Volume measurements of 28Si spheres using an interferometer with a flat etalon to determine the Avogadro constant

Abstract

The volumes of two 1 kg silicon spheres, AVO28-S5 and AVO28-S8, fabricated from a 28Si-enriched crystal were measured to determine the Avogadro constant by the x-ray crystal density method in the International Avogadro Coordination Project. The volumes were determined from diameter measurements of the two spheres using a laser interferometer with a flat etalon. In the diameter measurement, the sphere was placed between the two flat etalon plates. The gaps between the sphere and the etalon plates and the distance between the etalon plates were measured by phase-shifting interferometry with optical frequency tuning. The apparent volumes of the 28Si spheres were determined from the diameter measurement in many directions with relative combined standard uncertainties of 5.0 × 10−8 and 4.4 × 10−8 for AVO28-S5 and AVO28-S8, respectively. The effect of the surface layer on the diameter measurement was evaluated on the basis of the results of characterizing the sphere surface. By taking into account the effect of the surface layer, the silicon core volume excluding the surface layer and the actual volume including the surface layer were also determined. Details of the interferometer, data analysis and the uncertainty in the measurement are described.