Chemical Torque\nin Y<sub>14</sub>Ag<sub>39.3</sub>Zn<sub>12.1</sub>: Unwinding the\nDisordered Triangles of the Gd<sub>14</sub>Ag<sub>51</sub> Type

Elemental substitution is commonly used in materials\nchemistry\nto tune the Fermi energy of a compound or impart Chemical Pressure\n(CP) to atomic environments. In this Article, we illustrate how such\nsubstitution can also allow one to tune the relative orientations\nof geometrical units within a crystal structure, using the Gd<sub>14</sub>Ag<sub>51</sub> structure type as a demonstration. A key\nfeature of this structure type is the presence of hexagonal columns\nbased on the CaPd<sub>5+<i>x</i></sub> structure type, containing\ntriangles of atoms disordered over two orientations. Synthesis and\nstructure solution of a Zn-substituted variant of this structure,\nY<sub>14</sub>Ag<sub>39.3</sub>Zn<sub>12.1</sub>, reveal that the\nincorporation of Zn atoms into these triangles leads to their rotation\n relative to their surroundings. Distinct triangle orientations are\nfound depending on whether they are Ag<sub>3</sub> or Zn<sub>3</sub> units. A DFT-CP analysis of unsubstituted parent compound Y<sub>14</sub>Ag<sub>51</sub> elucidates these observations. The Ag<sub>3</sub> triangles lie within a large hexagon of Y atoms, with each\ntriangle corner being able to gain close contacts with up to two of\nthese Y atoms depending on the orientation. Obtaining an optimal alignment\nof the Ag<sub>3</sub> triangles with respect to these interactions,\nhowever, is prevented by repulsion from other Ag atoms in the columns\nderived from the CaPd<sub>5+<i>x</i></sub> type. Instead,\nthe triangles are twisted toward the Y neighbors with larger negative\nCP features. The replacement of Ag atoms with smaller Zn atoms provides\nthe opportunity to relieve these packing tensions, allowing the triangles\nto turn to a position that better optimizes their interactions with\nthe surrounding Y atoms. These results point to simple guidelines\nfor identifying, with CP analysis, rigid units within structures that\nmay be manipulated through elemental substitution.