Cécile Guianvarc'H

A determination of the Boltzmann constant from speed of sound measurements in helium at a single thermodynamic state

We report on acoustic and microwave measurements made with a purified helium sample maintained close to a single thermodynamic state (Texp ~ 273.16 K, pexp ~ 410 kPa) within a 2.1 L volume stainless steel spherical cavity. From these measurements and ab initio calculations of the non-ideality and the refractive index of helium, we determine a value for the Boltzmann constant kB which is consistent with the recommended 2006 CODATA value: (kB − k2006)/k2006 = (−7.5 ± 7.5) × 10−6. We discuss the current limits of the experiment and the prospects of a further reduction in the uncertainty associated with the determination of kB.

The IMERAPlus joint research project for determinations of the Boltzmann constant

To provide new determinations of the Boltzmann constant, k, which has been asked for by the International Committee for Weights and Measures concerning preparative steps towards new definitions of the kilogram, the ampere, the kelvin and the mole, an iMERAPlus joint research project has coordinated the European activities in this field. In this major European research project the Boltzmann constant has been determined by various methods to support the new definition of the kelvin. The final results of the project are reviewed in this paper. Determinations of the Boltzmann constant k were achieved within the project by all three envisaged methods: acoustic gas thermometry, Doppler broadening technique, and dielectric constant gas thermometry. The results were exploited by the interdisciplinary Committee on Data for Science and Technology (CODATA) in their 2010 adjustment of recommended values for fundamental constants. As a result, the CODATA group recommended a value for k with a relative standard uncertainty about a factor of two smaller than the previous u(k)/k of 1.7×10−6.To provide new determinations of the Boltzmann constant, k, which has been asked for by the International Committee for Weights and Measures concerning preparative steps towards new definitions of the kilogram, the ampere, the kelvin and the mole, an iMERAPlus joint research project has coordinated the European activities in this field. In this major European research project the Boltzmann constant has been determined by various methods to support the new definition of the kelvin. The final results of the project are reviewed in this paper. Determinations of the Boltzmann constant k were achieved within the project by all three envisaged methods: acoustic gas thermometry, Doppler broadening technique, and dielectric constant gas thermometry. The results were exploited by the interdisciplinary Committee on Data for Science and Technology (CODATA) in their 2010 adjustment of recommended values for fundamental constants. As a result, the CODATA group recommended a value for k with a relative standard uncerta...

New planar nano-gauge detection microphone: Analytical and numerical acoustic modeling

The miniaturization of microphones is of great interest for several fields, such as medical applications (audio implants), or consumer electronics (cell phones). Almost all existing miniature microphones rely on electrostatic transduction and offer good performances (sensitivity, frequency bandwidth). However, their sensitivity, proportional to the membranes area, would be dramatically reduced in case of extreme miniaturization. A new concept of microphones developed by CEA-LETI, which uses membranes moving in the plane of the substrate and inducing strain on piezoresistive Si nano-gauges (M&NEMS technology), seems promising for its miniaturization potential without significant decrease of sensitivity. The design and optimization of such planar piezo-resistive microphone require a deep understanding of its acoustic and vibroacoustic behavior. Regarding the small dimensions of the slits (1-100µm) and the sharp discontinuities in the microphones structure, viscous and thermal effects in the boundary layers and turbulent perturbations are of great importance, and must then be taken into account with high accuracy in device modeling. The aim of the present work is to provide accurate analytical and numerical (FEM) models able to gather all these effects in a consistent manner, and to suggest an experimental method to check their validity.

Microphone with planar nano-gauge detection: fluid-structure coupling including thermoviscous effects

This article presents the modeling of a MEMS microphone with an original architecture formed of mechanical structures moving in the plane of the substrate. On the contrary of most microphones generally constituted of an oscillating membrane, some transducers developed by the CEA-LETI with M&NEMS technology use micro beams moving in the plane of the silicon wafer under the effect of an acoustical wave. These micro-structures are connected to the substrate by flexible micro-hinge and strain silicon nano-gauge producing a variation in resistance by piezoresistive effect. After the description of the design and functioning of the microphone under study, the vibroacoustic model of the fluid-structure coupling is presented. Considering the dimensions of the MEMS transducer close to the thermal and viscous boundary layers thicknesses, this model has to include diffusion phenomena. The model is discretized using the finite element method and the weak formulation is implemented using COMSOL Multiphysics® software. The pressure sensitivity of the microphone is calculated and compared with an analytical lumped model to asses the numerical model. Pressure and velocity fileds are also computed. Solutions of simulations are interpreted by focusing on phenomena influencing the sensitivity of this novel sensor design. In particular, the influence of the geometry and the role of the different part of the transducer (back cavity, mechanical structures) are studied.

Improved apparatus to determine the Boltzmann constant using a large quasi-spherical acoustic resonator

There is currently great interest in a new definition of the SI unit of temperature based on a fixed value of the Boltzmann constant k. This paper describes work towards an improved determination of k from the measurement of the speed of sound in argon in a quasi-spherical resonator at constant temperature near 273.16 K. The speed is extracted from acoustic resonance frequencies extrapolated to ideal gas behavior while the dimensions of the resonator are determined from microwave resonance frequencies. We outline key aspects of the experiment namely thermometry and pressure measurement, acoustic and microwave resonances and gas handling.

Acoustic field in a spherical resonator: effect of modal coupling due to small perturbations

The international community recently recommended a re‐definition of the kelvin referring to the value of the Boltzmann constant k, which must thus be known with a relative uncertainty of 10‐6. The measurement of the acoustic resonance properties of a gas filled spherical or quasi‐spherical resonator is an appropriate method to do this with these requirements. Actually, a detailed modeling of the acoustic field in the resonator is required for the determination of k. Several phenomena must be taken into account including heat conduction, shear and bulk viscosity of the gas, the real shape of the resonator, the acoustic input impedance of small acoustic elements flush‐mounted on the wall (tubes, transducers)... . Significant theoretical studies have already been done in which these perturbations are accounted for separately, the coupling between them being neglected. The scope here is thus to provide a unified model for the acoustic field in the cavity including all these perturbations and the resulting mod...

Relative calibration and characterization of 1/4" condenser microphones under different environmental conditions

Measurement condenser microphones are commonly used in air at ambient temperature and pressure. However, several applications require to use such microphones in environments which are significantly different. In particular, for the determination of the Boltzmann constant by an acoustic method, measurements take place in a cavity filled with pure argon or helium over a wide pressure range at the temperature of the triple point of water. For this application, it is important to determine the microphone frequency response and acoustic input impedance with a low uncertainty in these gas conditions. A few previous works have examined the influence of static pressure, temperature and gas composition on microphone sensitivity. In one case, these results were supported by a theoretical investigation using a lumped‐element model. The aim of the present work is to compare theoretical results from different lumped‐element models with experimental relative calibration results obtained using an electrostatic actuator ...