CAPT OF A CESSNA CITATION V; C560; TURNED THE WRONG WAY WHEN CLRED DIRECT TO DEST DUE TO BEING OUT OF THE LOOP OF ATC FLC COMS. THE ARTCC RADAR CTLR INTERVENED AND DIRECTED THE CAPT TO TURN R TO A VECTOR HDG.

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DUE TO GND FOG AT THE DEST ARPT; AGS; THE ACFT WAS ESTABLISHED IN HOLD AT FL260 ON THE IRQ (COLLIERS) 180 DEG RADIAL; 20 MI LEGS; R TURNS. THE CREW ADVISED CTR THAT THEY COULD PROCEED TO AGS BECAUSE CONDITIONS HAD IMPROVED FOR LNDG. ZTL CLRED THE ACFT DIRECT AGS WITH DSCNT TO 11000 FT. THE CREW ACKNOWLEDGED AND COMPLIED. THE CO-CAPT IN THE R SEAT WENT OFF FREQ TO COMMUNICATE WITH THE DEST FBO. ZTL HANDED THE ACFT OFF TO THE NEXT SECTOR AND THE CAPT ACKNOWLEDGED AND COMPLIED. UPON INITIAL CALL; ZTL DIRECTED THE ACFT TO FLY HDG 180 DEGS AND CONTINUE DSCNT TO 11000 FT; WHICH THE CAPT ACKNOWLEDGED AND COMPLIED. THE CO-CAPT RPTED BACK ON FREQ AND THE CAPT WENT OFF FREQ TO ADVISE THE PAX OF THEIR INTENTIONS. AT THIS TIME; THE ACFT WAS S OF THE DEST (AGS) ON ASSIGNED HDG. WHEN THE CAPT RPTED BACK ON FREQ; THE CO-CAPT ADVISED THAT THEY WERE CLRED DIRECT AGS. THE CAPT ACKNOWLEDGED AND STARTED TO TURN THE ACFT TO THE L TO COMPLY. AFTER 30 DEGS OF TURN; ZTL QUESTIONED THE L TURN AND ADVISED THE CREW TO TURN R TO HDG 360 DEGS. THE CREW QUESTIONED THE CLRNC AND COMPLIED. NO TA/RA CONFLICT WAS GENERATED; NOR WAS SAFETY COMPROMISED. THE CREW REALIZED WHAT HAD OCCURRED -- BREAKDOWN OF CREW COMS.