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3.2 Tunnel Structures  95

                                               Figure 3.3  Schematic drawing of the crystal
                                               structure of ε-MnO 2 . The manganese atoms
                                               arc randomly distributed in the octahedral
                                               voids of the hexagonal close packing of oxy-
                                               gen atoms. (Adapted from Ref. [41].)





               structure of β-MnO 2 and ramsdellite. Depending on the relative fraction of the two
               parent components contributing to the crystal structure, the XRD patterns may
               resemble either one or the other component. The De Wolff model of γ -MnO 2 was
               confirmed by HRTEM investigations [4, 5, 40]. In this study the [1 × 1] and [1 × 2]
               tunnel domains in the structure could be visualized. Additionally, a large number
               of discontinuities and structural faults were observed. Even larger tunnels (e.g.,
               [2 × 2]) exist in the real lattice of γ -MnO 2 . These findings explain the relatively large
               amount of water in the compounds and the presence of foreign cations and anions
               (e.g., sulfate), incorporated during the chemical or electrochemical synthesis.
                As described above, the XRD patterns of most γ -MnO 2 samples differ signifi-
               cantly. Some patterns can be indexed on the basis of the orthorhombic ramsdellite
               lattice according to the De Wolff model. In these samples the intergrown β-MnO 2
               slices in the structure clearly do not destroy the orthorhombicity of the lattice. With
               an increasing number of defects and a decreasing order within the domains, the
               distribution of manganese in the octahedral voids of the hexagonally close packed
               oxygen atoms becomes more and more statistical. In this case the contribution of
               the manganese atoms to the coherent scattering of X-rays becomes very small and
               is sometimes only indicated by the presence of the very broad reflection around
                ◦
               21 (in 2θ, or at about 3.9–4.2 ˚ A). Ignoring this peak, all other reflections of such
               a diffraction pattern can be indexed with a small hexagonal cell (e.g., a = 278.3,
               443.7 pm [12]), describing the close packing of the oxygen matrix. These samples
               with a high degree of disorder at the manganese sites are called ε-MnO 2 (see
               Figure 3.3).
                This modification contains tunnels of irregular shape and a statistical distribution
               in the structure. The only limitation for the distribution of the manganese atoms,
               and thus for the shape and size of the tunnels, is that no face-sharing voids can
               be occupied by manganese atoms, since in this case the interatomic distance of
               the Mn 4+  ions would become too small. Usually, it is quite difficult to distinguish
               between the XRD patterns of γ -and ε-MnO 2 . This can only be done by careful
               analysis of the diffractograms using effective profile-fitting routines and an accurate
               determination of the orthorhombic or hexagonal lattice parameters [12].
                The De Wolff disorder model has been extended to the cation vacancy model for
               γ -MnO 2 and ε-MnO 2 by Ruetschi [42]. In this model the occurrence of manganese
               cation vacancies and the non stoichiometry of electrochemical MnO 2 have been
               taken into account. Furthermore, the vacancy model deals with the explanation of
               the different water contents of manganese dioxide. Ruetschi makes some simple
               assumptions:
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