If I get your idea correctly, the situation is as follows:

You CAN dissociate a perfect dislocation into two other perfect dislocations, however, then betwen these two new perfect dislocations you will NOT get a planar fault.

Thank you, Dr. Andreas Leineweber for your response. I still have a query how to visualize the same in a crystal? How it will exist as dissociated without getting a fault??

A perfect dislocation simply does not generate a fault. In my beginners lecture I visualize it on the (hypothetical) alpha-Polonium case (primitive cubic). The natural shortest Burgers vector is of the type . It may split (if the stacking fault is of low energy/area; which is unlikely) into 2 x . The strain energy decreases but the stacking fault energy will be large, so the splitting distance will be large. If you, however, start with a dislocation with a Burgers vector (being present for whatever reason) , than this can split to 2 x , and not being a stacking fault in between, because all dislocations with and integer n are perfect dislocations for this crystal structure. the splitting of the will release a siginificant amount of elastic energy without having the cost of a stacking fault. this can be taken as argument that dislocations are unlikely to exist.

Thank you Dr. Andreas Leineweber for clarifying it...

Sincere regards

Subha Sanket