Determination of coordination numbers and oxidation state of uranium atoms in β-U3O8 


Algorithm:
  1. Open the database Dirichlet. Choose U3O8/beta and compute Adjacency matrix for it. Open a Dirichlet window Program/Dirichlet (or Ctrl-D or click on the menu bar) and use the default options (Click on Default in the Dirichlet Option window).

  2. Run Dirichlet, choose all atoms as sublattice (the atoms that will form faces of Dirichlet domains) and uranium atoms as origin (the atom for which Dirichlet domains will be constructed).





    You will get the output like follows.


    Central atom:U1 CN:7 0.500 0.489 0.250 Rsd:1.326
      D(CP):0.129 ( 0.5000 0.4778 0.2500 )
      D(VDP):0.087 ( 0.5000 0.4814 0.2500 )
    Atom:2.014 < r < 2.396 =2.219 Top: 1.714 < R < 1.811 =1.758
    CN=7:0:0 NV=10 V=9.761/16.864 S=26.610 Cpac=0.438 Ccov=2.548
    G3=0.082506103
    Face distribution: {4/5 5/2 }
    Vertex distribution: {3/10 }
     
    N Atom x y z Dist. D1 D2 SAng.
    1 O_3 0.5000 0.6650 0.2500 2.01432 1.32578 0.68854 16.17405
    2 O_1 0.5000 0.5000 0.0000 2.07956 1.32578 0.75379 17.38460
    3 O_1 0.5000 0.5000 0.5000 2.07956 1.32578 0.75379 17.38460
    4 O_4 0.8180 0.5240 0.2500 2.28335 1.32578 0.95758 12.81750
    5 O_4 0.1820 0.5240 0.2500 2.28335 1.32578 0.95758 12.81750
    6 O_5 0.6810 0.3120 0.2500 2.39600 1.32578 1.07022 11.71087
    7 O_5 0.3190 0.3120 0.2500 2.39600 1.32578 1.07022 11.71087

    Central atom:U2 CN:7 0.000 0.350 0.250 Rsd:1.288
      D(CP):0.124 ( 0.0000 0.3609 0.2500 )
      D(VDP):0.032 ( 0.0000 0.3528 0.2500 )
    Atom:1.885 < r < 2.371 =2.175 Top: 1.688 < R < 1.722 =1.703
    CN=7:0:0 NV=10 V=8.952/15.564 S=25.195 Cpac=0.392 Ccov=2.389
    G3=0.082546290
    Face distribution: {4/5 5/2 }
    Vertex distribution: {3/10 }
     
    N Atom x y z Dist. D1 D2 SAng.
    1 O_2 0.0000 0.3520 0.0230 1.88492 1.28807 0.59685 19.49780
    2 O_2 0.0000 0.3520 0.4770 1.88492 1.28807 0.59685 19.49780
    3 O_3 0.0000 0.1650 0.2500 2.11732 1.28807 0.82926 14.90743
    4 O_5 0.3190 0.3120 0.2500 2.29657 1.28807 1.00850 12.20241
    5 O_5 -0.3190 0.3120 0.2500 2.29657 1.28807 1.00850 12.20241
    6 O_4 0.1820 0.5240 0.2500 2.37087 1.28807 1.08280 10.84607
    7 O_4 -0.1820 0.5240 0.2500 2.37087 1.28807 1.08280 10.84607

    Central atom:U3 CN:6 0.500 0.168 0.250 Rsd:1.350
      D(CP):0.058 ( 0.5000 0.1629 0.2500 )
      D(VDP):0.024 ( 0.5000 0.1701 0.2500 )
    Atom:2.086 < r < 2.278 =2.152 Top: 1.668 < R < 2.050 =1.901
    CN=6:0:0 NV=8 V=10.302/12.781 S=28.776 Cpac=0.462 Ccov=3.501 G3=0.085421206
    Face distribution: {4/6 }
    Vertex distribution: {3/8 }
     
    N Atom x y z Dist. D1 D2 SAng.
    1 O_5 0.6810 0.3120 0.2500 2.08645 1.34984 0.73660 17.93186
    2 O_5 0.3190 0.3120 0.2500 2.08645 1.34984 0.73660 17.93186
    3 O_4 0.6820 0.0240 0.2500 2.09079 1.34984 0.74095 16.80713
    4 O_4 0.3180 0.0240 0.2500 2.09079 1.34984 0.74095 16.80713
    5 O_2 0.5000 0.1480 -0.0230 2.27825 1.34984 0.92840 15.26102
    6 O_2 0.5000 0.1480 0.5230 2.27825 1.34984 0.92840 15.26102



    Pay attention to the atoms forming the Dirichlet domains; they all have large (> 10%) values of solid angles of corresponding Dirichlet domain faces; this means that all of them are strongly connected with uranium atoms and, hence the coordination numbers of U1, U2 and U3 are 7, 7 and 6, respectively.
    Now look at volumes of Dirichlet domains (V, Å3) and corresponding radii of spherical domains (Rsd, Å). They are characteristic for the atoms in a given oxidation state. In particular, for U(IV), U(V) and U(VI) in oxygen environment Rsd=1.39(3), 1.33(1) and 1.30(1) Å, respectively (Blatov V.A. (2004) Cryst. Rev. 10, 249-318). Comparing these values with computed ones we find that U1, U2 and U3 occur in oxidation states V, VI and V, respectively. This obey the rule of electrostatic balance in the formula U(+6)U2(+5)O8(-2).

  3. Draw the last computed Dirichlet domain together with the star of surrounding atoms by clicking Image/VDP&CP and also its Schlegel projection clicking Image/Schlegel Projection.
       



  4. To draw the Dirichlet domains for all uranium atoms open an additional IsoCryst window, select all uranium atoms and click button. Unselect all atoms.



    Check Polyhedra/Translucent and Show Vertices&Edges option to show the interior and exterior of the Dirichlet domains.





    Remove Dirichlet domains by clicking button, select uranium atoms again and construct Coordination Polyhedra by clicking button. Pay attention that, in general, coordination polyhedra are dual to the corresponding Dirichlet domains. Constructing coordination polyhedra for all cations you can get a polyhedral representation that is the most useful for inorganic compounds.



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