## 1 Introduction  
Electrochemical devices converting chemical energy of a fuel directly into electricity without the necessity for direct combustion as an intermediate stage are known as fuel cells. Solid oxide fuel cells are among the most promising of these, owing to their high efficiency of energy conversion and their adaptability to various kinds of hydrocarbon fuels including biofuels [1; 2; 3]. Fuel cells, utilizing proton conductors as electrolyte membranes (PCFS), possess some significant advantages, the most important of which relates to changes in the reactions taking place at the electrodes. Water is produced on the cathode side of the cell as a product of the reactions, thus enabling a more efficient fuel use. The open circuit voltage is maintained at a high level and there is no problem with reduced anode stability [1]. A recent trend in the development of solid oxide fuel cells is the practice of lowering the working temperature down to 550-700 \({}^{\circ}\)C in order to increase the long-term stability and broaden the choice of cheap functional materials applicable for the cells' production. The cells' performance is strongly dictated by the ohmic loss of the electrolyte and resistance due to the electrodes' polarization. Thus, effective operation at decreased temperatures requires the application of materials with advanced electrical properties and the development of cost-effective and versatile methods for the formation of cells' structures with reduced electrolyte thickness and improved electrode microstructure [4]. Solid state solutions based on BaCeO\({}_{3}\) are promising electrolyte materials for SOFCs due to their high co-ionic (oxygen-ion and proton) conductivity and low activation energy in the intermediate temperature range and in a humidified atmosphere [5; 6; 7]. Gd-doped BaCeO\({}_{3}\) exhibits one of the highest levels of ionic conductivity at temperatures below 800 \({}^{\circ}\)C among the electrolytes stable in a fuel cell environment [8; 9; 10]. There are several techniques for depositing thin electrolyte films on porous and dense substrates, including chemical vapor deposition, electrochemical vapor deposition, ceramic and colloidal processes, and various sputtering processes using ion beam, magnetron, electron beam, and others [11; 12]. Among them there are several studies on the formation of Gd-doped BaCeO\({}_{3}\)-based films; however, deposition was performed mainly on anode substrates using dip-coating [13], spray pyrolysis [14], and tape calendering [7]. Recently, our group has presented several studies on electrophoretic deposition (EPD) of BaCeO\({}_{3}\)-based films on dense cathode substrates [15; 16]. The EPD process is carried out on the electrodes immersed in a suspension of ceramic particles, between which a potential difference is set. The particles in a liquid medium are solvated, and an electric charge arises on them, thereby, on the one hand, the particles and their aggregates move under the action of an external electric field; on the other hand, the particles are deposited on the electrode and a deposit of the solvated particles is formed. Following the formation of the deposit, drying and sintering stages are carried out to finally form a coating [17]. EPD offers such advantages in deposition of thin-film electrolytes for SOFCs' applications as inexpensive equipment, short deposition time, simplicity of process management via current/voltage adjustment, and adaptability to the electrolyte composition and substrate shape [12; 18; 19]. The main problem, which appears during sintering Ba-containing thin films, consists of Ba loss at high temperatures due to evaporation and chemical interaction with the electrode substrate. Ba volatility is a well-known fact for BaCeO\({}_{3}\)- and BaZrO\({}_{3}\)-based electrolytes.