X-Ray Diffraction Study of Cs$sub 3$ZrF$sub 7$ Page: 4 of 8
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5
relationships on the films and space-group requirements
indicate that the metal ions must lie on or near the following
sites:
4Zr4+ at (0,0,0) + face centering
4Cs+ at (l/Zl/2,l/Z) + face centering
8Cs+ at (1/4,1/4,1/4; 3/4,3/4,3/4) + face centering.
In addition to the systematic absences due to the face
centering, the Oki reflections are strong only for k+i = 4n
while those reflections with k+i = 4n+2 are observable only
after long exposure. Although this type of absence is
usually indicative of a d-glide plane (or an approximation
to one), it arises from another cause in this crystal. If
only the heavy-atom contribution to the scattering is con-
sidered, the structure factor expression reduces, for atoms
in the above positions, to:
Fk ~ f(Zr4+) + 3f(Cs+) , k+j = 4n
FOki ~ f(Zr4+) - f(Cs+), k+9 = 4n+2.
The similarity in scattering power of Zr4+ and Cs+ makes the
second expression quite small, thus explaining the near
absences.
Because of the disorder in the arrangement of the
fluoride ions, they cannot be located in a straightforward
way; but a reasonable configuration may be assumed and the
resulting X-ray intensities compared with observation. In
the case of K3ZrF7 (and (NH4)3ZrF7) and in K UF7 , a ZrF7
and a UF7 ion, respectively, was assumed to exist;4,5
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Robbins, G. D. & Burns, J. H. X-Ray Diffraction Study of Cs$sub 3$ZrF$sub 7$, report, August 1, 1962; Tennessee. (https://digital.library.unt.edu/ark:/67531/metadc1058469/m1/4/: accessed April 25, 2024), University of North Texas Libraries, UNT Digital Library, https://digital.library.unt.edu; crediting UNT Libraries Government Documents Department.