In determining the Avogadro constant, the preferred method has been to use one of the high-precision spheres fabricated here at the ACPO. These come in the form of a highly polished 1 kg single crystal silicon sphere, fabricated with a roundness in range of 60 nm.
The nominal diameter of a 1 kg Si sphere is 93.6 mm. In order to obtain an accuracy of 0.01 ppm in volume, the diameter must be known to a range of 0.6 nm. In other words, within one atom spacing.
Such high accuracy requires specialised equipment and one such procedure is by optical interferometry using a precision etalon through a stabilised laser light. The measurements are sensitive to many parameters, particularly to those of temperature and pressure. An instability within the range of 2 mK would be sufficient to cause the silicon to expand by more than the allowable uncertainty. The refractive index of air (and hence the wavelength of the light) is sensitive to the surrounding air pressure. It is therefore necessary to carry out the measurements in a controlled environment.
Corrections must be applied for surface impurities such as oxides and absorbed water. Typically, silicon has an oxide layer 3 to 4 nm thick, which is a mixture of SiO and SiO2. It is also possible for the surface to absorb some monolayers of water. Since much of the absorbed water is removed in a vacuum, a number of the key measurements are made in a vacuum environment. A further correction must then be applied for the difference in bulk modulus between the air and vacuum.
This ball wants to be caught…