Layer structures considered as trial models in the short-range order determination of nanocrystalline δ-MnO2. (a) 31/2 × 3b C-centered orthogonal layer cell featuring 33% vacancies. (b) 2( 31/2) × 2b C-centered orthogonal layer cell featuring 25% vacancies. (c) 2( 31/2) × 6b C-centered orthogonal layer cell featuring 17% vacancies. The equivalent hexagonal 2( 31/2)b supercell is also represented. (d) Top view of the MnO2 layer for chalcophanite containing 14% vacancies. Arrows indicate the directions of the Mn (black) and O (red) displacements upon structural relaxation induced by Mn vacancies. The gray octahedra are interlayer Mn (a)–(c) or Zn (d).