Back bonding is a type of resonance that is exhibited by several chemical compounds. Back bonding is known to offer increased stability to chemical compounds. It is also known to affect the overall dipole moment of the molecule and its hybridization.
Back bonding occurs between the same size of orbitals of small atoms. 3p orbitals of Al and Cl are comparatively larger. So, back bonding doesn’t occur in AlCl3. In this case the octet of Al is completed by dimerization. The 3p-orbitals of Al and Cl are comparatively larger in size which eventually increases the bond length and thus, it can not attain the double bond character by back bonding. Here, one of the lone pairs of Cl atom is donated to vacant 3p orbital of Al atom of other AlCl3 molecules.