The Items of quality mystery of the Verditius allows you to bring forth a property of whatever you are making and have one of its material/form bonuses act on it. So a sword might get +4 to attack, a bow might get +5 to damage at a distance, etc.
I want to make a battle axe of quality for one of my magi. Looking up axes gives me +4 to destroy wood. Fair enough for a woodsmans axe, but hardly inspiring for a viking style battle axe.
So, what do i do? Would it be suitable to give a battle axe a bonus similar to a sword or is a battle axe of quality exactly the same as a mundane battle axe, but particularly awesome when it comes to felling lumber?
Well, going strictly by the listed S&M bonuses you could:
Bring out the +7 Harm or Repel Fairies in the iron axe head
Bring out the +4 mind (for increased clear-thinking ability in battle, increased resistance against guile or attempts to control the wielder's mental state in some way, etc.) if the handle were made of Walnut wood
Bring out the +7 protection from storms if the handle were made of Oak
Bring out the +4 Bloodshed if the handle were made from Cherry wood (most fitting IMO)
Bring out the +2 Harm People if the handle were made from Ash wood.
Those are as many as I can think of trawling through the full index. Otherwise just make up your own S&M bonus for the shape "Battleaxe" in keeping with its sword counterpart.