AFTER DEPARTING ATL; A B767 CREW OVERTAKE AN ATR72 CAUSING A TCASII ALERT AND REQUIRING EVASIVE ACTION.

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DEPARTED ATL RWY 27R ON INITIAL HDG OF 25 DEGS. PASSING 6000 FT MSL; DEP CTL GAVE US L TURN TO 160 DEGS. THERE WAS A LINE OF TSTM CELLS RUNNING E/W JUST S OF THE DEP CORRIDOR. ABOUT 20 DEGS INTO THE TURN; I GOT A 'TFC; TFC' TCASII ALERT. I LOOKED UP AND SAW AN ATR IN MY FORWARD WINDSCREEN DEAD AHEAD AND APPEARING LEVEL; FAIRLY CLOSE. I COULD SEE DETAIL ON THE ACFT -- PROPS; AILERONS; ETC. I WATCHED FOR A SECOND OR TWO LOOKING FOR RELATIVE MOTION AND SAW NONE. ALSO; BECAUSE OF THE FLAT GRAY CLOUD BACKGND; I COULD NOT BE CERTAIN OF HIS HDG. I REVERSED MY TURN HARD TO THE R; USING 45 DEGS ANGLE OF BANK FOR ABOUT 20-30 DEGS OF TURN; THEN ROLLED LEVEL TO VISUALLY REACQUIRE THE TFC. THE COPLT TOLD ATC WE WERE RETURNING TO A WESTERLY HDG AND ADVISED THEM OF THE TFC. ATC TOLD US TO MAINTAIN 7000 FT. WE WERE PASSING 7500 FT CLBING AND ACCELERATING PAST 280 KIAS IN CLB PWR (WE WERE PREVIOUSLY CLRED TO 10000 FT). I PULLED THE PWR BACK AND LET THE ACFT SLOW A LITTLE; THEN STARTED DOWN TO 7000 FT. WE TOPPED OUT AROUND 8000 FT. WE RPTED THE CONFLICT AND ASKED ATC TO 'MARK THE TAPE.' WE GOT THEIR PHONE NUMBER AND I CALLED.