Elastic softening of bulk modulus of monoclinic HfO2 under high pressure

In this study, the lattice compression properties of monoclinic HfO2 (m-HfO2) at room temperature are investigated by performing high-pressure powder x-ray diffraction experiments. The lattice constants are precisely determined from the Rietveld analysis. The linear compressibility of each crystal axis a, b, and c is estimated as 10.0 × 10−3, 3.8 × 10−3, and 12.7 × 10−3/GPa, respectively, indicating a strong anisotropy. The equation of state for m-HfO2 is obtained using the third-order Birch–Murnaghan equation based on the volume and pressure data. The obtained unit cell volume (V0), bulk modulus (B0), and its pressure derivative (B0′) at ambient pressure are 138.3(1) A, 195(2) GPa, and –5.4(5), respectively. The negative value of B0′ implies the bulk modulus softening with an increase in pressure. The fact that the elastic softening has also been observed in m-ZrO2 suggests that the abnormal behavior is a characteristic of the monoclinic structure (P21/c). The transition to the orthorhombic phase is observed at approximately 6.4 GPa. The transition is sluggish, and two phases coexist at a pressure of up to 10 GPa.