The Debye temperature of iron nanoparticles : how far from the bulk ?

Overview & Synopsis

The Debye temperature ΘD characterizes the vibrations of a solid and marks the transition be- tween quantized and classical behaviors of nuclear motion. While thermodynamical theories suggest that for nanoparticles ΘD should be lower than the bulk limit and increase with increasing nanoparti- cle size, various experimental measurements have reported intriguing variations with size, including values above the bulk limit and possibly decreasing with size. In this article we have theoretically determined the Debye temperature of iron nanoparticles of up to about 7 nm diameter at the atom- istic level of details, using complementary approaches based on the equilibrium heat capacity or the mean square atomic displacement. Both methods consistently indicate steady finite size effects in the scaling regime, with no evidence for values higher than the bulk or varying in opposite ways, but they also produce marked quantitative differences. Further comparison with the melting tempera- ture Tm indicates that the two quantities correlate with each other through Tm ∝ Θα D, but with an exponent α close to 3 that deviates from the expected value of classical thermodynamical theories based on pure bulk ingredients.