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.
An integral form of the quantum-mechanical virial theorem, applicable to ionic as well as neutral systems, is established. This theorem is used to derive an approximate expression for the potential curve for a doubly positive diatomic ion in terms of the corresponding curve for a related neutral molecule. The appearance potentials of a number of these ions are calculated and compared with values obtained from electron-impact measurements. Satisfactory agreement is found, but a crucial test of the theory is vitiated by uncertainties in the experimental value of either the appearance potential of the doubly charged ion or the dissociation energy of the corresponding neutral molecule. The accuracy of the approximations underlying the theory is estimated by a series of calculations on two-electron systems.
An expression is derived for the (e, 2e) differential cross section of a crystal, with allowance for dynamic diffraction of both the incident and outgoing electrons, all of which are assumed to be fast. Conditions for unique momentum determination on the one hand or for maximum enhancement of the (e,2e) signal on the other are discussed.
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