## W C Maskell

t,,,

1) as diffusion processes in the solid phase are slow and

this will produce the long-term drift mentioned above.

In fact the response is not instantaneous because of the omission of a number of factors as listed below and discussed in detail in the appendix.

(i) The double layer at the electrode-electrolyte interface acts as a capacitor requiring the transfer of charge when the sensor EMF responds to a change in oxygen pressure.

(ii) The electrode potential cannot stabilise until the stoichiometry of the electrolyte in the double layer has achieved equilibrium with the gas phase.

(iii) Changes in stoichiometry throughout the electrolyte result in overvoltages due to charge transfer and perturbation of the oxygen partial pressure at the gas-solid interface.

(iv) A low electrode resistance to charge transfer reduces the response time of the sensor.

(v) The hydrodynamics in the gas phase influence the rate at which a PO, change in the bulk gas is transmitted to the sensor interface.

## Ri

c3

2

Bulk

Groin boundary

1551

C? Electrode

# I - - ^{Frequency }

fi

R , + R zt R ?

Figure 1. (a)Equivalent circuit representation of a sensor. (b)Complex plane impedance response of a sensor. The zenith of the electrode semicircle occurs at frequencpfi .

## 2.3.2. Impedance analysis. In order to analyse its electrical

behaviour, the gas sensor can be represented by the equivalent circuit shown in figure l(a) (Bauerle 1969). The components

Rl/CI, R2/C2 and R3/C3 are associated with the electrode. the grain boundaries and the grain interiors in the ceramic respectively. The AC spectrum for such a circuit plotted in the complex plane is shown in figure l(b) with frequency of the applied signal, f, increasing from right to left, Z' and Z" represent the in and out of phase components of the complex

impedance concerned

respectively. The present with the processes indicated at

discussion is only the lowest frequencies

associated with the electrode: typically 100Hz and below. The point shown

the at

frequency range is the zenith of the

electrode semicircle occurs at a frequencyf l,such that 2Zfi Ci R I= 1

(16)

Consequently the time constant for the electrode process is (2zfi)-'. A typical value for f, at 700 OC is 10 Hz (Kleitz et al 1981) corresponding to a time constant of less than 20 ms.

In a recent work (Verkerk and Burggraaf 1983) more complex equivalent circuits have been proposed for the electrode

1158

processes involving Warburg impedances. These are introduced to account fGr diffusional processes that result in additional features in the impedance spectrum. Such processes might include the diffusion of oxygen atoms on the electrode or electrolyte surfaces or diffusion of elcctronic holes in the ceramic.

The impedance technique, by allowing separation of the various components of the sensor impedance, can provide a valuable insight into the factors controlling the response of the sensor. Note that deviation of the electrode impedance from a perfect semicircle indicates that the product R C is effectively varying and would result in a response curve deviating from that based on the simple theory where RC is taken as constant (Fewkes and Yaiwood 1956).

2.3.3. Experimental data. In this section only work in non- reactive gases is considered, i.e. in 02-inert gas (e.g. Ar or N2) mixtures.

(i) Step changes in oxygen partial pressure. Anderson and Graves (1982) applied a po, step to a zirconia sensor and observed the resulting EMF change. They found the response times to be an order of magnitude greater than suggested from the electrical response to a small current pulse: this suggests that transport processes in the gas phase were a controlling influence. The EMF responses in going from high-to-low and from low-to- high po2 were compared and showed an asymmetry. However, when EMF values were converted to indicated po, using equation (4), the asymmetry disappeared. This again was compatible with gas-phase diffusion control. Response time on a Z r 0 2 - Y 2 0 3 e l e c t r o l y t e w i t h a P t e l e c t r o d e w a s t y p i c a l l y - 1 s a t 6 0 0 O C f o a 90% change in sensor EMF compared with the equilibrium values. r

Fouletier et a1 (1974) carried out response measurements in which oxygen pressure changes were induced by connecting two vessels containing gases of the same composition but at different pressures and obtained data obeying the following relationship

## AE =4Eo{ 1- exp [ -( t / z ) ' I 2 ] }

(17)

where A E and AEo are the EMF changes after times t and infinity. The parameter zdisplayed Arrhenius behaviour and the activation energy, E A .was determined from the response time t,

(proportional to r) using the empirical equation

t_{r -}- A p ; 112 exP(-EdRT)

(18)

where A , is a constant andp, the mean pressure: i.e.

~m

= 4(pinitiai +Pfinal).

(19)

Both Pt and Ag electrodes responded according to equation (18) but with different A i and EAparameters: the response of the Ag electrodes was faster than that of the Pt electrodes. At 500 "C the response times for a 99% change in sensor EMF were 100 s and 3 s for Pt and Ag electrodes respectively on a Zr02-Yi03 electrolyte.

The dependence of t, on p i ' I 2 may have been significant, as other studies (Bauerle 1969, Kleitz et a1 1981, Verkerk et a1 1983) have shown the electrode resistance on zirconia-based electrolytes to display an inverse square root dependence onpo2, For a constant value of the double layer capacitance, the RC time constant would be expected to increase with decreasing po2 in accordance with equation (18).

Recently response measurements on a variety of systems, using relatively high gas flow rates onto the electrodes to minimise gas phase diffusion limitations, have been reported (Winnubst et al 1985). Results were found to be consistent with equations (1 7 ) and (18) for times longer than 0.5 s. The response was probably controlled by gaseous diffusion at times less than 0.5 s. Interestingly, Fouletier el al (1974) measured t, for