# Confirmation of the results obtained in the mass determination of the 28Si spheres AVO28-S5c and AVO28-S8c in 2013 and 2014

24.10.2018

Within the scope of comparison measurements with regard to the results of the determination of the Avogadro constant and the Planck constant with the aid of the first two monocrystalline silicon spheres AVO28-S5c and AVO28-S8c made of highly enriched silicon (degree of enrichment for 28Si: > 99.99 %), also the mass of the spheres in vacuum was determined again.

For this purpose, measurements were carried out with the aid of a mass comparator (Sartorius CCL1007 type) in a pressure range between 4 × 10‑5 hPa and 6 × 10‑6 hPa. Special sorption artefacts made of platinum-iridium served as transfer standards between the mass of a prototype of the kilogram in air and the mass of the 28Si spheres in vacuum [2]-[4].

Figure 1 shows a summary of the current results and a comparison with the results of the measurements carried out in 2013/14. For the new measurements, a different mass comparator, a modified measuring sequence and an updated link-up to the kilogram prototypes of the International Bureau of Weights and Measures (BIPM) were used. The measurement results agree within the standard uncertainties (= 1) indicated and thus confirm PTB’s previous results as well as the reference values for the 28Si spheres AVO28-S5c and AVO28-S8c [1].

Figure 1: Comparison of the results of the mass determinations in vacuum achieved for the 28Si spheres AVO28-S5c and AVO28-S8c. The uncertainty ranges indicated here correspond to the standard uncertainties (k = 1) of the respective measurements. The influence which the reproducibility of the cleaning has on the mass of the silicon spheres amounts to 3 µg (standard uncertainty) and is not included in the uncertainty ranges indicated here.

### Literature

[1]    Azuma, Y.; Barat, P.; Bartl, G.; Bettin, H.; Borys, M.; Busch, I.; Cibik, L; D’Agostino, G.; Fujii, K .; Fujimoto, H.; Hioki, A.; Krumrey, M.; Kuetgens, U.; Kuramoto, N.; Mana, G.; Massa, E.; Meeß, R.; Mizushima, S.; Narukawa, T.; Nicolaus, A.; Pramann, A.; Rabb, S. A.; Rienitz, O.; Sasso, C.; Stock, M.; Vocke Jr., R. D.; Waseda, A.; Wundrack, S.; Zakel, S.: Improved measurement results for the Avogadro constant using a 28Si-enriched crystal. Metrologia 52 (2015), pp. 360–375

[2]     Davidson S, Brown S and Berry J: A report on the potential reduction in uncertainty from traceable comparisons of platinum–iridium and stainless-steel kilogram mass standards in vacuum. NPL Report CMAM 88 (2004), National Physical Laboratory, Teddington, pp. 1–24

[3]     Picard, A.: Mass determinations of a 1 kg silicon sphere for the Avogadro project. Metrologia 43 (2006), pp. 46–52

[4]     Picard, A.; Barat, P.; Borys, M.; Firlus, M. and Mizushima, S.: State-of-the art mass determination of 28Si spheres for the Avogadro project. Metrologia 48 (2011), pp. S112–9

### Contact person:

Dr. Michael Borys, Department 1.8, Working Group 1.81, e-mail: michael.borys(at)ptb.de