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Strain and Structure in Nanocrystals

Y. Bae and R.E. Caflisch
University of California, Los Angeles, US

nanocrystals, strain energy, quantum yield and linear elasticity

Layered nanocrystals consist of a core of one material surrounded by a shell of a second material. Because of the small size of these systems, their atomic structure is epitaxial in many cases. Lattice mismatch between the materials in the core and shell leads to elastic strain in a layered nanocrystal. Quantum yield for a layered nanocrystal has been found to correlate with strain. We present computation of the atomistic strain energy density in a layered nanocrystal, using an idealized model with a simple cubic lattice and harmonic interatomic potentials. The present study employs a simple model for the structure and strain of layered nanocrystal. Simulation of this model for a range of geometric and elastic parameters shows that there is a critical shell size at which strain has maximal influence. Moreover, this critical shell size correlated well with the shell size at which quantum yield is maximal. Our main results are as follows. We find that the elastic energy density of nanocrystals is concentrated in the region of the shell, along the interface with the core. Moreover, Figure ef(fig:3D_energy_density} shows that the energy density is more concentrated for thicker shells and the largest values of the energy density are close to the diagonal. Figure ef(fig:max_shell} (a) shows that the maximum energy density as a function of shell thickness peaks with small shell thickness. We define this shell thickness as critical shell thickness $r_s^(*}$ and compare these results to known QY results from expeiments in cite(Uri_critical}. Figure ef(fig:max_shell} (b) shows that the critical shell thickness is the same as that of quantum yield . The robustness of these results with respect to variation of dimension, geometry and material parameters suggests that these results are qualitative and generally applicable. Therefore, our atomistic elastic model has allowed us to investigate the instabilities of nanocrystals which result in their irregular growth with large lattice mismatch.

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