Size and shape dependent cohesive energy and melting temperature in semiconducting nanomaterials

Predicting thermophysical properties at the nanoscale remains challenging due to the lack of a unified model that simultaneously accounts for key factors such as atomic packing of the crystal lattice, surface-bond relaxation effects, and particle shape, along with the particle size, leading to limited analytical accuracy in existing thermodynamic models. Thus, this work introduces a unified thermodynamic model that explicitly incorporates the combined effects of two key factors-the atomic packing factor (µ) and the shape factor (α) of nanoparticles-along with size. These factors are essential for accurately describing the thermophysical properties of semiconductor nanomaterials. The model is applied to InSb, ZnSe, CdS, and CdSe semiconductor nanomaterials with various shapes, including nanowire, spherical, octahedral, hexahedral, and tetrahedral. A significant finding is the strong size-dependent decrease in cohesive energy and melting temperature, with noticeable deviations seen below 5 nm. Shape effects become crucial at this scale. Nanowires show smaller reductions in both cohesive energy and melting temperature compared to tetrahedral nanoparticles of similar size, indicating reduced surface vibrational relaxation. In comparison to the universal liquid drop model, which uses a fixed shape factor (α = 2/3), the current model aligns more closely with theoretical data. These results suggest thermodynamic stability for nanowire formation in the size range of less than 5 nm, and also highlight the importance of the µ-α coupling and surface vibrational effects in accurately defining thermophysical properties at the nanoscale. The proposed model lays a solid foundation for the predictive design of semiconductor nanomaterials.