I know that it is very common to place the object after the phrasal verb 'lay down' as follows:
The soldiers laid down their arms.
But can we place the object between the verb and the particle in the above-mentioned construction?
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Sign up to join this communityYes, you can say They laid their arms down.
The rule of thumb is that a 'light' object—typically no more than two words—follows the verb directly; a pronominal object always takes this position. If the object is 'heavier' than that it usually follows the preposition (particle), to make the construction easier to parse; but this is not a rule, merely a courtesy to your reader.
John laid it down.
John laid his laptop down or
John laid down his laptop.John laid down the laptop he was carrying.
John laid the laptop he was carrying down is grammatically acceptable but awkward.
To lay down one's arms is a kind of image or metaphor to mean: stop engaging in war.
"What will it take for the soldiers to lay down their arms"= Stop fighting in a war or battle.
To lay arms down does not mean that. It would mean something like to place weapons or arms on the ground:
The soldiers laid their arms down [on the ground]. The mother laid the baby down [on the bed].
Some phrasal verbs can change meanings very subtly sometimes.
I would argue that lay down in the phrase lay down arms is a phrasal verb but lay arms down [some place] is actually not a real one. It's a verb with an implied prepositional phrase.