Thermal expansion of HfO₂ and ZrO₂

The thermal expansion of a low symmetry crystal can be much more interesting than the lattice parameter expansion would suggest. Here, the complete thermal expansion tensors for monoclinic and tetragonal phases of ZrO₂ and HfO₂ have been measured in air, by high-resolution, high-temperature X-ray diffraction. These results reveal the highly anisotropic nature of thermal expansion in the monoclinic phase as well as a cooperative movement of ions and the existence of a zero thermal expansion plane.