Structure of 3Â at.% and 9Â at.% Si-doped HfO2 from combined refinement of X-ray and neutron diffraction patterns

The crystal structure of 3 at.% and 9 at.% Si-doped HfO2 powder was determined through refinements using X-ray and neutron diffraction patterns. The lattice parameters, atomic positions, dopant occupancy, and the second phase fraction were determined with high precision using a combined full pattern fitting via the Rietveld method. The results show that both 3 at.% and 9 at.% Si-doped HfO2 powder exhibit the monoclinic crystal structure with P 1 21/c 1 space group. Through the combined refinement, the crystal structure parameters, especially for the positions and occupancies of the lighter atoms, were more precisely determined compared to independent X-ray diffraction refinement. Although the ionic radius of Si4+ is smaller than Hf4+, with increasing Si occupancy, the unit cell volume slightly increases; possible mechanisms for this effect are discussed. Moreover, the refined results provide evidence of the existence of a non-equilibrium phase of HfxSi1−xO2. The second phase (SiO2) fraction is determined as 0.17 at.% for 3 at.% Si-doped HfO2 powders and 1.7 at.% for 9 at.% Si-doped HfO2 powders.