In the present decade, considerable interest has been taken in the investigation of anharmonic properties of materials of various kinds [1, 2]. Many workers have contributed in the field through their experimental and theoretical approach. Several efforts have been made in the study of physical and anharmonic properties of solids of different types [3–6]. Utilizing different physical conditions and using several techniques. Some interesting results have been presented by several investigators while studying the anharmonic properties of the substances possessing various crystal structures. Some have studied temperature variation of anharmonic properties of mixed alkali halides and cyanides of rare gas materials [7] of alkali halides [8–10] using ultrasonic [11, 12] and Brillouin scattering [13] methods. The static and Dynamic structural properties of solid C60 are currently the subject of numerous investigations. At room temperature, the crystal has a face-centered cubic fcc structure, the fcc phase has the symmetry of the space group Fm3m with a lattice constant of a0=14.2 A where the C60 molecules rotate freely. With decreasing temperature, the rotational degrees of freedom of the C60 molecules becomes more and more hindered and the solid C60 undergoes a first order structural phase transition from orientationally disordered fcc phase to an orientationally ordered simple cubic structures with four molecules per unit cell located on four different cubic sub lattices having different orientations[14]. Since the discovery of superconducting properties of C60 and the ability to prepare large quantities of this material [15, 16] an enormous amount of work has been carried out on it. Since Krastchmer et al. [14] produced macroscopic quantities of fullerene, knowledge of the molecular and solid state chemistry