Anisotropic Deformation Behavior and Indentation Size Effect of Monocrystalline BaF₂ Using Nanoindentation

In this study, our objective is to investigate the anisotropic deformation behavior and the indentation size effect (ISE) of monocrystalline barium fluoride (BaF₂) using nanoindentation experiments with a diamond Berkovich indenter. BaF₂ is known for its anisotropy, which results in significant variations in its mechanical properties. This anisotropy poses challenges in achieving high processing quality in ultra-precision machining. Through our experiments, we observed numerous pop-in events in the load-displacement curves, indicating the occurrence of plastic deformation in BaF₂ crystals, specifically in the (100), (110), and (111) orientations; these pop-in events were observed as the indentation depth increased to 56.9 nm, 58.2 nm, and 57.8 nm, respectively. The hardness-displacement and elastic modulus-displacement curves were obtained from the tests exhibiting the ISE. The nanoindentation hardness of BaF₂ is found to be highly dependent on its crystallographic orientation. Similarly, for BaF₂ in the (100) orientation, the range is from 2.43 ± 0.74 and 1.24 ± 0.12 GPa. For BaF₂ in the (110) orientation, the values range from 2.15 ± 0.66 to 1.18 ± 0.15 GPa. For BaF₂ in the (111) orientation, the values range from 2.12 ± 0.53 GPa to 1.19 ± 0.12 GPa. These results highlight the significant influence of crystallographic orientation on the mechanical properties of BaF₂. To better understand the ISE, we employed several models including Meyer's law, the Nix-Gao model, the proportional specimen resistance (PSR) model, and the modified PSR (mPSR) model, and compared them with our experimental results. Among these models, the mPSR model demonstrated the best level of correlation (R2>0.9999) with the experimental measurements, providing a reliable description of the ISE observed in BaF₂. Our reports provide valuable insights into the anisotropic mechanical characteristics of BaF₂ materials and serve as a theoretical guide for the ultra-precision machining of BaF₂.