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3.3 Layer Structures  113

               are completely missing. Giovanoli [3] has developed a model that explains this
               somewhat extraordinary behavior of different δ-MnO 2 materials. In the model
               of birnessite-type materials proposed by Giovanoli, several arrangements of the
               Mn–O layer and the interlayer cations or water molecules are possible. The ideal
               is the perfect ordering of both types of sheets in the structure (see Figure 3.15a),
               thus building up a fully commensurate crystal lattice such as is realized in chal-
               cophanite. The XRD pattern of sample I in Figure 3.14 may be of a structure
               type with a high degree of order. In the second case a certain kind of disorder
               appears within the cation or water layer in terms of an inhomogeneous distribution
               of the interlayer species, while the distance between the main layers is constant
               (Figure 3.15b). A very similar situation is demonstrated in Figure 3.15c: a disorder
               of the interlayer species is combined with a shift of the main Mn–O layer within
               its own plane. This results in an incommensurate arrangement of the layers in the
               direction perpendicular to the layers. As a result the XRD patterns show only weak









                       Perfectly ordered Mn-O and    disorder of the foreign cation sublattice
                       foreign cation sublattices    Mn-O layers incommensurably shifted
                                                     (constant interlayer d-spacing)
               (a)                                  (c)









                   disorder of the foreign cation sublattice  disorder of the foreign cation sublattice
                   ordered arrangement of the Mn-O layers  ″turbostratic″ arrangement of the Mn-O layers
                                                      (order only within the Mn-O sheets)

                                                                               2+
                                                                           +
                             layer of                    Foreign metal cations (e.g. K or Ba )
                             MnO  octahedra                  O molecules
                                6                        or H 2
               (b)                                  (d)
               Figure 3.15  Arrangement of the Mn–O  distance, (c) disorder of the interlayer atoms
               layers and separating sheets according to  and an incommensurate shift of the com-
               Giovanoli [3]. The layer structure can be (a)  plete Mn–O sheet within the layer plane,
               completely ordered or (d) completely dis-  resulting in an incommensurate superstruc-
               ordered (turbostratic disorder). The cases  ture along the c-direction (perpendicular to
               (b) and (c) represent situations between the  the layer) and in a diffuse distribution of the
               two extremes: (b) disorder of the interlayer  electron density in this layer, resulting in a
               atoms or molecules but an ordered stack-  lower contribution of this layer to the 0 0 l
               ing of the Mn–O layers with constant layer  reflections. (Adapted from Ref. [41].)
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