Shape of d-orbitals:
For d-subshell, l = 2, there are five values of m, that is, -2, -1, 0, 1, 2. It means that d-orbitals can have five orientations. These are symbolized by dxy, dyz, dzx, dx2-y2 and dz2; for illustration, 3dxy, 3dyz, 3dzx, 3dx2-y2 and 3dz2 .The dxy, dyz and dzx orbitals have similar shape that is, clover leaf shape although they lie in XY, YZ and ZX- planes correspondingly. The dz2 orbital is symmetrical around Z-axis and has a dumb-bell shape with a doughnut shaped electron cloud in the centre. The dx2-y2 orbital is also clover leaf shaped however its leaves are directed all along the X and Y-axis.
The motive for the presence of four lobes in any nd orbital lies in the fact that the d-orbitals have two nodes, and therefore two changes in algebraic sign of ψ, that lead to four lobes.
Figure: Shapes of d-orbitals
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