Effect of crystal size reduction on lattice symmetry and cooperative properties

Size-induced changes in the crystal symmetry have been observed in ${\mathrm{Al}}_2$ ${\mathrm{O}}_3$, ${\mathrm{Fe}}_2$ ${\mathrm{O}}_3$, ${\mathrm{PbTiO}}_3$, ${\mathrm{PbZrO}}_3$, ${\mathrm{La}}_{1.85}$ ${\mathrm{Sr}}_{0.15}$ ${\mathrm{CuO}}_4$, ${\mathrm{YBa}}_2$ ${\mathrm{Cu}}_3$ ${\mathrm{O}}_{7\mathrm{-}\mathrm{\delta }}$, and ${\mathrm{Bi}}_2$ ${\mathrm{CaSr}}_2$ ${\mathrm{Cu}}_2$ ${\mathrm{O}}_8$. In these systems—and presumably in a large majority of partially covalent oxides—the crystal lattice tends to transform into a structure of higher symmetry with a decrease in the crystal size. We also find that the size dependence of many important physical properties can be ascribed directly to the lattice distortion. The physical mechanism responsible for these phenomena is intriguing and their complete understanding essential since they effectively define the practical lower limit to the miniaturization of devices based on these materials.