Neutron-diffraction study ofZr(Ca,Y)O2−x: Evidence of differing mechanisms for internal and external distortions

We have deduced from measurements of the neutron elastic cross section that below the order-disorder transition in $\mathrm{Zr}\left(\mathrm{Ca}\right)\mathrm{}{\mathrm{O}}_{2-x}$ and $\mathrm{Zr}\left(\mathrm{Y}\right)\mathrm{}{\mathrm{O}}_{2-x}$ the oxygen atoms are shifted from their fluorite positions. We find quantitative agreement with experiment for a model containing a rearrangement (internal shear deformation with amplitude 0.23 Å) of the oxygen sublattice. The (110) internal shear deformation is the same (in symmetry and magnitude) for $\mathrm{Zr}\left(\mathrm{Ca}\right)\mathrm{}{\mathrm{O}}_{2-x}$ and $\mathrm{Zr}\left(\mathrm{Y}\right)\mathrm{}{\mathrm{O}}_{2-x}$, however, only $\mathrm{Zr}\left(\mathrm{Y}\right)\mathrm{}{\mathrm{O}}_{2-x}$ exhibits an external distortion. These observations are consistent with the fact that the internal rearrangement is an inhomogeneous deformation and does not require the presence of an external strain. A successful test of Cooper's search criterion leads us to an internal rearrangement mode corresponding to a $\overrightarrow{\mathrm{q}}=(0,0,\frac{2\pi }{a})$ longitudinal phonon, and points to the dominance of cation-anion interactions in determining the nature of the lattice internal rearrangement.