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96  3 Structural Chemistry of Manganese Dioxide and Related Compounds

                    1) The manganese atoms are distributed in a more or less ordered manner at
                        the slightly distorted octahedral voids in the hexagonally close-packed oxygen
                        atoms (as described above).
                    2) A fraction x of the Mn 4+  ions is missing in the manganese sublattice. For
                        charge compensation, each Mn 4+  vacancy is coordinated by four protons in
                        the form of OH anions at the sites of the O 2−  ions.
                                    −
                    3) A fraction y of the Mn 4+  ions are replaced by Mn . This fraction determines
                                                              4+
                        the average valence of the manganese atoms. For each Mn 3+  there is a further
                        OH −  ion in the lattice, replacing an O 2−  anion in the coordination sphere
                        of the Mn 3+  cation. A schematic drawing of the Ruetschi model is shown in
                        Figure 3.4.
                                                                     3+
                                                               4+
                    4) Therefore the crystal structure is composed of Mn ,Mn ,O ,OH , and
                                                                               −
                                                                         2−
                        vacant sites. The water in the structure is present in the form of OH anions
                                                                             −
                        and Mn 4+  vacancies.
                    5) Chemisorbed water is considered to be present in the form of surface OH −
                        groups.
                    6) Electronic conductivity arises from delocalized electrons, tunneling or hopping
                        processes.
                      Therefore, Ruetschi proposes a general formula for γ -MnO 2 :
                                4+   3+  2−
                          Mn 1−x−y  Mn O 2−4x−y  OH 4x+y
                                     y
                    which replaces the formerly widely accepted, but unsatisfactory, formula:
                          MnO n .(2 − n + m)H 2 O
                    The terms x, y, n,and m can easily be transformed into one another by applying
                    Equations 3.1–3.4:
                               m
                          x =                                                   (3.1)
                             2 + m








                                                                  3+
                                                                Mn
                                                                      OH −






                    Figure 3.4  Vacancy (Ruetschi) model for the crystal struc-
                    ture of γ -MnO 2 . The shaded octahedra represent the
                    β-MnO 2 parts of the lattice. The small gray circles represent
                    protons attached to oxygen atoms.
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