Note: this is the first half of a slightly revised version of an article series that originally appeared in The International Neon Association (INA) newsletter (a wonderful but unfortunately no longer active association devoted to the betterment of the neon sign industry. Many thanks to them.)

Vacuum Measurement Units and Scientific Notation - Part 1

By Telford Dorr

When we measure very low pressures, as found inside neon tubes during the pumping process, we speak of these pressures in terms of absolute pressure. This is the pressure of a gas as compared to a perfect vacuum (which would have a numeric pressure value of '0'). This is different from the more common pressure measurement method used to measure the pressure in compressed air tanks. This pressure is referred to as 'gauge' pressure, and is measured relative to atmospheric pressure. In a sense, there is no such thing as a vacuum. What we commonly refer to as a vacuum is simply an area of pressure below that of the normal atmosphere.

As the first experiments involving vacuum were conducted with mercury barometers, one of the unit of pressure measurement used was 'inches of mercury'. It was discovered that our normal atmospheric pressure would support a column of mercury in a barometer approximately 30 inches (or approximately 760 mm) tall. In neon work in the USA, we measure the low pressure inside tubes in the unit of 'torr' (1 mm Hg). This system of units works well for measuring filling pressures of our tubes, as the range of normal fill pressures is from about 4 to 18 torr. However, it doesn't work as well for measuring the pressures needed to insure a clean an empty tube before the rare gas is inserted into it. For this, we use the unit of the micron, where 1000 microns = 1 Torr. 

In areas of Europe, the standard unit of pressure used is the 'bar', where atmospheric pressure is around 1.013 bar. This unit is a little large for vacuum work, so a more commonly used unit is the millibar, where atmospheric pressure is around 1013 millibars. As you can see, the unit 'millibar' is close in value to the 'torr'. You can convert between them by using the following conversion factors:

1 torr = 1.333 millibar
1 millibar = 0.750 torr

When we get involved with vacuum systems using secondary pumps, such as diffusion pumps, we find even the 'micron' can be too large. Rather than invent yet another unit of pressure measurement, we revert to what is called 'scientific notation', and express all pressures in terms of 'torr'. The value of this technique is that we can easily express an extremely wide range of measurement. This is because this notation involves using exponents, which is a multiplier factor expressed as a 'power of ten'. For example, the number 1000 can be expressed as '10 to the third power', which means '10 times 10 times 10'. This can be written as 103 or 10e3. Example:

1234.5 = 1.2345 x 103 =
'one point two three four five times ten to the third power'

We can also express numbers using negative exponents. Example:

0.00123 = 1.23 x 10-3 = 1.23 x 10e-3

Typically, the main number (or mantissa) is expressed with one significant digit to the left of the decimal point and everything else to the right. A trick to remember: to convert a number to scientific notation, move the decimal point either right or left such that it is to the right of the first significant (e.g. non-zero) digit. The number of positions you move it is the numeric value of the exponent. If you move it to the left, the exponent is positive; to the right, it is negative. Try this on the examples above. Simple!

How do we apply this knowledge to neon work? Suppose we have a pumping system which has a diffusion pump, and suppose we have a cold cathode type discharge gauge attached to our manifold, as well as the more common thermocouple gauge. My discharge gauge has a two scales, both calibrated in 'torr'. The 'high' scale has a range of 10-5 to 10-3. What does this mean? Well, per our discussion above, we see that 10-5 torr is the same as 0.00001 torr, and 10-3 torr is the same as 0.001 torr. Therefore, my discharge gauge reads from 0.00001 to 0.001 torr. As my thermocouple gauge indicates down to 1 millitorr (or 'micron'), which is the same as 0.001 torr, we see that the discharge gauge picks up nicely there the thermocouple gauge quits.

Now suppose I want to convert a measurement from one system of units to another. I can do this by multiplying the number by the proper conversion factor. For example, suppose my discharge gauge indicates a pressure of 1.23 x 10-4 torr, and I want to convert this to millibars. Scientific notation makes this easy. Example:

1.23 x 10-4 torr x 1.333 millibars per torr = 1.64 x 10-4 millibars

You create the mantissa value (the main number) by multiplying the two numbers together: 1.23 x 1.333 = 1.64. You create the exponent by adding the two exponent values together: -4 + 0 = -4. Note that the conversion factor can be expressed as 1.333 x 100, which is where the '0' came from. 

By knowing the principles of scientific notation, we can compare the scale calibrations of different gauges to each other, using the same basic unit of measurement. We can also easily convert from one system of units to another by multiplying by the proper conversion factor.