1. VISUAL AIDS for instruction in VACUUM TECHNOLOGY AND APPLICATIONS
Module 2:
Total Pressure Measurement in Vacuum
Second Edition
Section 3
Indirect Measurement of Pressure I
Gauges Using Properties of the Gas

2. Indirect Measurement of Pressure
The gauges described in this Chapter use bulk properties of gases as a measure of pressure
Clearly, such properties have to be pressure dependent to form the basis of a gauge
Suitable properties are heat transfer or viscosity
We first consider some fundamentals of heat transfer

3. Indirect Measurement of Pressure
Thermal Interactions
Often when we think about the behaviour of gas molecules in a vacuum system, we assume the system to be in equilibrium, with the gas molecules having a Maxwellian energy distribution
For this to apply, the system has to be at a uniform temperature
In this case, when a gas molecule strikes a surface, it stays on the surface for a relatively long period of time so that when it leaves the surface again, it has no memory of the direction from which it arrived
On average, gas molecules will leave the surface with the same average energy with which they arrived - i.e. at the same temperature
This is described as complete accommodation
Gas molecules will leave the surface with a cosine velocity distribution

4. Indirect Measurement of Pressure
Thermal Interactions
When different parts of the vacuum system are at different temperatures, the temperature of a gas molecule may, on average, be different from the temperature of a surface which it strikes
The velocity distribution of gas molecules leaving the surface may not be a simple cosine
Under these circumstances, thermal transfer (i.e. energy transfer) can occur between surfaces
The process can be described by an accommodation coefficient   1
The value of  will depend on the gas concerned and the surface involved

5. Indirect Measurement of Pressure
Thermal Interactions
Here, the gas atom or molecule coming in from the left has an energy equivalent to a temperature of Ti.
When it strikes the surface which is at the higher temperature Ts, the gas atom can gain some kinetic energy and leave with a temperature equivalent to Tr

6. Indirect Measurement of Pressure
Thermal Interactions
Here, a gas molecule is scattered between two surfaces at different temperatures T1 and T2
At point 1, it undergoes an elastic scattering from the lower surface at temperature T2
It is then, at point 2, adsorbed onto the upper surface at temperature T1

7. Indirect Measurement of Pressure
Thermal Interactions
It leaves this surface having gained energy and is adsorbed onto the lower surface at point 3
As T1>T2, the molecule gives up some energy to the surface before leaving at an intermediate temperature T3
The net effect is transfer of energy (heat) from the upper to the lower surface
The overall accommodation coefficient  is as shown

8. Indirect Measurement of Pressure
Thermal Interactions
This table shows some values of accommodation coefficients for a range of gas species and surfaces

9. Indirect Measurement of Pressure
Heat Transfer
Heat transfer from a hot to a cold surface can occur through two basic mechanisms dependent on the pressure of the gas, or more accurately on the mean free path of the gas molecules in the gas.
Where the mean free path is less than the dimensions of the gauge, then gas flow is viscous and the main mechanism of heat transfer is by convection
Where the mean free path is greater than the dimensions of the gauge, then gas flow is molecular and the main mechanism of heat transfer is by conduction
There is also a pressure independent transfer of heat by radiation
These processes are illustrated in the next two slides

10. Indirect Measurement of Pressure
Heat Transfer
This figure shows the various energy flows for a system whose configuration is typical for a thermal manometer

11. Indirect Measurement of Pressure Heat Transfer
We can see here the net energy transfer as a function of pressure.
At high pressures (Region III) the energy flow is almost independent of pressure as is the case at low pressures.
In Region II it is a strong almost linear function of pressure.
In Region 1 it is a less strong, but still useful function.

12. Indirect Measurement of Pressure
Thermal Manometers
Thermal manometers are devices in which heat transfer away from a hot wire in vacuum is measured to provide an analogue of pressure
The wire – often referred to as the filament – is usually heated by passing an electric current through it
The temperature of the filament may be measured directly, either with a thermocouple or a thermistor
Alternatively the power transferred from the filament to its surroundings may be measured electrically
In all such devices, the gauge sensitivity is dependent on the gas species being measured
We will illustrate thermal transfer gauges shortly by looking at Thermocouple gauges and Pirani gauges

13. Indirect Measurement of Pressure
Thermal Manometers
This is a typical set of relative sensitivities, , for a typical thermal manometer for some common gases
The sensitivities are relative to air (or nitrogen)
The precise ratios will depend on the actual gauge used

14. Indirect Measurement of Pressure
The Thermocouple Gauge
The simplicity of such a gauge can be seen here – a thermocouple is simply spot welded to the centre of the heated filament and the potential developed measured on the millivoltmeter
A thermistor may also be used and its resistance measured

15. Indirect Measurement of Pressure
The Thermocouple Gauge
The sensitivity of such a gauge (expressed here as millivolts) as a function of pressure is now shown
Again, the sensitivity is dependent on the gas species being measured

16. Indirect Measurement of Pressure
The Pirani Gauge
In a Pirani gauge, the filament (heated wire) forms one arm of an electrical bridge circuit
Here we can see the basic construction of the Pirani gauge head and a schematic of the external electrical bridge circuit

17. Indirect Measurement of Pressure
The Pirani Gauge
The Pirani gauge can be operated in one of two modes
a constant voltage is applied across the filament. The resistance will therefore vary as the temperature varies due to the varying heat transfer and the imbalance current of the bridge will be an indication of the pressure
the input voltage to the bridge is varied such that the bridge is always balanced with the filament maintained at a constant temperature i.e. the filament is maintained at a constant resistance. The voltage across the bridge is a measure of the pressure

18. Indirect Measurement of Pressure
The Pirani Gauge
Here we can see how the sensitivity of a Pirani gauge varies with pressure and gas species

19. Indirect Measurement of Pressure
The Pirani Gauge
Here we see in more detail a set of calibration curves for a Pirani gauge operated in constant filament temperature mode for a range of gases
The curves are the sensitivities of the gauge relative to nitrogen

20. Indirect Measurement of Pressure
The Pirani Gauge
The details of such a set of curves will depend on the exact gauge used, but the trends shown here will be typical
Note the great divergence of behaviour exhibited at higher pressures for the different gases where convection is important

21. Indirect Measurement of Pressure
The Pirani Gauge
These are typical scales found on analogue meters for both the constant voltage and constant resistance (constant temperature) types of Pirani gauges
The constant resistance type is seen to operate over a wider pressure range. Many modern Pirani gauge electronics will use a digital display so such differences will not be so immediately obvious

22. Indirect Measurement of Pressure
Thermal Manometer Accuracy
Thermocouple gauges operate between about 103 Pa and 0.1 Pa
These are not high accuracy gauges and contamination of the filament can cause serious shifts in sensitivity
Pirani gauges operate between about 104 Pa and 0.1 Pa
Again they are not high accuracy gauges, but clean gauges can exhibit short term reproducibility of the order of 10%
Any thermal gauge will have a relatively long time constant

23. Indirect Measurement of Pressure
Modern Developments
Modern developments in Pirani gauges have led to solid state sensors being developed
These sensors use the well known techniques developed for manufacturing integrated electronic circuits
The sensor is manufactured directly on silicon
An example is shown in the next slide

24. Indirect Measurement of Pressure Solid State Pirani Sensor
Construction of the sensor
Cross section of the sensor

25. Indirect Measurement of Pressure
The Spinning Rotor Gauge
A gauge which uses a different gas property, viscosity, is the spinning rotor gauge
Here a steel ball is set spinning and its deceleration measured
The higher the pressure, the greater the viscous drag on the ball and the greater the deceleration experienced
The rotation of the ball – which has a small magnetic moment – is sensed by a pickup coil
The sensitivity of the gauge is relatively independent of gas species and is very stable - the uncertainty is better that 3% and stability better than 2% per annum
The operating pressure range is 1 Pa to 10-4 Pa
The gauge can be used as a transfer standard for calibration

26. Indirect Measurement of Pressure
The Spinning Rotor Gauge
This is a typical example of such a gauge
The vacuum tube or thimble in which the spinning sphere is situated is often made of glass
To give an idea of size, the vacuum flange is 70mm in diameter

27. VISUAL AIDS for instruction in VACUUM TECHNOLOGY AND APPLICATIONS
Module 2:
Total Pressure Measurement in Vacuum
Second Edition
End of Section 3
Indirect Measurement of Pressure I
Gauges Using Properties of the Gas