Modeling the formation and growth of cubic sodium tungsten bronze during electrodeposition from a polytungstate melt

The experimental study of the formation/growth processes of crystals with Na0.74WO3 isostructural formula during potentiostatic electrolysis of 0.8Na2WO4–0.2WO3 and 0.9Na2WO4–0.1WO3 melts at 973 and 1023 K is performed. A mathematical model is proposed to describe the complex process mechanism, including the electroreduction of polytungstate anions [WnO3n+1]2– on the Pt cathode surface to [WnO3n]–, as well as the electrochemical and chemical reactions of Na+ with [WnO3n+1]2– and [WnO3n]–, respectively, on the crystal surface. The model considers the change in the concentration of lower reduced forms in the near-electrode layer, the ohmic drop in the melt, the mixed control of deposit growth, and the evolution of the new phase surface area and volume during the process. Exchange currents for electrochemical reactions, rate constants for reactions associated with deposit growth, surface concentration of lower reduced forms, formation time, and number density of nuclei are found from fitting chronoamperograms using this model. It is detected that the chemical reaction promotes the growth of crystals, while the electrochemical reaction leads to their electrodissolution under the studied conditions. The rates of forward and backward chemical reactions decrease as the temperature and the WO3 mole fraction in the melt decrease, respectively, while the kinetics of the electrochemical reaction depends weakly on these factors. The calculated crystal sizes and their numbers are in good agreement with the experimental ones. The proposed approaches to modeling are important for the development of technologies for the electrochemical synthesis of cubic NaxWO3.