For d-orbitals or d-subshell, Ɩ = 2, there are five values of m namely -2, -1, 0, 1, 2. It means d- orbitals can have five orientations. These are represented by dxy, dyz, dzx, dx2-y2 and dz2; for example, 3dxy, 3dyz, 3dzx, 3dx2-y2 and 3dz2. The dxy, dyz and dzx orbitals have same shape i.e., clover leaf shape but they lie in XY, YZ and ZX planes respectively. The dz2 orbital is symmetrical about Z-axis and has a dumbbell shape with a doughnut-shaped electron cloud in the centre. The dx2-y2 orbital is also clover leaf shaped but its leaves are directed along the X and Y- axis.
The reason for the presence of four lobes in any d orbital lies in the fact that the d – orbitals have two nodes, and hence two changes in algebraic sign of ψ, which lead to four lobes.
Fig: Shapes of d-orbitals