Precision Measurement Techniques for Avogadro Constant Determination

Determining the Avogadro constant with unprecedented accuracy demands a rigorous integration of complementary measurement strategies. Central to this endeavour is the x-ray crystal density method, which combines precise optical interferometry of near-perfect silicon spheres with lattice parameter determination via X-ray interferometry. Mass and volume measurements of polished spheres are reconciled with the lattice spacing of the enriched silicon crystal to count the number of atoms directly. High isotopic enrichment in 28Si crystals reduces uncertainty in the molar mass, while atom probe tomography verifies chemical purity and homogeneity at the nanometre scale. Progress in the fabrication of ultraprecise spheres, including advanced polishing and surface characterisation techniques, has minimised deviations from ideal sphericity and accounted for surface layers through ellipsometric and spectroscopic methods. More recently, in-process interferometric monitoring devices have been developed to assess diameter variation with sub-nanometre resolution during manufacturing. Together, these approaches interlink mass spectrometry, crystallography, optical and X-ray interferometry, and microscopy to yield a self-consistent value of the Avogadro constant, underpinning the redefinition of the kilogram and reinforcing global measurement standards.

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Precision Measurement Techniques for Avogadro Constant Determination publication trend

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Technical terms

Avogadro constant: The fixed number of constituent particles in one mole of a substance, defining the mole in the SI.

x-ray crystal density (XRCD) method: A technique combining sphere mass, volume, and crystal lattice measurements to count atoms in a crystal.

Atom probe tomography (APT): A microscopy method that maps the three-dimensional distribution of isotopes and impurities at near-atomic resolution.

Isotopic enrichment: The process of increasing the proportion of a specific isotope (e.g., 28Si) to reduce molar mass uncertainty.

Lattice parameter: The characteristic spacing between atoms in a crystal lattice, determined by X-ray interferometry.

Optical interferometry: A method using light interference to measure distances or displacements with sub-nanometre precision.

Sphericity: The degree to which a sphere approaches an ideal shape, critical for accurate volume determination.

References

1. Atom probe tomography investigation of highly-enriched 28Si crystal. Microchemical Journal (2024).
2. A new 28Si single crystal: counting the atoms for the new kilogram definition. Metrologia (2017).
3. A new generation of 99.999% enriched 28Si single crystals for the determination of Avogadro’s constant. Metrologia (2017).
4. Determination of the Avogadro constant by the XRCD method using a 28Si-enriched sphere. Metrologia (2017).
5. Si lattice parameter measurement by centimeter X-ray interferometry.. Optics Express (2008).
6. Interferometric device for the in-process measurement of diameter variation in the manufacture of ultraprecise spheres. Measurement Science and Technology (2021).