The Mott-Jones Electron Crystal: Patterning Atomic Positions for Pseudogap Formation in Hume-Rothery Phases

The valence electrons of Hume-Rothery intermetallics are envisioned to be so delocalized that together they approximate a free electron gas. However, electron count plays a key role in their structural preferences. This influence is generally attributed to the Mott-Jones (MJ) effect, in which the mixing of otherwise free electron states is induced by the presence of a periodic array of ions. Less clear, however, is how these interactions translate into the often complex local atomic configurations encountered in these materials. Here, we investigate this connection through the visualization of the partial electron densities associated with MJ planewave interactions. Over a series of structures with varying complexities, a simple mechanism emerges. In each case, essentially the same partial electron density distribution is obtained, which we refer to as the BCC-derived Mott-Jones electron crystal. The atomic centers are placed within channels in this density, corresponding to nodal surfaces in the underlying standing waves with different structures representing distinct ways of spreading atoms over the channels. These positions reinforce the splitting of s- and p-orbital character across pseudogaps, while the contributions of additional reciprocal lattice vectors fine-tune this effect. We comment on the potential existence of Mott-Jones electron crystals with other topologies.