Double-diamond NaAl via pressure: Understanding structure through Jones zone activation

Under normal conditions, sodium forms a 1:1 stoichiometric compound with indium, and also with thallium, both in the double-diamond structure. But sodium does not combine with aluminum at all. Could NaAl exist? If so, under what conditions and in which structural types? Instead of beginning with a purely computational and first-principles structure search, we are led to apply the early Brillouin and higher (Jones) zone ideas of the physics determining structural selection. We begin with a brief recapitulation of the higher zone concept as applied to the stability of metals and intermetallic compounds. We then discuss the extension of this concept to problems where density becomes a primary variable, within the second-order band structure approximation. An analysis of the range of applicability of pressure-induced Jones zone activation is presented. The simple NaAl compound serves us as a numerical laboratory for the application of this concept. Higher zone arguments and chemical intuition lead quite naturally to the suggestion that 1:1 compound formation between sodium and aluminum should be favored under pressure and specifically in the double-diamond structure. This is confirmed computationally by density functional theoretic methods within the generalized gradient approximation.