  Mono- and bi-alkali antimonides, X$_2$YSb (X and Y from Group I), are
promising for next-generation electron emitters due to their capability of
producing high-quality electron beams. However, these materials are not yet
well understood, in part due to the technical challenges in growing pure,
ordered alkali antimonides. For example, in the current literature there is a
lack of complete understanding of the mechanically stable crystal structures of
these materials. As a first step towards understanding this issue, this paper
presents an ab initio study of stability of single-crystal mono- and bi-alkali
antimonides in the $D0_3$ structure, the structure generally assumed in the
literature for these materials. Finding that many of these materials actually
are unstable in the $D0_3$ structure, we formulate a new set of
Goldschmidt-like tolerance factors that accurately predict $D0_3$ stability
using a procedure analogous to machine-learning perceptron-based analysis.
Next, we consider possible stable structures for materials that we predict to
be unstable in the $D0_3$ structure. Taking as examples the mono- and bi-alkali
antimonides Cs$_3$Sb and Cs$_2$KSb, which also are technologically interesting
for photoemission and photoabsorption applications, respectively, we note that
the most unstable phonon displacements are consistent with the cubic structure,
and we therefore perform extensive ab initio searches to identify potential
ground-state structures in a cubic lattice. Our X-ray diffraction experiments
confirm that indeed these two materials are not stable in the $D0_3$ structure
and show scattering that is consistent with our new, proposed stable
structures. Finally, we explore ab initio the implications of the breaking of
the $D0_3$ symmetry on the electronic structure, showing significant impact on
the location of the optical absorption edge.
