Chapter 6 Vacuum Guages

6.1 Primary Vacuum Guages (Gauges Measuring Pressure Directly)
U-tube Manometer
In the U-tube manometer pressure in a gas is opposed by a liquid surface acting as a piston which is converted to a pressure reading.It consists of transparent tubing, usually glass, that contains a liquid of known density ρ . The pressure difference p1 − p2 is measured by the difference in height h between the meniscus levels in the two columns, according to the equation
p1 – p2 = ρ g h
For work of the highest accuracy, the local value of g, the acceleration due to gravity, and the precise density of the liquid at the prevailing temperature would be employed. With one limb sealed at vacuum as shown in Figure(1), and mercury (relative density 13.6) as the sensing liquid, so that only mercury vapor exerting a vapor pressure of approximately 10−3 mbar at room temperature exists in the closed volume, it is possible to measure from atmospheric pressure ~1000 down to about 1 mbar in the other limb.
Fig1. (a) & (b) U-tube manometer configuration
In ordinary use, the accuracy of measuring h by eye against a scale graduated in millimeters would be limited to a millimeter or a little less. The transport of mercury vapor toward the measured vacuum has to be prevented by the use of a liquid nitrogen cooled trap.
Gauges Depending on Deformation of a Sensor
These gauges depend on the deformation within elastic limits induced by pressure changes applied to a sensor. There are various types. The relatively small movement created is magnified mechanically so as to move a pointer over a scale. Deflections vary linearly with pressure, and usually therefore, so do the scales.
Simple Diaphragm Guage
In diaphragm gauges, the pressure difference across a single circular corrugated diaphragm causes a deflection that is coupled with magnification to a pointer and scale. In an ingenious version of the device described by Wutz et al. (1989) and manufactured by the Leybold Company, the reference pressure on the side remote from the pressure being sensed is sealed off at a negligible value of 10−4 mbar. Its operating range is from 1000 down to 1 mbar, with an expanded scale in the lower range so that 1–20, 20–100, and 100–1000 mbar occupy comparable lengths of a generous 280° scale. This is accomplished by having a large, very sensitive diaphragm and a set of concentric circular stops that render it progressively less
sensitive at higher pressures. The accuracy quoted is ±1 mbar between 1 to 10 mbar and ± 10% of reading between 10 and 1000 mbar.
The Capacitance Diaphragm Gauge (Gauge Measuring Pressure indirectly)
When the flexure of a diaphragm is sensed electrically rather than mechanically, greater sensitivity and precision are possible. The basic principle employed is that the pressureinduced displacement of a metallic diaphragm with respect to a fixed partner electrode close to it causes a change in their mutual capacitance, which, by appropriate signal conditioning, is converted to a pressure reading. The flexure of a thin-plane circular diaphragm due to a pressure difference depends on how its edge is supported and whether or not it is pre-tensioned. Two possibilities are shown in Figure
1 for diaphragms of radius R across which there is a pressure difference Δp. In Figure 1(a), the edge is rigidly clamped by forces perpendicular to the plane. For Δp = 0, there is no stress in the diaphragm and no deformation. In Figure 1(b), however, the edge clamping is also made to exert a large outwardly directed tension T per unit length of the rim so that the diaphragm is radially stressed. These deformations are analyzed in Prescott (1961).
The result for the case illustrated in Figure 1(a) is given in a convenient form in Kempe’s Engineers Year-book (2001). The maximum displacement x0 at the center is.....
where t is the thickness, E is Young’s elastic modulus, and σ is Poisson’s ratio. Between the
center r = 0 and the edge at r = R, the displacement x decreases with r as (R2 − r2)2.
For the highly pretensioned diaphragm of case (b), the displacement x depends on r as (R2 −r2) and the central displacement x0 is....

Also, as proved in Feather (1961), the fundamental frequency f of vibration of such a tensioned diaphragm made of material of density ρ is...
Fig1. Deflection of diaphragms due to pressure difference
As a simple model of one type of this device, consider the arrangement of Figure 2 in which a tensioned diaphragm TT of radius R and thickness t separates two regions at different pressure, the left-hand side at high vacuum ~10−7 mbar, essentially zero for mechanical purposes, and the other side at a pressure p. In this mode, the device measures absolute pressure. In a differential mode, the left-hand-side pressure would be held at some reference value other than zero and Δp would be sensed. A fixed electrode E of area A is located close to the diaphragm, and pressure p causes bowing towards it, altering the capacitance. If p = 0, the undistorted diaphragm is parallel to E at a distance X so that, discounting edge effects, the
two approximate a parallel plate capacitor with capacitance C = ∈ 0A/X, in accordance with the well-known formula. Otherwise, for a finite pressure, regarding the central part of the diaphragm as being approximately flat and displaced according to Equation 2, the capacitance is increased to
Fig2. Simple form of diaphragm guage

The sensitivity and measuring range will depend on the stiffness of the diaphragm. For a device with a nominal range of 0–1000 mbar, in order to produce a reasonable change of capacitance, the high pressure must move the diaphragm close to electrode E without
touching it, and a relatively stiff diaphragm is required. For a version designed for, say, 10 mbar maximum, a weaker diaphragm will be appropriate.

6.2 Secondary Vacuum Guages: The Spinning Rotor Gauge (SRG)
First suggested by Beams et al. (1962) and subsequently intensively developed by Fremerey and coworkers (1982), this gauge is now a highly accurate and sophisticated, though expensive, instrument. It measures the slowing down by molecular drag of the spinning motion of a magnetically levitated steel sphere, and operates over a range from about 0.1 down to 10−7 mbar.
A schematic diagram of the SRG is shown in Figure 1. The rotor is a steel ball 4.5 mm in diameter, magnetically levitated inside a horizontal stainless steel tube, using permanent magnets and current-generated magnetic fields. In addition, there are drive and pick-up coils. The tube is closed at one end and the open end is attached to a flange and samples the vacuum. In use, the driving magnetic field is rotated and the ball accelerated to about 400–415 Hz. The driving field is then switched off and the reduction in the rotation rate of the ball, caused by the decelerating effects of gas-induced friction at its surface, is measured over a period of time by pickup coils that sense the ball’s rotating magnetic moment. Digital electronics in the control unit computes the slowing rate and hence the pressure, which is updated every few seconds using an average measuring period of 10s.
Fig1. Crossection of guage head of Spin Rotar Guage
The SRG samples the vacuum passively without producing thermal, chemical, or pumping effects and is bakeable to 400°C. Because of its potential accuracy and stability, it is used as a transfer standard. In a system containing a calibrated SRG, because of its range and reliability, it can be used to calibrate other gauges that overlap its range, such as ionization gauges and
capacitance manometers at its lower and upper limits, respectively.