The temperature and size dependences of atomic mean-squared thermal vibration amplitude of nanocrystals sigma(2) (T, D) are theoretically considered, where T is the temperature and D is the diameter of nanocrystals. It is found that when T is normalized by T-v = [T-m(D) -T] / T-m(D) where T-m(D) denotes the melting temperature, sigma(2)(T-v) function is size-independent, which is supported by simulation results of Co nanoparticles embedded in Ag matrix. (c) 2007 Elsevier B.V. All rights reserved.