Stress-induced Frequency Shifts Research Articles

Stress-Insensitive Resonant Graphene Mass Sensing via Frequency Ratio.

Herein, a peripherally clamped stretched square monolayer graphene sheet with a side length of 10 nm was demonstrated as a resonator for atomic-scale mass sensing via molecular dynamics (MD) simulation. Then, a novel method of mass determination using the first three resonant modes (mode11, mode21 and mode22) was developed to avoid the disturbance of stress fluctuation in graphene. MD simulation results indicate that improving the prestress in stretched graphene increases the sensitivity significantly. Unfortunately, it is difficult to determine the mass accurately by the stress-reliant fundamental frequency shift. However, the absorbed mass in the middle of graphene sheets decreases the resonant frequency of mode11 dramatically while having negligible effect on that of mode21 and mode22, which implies that the latter two frequency modes are appropriate for compensating the stress-induced frequency shift of mode11. Hence, the absorbed mass, with a resolution of 3.3 × 10−22 g, is found using the frequency ratio of mode11 to mode21 or mode22, despite the unstable prestress ranging from 32 GPa to 47 GPa. This stress insensitivity contributes to the applicability of the graphene-based resonant mass sensor in real applications.

Magnetostrictive stress induced frequency shift in resonator for magnetic field sensor

A static/quasi-static magnetic field sensor is developed by using a double ended trip-beam tuning fork (TBTF), a TbxDy1-xFe2-y plate and several piezoelectric Pb(Zr1−xTix)O3 (PZT) plates. The TBTF is boned horizontally across two ceramic supports which are fixed on the ends of the TbxDy1-xFe2-y plate. The magnetostrictive stress induces an axial force in the TBTF, which causes the resonance frequency of the TBTF to increase. The theoretical analysis shows that the magnetostrictive stress increases approximately linearly with the increase of the external DC field, and so does the resonance frequency shift of the TBTF. The magnetostrictive stress can get to 32.65MPa at the field of 1000Oe, and the total frequency shift respectively achieves 2.97% and 16.67% under the assumption of 10% and 60% transmission efficiencies (as the sectional area of the magnetostrictive plate being 6mm×1mm). A Be-bronze TBTF based sensor was fabricated, and the frequency shift of 2.1% was obtained by applying a DC magnetic field in the range of 0–1000Oe. The magneto-mechanical damping in the magnetostrictive plate has no influence on the quality factor of the TBTF which is found to be relatively constant after an initial increase. The results show the great potential to realize a high sensitivity magnetic sensor featuring high quality factor and digital frequency output.

Frequency response of curved bilayer microcantilevers with applications to surface stress measurement

Bilayer microcantilevers are normally curved because of fabrication-induced stresses. When used in biological/chemical sensing applications, the absorption of target agents onto the functionalized surface of the microcantilever creates a surface stress that shifts its resonance frequency. Despite numerous efforts, the mechanisms of surface stress-induced shift in the resonance frequency of microcantilevers remain elusive. To address this problem, this work presents a detailed analysis of the frequency response of microcantilevers, with different width-to-thickness ratios and curvature levels, using classical lamination theory and the Rayleigh–Ritz method. Based on the results of this analysis, a new relationship between resonance frequency shift and curvature variation due to differential surface stress loading is established. By comparing the strain energies associated with the in-plane and out-of-plane displacements of the microcantilever at different curvature levels, a new implicit model for surface stress-induced resonance frequency shift in microcantilevers is presented. Verified against the results of experiments carried out on gold/polysilicon microcantilevers, the new model is expected to provide a better understanding of surface stress-microcantilever resonator interaction, which is critical to systematic optimization of resonance-based micro sensors.

Stress- and temperature-compensated orientations for thickness-shear langasite resonators for high-temperature and high-pressure environment.

This paper describes an exhaustive study of the variations of the mean force sensitivity coefficients in the entire region of crystalline langasite (LGS). We also study the variation of temperature coefficients in the entire region of the crystalline LGS and its isomorphs. The computational results have been obtained from a procedure that has been successfully employed in the study of the planar and temperature stressinduced frequency shifts in thickness-mode resonators. Both the fast and slow thickness-shear modes have been studied. Among other things, the loci of orientations with zero stress and temperature coefficients of frequency have been identified for LGS.

Experimental measurement of the frequency shifts of degenerate thickness-shear modes in a rotated Y-cut quartz resonator subject to diametrical forces.

We report the first experimental measurement of the stress-induced frequency shifts of degenerate thickness-shear modes in a rotated Y-cut quartz resonator. Two distinct but nominally degenerate modes shifted toward higher frequencies at different rates and merged into a single mode as diametrical forces were applied gradually. The single mode split into the two distinctive modes progressively as the diametrical forces were released. The experimental results are in excellent agreement with previous theoretical results and may provide an insight into mode-coupling phenomena as a possible cause of frequency jumps in quartz resonators.

Stress-induced frequency shifts of degenerate thickness-shear modes in rotated Y-cut quartz resonators

We study stress-induced frequency shifts in a rotated Y-cut quartz resonator (theta = 23.7 degrees ) with degenerate fundamental thickness-shear modes when the biasing stress is not present. Using the recently derived perturbation procedure for degenerate frequencies in crystal resonators, we show that when a planar stress system is applied, the degenerate frequency splits into two. This phenomenon is expected to be typical for degenerate frequencies in crystal resonators and may be responsible in part for the jump discontinuities in frequency temperature curves and other frequency jump phenomena.

Stress-induced frequency shifts in langasite thickness-mode resonators

In this paper, we report on our study of stress-induced effects on thickness vibrations of a langasite plate. The plate is assumed to be doubly rotated, specified by angles phi and theta. The stresses are assumed to be uniform and planar. The first-order perturbation integral as developed by Tiersten for frequency shifts in resonators is used. The dependence of frequency shifts on phi and theta is calculated and examined, and loci of stress-compensation are determined.

Determining the stress tensor in strained semiconductor structures by using polarized micro-Raman spectroscopy in oblique backscattering configuration

We present a characterization technique for the determination of the stress tensor as well as of the crystallographic orientation of strained semiconductor structures. The technique is based on a polarized oblique incidence micro-Raman experiment in a backscattering configuration. A methodology relating the stress-induced frequency shifts and linewidths of the phonon peak to the stress tensor components within the adopted experimental configuration was developed. The method consists in monitoring the variations of the stress-sensitive peak frequencies and linewidths while rotating stepwise the sample about its normal. The practical application of the technique is illustrated on a Si∕SiGe sample microelectronic structure demonstrating a full plane stress tensor determination.

Stress-induced frequency shifts in rotated Y-cut langasite resonators with electrodes considered

Stress-induced frequency shifts of the thickness-shear vibration of rotated Y-cut langasite resonators are studied with the electrode considered. The relationship between mass loading and force-frequency coefficients is explored for several kinds of electrode materials. Comparisons between Y-cut langasite and AT-cut quartz resonators are also presented.

Insights into Structure and Mechanical Behavior of α and γ Crystal Forms of Nylon-6 at Low Strain by Infrared Studies

Stress-induced frequency shifts of spun-cast nylon-6 films with α and γ crystals are studied at low strains with particular emphasis on vibrations related to hydrogen bonding and to the methylene chains. With increasing stress in the α films, there is a frequency increase of the NH stretching mode in the crystals where the NH bonds are preferentially aligned parallel to the tensile stretching direction. The CH2 stretching modes undergo a downward shift. This is correlated with the weakening of the hydrogen bonds and opening up of the tightly packed α crystal structure during deformation, thereby increasing both the N−H- - -O and CH bond lengths. In the α crystals where the NH bond and stretching directions are perpendicular to each other, compressive forces do not lead to significant amounts of frequency shifting of the NH stretching peak. Tensile deformation has less effect in weakening the hydrogen bonds in the more dynamic amorphous regions. For the γ films, however, there is negligible frequency shift of the NH and CH2 stretching modes with deformation. The high sensitivity of the NH stretching frequency to mechanical stress (frequency shift coefficient, α = 100 cm-1/GPa) demonstrates the utility of using FTIR to study deformation micromechanics in hydrogen-bonded systems. An analysis was performed utilizing bond potentials which revealed that the observed FTIR shifts correspond to changes in X−H bond distances that are as small as 0.001%.

Dynamic Fourier Transform Polarized Raman Spectroscopy of Polyethylene Fibers under a Modulated Strain

The response of materials under stress is a critical aspect of the in-use performance of fibers and films. Dynamic infrared measurements have been shown to be very informative and have provided information about both chain reorientation and conformational state change during deformation. However, the use of infrared transmission techniques necessarily confines the measurements to thin films. Polymeric fibers present a real challenge to this approach. Raman scattering is extremely well suited for fibers. There is no real constraint on sample size, shape, or thickness. Dynamic measurements on fibers under deformation have been extended using a Raman probe. Step-scan FT-Raman spectroscopy has allowed the decoupling of the sample strain frequencies from the Fourier frequencies, and the sensitivity is sufficient to observe the small changes associated with an elastic tensile deformation. For polyethylene fibers, the dynamic spectra exhibit both stress-induced frequency shifts and intensity changes due to chain reorientation. Vibrational modes that are coupled to chain backbone motions are found to exhibit the strongest stress-induced frequency shifts, while decoupled motions, such as C–H stretching modes, exhibit the effects of chain reorientation.

Dynamic Step-Scan Two-Dimensional Fourier Transform Infrared Studies of Uniaxially Drawn Poly(Ethylene Terephthalate) Film

Dynamic infrared spectra of uniaxially drawn poly(ethylene terephthalate) (PET) under a sinusoidal strain were examined. A very intense dynamic band at 973 cm−1 assigned to the trans C-O stretching mode indicated stress-induced high mobility around the C-O bond in the ethylene glycol units. It was supposed that derivative-like skeletal bands observed in the dynamic spectra originated from the stress-induced frequency shift. Two-dimensional correlation analyses of the dynamic spectra were also carried out and revealed that the phenyl ring 18a band at 1018 cm−1 and the phenyl ring 19b band at 1410 cm−1 were composed of three and two independent components, respectively. The correlation peaks between the phenyl ring and CH2 vibrational modes showed that orientation of the methylene group in the ethylene glycol unit, induced by mechanical stretching, is faster than that of the phenyl ring in the terephthalate unit.

Crack Shielding in Ce‐TZP/Al2O3 Composites: Comparison of Fatigue and Sustained Load Crack Growth Specimens

Crack shielding stress intensities in in situ loaded compact tension specimens of two types of ceria‐partially‐stabilized zirconia/alumina (Ce‐TZP/Al2O3) composites with prior histories of subcritical crack growth in sustained and tension‐tension fatigue loading were directly assessed using laser Raman spectroscopy. Crack‐tip stress fields within the transformation zones were measured by measuring a stress‐induced frequency shift of a peak corresponding to the tetragonal phase. The peak shift as a function of the applied stress was separately calibrated using a ball‐on‐ring flexure test. Total crack shielding stress intensity was estimated from the far‐field applied stress intensity and the local crack‐tip stress intensity assessed from the measured near‐crack‐tip stresses. The shielding stress intensities were consistently lower in the fatigue specimens than in the sustained load crack growth specimens. The reduced crack shielding developed in the fatigue specimens was independently confirmed by measurements of larger crack‐opening displacement under far‐field applied load as compared to the sustained load crack growth specimens. Thus, diminished crack shielding was a major factor contributing to the higher subcritical crack growth rates exhibited by the Ce‐TZP/Al2O3 composites in tension–tension cyclic fatigue. Calculations of zone shielding considering only the dilatational strains in the transformation zones accounted for 81% and 86% of the measured values in the sustained load crack growth specimens, but significantly overestimated the shielding in the fatigue specimens. Possible reasons for the diminished crack shielding in the fatigue specimens are discussed.

Symmetry, stress alignment, and reorientation kinetics of the SiAs-H complex in GaAs.

The symmetry, reorientation kinetics, and coupling of the ground-state energy to stress have been determined for the ${\mathrm{Si}}_{\mathrm{As}}$-H complex in GaAs from uniaxial stress data. The stress-induced frequency shifts of the H-stretching vibration at 2094.5 ${\mathrm{cm}}^{\mathrm{\ensuremath{-}}1}$ are consistent with trigonal symmetry for the defect. The application of stress at temperatures above 85 K gives rise to a preferential alignment of the defect. The reorientation of the complex is thermally activated with an activation energy of 0.26 eV. The uniaxial stress data are consistent with the hydrogen atom being on the trigonal axis between the Si acceptor and a nearest-neighbor gallium atom.

Quasiharmonic treatment of infrared and raman vibrational frequency shifts induced by tensile deformation of polymer chains. II. Application to the polyoxymethylene and isotactic polypropylene single chains and the three‐dimensional orthorhombic polyethylene crystal

AbstractQuasiharmonic equations are derived for stress‐induced vibrational frequency shifts in the infrared and Raman spectra of polymer chains subjected to a tensile stress. The expressions are applied to the helical chains of polyoxymethylene and isotactic polypropylene. Observed frequency shifts can be reproduced well by using reasonable anharmonic force constants. A semiquantitative interpretation is given for the close relationship between stress‐induced vibrational frequency shifts and the deformation mechanism of the polymer chains. Stress‐induced frequency shifts are also calculated for an orthorhombic polyethylene crystal subjected to uniaxial tension along the chain axis or to hydrostatic pressure. The results consistently and reasonably reproduce observed data, not only for the intramolecular vibrational modes but also for the external lattice modes. © 1992 John Wiley & Sons, Inc.

Cathodoluminescence measurement of strained alumina single crystals

Abstract Alumina single crystals indented with a Vickers hardness indenter were investigated by cathodoluminescence (CL) imaging and spectroscopy in a scanning electron microscope. The spatial resolution of the CL images was approximately 0·4 μm. CL spectra were measured with wavelength resolution of 1·0 nm in the wavelength range of 200 to 900 nm; in the immediate region of the ruby lines (693 nm), spectra were measured with a resolution of 0·15 nm. Stress-induced frequency shifts of the ruby lines were utilized to measure the residual stresses in the region surrounding the indentation. Both hydrostatic and non-hydrostatic stresses were measured. The magnitude of the stresses was observed to vary with distance from the center of the indent and also with crystallographic orientation. After the samples were annealed at 1600°C for 10 h, no measurable stresses remained either in the center of the indent or in the surrounding area.

Characterization of short-period ZnTe-ZnS superlattices grown by MBE

Structural properties of short period ( <30 Å) ZnTe-ZnS strained-layer superlattices (SLSs) have been examined by Raman spectroscopy and low temperature photoluminescence (PL). The longitudinal optical (LO) phonon of ZnS shows a stress-induced frequency shift, which is in close agreement with theoretical calculation. Although ZnTe LO phonon frequency shifts depending on the SLS structure, there is a discrepancy between experiment and calculation, implying a relaxation in the layer. PL spectra are dominated by one intense peak, and the peak energy shows a trend to shifts according to layer thicknesses and SL period as expected from Kronig-Penney model, but the energy value is lower.

The Rayleigh phonon dispersion on Cu(100): A stress induced frequency shift?

The dispersion of the Rayleigh wave on Cu(100) has been measured by high resolution electron energy loss spectroscopy (EELS) throughout the two-dimensional Brillouin zone in the\(\overline {\Gamma M} {\text{ - direction}}\). The experimental data can be matched with a nearest neighbour central force model when the force constant between the first and second layerk12 is stiffened by 20%. However, the data are likewise explained by assuming stress within the surface layer. The stress could arise from a tendency of the surface layer to contract.

Uniaxial stress induced frequency shifts for muons in single crystal Fe

We report the first results on uniaxial stress-induced frequency shifts in an Fe single crystal. Stress was applied along the 〈100〉 axis, which was also the axis of magnetization induced by an external field. The observed frequency shift was −0.34±0.023 MHz per 100 microstrain, which corresponds to ∂Bμ/∂e=+25.1±1.6 G/100μe. The positive sign arises from the negative sign of Bμ itself. This result is interpreted as follows: The stress induces a statistical population shift between magnetically inequivalent sites. Extrapolations from the calculations of Sugimoto and Fukai from Nb and V to Fe yield order of magnitude agreement. The 4T(0) site system seems more likely.

Stress-Induced Frequency Shift of a Lattice Resonant Mode

Stress-Induced Frequency Shift of a Lattice Resonant Mode