ACR DC9 INBOUND TO PIT WAS ISSUED R TURN FOR VECTOR CLR OF OPPOSITE DIRECTION TFC AND DSCNT TO FL290. PIC THOUGHT L TURN WAS ISSUED. FO DID NOT INITIALLY OBSERVE PIC TURNING L. CTLR OBSERVED TURN INTO OPPOSITE DIRECTION TFC; ISSUED L TURN TO 360 DEGS. FLC RECEIVED TCASII RA AND CLBED.

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ACR X WAS AT FL330 INBOUND TO PIT. ACR Y WAS AT FL310. ACR X WAS EBOUND AND S OF ACR Y (WBOUND). I ISSUED A 20 DEG R TURN TO ACR X AND DIRECTED THAT WHEN HE WAS ESTABLISHED ON THE NEW HEADING TO DSND TO FL290. AS ACR X WAS ALREADY ABOUT 3 MI S OF ACR Y'S TRACK; I BELIEVED THE TURN WAS MORE THAN SUFFICIENT TO ENSURE SEPARATION. I THEN ISSUED CLRNCS TO OTHER ACFT; THEN I NOTICED CONFLICT ALERT ACTIVATING BTWN ACR X AND ACR Y. ACR X TRACK HISTORIES AND LEADER LINE BOTH SHOWED A CONSTANT L TURN. THE ACFT WERE BASICALLY NOW HEAD ON AT ABOUT 8 MI WITH ACR X DSNDING THROUGH 32000 FT. I TOLD THE PLT HE HAD TURNED L AND HE REPLIED THAT HE HAD TURNED R. AS I COULD NOT BE SURE WHAT HE WAS DOING I DID NOT BELIEVE IT WAS SAFE TO ISSUE A VECTOR TO ACR Y; I TOLD ACR X TO FLY A HDG OF 360 DEGS AND TO EXPEDITE A DSCNT TO FL280. I ISSUED THE CONTINUED DSCNT IN AN EFFORT TO MAINTAIN A SAFE SIT AS ACR X WAS ALREADY DSNDING. ACR X ADVISE THAT HE WAS GETTING A TCASII RA AND CLBING. I TOLD HIM TO CONTINUE THE TURN TO HDG 360 DEGS FOR OTHER TFC AT FL330; THEN DSNDED HIM TO FL240 WHEN CLR OF ACR Y. I WAS THEN RELIEVED UNTIL THE EDP COULD BE INVESTIGATED. SUPPLEMENTAL INFO FROM ACN 388003: IN LEVEL CRUISE AT FL330 ZID INSTRUCTED US TO TURN R 20 DEGS AND DSND TO FL290. THE FO REPLIED 'R 20 DEGS; DSND TO FL290;' BUT I HEARD THE CLRNC AS (L 20 DEGS). WHILE I BEGAN A GENTLE 10 DEG BANK TURN TO L; THE FO RESET THE CABIN AND TURNED HIS ATTN TO HIS FLT KIT FOR THE APPROPRIATE CHARTS. THE FO HAD NOT MONITORED THE ACTUAL ACFT TURN OR DSCNT; BUT UPON SELECTING 360 DEGS ON THE HEADING BUG HE NOTED THAT I HAD MADE LITTLE PROGRESS TOWARD THE ORIGINAL 20 DEG R. AT ALMOST THE SAME TIME THAT THE INSTRUCTION TO TURN L 360 DEGS WAS GIVEN; WE BEGAN TO EXPERIENCE MODERATE CHOP WHICH FURTHER LED TO CONFUSION/DISTR AS THE SEAT BELT SIGN AND AIRSPD WERE CHKED. VERY SHORTLY AFTER THESE EVENTS (APPROX 15-20 SECONDS) THE TCASII RA SOUNDED. I IMMEDIATELY ADDED PWR AND BEGAN TO CLB TO FOLLOW THE TCASII VERT GUIDANCE. THE FO RPTED TO ZID THAT WE WERE RESPONDING TO A TCASII RA AND HAD THE ACFT IN SIGHT AND WERE CLBING. THE TCASII THEN SOUNDED 'CLR OF CONFLICT.' I RESUMED DSCNT TO FL290. I DIDN'T HEAR THE CLRNC PROPERLY AND THE FO DIDN'T ENSURE MY RESPONSE TO THE CLRNC. DISTR FROM TURB AND CONFUSION FROM THE CTLR'S WORDS ALSO CONTRIBUTED. SUPPLEMENTAL INFO FROM ACN 387924: IN LEVEL CRUISE AT FL330 ZID INSTRUCTED 'TURN R 20 DEGS; THEN DSND TO FL290.' FO READ BACK CLRNC. PROB CAN BE AVOIDED BY ENSURING CLRNCS ARE FULLY UNDERSTOOD BY BOTH PLTS; AND CLOSER MONITORING BY PNF.