Nefreet
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If you can find rules to make an improvised weapon out of a special material, then said improvised weapon would benefit from said material.
The hangup is that not all materials have such rules.
For example, making a crowbar out of Mithral is easy. Mithral is 500gp/lb, and a crowbar is 5lbs, so a Mithral crowbar would cost 2502gp.
But you couldn't do the same with Adamantine, since there's no "per pound" price.
In a homegame, you could probably just petition your GM to treat crowbars as weapons, and pay the +3000gp pricetag. But for systems like PFS, players have to be creative in how they acquire improvised weapons (or farm for Chronicle Boons).
| Pizza Lord |
In most cases, if the item is almost entirely composed of the material or at least how you're believably wielding it.
There are numerous references to players with longspears or other reach weapons suddenly using them as improvised weapons (club-equivalent) to attack adjacent foes. In such cases a ruling would likely be that you aren't able to count the adamantine spearheard for overcoming DR because you're using the haft to smack them (though if the haft were a special material, like darkwood, that might count instead.) So it isn't always a sure thing, but in most cases if what you're striking an enemy with is of a special material, it will count.