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Semiconductor nanocrystals (NCs) experience stress and charge transfer byembedding materials or ligands and impurity atoms. In return, the environmentof NCs experiences a NC stress response which may lead to matrix deformationand propagated strain. Up to now, there is no universal gauge to evaluate thestress impact on NCs and their response as a function of NC size$d_{\mathrm{NC}}$. I deduce geometrical number series as analytical tools toobtain the number of NC atoms $N_{\mathrm{NC}}(d_{\mathrm{NC}}[i])$, bondsbetween NC atoms $N\mathrm{_{bnd}}(d_{\mathrm{NC}}[i])$ and interface bonds$N\mathrm{_{IF}}(d_{\mathrm{NC}}[i])$ 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 structuresrevealed here allow for major advancements in data interpretation andunderstanding of zb- and diamond-lattice based nanomaterials. The analyticalnumber series can serve as a standard procedure for stress evaluation in solidstate spectroscopy due to their deterministic nature, easy use and generalapplicability over a wide range of spectroscopy methods as well as NC sizes,forms and materials.

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