Mass Metrology: A small taste of Dave's job

From time to time, I hear, "So what exactly do you do anyway?" For some reason, metrology and calibration are unusual concepts for most people. My sister heard metrology, and wondered why I wanted to be a weatherman. The details of what I do really don't matter that much to most people. The world keeps on ticking as long as people like me are out doing our thing. Yeah, Dave, but what is your "thing"?

Don't worry if your eyes glaze over while reading this and you don't finish. I'm sure you'll be in the majority. I just present it in case anyone is interested in the arcane science of what I do.

I'm a small part of a large system linking measurement devices all over the world back to standard measurements somewhere. That's metrology, or the sturdy of precision measurements. Calibration is just the comparison of one measurement device back to something that is traceable through an unbroken chain of comparisons to one of those standards. Most measurements in this country are traced back to the National Institute of Standards and Technology (NIST), a part of the Commerce Department. NIST laboratories maintain the U.S. national standard for thousands of things. Some are basic measurements like the second or the meter and some are more obscure such as standard Columbia River beach sand or whatever.

I'm more concerned with the basic measurements. NIST has extensive experimental apparatus that can determine with a great deal of precision exactly how long a meter is using light speed and how long a second is using atomic fluctuations. Most basic units are defined this way. There is an accepted standard that the distance light travels in a certain fraction of a second equals one meter. Everybody agrees on that definition, so anyone can find the meter depending only the ability to isolate the fraction of a second and measure how far the light went.

It used to be that all measurements were based on artifacts, or specific things that defined a yard or a foot or what ever. In the beginning, the myth goes that a yard was the distance between the king's thumb and his nose. Someone decided that something more specific might be useful since different places had different kings, so he decided to use a particular stick that was about the right length. He then could make copies of that stick and pass them around so everybody was using the same yard. However, over time, this method begins to fail as the specific artifacts are used and damaged. You end up with a bunch of sticks that are something like a yard, but none of them are exact anymore and none of them completely agree with each other, which kind of defeats the purpose. So over the years, most units have been defined in terms of physical properties of certain materials, properties that will theoretically never change. Therefore everyone who can set up experiments to measure those properties can recreate the units as precisely as they can measure them.

The sole exception to this method is mass. Up until around 1800, the kilogram was defined as the mass of one cubic decimeter of water. A cubic decimeter was used instead of a liter because length is a base unit, while volume is derived based on length. However, since water can change due to temperature and pressure, a better method was needed. Again, like the stick, someone made a prototype kilogram, which was from that point considered the de facto definition of a kilogram. However, nobody has yet come up with a proper physical property measurement for mass to replace this old method of measurement.


The current, most exact kilogram was made in the 1880's, as were the various copies of it scattered around the world. The primary kilogram prototype (pictured above, inside concentric bell jars) is in France and the U.S. top kilogram (pictured below) is at NIST. The primary kilogram is kept sealed and locked in a vault almost all of the time. It is brought out once in a great while (maybe once every decade or two) for comparison with the various national standards. Other than that, it never gets touched. The U.S. national kilogram is then compared occasionally by NIST against several copies they use for checks against other weights. My company has a master set of weights that are sent to NIST every five years for comparison against that second tier of weights. Those are then compared against our other weights once a year and against another set that is used for customer weight calibrations. I then take my weights and calibrate balances and scales used in the world. We even work on other metrology balances that are used for further weight checks. The idea is to handle the sets closer to NIST as little as possible in order to keep them from changing too much between calibrations. There is a certain amount of uncertainty in each comparison, which increases for each step away from the prototype. If your weights change beyond that uncertainty, then you throw the work you've been doing into question. That's bad.


To put the precision into context, I have Class 1 weights (the best available) ranging from 20 kilograms (about 45 lb.) down to 1 milligram (a tiny piece of foil you would overlook if you didn't know about it). For the smaller of these weights, say below about 200 grams, I know the exact weight down 8 digits beyond the decimal point, with the uncertainty (different for each one) showing up in the 5th or 6th place. This means that I know the values of my weights to at least 7 significant figures. This is important since the best balance (precision scale) I work with has 20,000,000 divisions (2 grams to 0.1 micrograms, or 0.0000001 grams). For reference, the main prototype is known to about 10 significant figures.

The problem with all this is that the prototype kilograms are suffering the same fate as the sticks, despite all the care put into their handling. The main prototype has lost approximately 30 micrograms over the last century. That means that if you assume that it was once 1.000000000 kilogram when it was made, it is now 0.999999970 kilogram. Seems pretty insignificant doesn't it? It is, for now at least. There are almost no instruments in the world good enough to see that difference. However, the kilograms will get worse and instruments will get better, especially as we continue to try and probe further into the atom and deeper into space. Eventually, this definition will fail to be good enough.

So what to do about it? There are two options that scientists are pursuing right now.

The first is basically making a better kilogram prototype. A group of Australian scientists is working on just that. They are trying to make a perfect sphere of silicon (pictured below) that is exactly one kilogram. The atomic weight of silicon is known quite well as is it's crystalline structure. It's quite possible to grow a very large perfect crystal of silicon. That's how computer chips are made. Then you apply a little math. You can figure out how many atoms of silicon you need to make a kilogram based on its atomic weight, and knowing the crystalline structure, you can figure out how big a sphere needs to be to contain the proper number of atoms. The hard part is now to make a perfectly round sphere of exactly the right diameter (using length, which is known very well). By the time they are done with this thing, it will essentially be the roundest thing ever made. This is basically just making another prototype, which will have the same issues as the current one. Unlike the current one, however, someone in the future can do the same thing again and come up with an identical, or maybe even better version, limited only by measurement and machining capability.


The second option is the watt balance. It is designed to use electrical properties, which are known very well, to determine the mass of an oscillating body. The math is very intensive. This type of device exists. NIST is working very hard on this method of mass determination. In the long run, something like this will likely take the place of having an artifact that must be compared back to. However, for the moment the uncertainty of doing it this way is still higher than using the current shrinking French kilogram.

Most of this is mainly academic. We are many centuries away from these variations causing the common man any trouble. A half a pound of deli ham and a gallon of gas will still be the same things as far as you will be able to tell. This becomes a problem only at the edge of research and possibly into some VERY exacting manufacturing, although I can't think of an example. Nothing you could afford anyway.

There. I obviously find this interesting, and I assume that if you made it this far, it must at least hold passing amusement for you. Let me know if I left anything too muddy or if something doesn't make sense.