TABLE OF CONTENTS Figure 4.7 shows the MD-computed dimensionless phonon dispersion and DOS for the Ar FCC crystal. The atomic coordinates used in the generation of the dispersion data were obtained from MD simulations as discussed in Section 2.5 [232]. A structure at finite temperature is slowly quenched to a temperature of 0 K. The cut-off used is 2.5 ? LJ. As the crystal structure is monatomic (number of atoms per primitive cell, N o = 1, total number of modes is 3 N o), all modes correspond to acoustic phonons.
The plotted angular frequency is dimensionless and has been normalized by the L J time scale (Table 2.7, except for the constant), 
. Note that from (2.54), ? n is 22.88 time this ? scale, which is near the cut-off frequency in Figure 4.7(a). For Ar, the time scale has a value of 2.14 ps. The divisions on the horizontal axis (the wave number) are separated by 0.1 2 ?/ a (i.e., one-twentieth of the size of the first Brillouin zone in the [100] direction).
Note the degeneracies of the transverse branches in the [100] and [111] directions, but not in the [110] direction. Also, as seen in the [110] direction, the longitudinal branch does not always have the highest frequency of the three branches at a given point.
The volumetric density of states is based on a Brillouin zone with a grid spacing of 1/21 2
