Abstract
The high-temperature neutron diffraction measurements of UO
2
and CaF
2
made recently by Willis are examined by means of the generalized formulation of the structure factor which recognizes the antisymmetric properties of atoms occupying non-centrosymmetric lattice sites. Numerical analysis of the neutron data in terms of an anharmonic vibration formalism developed for effective one-particle potential fields of the type
V
j
(r) =
V
0
,
j
+ ½
α
j
(
x
2
+
y
2
+
z
2
) +
β
j
xyz
+ quartic terms shows that certain unusual features of the observations are readily accounted for by the antisymmetric (
β
) components associated with the tetrahedral point symmetry of the anionic sites. Values are derived for the
α
j
and
β
j
parameters in both UO
2
and CaF
2
, and their ability to reproduce the experimental observations over a wide range of elevated temperature is demonstrated. The parameters derived for CaF
2
are compared with theoretical estimates obtained from an Einstein-type model of the vibrating lattice, using the various expressions for the interionic interaction in fluorite that have been proposed by Benson & Dempsey. Despite evident limitations in this model, it is possible to conclude that the Pauling radii for Ca
2+
and F
-
cannot reproduce the physical behaviour of this system.
Reference21 articles.
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2. Proc. Boy;Benson G. C.;Soc. A,1962
3. Cochran W . 1951 Acta crystallogr. 4 81.
4. A ust. J;Dawson B.;Chem.,1965
5. Proc. Roy;Dawson B.;Soc. A,1967
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