Sunday, June 9, 2013

Rouding out my weekend

I was browsing around the interwebs yesterday when I came across this cool video about the definition of the kilogram. I was aware of the attempt to make a very round sphere of silicon, but didn't know the history behind it. Vive Lavoisier! [Well, requiescant in pace Lavoisier.] As Mr. Spock would say "fascinating."

I also didn't know why they used silicon. Silicon is the second most abundant element in the Earth's crust (after oxygen), and yet was unknown until the 19th century because it bonds so tightly in chemical compounds. It seems silicon was used for this because we know so much about its crystal structure.

Of course, after watching the video I went to find out more and found this article by the lab that produced the spheres. Interesting, btu I must take offense at their claim:
CSIRO’s Australian Centre for Precision Optics is the only place in the world capable of fabricating round objects with the accuracy required for the Avogadro Project.
The best sphere the ACPO team has ever made had a total out-of-roundness of 35 nanometres. That is, the diameter varies by an average of only 35 millionths of a millimetre, making it probably the roundest object in the world.
Now, as an amateur telescope maker I have to say that's good, but not great. I have made spheres accurate to 5nm, so these are certainly not the roundest objects in the world. Here is a graph of a mirror made by a friend of mine showing the surface error in nm (I'm assuming he doesn't mind me using an image displaying his optical fabrication prowess).

This is a 20" diameter paraboloid that's accurate to within 10nm. Makes the silicon sphere look bumpy! On the other hand, the mirrors we make are not complete spheres, but segments of spheres (or often paraboloids, as the optical design calls for different shapes). I don't think it would be any harder to make a complete sphere than a segment, but I can't say for sure.

I was also curious as to how they tested a convex sphere to that accuracy. It is easy to test a concave sphere, much harder to test a convex sphere. The video indicates that they used a laser spinning around the sphere. But that test would depend on the accuracy of the bearing the laser spun on. I guess that would have to be averaged out over many tests.

Either way, this is a fascinating topic, that bears witness to the beauty and complexity of even the simplest thing in nature.


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