E120 FLC CLB ON EXPECTED DEP CLRNC AND ARE CHALLENGED BY ZME CTLR.

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ON A LATE NIGHT SCHEDULED FLT FROM GTR TO AEX; OPERATED AS ACR X. CONFUSION ABOUT OUR CLRNC FROM ZME CAUSED A DEV FROM OUR ASSIGNED CLRNC. OUR NORMAL FLT PLAN IS FILED GTR DIRECT IGB V278 SQS DIRECT HEZ DIRECT AEX. SINCE A DEP FROM GTR REQUIRES BACKTRACKING TO GET TO IGB; IT IS A COMMON PRACTICE TO REMAIN ON RWY HDG TO CLR THE GTR TFC PATTERN; AT WHICH POINT WE ARE GENERALLY IN RADAR CONTACT; AND THE CTLR ASSIGNS DIRECT TO A FIX FURTHER ALONG THE RTE. ON THIS OCCASION; OUR CLRNC FROM GTR READ 'CLRED AS REQUESTED.' AFTER DEP; THE CAPT CALLED ZME AND INFORMED THEM WE WERE CLBING THROUGH 1000 FT ON RWY HDG. THE SINGLE WORD RESPONSE OF 'WHY?' WAS HEARD. THE CAPT ASKED FOR A REPEAT; AND THE ANSWER CAME 'CLRED TO ALEXANDRIA ON COURSE.' AS WE GENERALLY GET DIRECT TO AEX THIS LATE AT NIGHT; WE TURNED TO A HDG OF 240 DEGS; WHICH THE CAPT TOLD CTR. AFTER PROCEEDING FOR PERHAPS 30 SECONDS; CTR ANNOUNCED RADAR CONTACT; ASKED US WHY WE WERE WHERE WE WERE; AND HOW WE EXPECTED A 240 DEG HDG TO TAKE US TO IGB. THE CAPT SAID HE HAD MISUNDERSTOOD; THINKING WE WERE CLRED DIRECT TO AEX. THE CTLR PROCEEDED TO LECTURE US ON THE RULES OF IFR DEPS; THEN GAVE US A PHONE NUMBER FOR ZME TO CLARIFY OUR DEPS FROM GTR. WE WERE THEN CLRED DIRECT TO AEX; AS WE HAD INITIALLY EXPECTED. THE PROB WAS A CLR LACK OF UNDERSTANDING BTWN WHAT WAS SAID AND WHAT WE PERCEIVED. WHILE THE CTLR NEVER USED THE WORD 'DIRECT;' NOR DID SHE CORRECT US WHEN WE STATED WE WERE TURNING TO 240 DEGS; AS GTR IS SW OF IGB; SHE MUST HAVE KNOWN THAT THIS HDG WOULD NOT TAKE US THERE. SOME SORT OF STANDARD DEP HDG; AS USED BY OTHER ARPTS WITHOUT TERMINAL RADAR COVERAGE; WOULD BE VERY HELPFUL.