pLEASE mention the material name and better show us the dispersion curves,
Generally, for unit cells of two or more atoms. It is not possible to have more than three acoustic branches. The rest will be optical branches. Therefore, if we have a 3-D crystal with P atoms per unit cell, there are 3P vibration modes, distributed as follows:
📷 3 acoustic modes with the three directions of polarization,
📷 3P-3optical modes, from which P-1 longitudinal & 2P-2transverse modes.
For example, a 3-dimensional lattice with one atom per unit cell, such as simple, body-centered, only three acoustic modes exist. For a 3-D lattice with two atoms per unit cell such as Ge, Si and GaAs, there exist three acoustic modes (one longitudinal acoustic LA, and two transverse acoustic TA) and three optical modes (one longitudinal optical LO, and two transverse optical TO).