A new²⁸Si single crystal: counting the atoms for the new kilogram definition

Abstract

A new single crystal from isotopically enriched silicon was used to determine the Avogadro constant N A by the x-ray-crystal density method. The new crystal, named Si28-23Pr11, has a higher enrichment than the former 'AVO28' crystal allowing a smaller uncertainty of the molar mass determination. Again, two 1 kg spheres were manufactured from this crystal. The crystal and the spheres were measured with improved and new methods. One sphere, Si28kg01a, was measured at NMIJ and PTB with very consistent results. The other sphere, Si28kg01b, was measured only at PTB and yielded nearly the same Avogadro constant value. The mean result for both 1 kg spheres is N A = 6.022 140 526(70) × 10 23 mol −1 with a relative standard uncertainty of 1.2 × 10 −8 . This value deviates from the Avogadro value published in 2015 for the AVO28 crystal by about 3.9(2.1) × 10 −8 . Possible reasons for this difference are discussed and additional measurements are proposed.

The Planck Constant for the Definition and Realization of the Kilogram

“…By rotating the sphere, a complete diameter mapping of the sphere is possible (Figure ). Uncertainties of 2.0 × 10 −8 V and 7 × 10 −9 V were achieved at NMIJ and PTB, respectively, with perfectly consistent results . The setups not only differ in their optical configurations but also in the phase‐shifting algorithms to calculate the fractional fringe order of interference.…”

“…Two lamellas diffract the X‐ray beams and realize an interferogram with the periodicity of the lattice planes at the position of a third lamella, the “analyzer.” While the third lamella is moved through this moiré pattern, the lattice spacings are counted by observing the X‐ray interference and the movement of the lamella is measured by an optical interferometer. Up to now the lowest uncertainty has been achieved by INRIM (Istituto Nazionale di Ricerca Metrologica, Italy) resulting in a relative uncertainty contribution to the Avogadro and Planck constants of 5.2 × 10 −9 . At PTB a similar apparatus is set up which uses a continuous detection of the X‐ray photons while the analyzer is moving …”

Wie viele Moleküle enthält ein Mol?

“…Mit der Verfügbarkeit von angereichertem Silizium‐28 mit einer Isotopenreinheit von mehr als 99,99 % erhielt das Avogadro‐Projekt schließlich einen neuen Impuls. Unter der Leitung der PTB gelang es einem internationalen Konsortium schließlich, mit Hilfe eines nahezu perfekten, monoisotopischen Silizium‐Einkristalls die Avogadro‐Konstante mit der angestrebten Messunsicherheit zu bestimmen .…”

XPS study of silicon spheres as a density standard

“…The accurate determination of the Avogadro constant is one of the candidate methods for realizing a new definition of the kilogram . To accurately determine the Avogadro constant, measurements of the density, lattice constant, and mean molar mass of a single‐crystal Si sphere, which is called X‐ray‐crystal‐density (XRCD) method, have been performed within the International Avogadro Coordination (IAC) project …”

“…For accurate measurements of the density of the Si sphere, the effects of the surface layer (SL) must be carefully considered. Our previous studies indicated that one of the dominant sources of uncertainty in such density measurement was from the surface characterization . Surface characterization, including investigation of the SL model, analysis of the surface chemical composition, and measurement of the thickness of each SL, is critical for refining correction values required for accurate determination of the mass and volume of the spheres in order to reduce the uncertainty of the density measurements.…”