Load-dependent nanoindentation response of NaBi(MoO 4) 2 single crystals: PSR analysis and energy dissipation

Abstract

In the present study, NaBi(MoO 4) 2 single crystals grown by the Czochralski method were systematically investigated through structural characterization and depth-sensing nanoindentation. X-ray diffraction confirmed phase purity and tetragonal symmetry, while Williamson–Hall analysis provided complementary insight into crystallite-scale strain and defect-related broadening. Load-dependent nanoindentation measurements were evaluated using Oliver–Pharr analysis together with proportional specimen resistance and Meyer-based approaches to distinguish apparent indentation effects from intrinsic mechanical behavior. The results reveal a clear indentation size effect, a progressive decrease in apparent hardness/modulus-related indicators with increasing load, and a concurrent shift in energy partition from elastic to plastic contribution, consistent with increasing irreversible deformation at higher contact loads. By combining crystallographic, mechanical, and energetic analyses within a single framework, this work delivers a reliable property map for NaBi(MoO 4) 2 and provides practical guidance for its use in load-sensitive photonic, optoelectronic, and functional oxide applications where mechanical reliability is critical.