[Paper Review] Precision measurements of the Planck and Avogadro constants

H. Bettin, Kenichi Fujii+4 more|arXiv (Cornell University)|Mar 4, 2013

Scientific Measurement and Uncertainty Evaluation34 references15 citations

TL;DR

This paper presents high-precision measurements of the Planck and Avogadro constants using the watt-balance and 28Si sphere experiments, achieving a combined uncertainty of 1.5×10⁻⁸ for the Avogadro constant. These results underpin the redefinition of the kilogram in terms of fundamental constants, ensuring SI unit stability and universality.

ABSTRACT

Precision measurements of the fundamental constants are tour de force of basic metrology, where the useful information is usually beyond the last digit of the measured value. They challenge theoretical models and measurement technologies and set a network of measurement equations on which a universal system of units can be built, which stems from the most basic concepts of physics. Because of their connection with the mass unit, the Avogadro and Planck constants are on the spotlight.

Motivation & Objective

• To achieve sub-10⁻⁸ uncertainty in the Avogadro constant to support the redefinition of the kilogram.
• To resolve discrepancies between Planck constant values derived from different experimental methods.
• To improve the accuracy of silicon sphere mass and atom count measurements by addressing surface contamination and lattice parameter uncertainties.
• To ensure the new SI definition of the kilogram is consistent with the historical international prototype within measurement uncertainty.
• To validate the internal consistency of physical theories by comparing Planck constant values across energy scales from meV to MeV.

Proposed method

• Using the watt-balance experiment to measure the ratio h/m(K), where m(K) is the mass of the international prototype, by equating mechanical and electrical power.
• Employing a 28Si-enriched crystal sphere to determine the Avogadro constant by counting atoms via x-ray interferometry and precise lattice parameter measurements.
• Applying the relation h/m(X) = N_A h / M to compare Planck constant values derived from atomic, nuclear, and macroscopic experiments.
• Implementing advanced surface characterization techniques, including ultra-precision ion-beam figuring and plasma-jet machining, to reduce surface topography and contamination effects.
• Correcting for wavefront distortions in optical interferometry by measuring the impulse-domain width of the illuminating beam.
• Using first-principles atomistic simulations to model stress and strain fields in silicon surfaces and their impact on lattice parameter measurements.

Experimental results

Research questions

• RQ1 Can the Avogadro constant be measured with a relative uncertainty below 1.5×10⁻⁸ using a 28Si sphere?
• RQ2 What is the impact of surface contamination and roundness errors on the accuracy of atom counting in silicon spheres?
• RQ3 How do discrepancies between watt-balance and 28Si measurements of the Planck constant affect the consistency of fundamental constants?
• RQ4 To what extent do wavefront distortions and beam aberrations limit the accuracy of optical interferometric lattice parameter measurements?
• RQ5 Can surface stress and strain effects in silicon crystals be accurately modeled and corrected to improve lattice parameter precision?

Key findings

• The Avogadro constant was measured with a relative uncertainty of 1.5×10⁻⁸, meeting the target for SI redefinition.
• Surface contamination by copper and nickel silicides increased measurement uncertainty by affecting optical constants and oxide layer mass.
• Roundness errors and wavefront distortions in interferometry were found to distort phase profiles, with a non-trivial evolution from sphere surface to detector.
• The 2010 least-squares adjustment of fundamental constants yielded h = 6.62606957(29)×10⁻³⁴ J s, used as the best estimate for the new SI definition.
• Discrepancies between Planck constant values from different experiments indicate potential errors in measurement models or technologies, prompting further investigation.
• Theoretical modeling of surface stress and strain fields in silicon using atomistic simulations revealed critical effects on lattice parameters, necessitating correction in high-accuracy measurements.