The Hodgkin-Huxley theory and its extensions concerning squid axon nerve impulse conduction are based on concepts of movement of free cations in liquid water assisted by cation pumps. Those concepts have been disproven by recent experimental evidence indicating cell water is structured and cell cations are associated with macromolecules, suggesting that nerve excitation probably involves a phase transition. It is shown here that the Hodgkin-Huxley data on the rise of K+ conductance after depolarization of the squid axon fits closely the Avrami equation with an exponent of two. This fit implies that axon depolarization is indeed the result of a phase transition, the new phase growing from preexisting nuclei within the old phase. The nuclei grow in one or two (but not in three) dimensions until the new phase entirely replaces the old phase.