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

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.