# Why must the kilogram standard be based on a kilogram mass object?

Inspired by the accepted answer to a question about the Avogadro Project, why must an object used to define a new standard for the kilogram have a mass of one full kilogram?

If a smaller mass were used then it might be possible to use a diamond, since it is currently not possible to manufacture a 1kg diamond.

It doesn't need to be. You could equally well have an International Prototype Gram, say, and then (just to make things more confusing, of course) define your base unit, the kilogram, as one thousand times the mass of the IPG.

Why wasn't it done this way originally? Mostly, because history. At the time that the IPK was made, it was easier to do precision manufacturing on the kilogram scale than on the gram scale, so the IPK was built with the best that the cutting-edge technology of the day could provide (said entirely without tongue in cheek: it was an honest-to-goodness technological achievement).

Why aren't we doing it this way now? Because we're not setting up any artifact kilograms at all. The details are detailed in this longer thread, but the upshot is that the kilogram is being redefined by fixing the value of Planck's constant (with standards for length and time assumed as pre-existing dependences). The main mise en pratique as currently envisioned is via Kibble (a.k.a. watt) balances, which means that the Avogadro Project is unlikely to play that big of a role in practical implementations of the new kilogram, i.e. there generally won't be a kilogram-scale object as an ultimate mass reference in most national metrology labs.

However, it's important to note that the Avogadro Project also falls in this scheme: the goal is not to create a new artifact kilogram (which would be just as problematic as the IPK), it is instead to create a reference mass which can be (directly, accurately and stably) traced to the fundamental constants $\hbar$, $N_A$, $c$ and $\Delta \nu(\rm Cs)$. The rough route to doing this looks like this:

• First off you make your object. Say, a big shiny sphere manufactured out of a silicon-28 monocrystal.

• Then you characterize its volume (which requires a length standard), via optical interferometric techniques.

• Then you characterize the lattice constant of the monocrystal via x-ray crystallography, which together with the volume gives you the number of atoms in the sphere.

• Then you measure the mass of an individual silicon-28 atom in terms of Planck's constant via recoil spectroscopy (in essence, you take a photon with known wavelength $\lambda$ and therefore known momentum $p=h/\lambda$, and you measure how much of a kick it gives to the atom, which produces a measurable frequency shift proportional to $h/m(^{28}\rm Si)$).

This then gives you the mass of your sphere.

None of the above particularly singles out the one-kilogram scale as special, and neither does it single out silicon (over, say, carbon). If you wanted to repeat the whole process with a twenty-gram synthetic carbon, there's no fundamental definition to stop you ─ only technological hurdles.

So, why aren't we doing this? Because it's expensive, and because the Avogadro Project's main value (or at least, the way I see it) is act as a crucial independent-method test of the accuracy of the results obtained via Kibble-balance methods. Making a twenty-gram diamond is liable to be even more expensive than the Avogadro Project without offering substantially more accuracy, and you need a good reason to go through the whole thing. Wouldn't you rather spend the money on a couple of top-of-the-line watt balances, which offer much more flexibility and which create a framework of technological assets, both material and know-how, that can be used for other things?

We don't need just one reference standard. Other standards labs outside Paris need to be able to create their own secondary standard kilograms to be used for day-to-day measurements. So we can't just pick some arbitrary sample diamond and say its mass is some fraction of a kilogram, we have to have a standard that can be duplicated by other labs.

When the International Prototype Kilogram was created, it wasn't possible to manufacture any kind of diamond at all, so a diamond standard wasn't suitable given the technology of the late 19th century.

Given that it was chosen to make the prototype kilogram of platinum iridium alloy, and 1 kg of that material was available, it seems sensible to make the standard a full kilogram.

A smaller prototype artifact would also be more subject to errors when measuring it (or measuring other objects against it).

By the time it became obvious that the standard kilogram was not maintaining its mass adequately, it was already obvious that it would be better to create a natural standard (such as a fixed number of silicon atoms or a relationship with the standard unit of power via the watt balance) rather than continue to maintain an artifact standard, so there's been no movement (that I know of)to adopt a new artifact standard.

• Perhaps a review of the linked question and this might be in order. Oct 24 '17 at 0:13
• @Dennis, in what sense? It's not my intention to repeat material here that was already presented in answers to the other question. Only to answer your present question, about why the standard kilogram is made of metal rather than some other material. Oct 24 '17 at 0:16
• I meant to address your comment regarding adopting a new standard. I should have included that distinction in my question and I'll do that now. Oct 24 '17 at 0:24
• Nobody's proposing to define a new artifact standard for the kilogram. They're proposing to define the kilogram in terms of a number of silicon atoms which would allow anybody to create a 1-kg object without any reference to a particular artifact standard. If the kilogram were defined in terms of silicon atoms, you could easily make a o.5 kg or 1 g silicon mass by simply making an object with 1/2 or 1/1000 as many atoms. Oct 24 '17 at 0:54
• That's not the way I interpret the Avogadro Project. Perhaps I'm misunderstanding it though. Oct 24 '17 at 1:42