Structure prediction of stable sodium germanides at 0 and 10 GPa

In this paper we used 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 <a:math xmlns:a="http://www.w3.org/1998/Math/MathML"><a:mrow><a:mo>∼</a:mo><a:mn>1.5</a:mn></a:mrow></a:math> million structures to be relaxed. At ambient conditions we predict three new Zintl phases, <b:math xmlns:b="http://www.w3.org/1998/Math/MathML"><b:mrow><b:msub><b:mi>Na</b:mi><b:mn>3</b:mn></b:msub><b:msub><b:mi>Ge</b:mi><b:mn>2</b:mn></b:msub></b:mrow><b:mo>,</b:mo><b:mrow><b:msub><b:mi>Na</b:mi><b:mn>2</b:mn></b:msub><b:mi>Ge</b:mi></b:mrow></b:math>, and <c:math xmlns:c="http://www.w3.org/1998/Math/MathML"><c:mrow><c:msub><c:mi>Na</c:mi><c:mn>9</c:mn></c:msub><c:msub><c:mi>Ge</c:mi><c:mn>4</c:mn></c:msub></c:mrow></c:math>, to be stable and a number of Ge-rich layered structures to lie in close proximity to the convex hull. The known <d:math xmlns:d="http://www.w3.org/1998/Math/MathML"><d:mrow><d:msub><d:mi>Na</d:mi><d:mi>δ</d:mi></d:msub><d:msub><d:mi>Ge</d:mi><d:mn>34</d:mn></d:msub></d:mrow></d:math> clathrate and <e:math xmlns:e="http://www.w3.org/1998/Math/MathML"><e:mrow><e:msub><e:mi>Na</e:mi><e:mn>4</e:mn></e:msub><e:msub><e:mi>Ge</e:mi><e:mn>13</e:mn></e:msub></e:mrow></e:math> 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; <f:math xmlns:f="http://www.w3.org/1998/Math/MathML"><f:msub><f:mi>NaGe</f:mi><f:mn>3</f:mn></f:msub></f:math> and <g:math xmlns:g="http://www.w3.org/1998/Math/MathML"><g:msub><g:mi>NaGe</g:mi><g:mn>2</g:mn></g:msub></g:math> have simple kagome and simple hexagonal Ge lattices respectively with Na contained in the pores. <h:math xmlns:h="http://www.w3.org/1998/Math/MathML"><h:msub><h:mi>NaGe</h:mi><h:mn>3</h:mn></h:msub></h:math> is isostructural with the <i:math xmlns:i="http://www.w3.org/1998/Math/MathML"><i:msub><i:mi>MgB</i:mi><i:mn>3</i:mn></i:msub></i:math> and <j:math xmlns:j="http://www.w3.org/1998/Math/MathML"><j:msub><j:mi>MgSi</j:mi><j:mn>3</j:mn></j:msub></j:math> family of kagome superconductors and remains dynamically stable at 0 GPa. Removing the Na from <k:math xmlns:k="http://www.w3.org/1998/Math/MathML"><k:msub><k:mi>NaGe</k:mi><k:mn>2</k:mn></k:msub></k:math> results in the hexagonal lonsdalite Ge allotrope, which has a direct band gap. Published by the American Physical Society 2024