###### Abstract  
Layered _Ruddlesden-Popper_ (RP) lanthanide nickelates, Ln\({}_{n+1}\)Ni\({}_{n}\)O\({}_{3n+1}\) (Ln = La, Pr, and Nd; \(n=1,2\), and 3) have generated great interest as potential cathodes for proton conducting fuel cells (PCFCs). The high-order phase (\(n=3\)) is especially intriguing, as it possesses the property of a high and metallic-type electronic conductivity that persists to low temperatures. To provide the additional requirement of high ionic conductivity, a composite electrode is here suggested, formed by a combination of La\({}_{4}\)Ni\({}_{3}\)O\({}_{10\pm 8}\) with the proton conducting phase BaCe\({}_{0.9}\)Y\({}_{0.1}\)O\({}_{3-8}\) (40 vol%). Electrochemical impedance spectroscopy (EIS) is used to analyse this composite electrode in both wet (\(p_{\text{H2O}}\)\(\sim\) 10\({}^{-2}\) atm) and low humidity (\(p_{\text{H2O}}\)\(\sim\) 10\({}^{-5}\) atm) conditions in an O\({}_{2}\) atmosphere (400-550 \({}^{\circ}\)C). An extended analysis that first tests the stability of the impedance data through _Kramers-Kronig_ and _Bayesian_ Hilbert transform relations is outlined, that is subsequently complemented with the distribution function of relaxation times (DFRTs) methodology. In a final step, correction of the impedance data against the short-circuiting contribution from the electrolyte substrate is also performed. This work offers a detailed assessment of the La\({}_{4}\)Ni\({}_{3}\)O\({}_{10\pm 8}\)-BaCe\({}_{0.9}\)Y\({}_{0.1}\)O\({}_{3-8}\) composite cathode, while providing a robust analysis methodology for other researchers working on the development of electrodes for PCFCs. type: 25 February 2021  
Accepted: 6 April 2021  
Subject: 10 April 2021  
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Nonetheless, several drawbacks remain when working at such low temperatures, with the minimisation of polarisation resistance being one of the most critical challenges remaining to date [4; 5]. In this respect, the majority of published works have focused on the use of mixed ionic electronic conductors (MIECs) as potential PCFC electrodes, where materials selection is driven by that traditionally used in solid oxide fuel cells (SOFCs), based on both oxide-ion and electron (O\({}^{2-}\)/e\({}^{-}\)) conduction [6; 7; 8; 9; 10; 11; 12]. One good example is that of the layered _Ruddlesden-Popper_ (RP) lanthanide nickelates, Ln\({}_{n+1}\)Ni\({}_{n}\)O\({}_{3n+1}\) (Ln = La, Pr, and Nd; \(n=1,2\), and 3) [13; 14; 15; 16]. These interesting materials differ from typical, state-of-the-art, perovskite cathode materials, due to their unique crystal structures that are composed of a rock-salt LnO layer with a finite number (\(n\)) of perovskite-type LnNiO\({}_{3}\) layers along the main crystallographic axis. Importantly, one of the key attractions of these materials is their ability to offer metallic-type electronic conductivity over extensive temperature ranges [14]. In recent years, these materials have also been proposed as electrodes targeted for PCFCs [17; 18; 19; 20], with the main bulk of previous work having concentrated on the lower order, Ln\({}_{2}\)NiO\({}_{4}\)-based phase, where \(n=1\). In this respect, the electronic conductivity of the lower order nickelate phases (\(n=1\), 2) has been documented to suffer an abrupt depletion as the operating temperature decreases below 600 \({}^{\circ}\)C, in air, as a result of temperature dependent changes in crystallographic symmetry [16]. This drop in electronic conductivity below 600 \({}^{\circ}\)C is concerning, as it may bring into question the continued validity of these lower order nickelate materials for the intended PCFC operational temperature range of (400-600 \({}^{\circ}\)C).