The size-and shape-dependent band gap energy of semiconductor compound nanomaterials (SCNs) is formulated. The model theory is based on the cohesive energy of the nanocrystals compared to the bulk crystals. We have considered CdSe, CdTe, ZnS, ZnSe and ZnTe semiconductors compounds for the study of size-and shape-dependent band gap energy. It is found that the band gap energy of SCN depends upon the particle size and shape. The model predicts that the band gap energy increases as particle size of the semiconductor nanomaterials decreases. The results obtained are compared with the available experimental data, which support the validity of the model reported.

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A simple theory is proposed to study the size-and shape-dependent specific heat, melting entropy and enthalpy of nanomaterials. The particle size and shape are demonstrated to affect the specific heat, melting entropy and enthalpy of nanomaterials. The model is applied to Ag, Cu, In, Se, Au and Al nanomaterials in spherical, nanowire and nanofilms shapes. The specific heat is observed to increase with the decrease in particle size, whereas the melting entropy and enthalpy decrease as the particle size decreases. Our theoretical predictions agree well with available experimental and computer simulation results, thereby supporting the validity of formulation developed.

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