Physicists from Australia, the USA, Europe and Japan have obtained an accurate estimate of the Avogadro constant by “counting” the number of atoms in two kilogram silicon spheres.

Avogadro’s constant N_A – the number of particles contained in one mole of a substance – serves as a connecting link between micro- and macrophysics. Calculation of NA makes it possible to estimate the value of Planck’s constant h, since the molar “version” of the latter, equal to the product of N_A* h, calculated with great accuracy from the results of measurements of the Rydberg constant. Well, the value of h can become the basis for a new definition of the kilogram, which will replace the outdated platinum-iridium standard, made more than a century ago and stored at the International Bureau of Weights and Measures. It is assumed that its mass has changed by about 50 μg over 100 years.

When measuring Avogadro’s constant using silicon samples, it is taken into account that the atoms in the crystal are arranged in an orderly manner. The formula for the calculation looks like this:

[tbcenter] (N_A = n * M / (p * a ^ 3) )[/tbcenter]where n = 8 is the number of atoms in the unit cell of the lattice, M is the molar mass, ρ is the density, a³ – the volume of the unit cell.

One of the most difficult tasks is to determine the isotopic composition of silicon, and in their work the authors used a crystal artificially enriched in the 28Si isotope. At the first stage of the project, which started in 2004, SiF was enriched at the Russian Central Design Bureau of Mechanical Engineering.₄ centrifugation; then the gas was converted to SiH₄, after which the staff of the Institute of Chemistry of High-Purity Substances. GG Devyatykh RAS grew a polycrystal by chemical vapor deposition. The manufacturing process was completed in 2007 in Berlin, where a 5 kg single crystal was grown.

Taking a ready-made sample, physicists made two silicon spheres to reduce the volume estimate to the definition of the diameter. After all the necessary quantities were measured, the scientists calculated Avogadro’s constant from two sets of data, obtaining values ​​of 6.022 140 93 (21) * 10²³ and 6.022 140 75 (22) * 10²³ mole^-one…

Averaging gave the final value N_A = 6.022 140 84 (18) * 10²³ mole^-one; the relative error here is 3.0 * 10^-eight…

According to the representative of the International Bureau of Weights and Measures Richard Davis, it will be possible to raise the question of redefining the kilogram only when the relative error drops below 2.0 * 10^-eight…

Note that the described method of estimating N_A there is a serious competitor – the watt-scale method. So far, the results of these two experiments (see figure below) do not agree very well with each other.