The Strongest Particle: Size-Dependent Elastic Strength and Debye Temperature of PbS Nanocrystals

Abstract

We investigated the elastic compressibility of PbS nanocrystals (NCs) pressurized in a diamond anvil cell and simultaneously probed the structure using synchrotron-based X-ray diffraction. The compressibility of PbS NCs exhibits bimodal size dependence. The elastic modulus of small NCs increases with increasing diameter and peaks near a particle diameter of approximately 7 nm. For large NCs the elastic modulus decreases toward the bulk value with increasing NC diameter. We explain the bimodal size-dependence of the elastic modulus in terms of a core-shell model based on distinct elasticity of the crystal near the surface and in the core of the particle. We combined insights into the size-dependent elasticity and lattice spacing to determine the Debye temperature of PbS NCs as a function of particle diameter. Understanding the size-dependent elasticity of defect-free colloidal NCs provides new insights into their crystal structure and mechanical properties.

Quantum-dot-in-perovskite solids

“…This can be explained by the fact that PbS is much stiffer than perovskite: the bulk modulus of PbS is B PbS 5 53 GPa (ref. 38), whereas for perovskite it is B perovskite 5 12.2 GPa (ref. 39).…”

Size dependent compressibility of nano-ceria: Minimum near 33 nm

“…22 They describe a core-shell model. Following this analysis, the synthesis methods for our nanoceria, as well as Bian's PbS, yield highquality crystallites that are defect-free, as evidenced by highresolution TEM, 5 and therefore Chen's explanation of bulk modulus trends depending on dislocations does not apply.…”

High‐Pressure‐Induced Comminution and Recrystallization of CH3NH3PbBr3 Nanocrystals as Large Thin Nanoplates

“…Nanocrystals (NCs) respond specifically to pressure with respect to phase progression, coherent crystal domain size, particle agglomeration, and morphology, accompanied by physical and chemical property modification. For example, high pressure can induce distinct textural coalescence of metallic Au/Ag NCs along with tuning the corresponding plasmonic resonance; (meta)stable phases in conventional semiconductors including CdSe and PbS/Pt;[15a,16] and alternation in the carrier dynamics in CdTe NCs and CsPbBr 3 perovskite nanocube superlattices …”