Size and shape-dependent thermodynamic properties of nickel nanoparticles: impact of carbon impurity

Based on the bond energy model, we investigate the particle size and shape effects on the melting temperature, Debye temperature, and specific heat at constant pressure of Ni nanoparticles with carbon impurity. We have derived analytical expressions for these thermodynamic quantities as functions of the size and shape of nanoparticles. Numerical calculations have been implemented for nickel nanoparticles with carbon impurity up to 20 nm of size. Our theoretical melting temperatures are compared with molecular dynamics simulations showing the good agreement. Our research indicates that the Debye temperature and melting temperature of nickel nanoparticles increase rapidly while the specific heat decreases significantly for particle diameters smaller than 5 nm. At larger sizes, these thermodynamic quantities gradually approach saturation values of bulk material. This indicates that surface area plays an important role in the thermodynamic properties of nickel nanoparticles. And carbon substitution leads to a reduction in the values of the studied thermodynamic quantities.