The study of defects or vacancies helps to understand the transport mechanism that occurs electrically and thermally in materials. It also deals with the mechanical properties of materials. In the present study, the extension of qualitative size-dependent model proposed by Jiang for cohesive energy of nanomaterials is done and size dependence of vacancy formation energy, vibrational frequency and vacancy concentration in nanomaterials is studied. The variation in vacancy concentration in nanomaterials is studied using the extended Jiang model for different dimensional nanomaterials with size and temperature. The model calculations depict the increase in vacancy concentration in free-standing nanomaterials as size of the nanomaterial is reduced and temperature is increased. The behaviour of concentration variation is found just opposite in embedded nanomaterials. The present predicted results of variation in concentration of vacancies follow the same trend as explained in previous studies. The study validates that defects help in the displacement of atoms. The variation in melting temperature and vibrational frequency of nanomaterials with size-dependent vacancy concentration is also discussed.

Three different models, viz. Qi model, Jiang model and Lu model, have been used in the present paper for studying the size and shape dependence of magnetic properties of the nanomaterials. The magnetic propertiesconsidered here are Curie temperature ($T_C$), magnetisation ($M_S$) and Neel temperature ($T_N$),. It is observed that Curie temperature, magnetisation and Neel temperature decrease with decrease in the size of the nanomaterial. Thisdecrease is due to the increase in the surface atoms with reduction in size. The variations in Curie temperature, magnetisation and Neel temperature are studied for cylindrical nanowires, thin films, spherical, regular tetrahedralnanoparticles, and regular triangular cross-section nanowires. The models used in the study give similar trend of variation and after the comparison of the computed results with experimental data, it is found that Qi model workswell compared to Lu and Jiang models. A close agreement between the available experimental results and the calculated results from Qi model justifies the validity of the present work.

In the present study, the thermal conductivity relation equation given by Leibfried and Schlomann is extended and thermal conductivity is estimated at different pressures and temperatures by predicting the variationof Debye temperature, Gruneisen parameter and volume compression with temperature and pressure. The change in volume under variable pressure and temperature for the materials considered, viz. NaCl, NaI, KCl and KBr, arepredicted from Goyal–Gupta pressure–volume–temperature equation. The results obtained for variation of volume with temperature and pressure using Goyal–Gupta equation are compared with the available experimental dataand theoretical values obtained using Stacey’s equation. The thermal conductivity values are estimated at different temperatures with pressure along different isotherms and results are compared with thermal conductivity data available in previous studies for pressure dependence as well as for temperature dependence to justify the present model.