The Theoretical Study on the Second-order Doppler Shifts of Simple Cubic Monatomic Nanocrystalline Particles

The formula of the second order Doppler shift of simple cubic monatomic nanocrystalline particle is reduced by means of the Green's function. The numerical results show that when the temperature is finite, the second order Doppler shifts of atoms on the surface are smaller than those in the inner, the second order Doppler shifts of inner atoms are almost equal. It is also shown that the second order Doppler shifts of the atoms on surface increase more rapidly than those of atoms in the inner when temperature increases, at the high temperature limit, the second order Doppler shifts of all atoms are equal. The sizes of nanocrystalline particles almost do not affect the second order Doppler shifts of all atoms, but the second order Doppler shifts of the whole nanocrystalline particle increase when the size of nanocrystalline particle increases.