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My question is, why use silicon-28 atoms to calculate the kilogram when you already have carbon-12 atoms defining the constant?

Does the Avogadro Project intend to define the constant by replacing the idea of carbon-12 and putting silicon-28 in its place?

Emilio Pisanty
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  • Note that there is no intention to elevate the mass of the silicon-28 atom to a unit-defining constant the way the carbon-12 mass currently functions. That route to the kilogram involves fixing two constants (the Avogadro number and Planck's constant $\hbar$), and it has two stages: (i) the silicon sphere allows you to measure the (macroscopic) mass of a known number of atoms, and (ii) you can measure the ratio $\hbar/m(^{28}\rm Si)$ via atomic recoil spectroscopy. Since $\hbar$ is fixed, that gives you the mass of each individual atom. – Emilio Pisanty Oct 22 '17 at 14:02
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    Related: What are the proposed realizations in the New SI for the kilogram, ampere, kelvin and mole? – Emilio Pisanty Oct 22 '17 at 14:03
  • @EmilioPisanty With (i) alone, if we were to keep the definition of the unified atomic mass unit (u), or dalton (Da), as $\frac{1}{12}$ of the mass of a carbon-12 atom, we could change the definition of the gram (or kilogram) to "the mass of exactly $6.0221408{?}{?}{?}\cdot 10^{23}$ unified atomic mass units". So we need (ii) only if we want to get rid of carbon-12-based definitions, as far as I can see. – Jeppe Stig Nielsen Oct 22 '17 at 16:52
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    Yes, that's correct. But keep in mind that the ultimate goal is metrology that's stable, scalable, reproducible and high-accuracy, and that is cheap enough to be accessible at the national-metrology-lab level beyond a few rich countries. Those concerns drive the choice of the Planck constant as the keystone to the kilogram and the watt balance as its main implementation. – Emilio Pisanty Oct 22 '17 at 17:17
  • Most researchers working in technical fields are male, and males are known for having a very peculiar fondness for that particular metal. – Lucian Mar 23 '18 at 10:19

2 Answers2

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The idea is to create a sphere of about 1 kilogram and then both weight it and count the number of atoms in it. This is only possible by using crystalline matter, by taking advantage of the regular arrangement of the atoms.

Diamond would be indeed a perfect candidate but machining diamond is a hell of a lot more difficult than machining a crystal of silicon, because of the huge difference in hardness, a problem which pales in comparison with the sheer impossibility of making a diamond mono-crystal weighing one kilogram! The world record is about 20 grams. The difficulty is the need to apply a pressure of the order of 100,000 atmospheres, which is only possible in too small a volume for the target weight of 1 kilogram, which would be a cube with 6.5 cm sides. We could imagine settling for a bunch of smaller diamonds of course but this would introduce an extra source of uncertainty. Since it is possible to make a monocrystal of silicon weighing one kilogram, by using refinements of the growth methods developed and refined by the electronic industry, it would not make sense to consider diamond.

Why not graphite instead? Unlike diamond, it is possible to carefully make big enough mono-crystals. Unfortunately, graphite is made of a regular arrangement of carbon atoms strongly bonded in sheets, and those sheets do then stack up and keep together because of weaker forces between them: in particular they can easily shift with respect to each other. As a result, this makes graphite much less suitable for the described precision experiment where pinpointing the atomic arrangement is key.

With graphite and diamond, we have exhausted the crystalline phases of carbon. Thus exit carbon!

  • Comments are not for extended discussion; this conversation has been moved to chat. – David Z Oct 23 '17 at 09:56
  • This answers the first question but not the second. – J... Oct 24 '17 at 12:08
  • Your first sentence is rather misleading and, upon further reflection, ultimately not true. The idea isn't to create a sphere that matches the current value of the kilogram: it's to create a reference object whose mass can be directly traced, via optical and x-ray interferometry and atomic spectroscopy, to the fundamental constants used to define the new SI kilogram. – Emilio Pisanty Oct 24 '17 at 17:27
  • As I explained in the comment, making a ball of 1kg is indeed an implementation detail. I rushed the introduction of that answer and it shows indeed. Better fix it with all those votes… –  Oct 24 '17 at 18:52
  • Well, actually, I don't see this is so far fetched what I wrote. I mean, you agree that the goal is to make a ball of 1 kg and then to count the numbers of atoms in it? If what you mean is that my phrasing reversed that, i.e. fixing the number of atoms, then I see your point. Otherwise? –  Oct 24 '17 at 19:02
  • Well, for one, your phrasing is ambiguous (is it just roughly 1kg, or do you mean precisely one kilogram? both are reasonable interpretations and I suspect most of the audience takes home the wrong message). But I do see a strong distinction between your original phrasing and the one I suggested above. – Emilio Pisanty Oct 27 '17 at 08:58
  • @EmilioPisanty I see your point indeed. Hopefully this time there is no ambiguity left! –  Oct 27 '17 at 09:22
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The production of large, pure silicon crystals is a mature technology that's feasible for any standards body to implement. Silicon crystals are produced at industrial scales for the manufacture of integrated circuits.

Spencer Joplin
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