The electrolytic growth of dendrites from ionic solutions

Abstract

Measurements have been made of the electrolytic growth on silver spheres of dendrites from the silver + silver nitrate system in liquid sodium nitrate + potassium nitrate. The potential and current density for initiation have been determined as a function of concentration and purity of the solution. Rates of growth have been measured as a function of potential at constant overpotential. The radius of the tips has been determined by electron microscopy. At constant current, the current density on to the base electrode during dendritic growth is proportional to the overpotential and the slope of the current density-overpotential relation is proportional to the concentration of silver ions. A critical current density ( i crit ) exists for initiation of dendritic growth. It is proportional to the silver ion concentration and increases as the radius of the substrate electrode decreases. i crit corresponds to an overpotential of 3 mV and increases with increasing purity of the solution. Dendrites are initiated up to 1 h after a constant current is switched on. At a given overpotential, a number of dendrites grow at a characteristic rate ( v ). Dendrites initiated at higher potential grow faster than those initiated at lower potential. The growing tip is parabolic and r tip ≏ 10 -5 cm. Twins are in some dendrites. The current density to the substrate is controlled by diffusion at all conditions and obeys laws characteristic of spherical diffusion for small radii of the substrate. The rate of growth of the dendrites is controlled by the kinetics of the Ag + ion deposition on the dendrite tip (activation and (spherical) diffusion control) and the effect on the Ag + + e ⇌ Ag reaction of the tip radius. For low exchange currents ( i 0 ) v ∝ η: for high i 0 , v α η 2 . The calculated rate of growth agrees with experimental data on maximum growth rate to some 50 %. The calculated r tip for maximum growth is essentially in agreement with that observed. At IηI < 3mV, the theoretical r tip for maximum growth rate increases rapidly, and an alternative electrode process succeeds that of dendritic growth. The theory shows that the optimum radius for growth undergoes a rapid increase in the neighbourhood of the critical overpotential for cessation of growth. Dendrites are initiated only after a preliminary prismatic growth passes through the diffusion layer characteristic of the substrate electrode. Not all prismatic protrusions from the substrate are growth sites. Conditions for the stability of the tip shape during growth are deduced. Dendrites which grow with v less than v max are those with a stable r less than r opt . It is a good approximation to apply equations for diffusion to a stationary surface for the moving dendrite tip. The model is consistent with an observed increase in the number of dendrites with potential and with aspects of side-arm growth.