I'll have to agree with Dewo on the atma... and banshee can be very situational, I do Phantom most of the time cause of it boosts your M. Speed but thats late game if it lasts long enough... I'd pick the black cleaver instead of atma cause it boost both your atk speed and hp (I usually do a pure AD build but always include Rageblade) or the Triforce should be good instead of Phantom and Atma. That's MHO. I'm just lvl 16 xD. But imma try out this build and see how it works.

PS: Forzen Mallet could be a good option IF u cant think of anything else... The slow would help a lot... IDK i guess i gotta try it... just wondering about it xD

The phantom dancer costs way too much for what it provides and is a very late game item. I would change it to Banshee's Veil for magic resist but most games do not last that long with this build.

Atma will not be "major damage boost" that early. at the moment you get it you will poorly have 1400-1800HP so at best 36 damage boost.
Also getting phantom dancer that late with jax? I would swap those 2 items together. Anyway good standard build.