Surface specific heats of metal nanocrystals at low temperatures

In order to quantitatively explain the enhanced specific heat of metal nanocrystals measured from 4.2 K to 80 K, an analytical expression has been deduced to determine the surface specific heat in nanocrystals, which is proportional to T(2.5) at low temperatures. The consequently calculated specific heat and surface Debye temperature of copper nanocrystals are in good agreement with the experimental data. This explains why the experimental specific heat of copper nanocrystals is enhanced with respect to the bulk and why it exhibits a different feature as a function of temperature from that of the bulk at low temperatures. The first experimental evidence is presented that the spatial dimension of surfaces should be neither pure 2D nor 3D, but between 2D and 3D, due to the effect of atoms in the core of the nanocrystals.