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

Ab initio study of the crystal and electronic structure of mono- and  bi-alkali antimonides: Stability, Goldschmidt-like tolerance factors, and  optical properties