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Title: International determination of the Avogadro constant
(Foreword to Metrologia 48(2)- Special Issue)
Author(s): Massa, E.; Nicolaus, A.
Journal: Metrologia
Year: 2011, Volume: 48, Issue: 2
DOI: 10.1088/0026-1394/48/2/E01
Funding programme: iMERA-Plus: Call 2007 SI and Fundamental Metrology
Project title: T1.J1.2: NAH: Avogadro and molar Planck constants for the redefinition of the
kilogram
Copyright note: This is an author-created, un-copyedited version of an article accepted for
publication in Metrologia. IOP Publishing Ltd is not responsible for any errors or omissions in this
version of the manuscript or any version derived from it. The definitive publisher-authenticated
version is available online at doi:10.1088/0026-1394/48/2/E01.
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Foreword
This issue of Metrologia collects papers about the results of an international research project aimed
at the determination of the Avogadro constant, NA, by counting the atoms in a silicon crystal highly
enriched with 28Si isotope. Fifty years ago, Egidi1 thought about realizing an atomic mass standard.
In 1965, Bonse and Hart2 operated the first X-ray interferometer, thus paving the way to the
achievement of Egidi’s dream and soon Deslattes3 completed the first counting of the atoms in a
natural silicon crystal.
The present project, outlined by Zosi4 in 1983, started in 2004 by combining the experiences and
capabilities of the BIPM, INRIM, IRMM, NIST, NPL, NMIA, NMIJ, and PTB. The start signal,
ratified by a memorandum of understanding, was a contract for the production of a Si crystal highly
enriched with 28Si. The enrichment process was undertaken by the Central Design Bureau of Machine Building in St. Petersburg. Subsequently, a polycrystal was grown the Institute of Chemistry
of High-Purity Substances of the Russian Academy of Sciences in Nizhny Novgorod and a 28Si
boule was grown and purified by the Leibniz-Institut für Kristallzüchtung in Berlin. Isotope enrichment made it possible to apply isotope dilution mass spectroscopy, the determination of the
Avogadro constant with unprecedented accuracy, and the fulfilment of the Egidi’s dream.
To convey the Egidi’s “fantasy” into practice, two 28Si kilogram prototypes shaped as quasi-perfect
spheres were manufactured by the Australian Centre for Precision Optics; their isotopic composition, molar mass, mass, volume, density, and lattice parameter were accurately determined and their
surfaces were chemically and physically characterized at the atomic scale. The Andreas’ paper reviews the work carried out; it collates all the findings and illustrates how the Avogadro’s constant
was obtained. Impurity concentration and gradients in the enriched crystal were measured by infrared spectroscopy and taken into account; Zakel relates about these measurements in detail. Next,
Pramann illustrates how the molar mass of the enriched crystal was measured by exploiting isotopic
enrichment and isotope dilution mass spectrometry. Valkiers reports about re-measurement of the
molar mass of a natural Si crystal, a measurement prompted by the exigency of clarifying the origin
of the discrepancy between the NA value given in the present issue and the value obtained with use
of natural Si crystals. A consistency analysis of the different isotopic-composition determinations is
illustrated in the Bulska’s paper. As reported in two papers by Massa, to determine the lattice parameter a X-ray interferometer was manufactured from the material between the already mentioned
spheres. The measurement result was combined with lattice comparisons between different crystal
samples and with the impurity gradient to extrapolate the sphere lattice-parameter. Ferroglio’s contribution analyzes the self-weigh deformation of the X-ray interferometer. Fujimoto reports about
the lattice-perfection investigations carried out by a novel self-referencing diffractometer at the National Laboratory for High-Energy Physics (KEK) in Japan. A really great effort was made to characterize the sphere surfaces and to correct for the oxide layer and the contaminating atoms. The res ults of these investigations are given by Bush. The sphere diameter and topography were measured
by optical interferometry to nanometer accuracy; Bartl’s and Kuramoto’s papers describe how the
sphere volumes were determined. Andreas’ paper relates about the calculation of phase corrections
for the diameter measurements. The results of mass comparisons against the Pt-Ir standards of the
BIPM, NMIJ, and PTB are given by Picard.
The results reported in the present issue need to be completed. One of the necessary activities is to
relate the mass of the 28Si atom to its Compton’s wavelength to test the mass-energy-frequency
equivalence. Another effort is to monitor the stability of the Pt-Ir prototype: the technologies described in the present issue can be refined and finalized to calculate the mass variation of 1 kg 28Sispheres by monitoring the surface evolution without weighing them on a balance. The last activity
is the determination of the mass of a 28Si sphere by electrical measurements using a watt balance
and without any reference to the Pt-Ir prototype. In this framework, it will be necessary to demonstrate the mutual consistency and the stability of both the electrical and crystal mise en pratique of a
kilogram definition based on a conventional value of the Planck constant. A related issue is to develop suitable procedures and protocols to disseminate the unit of mass from the new realizations.
Since the molar Planck constant is well known via the measurement of the Rydberg constant, the
accurate measurement of NA also provides an accurate and independent determination of the Planck
constant, h. The comparison of the Planck constant values obtained via the watt-balance experiment
and the NA determination tests quantum mechanics. In fact, the watt-balance value of h depends on
solid state physics through the theories of Josephson and quantum Hall effects, whereas the value of
h derived from NA depends on atomic physics through the energy level differences in hydrogen and
deuterium whose associated transition frequencies yield information on the Rydberg constant.
Grateful thanks are addressed to H-J Pohl for his outstanding project management in Russia, to
A.K. Kaliteevski and his colleagues of the Central Design Bureau of Machine Building and the Institute of Chemistry of High-Purity Substances for their dedication and the punctual delivery of the
enriched material, to H. Riemann and his staff of the Institut für Kristallzüchtung for the crystal
growth, to our directors for their advice and financial support, and to our colleagues for their daily
work.
A special thank is addressed to Peter Becker, to whom this issue is dedicated on the occasion of his
retirement from work at the Physikalisch-Technische Bundesanstalt. In 1974, young Peter joined
the PTB’s Avogadro group which, under the direction of Peter Seyfried, followed Bonse’s work
and improved the measurements of the lattice parameter and the Avogadro constants 5,6. In 2004,
Peter proposed and backed this project by taking on his shoulders the risks, the management burden, and the coordination of the many relevant activities.
Enrico Massa
Arnold Nicolaus
1
2
3
4
5
6
Egidi, C. Phantasies on a natural unity of mass. Nature 200, 51-52 (1963).
Bonse, U. and Hart, M. An X-ray interferometer. Appl. Phys. Lett. 6, 155-156 (1965).
Deslattes, R.D. et al. Determination of the Avogadro constant. Phys. Rev. Lett. 33, 463-466 (1974).
Zosi, G. A neo-Pythagorean approach towards an atomic mass standard. Lettere al Nuovo Cimento, 38, 577580 (1983).
Becker P, Dorenwendt K, Ebeling G, Lauer R, Lucas W, Probst R, Rademacher H-J, Reim G, Seyfried P, and
Siegert H Absolute Measurement of the (220) Lattice Plane Spacing in a Silicon Crystal Phys. Rev. Lett. 46,
1540–1543 (1981).
Seyfried P, Becker P, Kozdon A, Luedicke F, Stuempel J, Wagenbreth H, Windisch D, De Bièvre P, Ku H H,
Lenaers G, Murphy T J, Peiser Hs, and Valkiers S A determination of the Avogadro constant Z. Phys. B
87 289-98 (1992).