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The polytypes of birnessite with a periodic stacking along the c* axis of one-, two-, and threelayers are derived in terms of an anion close-packing formalism. Birnessite layers may be stacked so as to build two types of interlayers: P-type in which basal O atoms from adjacent layers coincide in projection along the c* axis, thus forming interlayer prisms; and, O-type in which these O atoms form interlayer octahedra. The polytypes can be categorized into three groups that depend on the type of interlayers: polytypes consisting of homogeneous interlayers of O- or P-type, and polytypes in which both interlayer types alternate. Ideal birnessite layers can be described by a hexagonal unit cell (ah = bh ≈ 2.85 Å and γ = 120°) or by an orthogonal C-centered cell (a = √3 b, b h  ≈ 2.85 Å, and γ = 90°); and, hexagonal birnessite polytypes (1H, 2H1, 2H2, 3R 1 , 3R 2 , 3H 1 , and 3H 2 ) have orthogonal analogs (1O, 2O 1 , 2O 2 , 1M 1 , 1M 2 , 3O 1 , and 3O 2 ).

Birnessite polytype systematics and identiÞ cation by powder X-ray diffraction