Structure prediction of stable sodium germanides at 0 and 10 GPa

In this paper we used ab initio random structure searching (AIRSS) to carry out a systematic search for crystalline Na-Ge materials at both 0 and 10 GPa. The high-throughput structural relaxations were accelerated using a machine-learned interatomic potential (MLIP) fit to density-functional theory (DFT) reference data, allowing ∼1.5 million structures to be relaxed. At ambient conditions we predict three new Zintl phases, Na₃⁢Ge₂,Na₂⁢Ge, and Na₉⁢Ge₄, to be stable and a number of Ge-rich layered structures to lie in close proximity to the convex hull. The known Na_𝛿⁢Ge₃₄ clathrate and Na_4⁢Ge₁₃ host-guest structures are found to be relatively stabilized at higher temperature by vibrational contributions to the free energy. Overall, the low-energy phases exhibit exceptional structural diversity, with the expected mixture of covalent and ionic bonding confirmed using the electron-localization function (ELF). The local Ge structural motifs present at each composition were determined using smooth overlap of atomic positions (SOAP) descriptors and the Ge-K edge was simulated for representatives of each motif, providing a direct link to experimental x-ray absorption spectroscopy (XAS). Two Ge-rich phases are predicted to be stable at 10 GPa; NaGe₃ and NaGe₂ have simple kagome and simple hexagonal Ge lattices respectively with Na contained in the pores. NaGe₃ is isostructural with the MgB₃ and MgSi₃ family of kagome superconductors and remains dynamically stable at 0 GPa. Removing the Na from NaGe₂ results in the hexagonal lonsdalite Ge allotrope, which has a direct band gap.