Realization of the kilogram by the XRCD method

Abstract

When the kilogram is redefined in terms of the fixed numerical value of the Planck constant h, the x-ray-crystal-density (XRCD) method, among others, is used for realizing the redefined kilogram. The XRCD method has been used for the determination of the Avogadro constant N A by counting the number of atoms in a 28 Si-enriched crystal, contributing to a substantial reduction of uncertainty in the values of N A and h to 2 parts in 10 8 . This method can be therefore used reversely for the mass determination of a 1 kg sphere prepared from the crystal. This is realized by SI-traceable measurements of its lattice parameter, isotopic composition, volume, and surface properties. Details of the corresponding measurements are provided, as well as the concept of the XRCD method, isotope enrichment, crystal production, sphere manufacturing, and evaluation of impurities and self-point defects in the crystal, together with mass comparison with respect to the silicon sphere for disseminating mass standards.

The Avogadro Constant for the Definition and Realization of the Mole

“…[42,43,47] These efforts led to the so-called "Avogadro-Project" by setting up experiments to count the atoms in silicon with natural isotopic composition. [48] In the XRCD method, the lattice parameter of the single crystalline silicon is measured as well as the volume of the silicon sphere used with a mass of 1 kg, the molar mass of the silicon, the density and mass of the sphere, its surface properties, and impurities of the crystal (chemical impurities and vacancies). A polishing technique for silicon spheres with a mass of 1 kg has been developed and the respective experiments for the determination of N A with further reduced uncertainty have been improved.…”

Determination of the Avogadro constant by the XRCD method using a28Si-enriched sphere

“…On the other hand, the XRCD method will be used to realize the kilogram from the new definition of the kilogram based on the value of h [10]. From equation (2), the mass of the Si sphere m sphere is related to h as…”

Naturally occurring 32Si and low-background silicon dark matter detectors

“…Over the last 25 years a research program -often collectively referred to as the "Avogadro Project" -has focused on redefining the kilogram using monocrystalline silicon that is highly enriched in 28 Si [54][55][56][57][58][59], encompassing a variety of materials and metrological techniques for achieving an improved, lower-uncertainty definition of the kilogram mass. The use of a single crystal of 28 Si with ultra-high purity, both chemically and isotopically, has the following benefits for metrology: i) Minimizing chemical impurities reduces uncertainty in lattice defects and total crystal mass [60]; ii) Minimal lattice defects and the physical regularity of the crystal structure allow for high-precision atom counting [55]; and iii) Having high isotopic purity (and thus a single atomic mass) further reduces uncertainty when estimating the total mass of an enriched crystal [61]. This research program is made possible via gaseous ultracentrifugation followed by chemical reduction to metal [55,62].…”

“…The use of a single crystal of 28 Si with ultra-high purity, both chemically and isotopically, has the following benefits for metrology: i) Minimizing chemical impurities reduces uncertainty in lattice defects and total crystal mass [60]; ii) Minimal lattice defects and the physical regularity of the crystal structure allow for high-precision atom counting [55]; and iii) Having high isotopic purity (and thus a single atomic mass) further reduces uncertainty when estimating the total mass of an enriched crystal [61]. This research program is made possible via gaseous ultracentrifugation followed by chemical reduction to metal [55,62]. The enrichment process begins with Na 2 nat SiF 6 conversion to nat SiF 4 gas.…”