High -resolution neutron elastic- diffraction data have been collected
for the cubic perovskites CsPbCZ₃, RbCaF₃, KMnF₃ and SrTiO₃ at a few
degrees above their cubic -- tetragonal phase transition temperatures, Tᶜ.
Similar data have also been collected for RbCaF₃ and KMnF₃ at room temperature - well above the transition.
Use of both cumulant- and Fourier -invariant -expansion formalisms in
the characterisation of anharmonic temperature factors is examined.
The relative merits of each formalism are compared with particular
reference to computational aspects and to the ease with which reliable
descriptions of atomic probability density functions may be derived.
It is found that the regimes of validity of both formalisms fall
considerably short of systems displaying classically disordered microstructure. The superiority of Fourier -invariant techniques in the
regime of relatively small anharmonic thermal motion is, however,
Cumulant and Fourier -invariant expressions have been used in the
analysis of the data collected for the cubic perovskites. It is
found that such anharmonicity as does exist in these crystals just
above Tᶜ is predominantly associated with the thermal motion of the
cations; that the magnitude and significance of this anharmonicity
varies considerably between the different cations; but that its
structure shows similar features in each. The motion of the cations
is shown to be preferentially in the plane of the cubic unit cell
face; a further slight preference is established for motion in the
directions along which the ions are known to displace on passing to the
lower- temperature phase. Clear evidence is found, for RbCaF₃ and
KMnF₃, that the thermal anharmonicity of the cations is anomalously
enhanced just above Tᶜ, while that of the anions is qualitatively as expected.
Suggestions are made as to the nature of further work which will
be required in order to clarify the full range of anharmonic atomic
distributions susceptible to meaningful analysis by elastic- diffraction