Sensors and Actuators B, 12 (1993)195-198 195 Operation of leaky zirconia pump-gauge oxygen sensors in the a.c. mode: theoretical analysis M. Benammar and W. C. Maskell* Energy Technology Centre, Middlesex University, Bour& Green Rd., London Nl I 2NQ (UK) (Received March 17, 1992; accepted in revised form December 1, 1992) Abstract A theoretical analysis of the behaviour of non-hermetically sealed devices operated in the a.c. mode is presented. The analysis reveals that a pump-gauge device with substantial leak may still be used for oxygen partial-pressure measurement with a concomitant substantial simplification in the electronics required when compared to fully sealed devices. In addition, theory suggests that the device may provide a measurement of the barometric pressure. 1. Intmduction Leakage can, in some instances, be a problem with ostensibly fully-sealed zirconia oxygen pump-gauge devices. This problem is compounded by the use of small pumping currents and small internal volumes, which are usually associated with the miniaturization trend in sensor making. Kaneko et al. [l] have studied the leakage mechanism in sensors with a metal seal. The three modes of leakage identified were physical, semipermeability of the ceramic and electrochemical via the metal seal. Under the given operating conditions [I], electrochemical leakage was found to be the domi- nant mechanism. In the present communication, the effects of physical leakage on pump-gauge devices oper- ating in the a.c. mode [2] are discussed at length. Physical leakage of ostensibly fully sealed sensors some- times occurs resulting from flaws in the ceramic-metal seal or porosity in the ceramic: the leakage rate may increase with sensor ageing. The theory developed is equally applicable to a pump-gauge device caused to leak by the deliberate inclusion of a diffusion barrier in the, sensor. 2. Theory A schematic diagram of the leaky sensor is shown in Fig. 1. It consists of a pump, enabling oxygen to be electrochemically pumped between the external gas and *Author to whom correspondence should he addressed. DIFFUSIO N IA RRIER _ 0 PI ZRCONIA ELEC IRO DES GAUGE ELEC TRO DE C O NNEC TIO NS - Fig. 1. Schematic diagram of a leaky pump-gauge sensor. the internal volume, and a gauge, dlowing the Nemst e.m.f. to be sensed between the inner and outer gases. A hole was included in the device to provide a physical leakage path. The analysis incorporated the following assumptions: (a) uniformity of the oxygen partial pressure within the internal volume; (b) linearity of the concentration profile within the diffusion hole; (c) complete Faradaic transfer of oxygen by the current applied to the pump. (d) the theory is developed for a hole of uniform cross section but may readily be generalized to diffusion barriers with geometry of any complexity. These are reasonable assumptions if the frequency of operation is low, for example, not greater than 10 Hz. The convention adopted was that a positive current 09254005/93/$6.00 @ 1993 - Else&r Sequoia.All rights reserved