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

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

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

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

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

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

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

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

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

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

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.

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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