Particle adverbs and modifying adverbs and where they are positioned

When modifying adverbs are used alongside particle adverbs intransitively (as particle adverbs usually are), the adverbs can appear in any verb/particle/adverb positions:
“He unhappily looked round.”
“He looked unhappily round.”
“He looked round unhappily.”

The particle adverb here is "round" and the modifying adverb is "unhappily". ("Round" is a particle because it is not inflected — does not take affixes and alter its form. "Unhappily" is a modifying adverb because it modifies the verb "look").

With a transitive verb, the adverb goes either before the verb of after the object or particle, whichever is last:
“He cheerfully picked the book up.”
“He picked up the book cheerfully.”
“He picked the book up cheerfully.”

(The particle adverb is "up" because it uninflected, and "cheerfully" is the modifying adverb because it modifies the verb "pick").