The influence of Young's modulus on roundness in silicon sphere fabrication [Avogadro constant]

Silicon single-crystal spheres for use in accurate determination of the Avogadro constant are fabricated by optical grinding and polishing. Surface profiling of the deviation from sphericity of the spheres shows a strong cubic symmetry on the scale of (20 to 40) mm, which is well correlated with the orientation of the silicon crystal axes and sets a limit on the ultimate shape that can be obtained. This deviation from sphericity can be explained in terms of the variation of Young's modulus with crystal orientation.