It's possible to form an aliphatic diazonium ion (R attached to a N triple bonded to another N, with + charge on one of the N). But, this aliphatic diazonium ion is very unstable, because although the aliphatic R group can inductively stabilize the + charge, this isn't as good as having an aromatic Ar group that can stabilize that + charge on N through resonance.
So the aliphatic diazonium ion will spontaneously split into a carbocation R+ and nitrogen N2. Then, the carbocation could undergo elimination reactions or whatever, possibly, and since we have nitrogen gas evolved (stable), that drives forward the dissociation of the aliphatic diazonium ion.
An aryl diazonium ion, on the other hand, is pretty stable due to resonance. So aryl diazonium salts (ex: benzene ring attached to a N triple bonded to another N, with the + charge on the N balanced by a Cl-), are actually stable enough to stay in the salt form when kept cold.
To form an aryl diaonium ion or salt, you'd have to start with a primary aryl amine, i.e. Ph-NH2, for example.
You CAN start with a primary amine (R-NH2, where R is aliphatic), but you'll end up with R+ and N2.
If you start with a secondary amine (R2-NH), you'll get a secondary N-nitrosamine (R2N-NO).
Sorry for the lengthy explanation, I can't draw out the molecules. Hope that helps.
