Higher Dimensionality in the Mg-Co-B System: Synthesis and Structure of Incommensurate Composite Mg_1+εCo₄B₄

Guided by high-temperature in situ X-ray diffraction, the discovery and synthesis of Mg_1+εCo₄B₄ (ε ≈ 0.272) using a MgH₂ hydride precursor is reported, along with a detailed crystal structure description and measurement of magnetic properties. The mismatch in lattice periodicities between Mg and Co-B substructures places Mg_1+εCo₄B₄ in the family of incommensurate composite crystals and prompted structural refinement in a (3 + 1)-dimensional model. The structure of Mg_1+εCo₄B₄ (P4₂/ncm(00γ)s00s, a = 6.75847(7) Å, c = 3.94007(8) Å, q = (0, 0, 1.2721(3))) was refined from neutron powder diffraction and high-resolution powder X-ray diffraction data and confirmed by scanning transmission electron microscopy and electron diffraction. Mg_1+εCo₄B₄ is isostructural to Nd_1+εFe₄B₄ and several related ternary borides with 0.07 ≤ ε ≤ 0.17, with Mg occupying the rare-earth site. Satellite reflections in the electron diffraction patterns hinted at positional modulation of the transition metal-boron substructure by Mg atoms, but this could not be refined from the neutron or X-ray diffraction data. Low-temperature magnetic measurements show no indications of long-range magnetic ordering or superconductivity down to 5 K. DFT calculations confirmed the absence of a magnetically ordered ground state and the stability of a 5:4 supercell (ε = 0.25) relative to the fully commensurate structure. Neutron diffraction and synthesis from elemental Mg demonstrated that Mg_1+εCo₄B₄ is not a hydrogen-stabilized phase. Mg_1+εCo₄B₄ represents the second compound reported in the Mg-Co-B system and the first superspace symmetry model of a Nd_1+εFe₄B₄-type incommensurate composite compound refined from powder diffraction data.