Molar-mass measurement of a²⁸Si-enriched silicon crystal for determination of the Avogadro constant

Abstract

The molar mass of a 28Si-enriched crystal was measured at the National Metrology Institute of Japan to determine the Avogadro constant by the x-ray crystal density method as part of the International Avogadro Coordination project. The molar mass was determined by isotope ratio measurements using a multicollector inductively coupled plasma mass spectrometer combined with an isotope dilution technique. The 28Si-enriched crystal was dissolved in tetramethylammonium hydroxide and three different blended solutions were used to correct for mass bias in the measurement. The molar mass of the 28Si-enriched crystal was determined to be 27.976 970 09 g mol−1 with a standard uncertainty of 0.000 000 14 g mol−1. This corresponds to a relative standard uncertainty of 5.2 × 10−9. This result is consistent with measurements reported by the Physikalisch-Technische Bundesanstalt, Germany.

The Correlation of the NA Measurements by Counting 28Si Atoms

“…In (1), m and V are the mass and volume, M is the mean molar mass, a 3 /8 is the atom volume, and 8 is the number of atoms in the cubic unit cell. From (1), it follows that the N A determination requires the measurement of (i) the lattice parameter-by combined x-ray and optical interferometry, 7,8 (ii) the amount of substance fraction of the Si isotopes and, then, of the molar mass-by absolute mass-spectrometry, [9][10][11][12] and (iii) the sphere mass and volume. [13][14][15] Silicon crystals contain impurities, interstitial atoms, and vacancies, which implies that the measured mass value does not correspond to that of an ideal Si crystal and that the crystal lattice may be distorted.…”

The Avogadro Constant for the Definition and Realization of the Mole

“…[74][75][76][77] Currently, a CCQM-pilot study is pending aiming at the screening of the ability of the participants of the study to measure the molar mass M of highly enriched silicon with sufficiently small associated uncertainties applying the VE-IDMS method. [74][75][76][77] Currently, a CCQM-pilot study is pending aiming at the screening of the ability of the participants of the study to measure the molar mass M of highly enriched silicon with sufficiently small associated uncertainties applying the VE-IDMS method.…”

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

“…For the N A determination by IAC in 2015, the molar mass M of AVO28-S5c was measured independently by the Physikalisch-Technische Bundesanstalt of Germany (PTB), NIST and NMIJ using isotope dilution and multicollector inductively coupled plasma mass spectrometers [28][29][30][31]. The measured amount of substance of 30 Si was confirmed by the measurement results with instrumental neutron activation analysis (INAA) by INRIM [32].…”