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

Abstract

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.

Anisotropy Dependence of Material Deformation Mechanisms in Nanoscratching Monocrystalline BaF2: Experiments and Atomic Simulations

“…Based on Bhushan’s research, the coefficient of adhesive friction (μ a ) is calculated using eq S6, where s represents the interfacial effective shear strength, and σ y , the yield compressive stress, is determined by eq S7. The elastic modulus E and the hardness H can be inferred from our prior investigation …”

“…Employing the results from anisotropic nanoscratch experiments, we can predict the material’s critical DBT value. Based on nanoindentation experiments on monocrystalline BaF 2 , the reliable reference hardness H of the (111) surface is 0.927 GPa, and the elastic modulus E is 70.82 GPa . Substituting these parameters into eqs and yields predicted DBT depths of 993 and 1052 nm for the [−110] and [−1–12] directions, respectively, on the BaF 2 (111) plane.…”

“…Based on nanoindentation experiments on monocrystalline BaF 2 , the reliable reference hardness H of the (111) surface is 0.927 GPa, and the elastic modulus E is 70.82 GPa. 47 Substituting these parameters into eqs 4 and 5 yields predicted DBT depths of 993 and 1052 nm for the [−110] and [−1−12] directions, respectively, on the BaF 2 (111) plane. These predictions align closely with the experimentally determined critical DBT depth of the BaF 2 (111) plane, measured at * d c = 1008 ± 46 nm, validating the model's accuracy.…”

“…The elastic modulus E and the hardness H can be inferred from our prior investigation. 47 By decomposing the COF into the coefficients of adhesive and plowing friction and incorporating the effects of elastic recovery of the monocrystalline BaF 2 surface using eqs 6, 9, S6, and S7, we developed a quantitative model for the COF of the monocrystalline BaF 2 workpiece as follows:…”