Improvement in the Volume Determination for Si Spheres With an Optical Interferometer

Accurate volume measurements for silicon spheres using optical interferometers play an important role in the determination of the Avogadro constant using the X-ray crystal-density method. To reduce the uncertainty in the volume determination, a new vacuum chamber with a radiation shield has been developed. A new sphere temperature-measurement system has also been installed. Using this system, the sphere temperature has been measured with an uncertainty of 0.71 mK. Details of the improvements are described. The relative uncertainty in the volume determination has been reduced to 2.4 times 10^-8 by the improvement in the sphere temperature measurement. This will be reduced to 1.7 times10^-8 using a direct chemical composition analysis to the oxide layers on the silicon spheres.