Catégorie : Article

Felipe Aguilar Sandoval, Mickael Geitner, Éric Bertin, and Ludovic Bellon, Journal of Applied Physics 117, 234503 (2015)

doi: 10.1063/1.4922785

In optical detection setups to measure the deflection of micro-cantilevers, part of the sensing light is absorbed, heating the mechanical probe. We present experimental evidences of a frequency shift of the resonant modes of a cantilever when the light power of the optical measurement set-up is increased. This frequency shift is a signature of the temperature rise and presents a dependence on the mode number. An analytical model is derived to take into account the temperature profile along the cantilever; it shows that the frequency shifts are given by an average of the profile weighted by the local curvature for each resonant mode. We apply this framework to measurements in vacuum and demonstrate that huge temperatures can be reached with moderate light intensities: a 1000 °C with little more than 10 mW. We finally present some insight into the physical phenomena when the cantilever is in air instead of vacuum.

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Tianjun Li, Anthony Ayari and Ludovic Bellon,  Journal of Applied Physics 117, 164309 (2015)

doi:10.1063/1.4919355

The physics of adhesion of one-dimensional nano structures such as nanotubes, nano wires, and biopolymers on different substrates is of great interest for the study of biological adhesion and the development of nano electronics and nano mechanics. In this paper, we present force spectroscopy experiments of individual single wall carbon nanotube loops using a home-made interferometric atomic force microscope. Characteristic force plateaus during the peeling process allow the quantitative measurement of the adhesion energy per unit length on various substrates: graphite, mica, platinum, gold, and silicon. Moreover, using a time-frequency analysis of the deflection of the cantilever, we estimate the dynamic stiffness of the contact, providing more information on the nanotube configurations and its intrinsic mechanical properties.

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Roberto Pérez-Aparicio, Caroline Crauste-Thibierge, Marius Tanase, Pascal Metz, Ludovic Bellon, Antoine Naert, and Sergio Ciliberto,  Rev. Sci. Instrum. 86, 044702 (2015)

doi: 10.1063/1.4916260

We present an innovative technique which allows the simultaneous measurement of the dielectric constant of a material at many frequencies, spanning a four orders of magnitude range chosen between 10-2 Hz and 104 Hz. The sensitivity and accuracy are comparable to those obtained using standard single frequency techniques. The technique is based on three new and simple features: a) the precise real time correction of the amplification of a current amplifier; b) the specific shape of the excitation signal and its frequency spectrum; and c) the precise synchronization between the generation of the excitation signal and the acquisition of the dielectric response signal. This technique is useful in the case of relatively fast dynamical measurements when the knowledge of the time evolution of the dielectric constant is needed.

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M. Adier, F. Aguilar et al.,  General Relativity and Gravitation 46, 1749 (2014)

doi: 10.1007/s10714-014-1749-4

The Amaldi 10 Parallel Session C3 on Advanced Gravitational Wave detectors gave an overview of the status and several specific challenges and solutions relevant to the instruments planned for a mid-decade start of observation. Invited overview talks for the Virgo, LIGO, and KAGRA instruments were complemented by more detailed discussions in presentations and posters of some instrument features and designs. This article is a collection of the abstracts of this session, including the presentation by my collaborator Massimo Granata :

Results from Raman spectroscopy and direct thermal noise measurements on tantala and silica coatings (Presenter: M. Granata)

In order to isolate the mechanisms behind thermal-noise fluctuations in optical coatings, the Laboratoire des Matériaux Avancés has started a collaboration with the Institut Lumière Matière to investigate the Raman spectra of ion-beam sputtered tantala samples with different annealing history. Work is presently ongoing to understand the observed behaviours, in order to correlate the mechanical loss to the evolutions of the Raman spectra. The same analysis will be shortly carried out on fused silica coatings too.

A novel technique of direct thermal noise measurements, developed by the École Normale Supérieure de Lyon, is presented. Measured samples are tipless cantilevers with ion-beam sputtered coatings of tantala or fused silica, annealed before and after the coating. In all cases, the power spectral density of the measured noise is inversely proportional to the frequency, as predicted by the structural noise model with constant loss.

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C. Devailly, J. Laurent, A. Steinberger, L. Bellon, S. Ciliberto,  EPL 106, 54005 (2014)

doi: 10.1209/0295-5075/106/54005

We analyze the advantages and drawbacks of a method which measures the viscosity of liquids at microscales, using a thin glass fiber fixed on the tip of a cantilever of an ultra-low-noise Atomic Force Microscope (AFM). When the fiber is dipped into a liquid, the dissipation of the cantilever-fiber system, which is linked to the liquid viscosity, can be computed from the power spectral density of the thermal fluctuations of the cantilever deflection. The high sensitivity of the AFM allows us to show the existence and to develop a model of the coupling between the dynamics of the fiber and that of the cantilever. This model, which accurately fits the experimental data, gives also more insights into the dynamics of coupled microdevices in a viscous environment.

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Tianjun Li, Felipe A. Aguilar Sandoval, Mickael Geitner, Gianpietro Cagnoli, Vincent Dolique, Jérôme Degallaix, Raffaele Flaminio, Danièle Forest, Massimo Granata, Christophe Michel, Nazario Morgado, Laurent Pinard, and Ludovic Bellon,  Phys. Rev. D 89, 092004 (2014)

doi: 10.1103/PhysRevD.89.092004

In recent years, an increasing number of devices and experiments are shown to be limited by mechanical thermal noise. In particular, subhertz laser frequency stabilization and gravitational wave detectors that are able to measure fluctuations of 10^-18 m/rtHz or less are being limited by thermal noise in the dielectric coatings deposited on mirrors. In this paper, we present a new measurement of thermal noise in low absorption dielectric coatings deposited on microcantilevers, and we compare it with the results obtained from the mechanical loss measurements. The coating thermal noise is measured on the widest range of frequencies with the highest signal-to-noise ratio ever achieved. In addition, we present a novel technique to deduce the coating mechanical losses from the measurement of the mechanical quality factor which does not rely on the knowledge of the coating and substrate Young’s moduli. The dielectric coatings are deposited by ion beam sputtering. The results presented here give a frequency-independent loss angle of (4.7±0.2)x10^-4 with a Young’s modulus of 118 GPa for annealed tantala from 10 Hz to 20 kHz. For as- deposited silica, a weak frequency dependence (~ f^-0.025) is observed in this frequency range, with a Young’s modulus of 70 GPa and an internal damping of (6.0±0.3)x10^-4 at 16 kHz, but this value decreases by one order of magnitude after annealing, and the frequency dependence disappears.

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Pierdomenico Paolino, Felipe A. Aguilar Sandoval and Ludovic Bellon,  Rev. Sci. Instrum. 84, 095001 (2013)

doi: 10.1063/1.4819743

In this article, we present a deflection measurement setup for Atomic Force Microscopy (AFM). It is based on a quadrature phase differential interferometer: we measure the optical path difference between a laser beam reflecting above the cantilever tip and a reference beam reflecting on the static base of the sensor. A design with very low environmental susceptibility and another allowing cal- ibrated measurements on a wide spectral range are described. Both enable a very high resolution (down to 2.5 × 10^-15 m/√Hz), illustrated by thermal noise measurements on AFM cantilevers. They present an excellent long-term stability and a constant sensitivity independent of the optical phase of the interferometer. A quick review shows that our precision is equaling or out-performing the best results reported in the literature, but for a much larger deflection range, up to a few μm.

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Justine Laurent, Audrey Steinberger and Ludovic Bellon,  Nanotechnology 24, 225504 (2013)

doi: 10.1088/0957-4484/24/22/225504

The functionalization of an atomic force microscope (AFM) cantilever with a colloidal bead is a widely used technique when the geometry between the probe and the sample must be controlled, particularly in force spectroscopy. But some questions remain: how does a bead glued at the end of a cantilever influence its mechanical response? And more importantly for quantitative measurements, can we still determine the stiffness of the AFM probe with traditional techniques? In this paper, the influence of the colloidal mass loading on the eigenmode shape and resonant frequency is investigated by measuring the thermal noise on rectangular AFM microcantilevers with and without beads attached at their extremities. The experiments are performed with a home-made ultra-sensitive AFM, based on differential interferometry. The focused beam from the interferometer probes the cantilever at different positions and the spatial shapes of the modes are determined up to the fifth resonance, without external excitation. The results clearly demonstrate that the first eigenmode is almost unchanged by mass loading. However the oscillation behavior of higher resonances presents a marked difference: with a particle glued at its extremity, the nodes of the modes are displaced towards the free end of the cantilever. These results are compared to an analytical model taking into account the mass and inertial moment of the load in an Euler–Bernoulli framework, where the normalization of the eigenmodes is explicitly worked out in order to allow a quantitative prediction of the thermal noise amplitude of each mode. A good agreement between the experimental results and the analytical model is demonstrated, allowing a clean calibration of the probe stiffness.

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Tianjun Li, Ludovic Bellon,  EPL 98, 14004 (2012)

doi: 10.1209/0295-5075/98/14004

In this letter, we characterize the internal dissipation of coated micro-cantilevers through their mechanical thermal noise. Using a home-made interferometric setup, we achieve a resolution down to 10-14 m/rtHz in the measurement of their deflection. With the use of the fluctuation dissipation theorem and of the Kramers-Kronig relations, we rebuilt the full mechanical response function from the measured noise spectrum, and investigate frequency dependent dissipation as a function of the air pressure and of the nature of the metallic coatings. Using different thicknesses of gold coatings, we demonstrate that the internal viscoelastic damping is solely due to the dissipation in the bulk of the coating.

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Julien Buchoux, Ludovic Bellon, Sophie Marsaudon, Jean-Pierre Aimé, European Journal of Physics B 84, 69–77 (2011)

doi: 10.1140/epjb/e2011-20204-1

Applications based on Single Walled Carbon Nanotube (SWNT) are good example of the great need to continuously develop metrology methods in the field of nanotechnology. Contact and interface properties are key parameters that determine the efficiency of SWNT functionalized nanomaterials and nanodevices. In this work we have taken advantage of a good control of the SWNT growth processes at an atomic force microscope (AFM) tip apex and the use of a low noise (10-13 m/rtHz) AFM to investigate the mechanical behavior of a SWNT touching a surface. By simultaneously recording static and dynamic properties of SWNT, we show that the contact corresponds to a peeling geometry, and extract quantities such as adhesion energy per unit length, curvature and bending rigidity of the nanotube. A complete picture of the local shape of the SWNT and its mechanical behavior is provided.

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