Anisotropic Fracture in Gadolinium Zirconate Single Crystal: Micromechanical Testing and Modelling

Abstract

We report a study on anisotropic fracture in gadolinium zirconate (GZO) using a combination of micromechanical testing and modelling. A GZO single crystal was grown using the floating zone method, and its fracture toughness in 8 different orientations was measured through the microcantilever beam bending tests. The fracture toughness, $K_{IC}$$K_{IC}$, of the GZO single crystal depends on its crystal orientation and follows this ranking order:$K_{IC}^{\left(7\overline{7}3\right)}>K_{IC}^{\left(1\overline{1}5\right)}>K_{IC}^{\left(1\overline{1}1\right)}>K_{IC}^{\left(1\overline{1}2\right)}>K_{IC}^{\left(3\overline{3}1\right)}>K_{IC}^{\left(001\right)}>K_{IC}^{\left(1\overline{1}3\right)}>K_{IC}^{\left(1\overline{1}0\right)}$$K_{IC}^{\left(7\overline{7}3\right)}>K_{IC}^{\left(1\overline{1}5\right)}>K_{IC}^{\left(1\overline{1}1\right)}>K_{IC}^{\left(1\overline{1}2\right)}>K_{IC}^{\left(3\overline{3}1\right)}>K_{IC}^{\left(001\right)}>K_{IC}^{\left(1\overline{1}3\right)}>K_{IC}^{\left(1\overline{1}0\right)}$. Fractographic analysis reveals that the crystal planes with low fracture toughness (e.g., $\left(001\right)$$\left(001\right)$) exhibit atomically smooth fracture surfaces. In contrast, planes with higher fracture toughness (e.g., $\left(1\overline{1}5\right)$$\left(1\overline{1}5\right)$) show distinct cleavages and zig-zag crack paths at the atomic scale, with crack deflection toward orientations with lower resistance to cracking. The cleavages and crack deflection increase the fracture surface area, which enables more energy dissipation during the fracture process and leads to higher fracture toughness. Surface energy of crystal planes determined by first-principles calculations is broadly consistent in ranking with the fracture toughness measured by experiments, which further confirm the anisotropic nature in fracture of the GZO single crystal. Finally, we calculate the broken bond energy density in different crystal planes during fracture and identify its strong correlation with fracture toughness.