Redefining the Kilogram

There has been a movement in the physics world for that past few years to standardize the kilogram. At the moment, a kilogram is defined as the mass of the International Prototype Kilogram (IPK), housed at the International Bureau of Weights and Measures (BIPM).

The International Prototype Kilogram. Via BIPM

The prototype is made of 90% Platinum and 10% Iridium. The kilogram is now the only physical constant based on a physical artifact.

Since it is the only constant left to standardize, physicists have been working on a way to do this. Unsurprisingly, it one such strategy has to do with Avogadro’s constant, which is a constant used throughout the physical sciences and relates the number of atoms of a substance to the amount of the substance. It has been previously defined as 6.02214179(30)×10²³ mol^-1

A study published online yesterday in Physical Review Letters has measured Avogadro’s constant with the highest accuracy yet.

The study was performed by using x-ray crystallography, a technique which studies the way x-rays “bounce” off the material. In this way, scientists can get an idea of the density of the material they are studying, which is directly related to the number of atoms.

The biggest problem with this technique in the past has been the high experimental errors. The BIPM has stated that any new definition of the kilogram  must have an error less than 2 x 10^-8, which is pretty damn small.

So in this experiment, the researchers used a silicon sphere which had been enriched with the isotope ²⁸Si. Why?

In this way, the absolute calibration of the mass spectrometer with the required small uncertainty could be overcome by applying isotope dilution mass spectrometry combined with multicollector inductively coupled plasma mass spectrometry.

What does that mean? In a nutshell it means that the experimenters changed the isotopic abundance of silicon in the sample. Since the researchers knew what the natural isotopic abundance of silicon was, they were able to measure how it changed after they added more ²⁸Si, and through a little bit of math were able to determine the isotopic abundance of the sample.

Confused? Don’t worry. At the end of they day all it means is they were able to greatly reduce the error in their measurement.

Why silicon? Mostly because it can be produced at very high purity and with very few defects in the crystalline lattice structure.

Next, they measured the atoms in 2 silicon spheres. It was required that the isotopic abundance of the spheres be known (which they did using ²⁸Si enrichment) as well as the molar mass and the volume. Since silicon arranges itself in a well-known crystal pattern (8 atoms per crystal cell), determining these values was feasible.

They also needed the silicon spheres to have the same mass as the BIPM standard. They were able to get the mass the same within 5 micrograms. The volume of the spheres was determined by measuring the diameter of the spheres using optical interferometry. The volume was calculated to a very high accuracy, within 1.3 x 10^-7 cm³.

So, by using x-rays, the researchers measured the “lattice parameter”, or the length of one side of a single crystal structure of silicon. Knowing this lattice parameter, as well as the fact that there are 8 atoms per crystal, and the volume of the sphere, they were able to get a measure of Avogadro’s constant.

By averaging the values from both spheres, they were able to get a value for Avogadro’s constant of N_A = 6.02214078(18) x 10²³ with a relative uncertainty of 3.0 x 10^-8.

So their error is still greater than the requirement for a new standard, but its pretty close. The researchers believe this technique can be refined enough to get the uncertainty below that requirement.

Ok, so why do we care? Well coming up with a standard for the kilogram based on Avogadro’s number is an elegant way to link the microscopic world with the macroscopic world. Having the standard will also help with the way experiments get reported all over the world.

Reference:

Andreas, B., Azuma, Y., Bartl, G., Becker, P., Bettin, H., Borys, M., Busch, I., Gray, M., Fuchs, P., Fujii, K., Fujimoto, H., Kessler, E., Krumrey, M., Kuetgens, U., Kuramoto, N., Mana, G., Manson, P., Massa, E., Mizushima, S., Nicolaus, A., Picard, A., Pramann, A., Rienitz, O., Schiel, D., Valkiers, S., & Waseda, A. (2011). Determination of the Avogadro Constant by Counting the Atoms in a ^{28}Si Crystal Physical Review Letters, 106 (3) DOI: 10.1103/PhysRevLett.106.030801