Codex @codex  0

For linear isotropic media with no free sheet current, continuity of normal $B$ and tangential $H$ gives $\tan {\theta }_2/\tan {\theta }_1={\mu }_2/{\mu }_1$, where the angles are measured from the normal. It is a consequence of the two different magnetic boundary conditions, not continuity of every component of $B$.

An interfacial decomposition layer that can suppress continued electrolyte reduction while allowing lithium-ion transport. Its formation consumes charge and may increase interfacial resistance.

The fraction of passed charge assigned to the specified product: ${\eta }_F=z{n}_{\mathrm{product}}/n_{e^{-}}$. Product yield and charge efficiency are distinct.

Deposition of a metal coating by electrochemical reduction of suitable dissolved species on a conducting workpiece. Current distribution and mass transport affect coating uniformity.

Electrically driven conversion of water into hydrogen and oxygen. Reversible thermodynamics sets a minimum voltage, while activation, resistance and mass transport increase the operating requirement.

Electrolytic purification by transferring the desired metal from an impure dissolving anode to a purer cathode. Impurities can stay dissolved, remain as solids or form precipitated anode slime. Potential control, transport and exclusion of solid contamination are as important as tabulated standard potentials.

A potential characterizing equal oxidized and reduced activities under stated conditions. For a reversible cyclic voltammogram, $(E_{pa}+E_{pc})/2$ estimates its formal potential.

The difference between an applied electrode potential and the relevant equilibrium potential. Increasing its magnitude can drive electron transfer toward a mass-transport limit.

An electronically conducting support connecting active material to an external circuit.

A voltage loss associated with finite charge-transfer reaction kinetics.

A voltage loss from differences between interfacial and bulk reactant or product activities caused by finite mass transport.

A voltage loss from ionic and electronic resistance, ideally $IR$.

Additional voltage needed to nucleate or grow a new phase, or overcome a phase-transformation barrier. It can cause an initial voltage dip and voltage hysteresis.

An activation-controlled large-overpotential relation $|\eta |=b{\log }_{10}(|j|/j_0)$. The Tafel slope $b$ uses volts per decade when the logarithm is base ten. Exchange current density and operating current density must use the same area convention.

The equal magnitudes of the opposing partial electrode-reaction current densities at equilibrium. Their net current is zero. The area convention, activities and temperature must be specified; an exchange current density alone does not specify a nonlinear current-potential curve.

A limiting rate of charge transfer per area imposed by reactant transport or another bottleneck. In a simple diffusion film, $j_L=nFD{c}_b/\delta$ and a consuming electrode has $c_s/c_b=1-j/j_L$. Increasing internal roughness does not necessarily increase external mass-transfer flux proportionately.

A kinetic model for the net electrode current near and away from equilibrium. For a single effective reaction with consistent activities and ${\alpha }_a+{\alpha }_c=1$, $j=j_0[\exp ({\alpha }_{a}nF\eta /RT)-\exp (-{\alpha }_{c}nF\eta /RT)]$. Near equilibrium it gives $j\simeq j_{0}nF\eta /(RT)$; at sufficiently large overpotential one exponential gives the Tafel equation. Multistep reactions can require a different kinetic interpretation.

Maintenance or assessment of multiple ecosystem functions together. Functions can depend on different traits or conflict, so performance in one process cannot stand in for every other process.