[Show abstract][Hide abstract] ABSTRACT: Despite their wide spread applications, the mechanical behavior of helically coiled structures has evaded an accurate understanding at any length scale (nano to macro) mainly due to their geometrical complexity. The advent of helically coiled micro/nanoscale structures in nano-robotics, nano-inductors, and impact protection coatings has necessitated the development of new methodologies for determining their shear and tensile properties. Accordingly, we developed a synergistic protocol which (i) integrates analytical, numerical (i.e., finite element using COMSOL®) and experimental (harmonic detection of resonance; HDR) methods to obtain an empirically validated closed form expression for the shear modulus and resonance frequency of a singly clamped helically coiled carbon nanowire (HCNW), and (ii) circumvents the need for solving 12th order differential equations. From the experimental standpoint, a visual detection of resonances (using in situ scanning electron microscopy) combined with HDR revealed intriguing non-planar resonance modes at much lower driving forces relative to those needed for linear carbon nanotube cantilevers. Interestingly, despite the presence of mechanical and geometrical nonlinearities in the HCNW resonance behavior the ratio of the first two transverse modes f2/f1 was found to be similar to the ratio predicted by the Euler-Bernoulli theorem for linear cantilevers.
[Show abstract][Hide abstract] ABSTRACT: A recent scheme for calculating approximate vibrational mode lifetimes in solids (Dickel and Daw, 2010) [1,2] is extended to the next level (fourth-moment). The extension is tested in two cases: (1) simple, low-dimensional anharmonic systems, and (2) on a simple lattice model of vibrations. We show that, for systems where the mode-resolved density of states is well-approximated by a single broadened peak, the fourth-moment approximation works well over a wide range of temperatures.
[Show abstract][Hide abstract] ABSTRACT: A recent proposal for practical calculation of vibrational mode lifetimes is
tested on simple, low-dimensional anharmonic models. The proposed scheme
approximates the mode lifetime in terms of ensemble averages of specific
functions in phase-space; various levels of approximation correspond to
ensemble moments of the Liouvillian. It is shown that, for systems where the
vibrational density of states is well-approximated by a single broadened peak,
the fourth-moment approximation works well over the full range of temperature.
[Show abstract][Hide abstract] ABSTRACT: Helically coiled carbon nanowires (CCNW) and nanotubes are promising
elements for use in MEMS/NEMS devices and nanorobotics, as
nano-inductors and sensors, and for impact protection (e.g. Bell et al.
2007 IEEE International Conference, J. Appl. Phys. 100, 064309 (2006)).
Understanding and characterizing their mechanical resonance behavior is
essential for the reliability in applications. In this study, we have
electrically actuated an individual CCNW in a diving-board cantilever
configuration inside a scanning electron microscope, and electrically
detected its mechanical resonance modes. By oscillation at low frequency
we confirmed the induced-charge actuation mechanism. Among the modes we
observed, some appeared to have both axial and lateral components. We
also observed closely spaced resonance modes which we attribute to the
splitting of degenerate modes, consistent with our COMSOL simulations.
We suggest that the helical morphology facilitates inter-mode coupling
that results in the observed complex resonance behavior.
[Show abstract][Hide abstract] ABSTRACT: In this study, we elucidate the fundamental mechanism for electrically actuated mechanical resonances in semiconducting ZnO nanowhiskers (NWs). Based on visual detection and measurement of mechanical resonances in ZnO NWs using a scanning electron microscope (SEM), previous studies have attributed dynamic charge induction as the fundamental mechanism for the observed resonances. We show that the use of an electron beam as a resonance detection tool alters the intrinsic electrical character of the ZnO, and makes it difficult to identify the source of the charge necessary for the electrostatic actuation. A systematic study of the amplitude of electrically actuated as-grown and gold-coated ZnO NWs in the presence (absence) of an electron beam using a SEM (dark-field optical microscope) suggest that our ZnO NWs intrinsically support static charge actuation.
Physical Review B 11/2012; 86(20-20). DOI:10.1103/PhysRevB.86.205312 · 3.74 Impact Factor
[Show abstract][Hide abstract] ABSTRACT: Bismuth is a fascinating material system owing to its unusual Fermi surface topology, which depends on size and temperature. Theoretical calculations predict that Bi should undergo a semimetal-to-semiconductor transition as at least one of its dimensions becomes < 50 nm. This prediction was experimentally confirmed by infrared (IR) absorption spectra, which is largely underlain by transitions between the L (electron) and T (hole) pockets of the Fermi surface. In this work, however, we report that in our nanosize samples, the observed IR peak positions are practically independent of temperature, which is hard to reconcile with the predicted behavior of the L–T transition. To help elucidate the origin of these IR peaks, we performed a careful analysis of the IR spectra of Bi nanorods, as well as those of bulk Bi, Bi samples prepared under different conditions and Bi2(CO3)O2 using Fourier transform infrared and photoacoustic spectroscopy measurements. We propose that the observed IR peaks in Bi nanorods arise from the oxygen–carbon containing secondary phases formed on the surface of Bi rather than from the Bi itself. We believe that secondary phases must be taken into account on a general basis in modeling the IR spectra of Bi and that the scenario that ascribes these IR peaks solely to the L–T transitions may not be correct. The results reported herein may also impact the research of Bi-based thermoelectric nanostructures and bulk materials.
[Show abstract][Hide abstract] ABSTRACT: Helically coiled Carbon Nanowires (HCNWs) are promising elements, both
for their promise as components for NEMS devices as well as for
fundamental research. This is due primarily to their exotic geometry. We
present here the electrostatic excitation of a HCNW cantilever to
resonance and an entirely electrical measurement of the same using
harmonic detection of resonance (HDR). The correlation between the
directly observed resonance and the electrical signal is shown and, in
addition to calculating a lateral spring constant from the observed
resonance frequency, we examine the nonlinear behavior of the HCNW when
driven to large amplitudes of vibration. Specifically, elliptical
oscillation is visually evident and we have measured the electrical
response of the corresponding combination mode.
[Show abstract][Hide abstract] ABSTRACT: Here, we present the fundamental mechanism for the observation of
electrically actuated resonances in semi-conducting ZnO nanowhiskers
(NWs). Previous studies have claimed that various mechanisms including
charge induction lead to a mechanical resonance in NWs. Many of such
studies employ an electron beam to visualize the resonance of NWs.
However, we find that the use of an electron beam changes the electrical
character of the NWs making it difficult to understand fundamental
actuation mechanism. In this article, we developed a novel, fully
electrical harmonic detection of resonance (HDR) method that enables us
to probe mechanical resonances of NWs even in the absence of an electron
beam. In contrast to the traditional optical detection scheme, the HDR
method allows us to successfully decouple the effects of the electron
probe beam from the actual driving force. Interestingly, we find that
the observed mechanical resonance of ZnO NWs is dominated by their
interactions with the electron probe beam. Importantly, ZnO NWs exhibit
strong (weak) mechanical resonance only in presence (absence) of the
electron probe beam suggesting that the observed behavior originates
from dynamically induced (static) charges.
[Show abstract][Hide abstract] ABSTRACT: We report a fully electrical microcantilever device that utilizes capacitance for both actuation and detection and show that it can characterize various gases with a bare silicon microcantilever. We find the motion of the cantilever as it rings down when the oscillating force is removed, by measuring the voltage induced by the oscillating capacitance in the microcantilever∕counterelectrode system. The ringdown waveform was analyzed using an iterative numerical algorithm to calculate the oscillator motion, modeling the cantilever∕electrode capacitance to calculate the electrostatic force. We find that nonlinearity in the motion of the cantilever is not necessarily a disadvantage. After calibration, we simultaneously measure viscosity and density of several gaseous mixtures, yielding viscosities within ±2% and densities within ±6% of NIST values.
The Review of scientific instruments 05/2011; 82(5):055103. DOI:10.1063/1.3585977 · 1.61 Impact Factor
[Show abstract][Hide abstract] ABSTRACT: In a two-part publication, we propose and analyze a formal foundation for practical calculations of vibrational mode lifetimes in solids. The approach is based on a recursion method analysis of the Liouvillian. In the first part, we derived the lifetime of vibrational modes in terms of moments of the power spectrum of the Liouvillian as projected onto the relevant subspace of phase space. In practical terms, the moments are evaluated as ensemble averages of well-defined operators, meaning that the entire calculation is to be done with Monte Carlo. In this second part, we present a numerical analysis of a simple anharmonic model of lattice vibrations which exhibits two regimes of behavior, at low temperature and at high temperature. Our results show that, for this simple model, the mode lifetime as a function of temperature and wavevector can be simply approximated as a function of the shift in frequency from the harmonic limit. We next compare these calculations, obtained using both Monte Carlo and computationally intensive molecular dynamics, with those using the lowest order moment formalism from the Part I. We show that, in the high-temperature regime, the lowest order approximation gives a reliable approximation to the calculated lifetimes. The results also show that extension to at least fourth moment is required to obtain reliable results over a full range of temperatures. Comment: 17 pages, 7 figures
[Show abstract][Hide abstract] ABSTRACT: We propose a formal foundation for practical calculations of vibrational mode lifetimes in solids. The approach is based on a recursion method analysis of the Liouvillian. From this we derive the lifetime of a vibrational mode in terms of moments of the power spectrum of the Liouvillian as projected onto the relevant subspace of phase space. In practical terms, the moments are evaluated as ensemble averages of well-defined operators, meaning that the entire calculation is to be done with Monte Carlo. These insights should lead to significantly shorter calculations compared to current methods.
[Show abstract][Hide abstract] ABSTRACT: We propose here a formal foundation for practical calculations of vibrational mode lifetimes in solids. The approach is based on a recursion method analysis of the Liouvillian. From this we derive the lifetime of a vibrational mode in terms of moments of the power spectrum of the Liouvillian as projected onto the relevant subspace of phase space. In practical terms, the moments are evaluated as ensemble averages of well-defined operators, meaning that the entire calculation is to be done with Monte Carlo. These insights should lead to significantly shorter calculations compared to current methods. A companion piece presents numerical results. Comment: 18 pages, 3 figures
[Show abstract][Hide abstract] ABSTRACT: While it has proven useful as a sensor and as a system for exploring and examining nonlinear oscillation, the harmonic detection of resonance (HDR) method has not been fully derived and explained analytically. We develop the equation of motion for the oscillation of a cantilever which is electrostatically driven into resonance and compared to experiment. The resonance signal is measured both by a photodetector (mechanical signal) and a charge amplifier (electrical signal) and is found to be in good agreement with the derived equation of motion. Finally, a few nonlinear phenomena observed in our HDR experiments will be examined analytically.
[Show abstract][Hide abstract] ABSTRACT: Harmonic Detection of Resonance (HDR) method has been shown to be an effective method of electrically determining the resonant frequency of cantilevered structures at both the micro- and nanometer scale. Previously, HDR has been used effectively to study nonlinear behavior in highly anharmonic systems, as a gas sensor, and to determine the resonant frequency of nanoscale structures such as a Multi-wall Carbon Nanotube (MWNT). In addition, HDR method has been used for determining material properties such as the Young's Modulus. Here, we provide a simple model describing the theory underlying the HDR method and a demonstration of its use to determine the resonant behavior of a MWNT. Finally, we report the effects of varying pressures on both the resonant frequency and quality factor of the MWNT. We also estimate the intrinsic damping inherent in the MWNT from these effects and show its correlation with defect density. The MWNT examined was found to have a resonant frequency for its primary mode of oscillation of 2.79 MHz with a quality factor of 10.15 at a pressure less than 1 Pa.