These results suggest an explanation for why the (quasi)harmonic models fail to show any signature of the superionic transition in α-Li 3 N. A quadratic potential, even when it is allowed to soften, or harden, in response to temperature effects misses the physics involved. The superionic state can only be described by including changes in the potential energy surface sampled by the mobile Li ions and thus requires higher-order anharmonic terms from Equation 2 to be included.