theta, block, and common-coil. Both traditional designs and more advanced stress-management options are considered.

43 PARTICLE ACCELERATORS↗

DOE OSTI2025

Analysis of Screening Current Effects in a Hybrid Nb$_{3}$Sn/REBCO Superconducting Accelerator Magnet Using a T - A Formulation

To explore the feasibility of using high-temperature superconducting (HTS) REBCO coated conductors in future accelerator magnets, two REBCO flat racetrack coils were fabricated using 4-mm wide EuBCO tapes at the High Energy Accelerator Research Organization (KEK). These coils were tested as an insert inside a Nb$_{3}$Sn common-coil dipole magnet, which provides a background field of up to $\sim$ 9.5T, at the Brookhaven National Laboratory (BNL). REBCO tapes offer exceptionally high critical current density under strong magnetic fields; however, they also exhibit significant magnetization due to screening currents, leading to magnetic field errors. Here, this study presents a 2D finite element model of screening current-induced fields (SCIF) in REBCO coils using the T-A formulation, along with the results obtained. Simulations were then performed for two KEK test cases: one where the REBCO conductors were oriented with the HTS tapes parallel to the background field, and another where the tapes were perpendicular to it. Since screening currents also influence the stress distribution and increase the peak stress in the coils, the mechanical effects of these currents were analyzed. The implications of these simulation and test results for the design of Nb$_{3}$Sn/REBCO superconducting accelerator magnets are discussed.

Accelerator magnets↗

DOE OSTI2022

Magnetostrictive Ultrasonic Waveguide Transducer for In-Pile Thermometry

Real-time and reliable temperature measurement on nuclear fuels is crucial for the safe operation of existing pressurized-water reactors and future advanced nuclear reactors. Magnetostrictive materials deform when subjected to a magnetic field or exhibit magnetization variation when stressed. Here, based on these properties, this study prototyped an ultrasonic thermometer (UT) consisting of a magnetostrictive waveguide, a dc coil providing appropriate magnetic biasing, and an ac coil generating an acoustic impulse and detecting the resulting acoustic echoes. By tracking the time of flight between the excitation pulse and the echoes, the UT can potentially detect nuclear fuel cladding temperature from a long distance. In this study, magnetostrictive iron–gallium alloys, or Galfenol, were selected as the waveguide due to their large magnetostriction, superior temperature survivability, excellent radiation resilience, and high mechanical robustness. A multiphysics finite-element model considering electrical, magnetic, and mechanical dynamics in the magnetostrictive UT was then developed. The model exhibited an error of 0.24% in time-of-flight simulation and, therefore, enabled computer-aided design and guided signal processing. Between room temperature and 120 °C, the new Galfenol-based UT exhibits a linear sensitivity of 162.8×10 ₋6 °C ₋1 , which is 51.7% higher than a previous magnetostrictive UT based on iron–cobalt–vanadium alloys.

46 INSTRUMENTATION RELATED TO NUCLEAR SCIENCE AND ↗

DOE OSTI2020

Piezoelectric Actuation of Graphene-Coated Polar Structures

Ferroelectric materials based on lead zirconate titanate (PZT) are widely used as sensors and actuators because of their strong piezoelectric activity. However, their application is limited because of the high processing temperature, brittleness, lack of conformal deposition, and a limited possibility to be integrated with the microelectromechanical systems (MEMS). Recent studies on the piezoelectricity in the 2-D materials have demonstrated their potential in these applications, essentially due to their flexibility and integrability with the MEMS. In this work, we deposited a few layer graphene (FLG) on the amorphous oxidized Si 3 N 4 membranes and studied their piezoelectric response by sensitive laser interferometry and rigorous finite-element modeling (FEM) analysis. Modal analysis by FEM and comparison with the experimental results show that the driving force for the piezoelectric-like response can be a polar interface layer formed between the residual oxygen in Si 3 N 4 and the FLG. The response was about 14 nm/V at resonance and could be further enhanced by adjusting the geometry of the device. These phenomena are fully consistent with the earlier piezoresponse force microscopy (PFM) observations of the piezoelectricity of the graphene on SiO 2 and open up an avenue for using graphene-coated structures in the MEMS.

36 MATERIALS SCIENCE↗