A B727 FLC WAS INSTRUCTED TO TURN L 10 DEGS; BUT THE PF THOUGHT THAT THE CLRNC WAS FOR A R TURN. THE ARTCC INTERVENED; THIS TIME ISSUING A 25 DEG TURN TO BOTH ACFT. AS THE FLC INITIATED THE TURN; THEY RECEIVED A SINGLE TCASII TA.

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WHILE CRUISING AT FL310 ON DIRECT ROUTING (ADJACENT TO J89; APCHING LVT VOR; AND APPROX 60 NM S); ATC GAVE INSTRUCTION OF 10 DEGS L FOR TFC. I ACKNOWLEDGED 10 DEGS L; SET MY HDG BUG ACCORDINGLY; AND TURNED ON MY FLT DIRECTOR (USED AS A MEMORY AID WHEN I'M ON VECTORS). THE FO; WHO WAS FLYING; UNCOUPLED THE AUTOPLT FROM THE OMEGA NAV SYS AND INITIATED THE TURN. I HAD BEEN PREVIOUSLY OCCUPIED WITH COLLECTING DATA AND MAKING NOTES ABOUT AN EARLIER MAINT PROB. I HAD RESUMED WRITING AFTER THE FO INITIATED THE TURN. SHORTLY THEREAFTER (ESTIMATED 2-3 MINS) ATC QUESTIONED THE TURN. I LOOKED UP AND FOUND THAT WE HAD IN FACT TURNED IN THE WRONG DIRECTION. ATC GAVE US 25 DEGS L NOW (WITH SOME URGENCY) AND GAVE AN IDENTICAL DIRECTION TO ANOTHER (SBOUND) ACFT. AS WE INITIATED THE TURN; WE RECEIVED A SINGLE TCASII TA. WE WERE GIVEN A DIRECT CLRNC SHORTLY FOLLOWING; WITH NO ADDITIONAL INCIDENT. THE PROB COULD HAVE BEEN PREVENTED BY NOT PERFORMING NONESSENTIAL PAPERWORK IN FLT. SUPPLEMENTAL INFO FROM ACN 335830: FATIGUE WAS A CONTRIBUTING FACTOR. WE HAD A TRIPLE GENERATOR FAILURE ON THE FIRST TKOF WHEN LEAVING FLL AND EXPERIENCED A 3 HR DELAY. THE ACFT RADIO VOLUME BEING ACCIDENTALLY TURNED DOWN WAS THE LARGEST FACTOR. I HAD HEARD 'FOR TFC;' BUT NOT CLRLY WHICH DIRECTION TO TURN. TO PREVENT A RECURRENCE I WILL ABSOLUTELY BE INSISTENT THAT BOTH CREW MEMBERS REPEAT ATC INSTRUCTIONS. IN FUTURE WHEN I AM TALKING ON THE RADIO; I WILL MAKE AN EFFORT TO GIVE ATC THE NEW HDG.