Observation of the negative pressure derivative of the bulk modulus in monoclinic ZrO2

Abstract

Using synchrotron radiation x-ray diffraction techniques, the equation of state of monoclinic ZrO2 has been investigated under a hydrostatic pressure condition at 298 K. Monoclinic ZrO2 transformed to the orthorhombic I phase at between 5.7 and 7.0 GPa. Lattice constants of monoclinic ZrO2 refined from the Reitveld analysis showed extreme anisotropic pressure dependence. From the pressure–volume data, using least-squares fit of the Birch–Murnaghan formula, the bulk modulus, K0 and its pressure derivative: K0′, were estimated to be 159(3) GPa and −3.6(6), respectively. A negative K0′ suggests the abnormal softening of the elastic modulus in monoclinic ZrO2 with compression. First-principles calculations supported present experimental results.

Structure change of monoclinic ZrO2 baddeleyite involving softenings of bulk modulus and atom vibrations

“…It was confirmed that the linear compressibility of the c axis was larger than those for the other two axes and became larger with increasing pressure, whereas the length of the b axis was hardly changed or rather elongated ( Fig. 3), as observed in the previous XRD study (Fujimoto et al, 2018). We found the direction showing the largest linear compressibility is not along the c axis but between the c and -a directions and makes an angle of $24 with the c axis.…”

“…The relationship between pressure and the volume is based the third-order Birch-Murnaghan equation-of-state (Birch, 1952). The parameters for the equation were determined in the previous study (Fujimoto et al, 2018). The incident beam size was 5 mm in diameter.…”

“…Solid circles, squares and triangles corresponds to those along the crystallographic a, b and c axes, respectively. Open triangles and circles indicate those along the G and H axes, respectively (see text and Fujimoto et al (2018) suggested that the abnormal softening might be a result of a change in the chemical bonding properties. We, therefore, calculated the electron localization functions (ELFs) to check the pressure change in bonding nature between Zr and O.…”

“…Dynamical behaviors of the atoms are analyzed based on the Raman spectroscopy results with the assistance of ab initio calculations. Finally, we discuss the relationship between the change of the crystal structure and the two anomalous behaviors of the bulk modulus found using XRD (Fujimoto et al, 2018) and atom vibrations found using Raman spectroscopy (Arashi & Ishigame, 1982).…”

“…Details of the anomalous softening were not discussed there. A more recent study using X-ray powder diffraction (XRD) revealed that baddeleyite shows a highly anisotropic compression and an anomalous softening of the bulk modulus with compression (Fujimoto et al, 2018). In that paper, the softening in the bulk modulus was discussed as being related to the compression along the crystallographic c axis.…”