Secondary Reduction of Refractory Metal near Smooth Cathode during the Salt Melt Electrolysis. 3. Numerical Reproducing of Natural Experiment with the Nb Cathodic Reduction in KNaCl2–NaF–K3NbF7 Melt

In terms of the model of steady-state process of a refractory-metal ion secondary reduction with an alkali (or alkali-earth) metal formed on a smooth cathode during salt melt electrolysis, numerical reproducing of a natural experiment is carried out. The model calculations are based on the polarization measured during the cathodic reduction of Nb in chloride―fluoride melt: [Nb] = 2.4 mol %, 800°C, current density i up to 5.4 A/cm2. On a smooth cathode in the overvoltage range from 0.21 to 0.41 V (i = 0.75―1.17 A/cm2), the reduction mechanism is shown to completely change from primary to the secondary reduction. The secondary reduction zone is located inside the diffusion layer and moves away from the cathode with increasing i. Even at maximal i, this zone remains inside δ (δ is the thickness of the diffusion layer): with i = 0.96 A/cm2, the coordinate of the maximum of the secondary reduction rate xm = 0; with i = 5.4 A/cm2, xm = 0.93δ (in the experiment, the value of i at which xm ≥ δ was not achieved). At i = 5.4 A/cm2, the fraction of secondary reduction in the bulk is insignificant, ≈10−5 A/cm2. The δ vs. E curve is calculated: when E is shifted from the equilibrium value toward the negative values, |i| increased from zero and higher, whereas δ first decreased by an order of magnitude and then increased. Correspondingly, the limiting diffusion current is not constant at a constant Nb concentration in the bulk. This is the reason of uncertain limiting current on steady-state cathodic polarization curves during the electrolysis of metals in melts. A hypothesis is proposed on the dependence of the Nernst diffusion layer thickness near the cathode on the current density exceeding the limiting diffusion current density under the conditions of secondary reduction.