Number series of atoms, interatomic bonds and interface bonds defining zinc-blende nanocrystals as function of size, shape and surface orientation: Analytic tools to interpret solid state spectroscopy data

Semiconductor n anocrystals (NCs) experience stress and charge transfer by embedding materials or ligands and impurity atoms. In return, the environment of NCs experiences a NC stress response which may lead to matrix deformation and propagated strain. Up to now, there is no universal gauge to evaluate the stress impact on NCs and their response as a function of NC size d(NC). I deduce geometrical number series as analytical tools to obtain the number of NC atoms N-NC(d(NC)[i]),bonds between NC atoms N-bnd(d(NC)[i]) and interface bonds N-IF(d(NC)[i]) for seven high symmetry zinc-blende (zb) NCs with low-index faceting: {001} cubes, {111} octahedra, {110} dodecahedra, {001}-{111} pyramids, {111} tetrahedra, {111}{ 001} quatrodecahedra and {001}-{111} quadrodecahedra. The fundamental insights into NC structures revealed here allow for major advancements in data interpretation and understanding of zb- nd diamond-lattice based nanomaterials. The analytical number series can serve as a standard procedure for stress evaluation in solid state spectroscopy due to their deterministic nature, easy use and general applicability over a wide range of spectroscopy methods as well as NC sizes, forms and materials. (C) 2016 Author(s).