Ion beam figuring machine for ultra-precision silicon spheres correction

•Development of a new ion beam figuring machine for ultra-precision machining of silicon spheres for Avogadro project.•Concept for alignment procedure for sphere machining.•Development of dwell time calculation for deterministic machining. In the framework of the Avogadro project, isotopically enriched 28Si spheres had been manufactured as artifacts for the assessment of various physical quantities including the sphere volume which finally leads to a very accurate determination of the Avogadro constant NA. The Avogadro constant is an important input datum for the redefinition of the unit of mass, the kilogram, on the basis of fundamental physical constants. During the recent measurement campaign, it has turned out that one of the main contributions to the overall uncertainty of NA is the sphericity error and consequently the interferometric volume measurement. Since chemical–mechanical polishing has reached its limits with respect to form accuracy due to the sensitivity of material removal rate to crystal orientation, it has been proposed to use ion beam figuring for further reduction of sphericity error from currently 50nm PV to values