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Overview

Current realisations of the pascal rely on piston gauges (also known as pressure balances) and liquid manometers containing toxic mercury, both of which measure force per area. Their performance however has remained essentially unchanged over the past few decades and they suffer from practical and environmental limitations. This project will develop photon‑based standards, which determine the pressure via gas density using the gas law. Following the implementation of the redefined SI in May 2019, the uncertainty of the Boltzmann constant has been eliminated, so at a given temperature, photon-based standards promise primary measurements limited only by the accuracy of the quantum calculations. In the longer term, such primary standards could be miniaturised, providing faster and calibration-free pressure measurements for industry at a fraction of the present cost.

Need

Accurate and fast gas pressure measurements are needed to ensure control and safety in a variety of critical industrial processes. In addition, manufacturers of pressure sensors require reliable, fast and automated calibration, preferably for a wide pressure range which will depend on the particular application. Conventional methods for the realisation of the pascal are based on force per area with relative uncertainties of a few parts in 106 at 100 kPa and a few parts in 104 at 1 Pa and have remained basically unchanged over recent decades. Currently, piston gauges are replacing mercury manometers due to their superior accuracy and lack of environmental hazards. However, the fact that weights have to be exchanged on the piston gauge during a calibration leads to drawbacks such as slowness, bulkiness, fragility and complexity of operation. For pressure measurements below 3 kPa, other methods involving static or continuous expansion of gases have to be used which significantly increases the effort required for operation.

The importance of overcoming these limitations has been identified as a strategic goal by the CIPM (Comité international des poids et mesures) Consultative Committee for Mass and related quantities (CCM) and the EURAMET Technical Committees for Mass and related quantities (TC-M), and in recent publications where optical quantum-based methods are proposed for calibration-free sensors. The drawbacks can be overcome by photon‑based devices, that could become inherent primary pressure standards significantly outperforming conventional standards, and which can potentially be implemented as desktop or even as an on-chip versions.

Two national metrology institutes, NIST (USA) and NIM (China), have recently invested significant resources in developing quantum-based pressure standards utilising Fabry-Pérot (FP) cavities. Further research and development are however required to address limiting effects such as outgassing, cavity deformation, gas permeation as well as thermal and temporal instabilities.

Due to the very wide range of pressures that need to be addressed, it is not feasible for this to be covered by one technique alone. The potential of other quantum-based techniques to act as pressure standards such as superconductive microwave resonators, Rayleigh scattering, multi reflection interferometry, gas thermometry methods and absorption spectroscopy therefore also need to be investigated and evaluated.

In addition, a prerequisite for developing quantum-based primary pressure standards is accurate knowledge of the thermodynamic and electromagnetic properties of the gas used, however the information currently available is often limited or insufficiently accurate.

Objectives

The overall aim is to develop novel quantum-based pressure standards based on optical, microwave and dielectric methods and to assess their potential with the aim of replacing existing mechanical based pressure standards. Therefore, the specific objectives of this project are:

  1. To improve the accuracy and extend the working range of Fabry‑Pérot refractometry quantum-based methods that have the potential to become primary standards of the SI unit of pressure, the pascal. The target uncertainties (k=1) and pressure ranges are 500 ppm in the range 1 Pa - 1 kPa and 10 ppm in the range 1 kPa ‑ 100 kPa.
  2. To improve the accuracy and evaluate the potential of alternative pioneering (non Fabry‑Pérot based) quantum-based approaches and detection methodologies for the realisation of absolute and partial pressure standards, including superconductive microwave resonators, Rayleigh scattering, multi‑reflection interferometry, gas thermometry methods, absorption spectroscopy of selected molecular species with very long optical pathways and modulation techniques, with target uncertainties (k=1) less than 500 ppm between 1 Pa and 10 Pa, less than 50 ppm between 1 kPa and 100 kPa, less than 500 ppm between 100 kPa and 1 MPa and less than 5 ppm between 1 MPa and 3 MPa, depending on the measurement technique.
  3. To develop improved ab-initio calculations of the thermodynamic and electromagnetic properties (static and dynamic polarisability, diamagnetic susceptibility along with dielectric- and density virial coefficients) of He, Ne, and Ar and the electromagnetic properties (intensities of specific absorption lines) for CO and CO2 of gases as needed to meet objectives 1 and 2. For gases other than He, the accuracy of the calculations (targeted uncertainty contributions of 1 ppm to 5 ppm at 100 kPa, equivalent to an improvement of at least a factor of 5) to be validated by comparisons with the results from experiments using He as a calibrating reference substance.
  4. To demonstrate the performance of the methods (FP-based refractometers, Rayleigh scattering, multi‑reflection interferometry, gas thermometry, superconductive microwave cavity) developed in objectives 1 and 2 by comparison with conventional primary absolute pressure standards such as pressure balances.
  5. To facilitate the take-up of the technology developed in the project by end users, i.e. the scientific, metrological, and industrial communities and standards developing organisations.

Progress beyond the state of the art

The project is taking advantage of recent advances in optical, microwave and dielectric measurement techniques, combined with the outstanding progress of quantum-based calculations of gas properties, to develop novel, improved pressure standards.

Refractivity or permittivity Fabry-Pérot cavity-based techniques for the realisation of the pascal (Obj. 1)

At present NIST is the world leader in the development and utilisation of FP-cavity based refractometry for pressure assessment, with claimed relative uncertainties of 9x10-6 at 100 kPa and 2x10-3 at 1 Pa. This project will develop techniques to overcome some of the current limitations of FP-cavity based refractometry by minimising the influence of cavity deformations induced by pressure, thermal expansion and instabilities, and gas diffusion, with the aim of developing standards for the assessment of pressure with relative uncertainties of 500 ppm in the 1 Pa to 1 kPa range and 10 ppm between 1 kPa and 100 kPa.

Alternative non Fabry-Pérot based techniques for the realisation of the pascal (Obj. 2)

No single technique can cover the extensive pressure range required, hence it is necessary to investigate other techniques, alternative to FP-cavity based refractometry, to expand the working range of existing quantum-based instrumentation for realisations of the pascal. Other quantum-based optical methods for pressure assessment are currently under development, including a simple and compact device for gas density/pressure measurements based on Rayleigh scattering, an optical pressure standard based on a homodyne interferometer with one arm folded by a multi‑reflection assembly, two different polarising gas thermometry techniques, dielectric-constant gas thermometry (DCGT) and refractive index gas thermometry (RIGT), a prototype superconducting microwave cavity suitable for use in the low-pressure range and absorption spectroscopy for the optical measurement of partial pressures. The targeted uncertainties are less than 500 ppm between 1 Pa and 10 Pa, less than 50 ppm between 1 kPa and 100 kPa, less than 500 ppm between 100 kPa and 1 MPa and less than 5 ppm between 1 MPa and 3 MPa, depending on the measurement technique.

Improved ab initio calculations for the thermodynamic and electromagnetic properties of gases (Obj. 3)

Ab-initio calculations of gas properties are a prerequisite to make these quantum-based methods primary, for example, the uncertainties in the calculations for helium contribute 1 ppm to the overall uncertainty of pressure assessment at 100 kPa. Gases other than He provide higher polarisabilities and thus higher sensitivities, but due to their complexity existing gas parameters data is insufficiently accurate. The thermodynamic and electromagnetic properties of He, Ne and Ar and the electromagnetic properties of CO and CO2 will therefore be determined to enable a link between calculations of the thermodynamic and electromagnetic properties of gas species on the quantum level and macroscopic pressure determinations. The targeted uncertainties of the theoretical values of the gas properties constitute an improvement of at least a factor of 5.

Demonstration of the performance of the novel and improved methods compared with conventional primary absolute pressure standards (Obj. 4)

The performance of improved FP cavity refractometry and alternative novel methods (Rayleigh scattering, absorption spectroscopy, and gas thermometry techniques) will be assessed by comparing them with conventional primary pressure standards such as pressure balances. In addition, a comparison will be undertaken between conventional pressure standards using a portable optical refractometer, with the aim of comparing conventional pressure standards and assessing how well the portable optical refractometer works as a transfer standard.

Results

Refractivity or permittivity Fabry-Pérot cavity-based techniques for the realisation of the pascal (Obj. 1)

In order to characterise potential cavity-spacer materials, investigations of the diffusion and permeation of He in ULE-glass, Zerodur and sapphire have been performed by PTB at 23°C and especially for sapphire by IMT for temperatures up to 426°C. It was found that there was no detectable permeation of He through sapphire. It has also been established that the permeability of He in Zerodur is orders of magnitude smaller than that through ULE-glass.

Using the new Gas modulation refractometry (GAMOR) method in combination with a recently realised Fabry-Pérot cavity system bored in Invar, it has been shown, that even materials with much higher thermal expansion coefficients than ULE-glass and Zerodur can be used for refractometers with highest precision. This enables for new designs of refractometers offering benefits for the photonic pressure assessment like orders of magnitude lower gas permeabilities (as shown for sapphire) and lower thermal gradients within the material of the cavity spacers.

The Gas Modulation Refractometry (GAMOR) technique has been further developed. A system with smaller volumes, which comprises an important step towards extending the working range up to 100 kPa, has been constructed and a method has been used to assesses the cavity deformation, using two gases whose molar polarizabilities are known (He and N2). The procedure is devised so that the assessment of the cavity deformation is independent of systematic errors in the reference pressure and in the assessed temperature, and, to a large extent, insensitive of gas leakages and outgassing. This implies that it will allow for the assessment of cavity deformation with extraordinary small amounts of uncertainties. Hence, it will reduce the influence of cavity deformation on the assessment of N2 by the use of FP-based refractometry and it is concluded that, when a high-precision refractometer and high purity gases are used, the pressure-induced cavity deformation can be assessed to such a degree that its uncertainty plays an inferior role on the assessment of pressure of N2. Finite-Elemente-Methode (FEM) simulations have been compared for different software and numbers of mesh points. It has been shown that FEM simulations of a given cavity can be performed by the utilisation of dissimilar programs, namely COMSOL Multiphysics and ANSYS, with such small discrepancies that the confidence interval of the simulated on-axis deformation represents sub-ppm uncertainties in the assessments of refractivity for both N2 and He as long as the number of mesh points is sufficient.

To assess the influence of the macroscopic properties of the cavity spacer block and the mirrors on the deformation of FP cavities, modelling of five different cavities including systems bored in Zerodur, Invar and Sapphire which will be used in the experimental setups have been performed based on the earlier verified FEM modelling procedures.

Based on the FEM simulations, a new 50x 50 mm squared cavity has been designed bored in a Zerodur spacer with bonded silica mirrors. The expected deformation has been evaluated: -6.8 × 10-12/Pa. In addition, to fit this new cavity pursues development of a system for temperature regulation based on the gallium melting point. Additionally, a more compact gas/vacuum enclosure in copper has been designed to ensure better temperature stability. Cavity and enclosure are in progress for manufacturing, while the current setup has shown that it is possible to reach a short-term pressure stability of ± 2 mPa at 53 kPa under N2.

A system based on a thermocouple referenced to a gallium fixed-point cell has been jointly realized assessing the cavity temperature with higher accuracy than what the classical thermistors could do with a total uncertainty of 1.2 mK (4 ppm), dominated by the stability of the nano voltmeter used for assessment of the thermocouple voltage. Additionally, a more compact gas/vacuum enclosure in copper has been designed in order to ensure a better temperature stability.

A double-walled, insulated structure with the aim of reducing the influence of room temperature fluctuations on the measurement device by at least four orders of magnitude has been designed together with a new vacuum chamber, which will be thermalised by a fluid. To realise traceable temperature assessments, four SPRTs will be part of this FP-refractometer and have been calibrated providing an uncertainty of less than 350 µK (k=1 @ 0.1°C).

Alternative non Fabry-Pérot based techniques for the realisation of the pascal (Obj. 2)

The design phase of the innovative non Fabry-Perot based systems for pressure standard realisations has been concluded.

In detail, setups for Rayleigh scattering-based system (RAY), as well as the optical pressure standard based on a multi-reflection interferometric technique (UINT) have been designed. A multi-step stray-light analysis has been performed to estimate its influence on the accuracy of the RAY system. Preliminary tests on RAY are ongoing inside a suction hood with molecular filtration. The new realization of UINT is also under development, including a double-step temperature control, and benefits from a series of optical simulation: after a predictive estimate of the nominal optical path, the optical simulations regarding the double mirror assembly, continued with a Gaussian beam propagation study to predict the value of misalignment of the laser beam. The DCGT and RIGT based pressure standard are under realisation. After checking the working equations, the DCGT based pressure standard has been successfully tested in argon at 296 K, in comparison with a traditional primary standard. A precise estimate of the effective compressibility of a RIGT microwave resonator made of copper (Cu-ETP) has been obtained at 273.16 K, in agreement with the results obtained using a RUS technique. The evaluation of compressibility allowed for a re-examination of previous RIGT experiments, obtaining an estimate of pressure which resulted in good agreement with a calibrated quartz transducer.

The realisation of a pressure standard based on a superconductive microwave cavity is ongoing and after a feasibility study and an evaluation of alternative solutions, the chosen solution consists of a copper cavity with internal Nb coating. Preliminary tests of its microwave, thermal and mechanical performance at ambient room temperature and atmospheric pressure, has been performed. After further preliminary tests, the implementation of a second cryogenic apparatus is scheduled with the aim of reducing the thermomolecular effect which occurs at low pressure and suitable for testing the superconducting microwave cavity at temperatures below 10 K.

In order to improve the precision of the absorption spectroscopy for measurements of partial pressures, first test-measurements on water vapor with an existing Herriot-cell setup have been performed, an improved Herriot-cell design has been finalised by modelling the mirror shapes and parameters to optimise the optical path length for the given dimensions of the vacuum chamber and a feasibility study has been performed, revealing the Laser-linewidth necessary to archive the targeted uncertainties. As a result of this feasibility study two new laser systems have been implemented, covering the absorption bands of CO and CO2 at 2160 cm-1 and 2330 cm-1. Both will be used quasi-simultaneously in the multiplexed setup, which is under realisation.

Improved ab initio calculations for the thermodynamic and electromagnetic properties of gases (Ob. 3)

The calculations of the desired thermodynamic and electromagnetic gas properties (static and dynamic) are in progress and several results have already been obtained and published.

The calculation of the magnetic susceptibility of neon is finished and published.

The nonrelativistic Born-Oppenheimer part for the two-body pair polarizability of He and Ne is finished. For helium, the calculation of the collision-induced three-body polarizability tensor is finished on a large grid of trimer configurations. The remaining work to find a satisfactory analytical fit and uncertainty estimates has started.

A path integral method for the calculation of the second dielectric virial coefficients was developed, published and tested using state-of-the-art potentials and polarizabilities from the available literature for the noble gases He, Ne and Ar.

A program to calculate the third dielectric virial coefficient with no uncontrolled approximations has been developed and will be validated by comparing the results to the best values available in the literature using state-of-the-art potentials.

Coupled DCGT and expansion experiments on the dielectric virial coefficients of helium and argon are finished. To verify the computations on helium with the required level of uncertainty further highly precise DCGT measurements were taken into account at the triple point of water. Measurements with argon were carried out at 253 K, 273 K, 296 K and 303 K. Currently a relative standard uncertainty in the order of 15 % can be reported for the second dielectric virial coefficient which was reached by application of a constraint on the apparatus constant based on the measurements with helium. The measurements with neon as well as the RIGT measurements with argon are currently under preparation.

The dispersions of the atomic polarizabilities of He and Ne were calculated and published. Work on argon as well as on the dispersion of the collision induced polarizabilities is in progress. The development of the quantum computer code for the frequency dependence of the dielectric virial coefficients has started. A second method to calculate the frequency dependence of the dielectric virials based on a path integral approach was already developed and published.

The activities covering the experimental verification of the calculated dispersions are either fully, or partly dependent on the use of RISE’s transportable refractometer. Although the refractometer has been completed and is fully capable of performing the measurements planned, travel restrictions due to Covid-19 have halted the work towards the corresponding activities at this point.

Calculations of the absorption line strength for CO and CO2 have been carried out using the MOLPRO package for the Dipole moment surface ab initio points and the nuclear motion programs DUO for CO and DVR3D for CO2 for the actual line intensities. The targeted discrepancy between calculations and observations of better than 0.1% for 0-3 band of CO has been achieved. Theoretical uncertainty for 0-2 and 0-1 bands is also better than 0.1%. Work on CO2 was prepared by collecting rovibrational energy levels. To probe the uncertainty of the computation for the desired absorption lines, the values calculated for the second and third overtones were compared to the most accurate available experimental data. The deviations for the 30014 and 30013 bands, which were measured with 0.1% accuracy are better than 0.1%. For other 3 bands the discrepancy is between 0.1% and 0.5% which corresponds to changes of less than 0.1 % for the first band including the absorption lines relevant for this project. A publication on the results for CO2 was submitted.

Demonstration of the performance of the novel and improved methods compared with conventional primary absolute pressure standards (Obj. 4)

The preparation of the portable optical refractometer utilising the GAMOR method as a suitable transfer standard has been completed and the setup is ready for use with improvement on the performance in terms of transportability, usability, and measurement quality. As soon as the pandemic travel restrictions will allow it, the portable refractometer setup will be sent to the next project partner for comparison measurements.

The transportable refractometer using GAMOR methodology has been upgraded to improve the performance in terms of transportability, usability, and measurement quality. The setup is now fully operational and ready to be transported and used at different facilities. Due to pandemic situation and travels restrictions, measurements in different locations are pending.

The key aspects of the calibration of the piston cylinder assembly used for RIGT measurements are ready and preparatory work for the calibration as the primary absolute pressure standards for comparison has been performed.

Impact

Dissemination activities include successful publication of 10 peer reviewed articles in international journals, the last one in the journal Physical Review A; Consortium members had 6 presentations of their results in international and national conferences (IVC-21, 26th Colloquium on High-Resolution Molecular Spectroscopy HRMS 2019, 66th AVS International Symposium and exhibition à Columbus, Warsaw Molecular Electronic Structure virtual conference 2020, and DKD annual meeting 2019); training to higher education students on Vacuum physics and metrology and Research Topics in Physics; and stablishing the website of the project to make available general information and publications to the public.

Impact on industrial and other user communities

The development of improved pressure standards will provide a major economic benefit to calibration laboratories and sensor and instrument manufacturers. This project will yield innovative approaches to perform automated calibrations between 1 Pa to 3 MPa. This is important because currently the portfolio of available methods is small and calibrations in this pressure range can only be covered by a combination of methods, hence they are relatively time-consuming and expensive for the end users.

As NIST has already patented a FP-based approach for the US market, it is very important for Europe to keep pace in order to drive forward the development of European companies. The active engagement of accredited laboratories and manufacturers of pressure measuring equipment and sensor instrumentation that rely on highly accurate pressure measurements will ensure benefit for all users who require improved, traceable measurements. Research papers will also be submitted for publication in high impact peer-reviewed journals and a workshop organised and held, to which representatives of industry (both manufacturers and users), academia and NMIs/DIs will be invited.

Impact on the metrology and scientific communities

The metrology and scientific communities will be the first to benefit from the project’s outputs. As a consequence of the revision of the SI in May 2019, in which the uncertainty of the Boltzmann constant kB was eliminated, it will be advantageous to realise the pascal through number density measurements, instead of force-per-area measurements. By exploring a novel, quantum-based traceability route to the pascal, the project’s developments will promote the improvement of pressure and density measurements and standards that promise to be more accurate and versatile compared to those currently in use.

The consortium will liaise closely with the key metrological bodies CIPM CCM, its working group on pressure and vacuum WGPV and the EURAMET TC-M, as they are the prime repositories of developments related to pressure metrology, to ensure that they are kept up‑to‑date on developments within the project and that their feedback is obtained. The active engagement of these key stakeholders will ensure that the outcomes of the project will be disseminated worldwide to NMI laboratories and subsequently to any user who needs improved, traceable measurements of pressure, thus enabling broad industrial uptake. The improved pressure standards and methods developed in this project will also have an immediate impact on other fields of metrology, in particular primary thermometry and interferometric-based dimensional metrology.

Scientific impact is expected from the application of the experimental methods developed within the project to extremely accurate, SI traceable determinations of the permittivity and the refractive index of pure gases and mixtures. The knowledge gained by the technical improvements will lead to advances in the field of optical cavity design. Furthermore, significant advances in the fields of atomic and molecular physics are expected by combination of refractometry and absorption spectroscopy, leading to highly accurate determination of absorption line strengths, which are otherwise subject to extremely complex theoretical calculations.

Impact on relevant standards

The development of photon-based measurements is still at an early stage hence no documentary standards are affected directly. Once the novel measurement standards are established, existing documentary standards on vacuum gauges will need to be adapted to also account for the quantum-based methods. In the longer term, standards analogous to existing standards on vacuum gauges will also have to be developed for the quantum‑based methods, however work on these documentary standards is beyond the scope and timeframe of this project. In the meantime, ISO TC 112 "Vacuum Technology" will receive reports on the results achieved, in preparation for possible changes to existing standards and the development of emerging standards.

Longer-term economic, social and environmental impacts

This project paves the road to the realisation of the vacuum scale in terms of density instead of pressure, and for most vacuum applications the density of gas molecules is the crucial quantity. The project will meet a growing demand from industry for high accuracy pressure and vacuum calibration services in Europe, whilst making calibration procedures less time consuming. Vacuum and pressure related processes are key to many industrial applications that require very clean and well-controlled environments, such as semiconductor, photovoltaic, lighting, nanotechnology, surface engineering, pharmaceutical developments and food packaging. Better control of the vacuum and pressure processes will lead to improved cost efficiency, better overall environmental control over the complete process (higher quality products, fewer rejections), and hence increased profit margins and reduction of waste for the stakeholders.

The European vacuum and pressure industry are at the forefront worldwide, with a number of companies in Europe manufacturing pressure gauges, vacuum pumps and process tools. The introduction of optical measurement techniques will lead to the development of new technology of optical vacuum gauges that are less expensive than the primary ones. It is highly probable that these will be self-calibrating and require less maintenance. In the long run, this will enable manufacturers to produce a completely new generation of vacuum gauges that are more precise and in the long term more economical.

There will be advantages for aviation transport, where the height of an aircraft is measured by an altimeter that is based on an absolute pressure measurement. Further reduction in the standard vertical separation of aircraft will be needed in the future, which will increase the demands on the accuracy of pressure measurements. Not only will manufacturers of avionic measurement equipment and the aircraft industry benefit directly from the enhanced measurement capabilities at the NMI level, but the technology developed also has the potential to be directly utilised in future avionic pressure measurements, thus, supporting future transport demands.

For power plants and the storage of nuclear and toxic waste, it is crucial to reliably assess gas pressure due to strict requirements on safety and sterility. The developments within this project will in the longer term provide more accurate means to monitor the operational conditions and will hence contribute to safer and more efficient conditions at power plants and critical facilities that handle toxic substances. Public agencies involved in environmental monitoring of atmospheric parameters and air pollution will profit from the improvements in absorption spectroscopy, which will lead in the longer term to the extremely accurate determination of the concentration of greenhouse gases, and hence have a significant effect on the detection of polluting sources and the improvement of climate models. Finally, the measurement of differential pressure is important for climate control in critical environments such as cleanrooms, hospitals, and biological/medical research laboratories. However, an additional 1 Pa of differential pressure in a medium‑sized cleanroom requires around 3000 kWh of additional energy per year. More accurate differential pressure measurements would therefore contribute to reducing energy consumption in this environment.