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3.2 Tunnel Structures  101

               discussed above, the larger [2 × 2] tunnel allow various cations to be located in the
               middle of the cavity.
                Hence, it is not surprising that a large number of different minerals with more
               or less ideal α-MnO 2 types of structure are known. Minerals containing sodium
               (manjiroite), potassium (cryptomelane), barium (hollandite), and lead (coronadite)
               have been structurally characterized in detail. The crystallographic data for some
               α-MnO 2 compounds are summarized in Table 3.1, from which it can be seen that
               the members of the structural family with [2 × 2] tunnels can be described either
               by an ideal tetragonal or by a monoclinic cell with very similar dimensions, but an
                                           ◦
               angle slightly differing from β = 90 . Generally, α-MnO 2 type compounds have a
               stoichiometry of A 2−y B 8−x O 16 (A = large cations, e.g., K ,NH 4 ,Ba ,orwater;
                                                          +
                                                                +
                                                                    2+
                                                   3+
                                4+
                                     3+
               B = small cations, Mn ,Mn ,V ,Fe ,A1 ). Each large cation is surrounded
                                         4+
                                              3+
               by eight oxygen atoms forming a slightly cubic environment and additionally by
               four oxygen atoms outside the lateral faces of the cube. The octahedrally coordinated
               manganese atoms can be replaced by other small transition-metal cations with a
               similar ionic radius. Natural α-MnO 2 samples usually contain one large cationic
               species as the major component (e.g., Ba 2+  in hollandite) and the other possible
               elements (e.g., K ) in minor amounts. Water molecules have similar dimensions
                            +
               to the large ions mentioned above and therefore they can replace these cations in
               the tunnels. The crystallographic c-axis of the tetragonal description of α-MnO 2 or
               the b-axis of the monoclinic setting, respectively, has a dimension of about 280–290
               pm. Hence, the shortest distances between the large cations A would be in the same
               range if their respective sites were completely filled. Since such a short distance
               does not usually occur in oxides (in contrast, in intermetallic compounds or the
               elemental structures such distances can be observed), the A site has an occupancy
               factor of about 50% or lower. This does not mean that a superstructure due to
               cation ordering will necessarily be observed, although some examples are known
               in the literature (see Table 3.2, Ba 2−x (Mn,Fe) 8 O 16 , with a doubled monoclinic
               b-axis). Usually the ordered domains of the cations in the α-MnO 2 are too small
               to be detected by the occurrence of superstructure reflections. Thus, the α-MnO 2
                                                                             ◦
               structure is mostly described by the tetragonal, pseudotetragonal (all angles 90 ,
               Table 3.2  T(m,n) nomenclature scheme for manganese ox-
               ides, according to Turner and Buseck [4].

               Common                       Variable dimension
               dimension

                        n = 1  n = 2      n = 3     n = 4    n = 5     n =∞
               m = 1    T(1,1)  T(1,2)    T(1,3)    T(1,4)   T(1,5)    T(1, ∞)
               Examples  β-MnO 2  Ramsdellite                          Birnessite
               m = 2    T(2,1)  T(2,2)    T(2,3)    T(2,4)   T(2,5)    T(2, ∞)
               Examples        α-MnO 2    Roman` echite  Rb 16.64  Rb 0.27 MnO 2  Buserite
                                                    Mn 24 O 48
               m = 3    T(3,1)  T(3,2)    T(3,3)    T(3,4)   T(3,5)    T(3, ∞)
               Examples                   Todorokite
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