Theory of one-dimensional ionic and solitary-wave conduction in potassium hollandite

It is argued that ions moving in hollandite crystals should not be significantly scattered by impurities. This could lead to large conductivities for low ionic concentrations. Ionic conduction for high concentration of ions occurs by motion of solitary-wave-like defects whose motion is damped by phonon radiation. An expression for the electrical conductivity is found using models for the motion of such solitary waves which were previously applied to the study of dislocation motion under an applied stress. Comparison is made with experiments on hollandite with the aid of an interrupted-strand model.