I'm doing a little "thinking out loud" about Robert Cohen's questions
about using a silicon standard for the kilogram.
First, some information and some restrictions...
(a) How good are we at making comparisons to the IPK? One of the NIST
copies of the IPK seems to be off by about 0.03 mg, but this varies
from year to year ranging from about 0.019 to 0.039 mg different from
the IPK. It is not known whether the IPK is changing, the copy is
changing, the cleaning method varies, etc.
Anyway, this gives an idea of how well we can maintain and reproduce the
current standard... approximately three parts per hundred-million.
(b) If we are going to change the standard we want the new standard to
be some combination of more stable, more accessible, and as good or
better accuracy than copying the current standard.
(c) We also want the new standard to be close enough to the current
standard that we don't have to retabulate all the published data and
constants that are based on the current standard.
Now thinking of silicon...
(1) I believe it is correct that we would make a silicon cube (or
other convenient shape) that has a particular volume. If a cube, then
the length of the edges would be about 7.54 cm. If we want to hold the
volume to +- 4 parts per 10^8 then I calculate we need to hold this
length to approximately +- one nanometer. (I used 4 because it comes
out to one-nanometer maching.)
Using electron-beam etching and interferometry I am aware that some labs
at Los Alamos were doing nanometer machining when I worked there in
1976. This was done on small parts, I don't know if they were able to
that on something as big as a 7.54-cm cube at that time.
However, a Google search on nanometer machining pulled up over 6000 hits
and I looked at some of them. I found one company claiming to have a
milling machine with a stroke of 20x20 cm with a resolution of 0.5 nm.
Wow!
I think this means fabricating a silicon object to the required accuracy
is probably within our grasp.
(2) Now we have to decide if we know the density to the requisite
accuracy. This depends on the lattice, the isotopic abundance, and the
purity. One reason for working with silicon is the semiconductor
industry has been working on these kinds of things for the past 50 years
or so. I think the purity is good enough, but I am not sure about the
lattice knowledge and the isotopic abundance knowledge.
I suspect it is determining the density that will make or break this
method of replacing the IPK. And I think it is lattice measurements and
isotopic abundance uncertainties that need to be worked out. Once we
have a large enough crystal for which the density is known to sufficient
accuracy, I think we can machine it.
I think the machining capabilities will exist in a lot of places.
Therefore, if we can make and distribute silicon crystals with
sufficiently known density, we should be able to crank out 1-kg masses
that are as good or better than the IPK. More important, the definition
of one kilogram would indeed be based upon obtaining a certain number of
silicon atoms as opposed to being based upon any single macroscopic
artifact.
Michael D. Edmiston, Ph.D.
Professor of Physics and Chemistry
Bluffton University
Bluffton, OH 45817
(419)-358-3270
edmiston@bluffton.edu