Measurement of the tpb Length

Several approaches have been proposed to measure the three phase boundary (tpb) length, Ntpb in solid state electrochemistry. The parameter Ntpb expresses the mol of metal electrode in contact both with the solid electrolyte and with the gas phase. More commonly one is interested in the tpb length normalized with respect to the surface area, A, of the electrolyte. This normalized tpb length, denoted by Ntpb,n equals Ntpt/A. 

It is also common to express the tpb length as an actual length, Apb, computed from APb=NtpbdMNAv, or Apb.n=N,pb.ndMNAv where dM is the atomic diameter of the metal (electrode) and NAv is Avogadro s number. 

A first approximate approach for estimating N,pb, or /tpb.n is to use scanning electron microscopy to estimate the average grain size, d, of the electrode. One then assumes spherical grains for the electrode film and semispherical grains in contact with the solid electrolyte to obtain  

The second approach, followed by Vayenas et al39 is direct measurement of Ntpb and N n using cyclic voltammetry, as in aqueous electrochemistry,49 and measuring the height, Ip, or the area fldt of the cathodic oxygen reduction peak (Fig. 5.28a). Then Ntpb can be estimated from  

due to the lack of sufficient Ds data for most metals, other than Pt, the most reliable method for measuring Kpb and N,Pb,n is based on AC Impedance spectroscopy as outlined in the previous section and using equation (5.62), i.e. 

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Wilson et al. [74] pioneered this technique using a Focussed Ion Beam slice and view method to allow the electrochemical performance and microstmcture of materials to be quantitatively connected. In their pioneering work, a direct measurement of the TPB length was achieved through analysis of the reconstructed 3D anode, Fig. 19.11. From the analysis, they differentiate between interconnected and unconnected pathways, finding 63% of TPBs are interconnected. A high level of interconnection is required for electrochemical reactions to occur, and quantifying the microstmcture in this way enables further optimization to proceed. 

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