ZJX CTLR INSTRUCTED ACFT DEVIATING AROUND A TSTM NEAR A MIL RESTR AREA TO SQUAWK 7700 EMER.

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CAPT'S EMER AUTH USED. Z TIME: XA07Z. FREQ/ALT: ZJX/FL310. ATC FACILITY: ZJX. LOCATION: CTY/285 DEG RADIAL/42 DME. LINE OF TSTMS FROM N OF LAL TO CTY AND E. DEVIATED TO W OF LINE. ZJX AN ACMI EXTENSION; WHICH IS NOT SHOWN ON THE US HI 5-6 CHART 'ACCORDING TO JAX' OR WARNING AREA 470 AND TOLD ME TO TURN R 15 DEGS INITIALLY; AND LATER TOLD ME TO TURN R 40 DEGS. THIS WOULD HAVE PUT ME SQUARELY INTO THE MIDDLE OF BOTH A SEVERE TSTM; AND THE LINE OF SEVERE STORMS I WAS TRYING TO AVOID. IN THE INTEREST OF FLT SAFETY; I TOLD JAX I WOULD NEED A L TURN TO APPROX 275 DEGS FOR TSTM AVOIDANCE. THE CTLR TOLD ME TO SQUAWK 7700; AND ASKED IF I WAS EXERCISING MY EMER AUTH. I SAID IF NECESSARY; YES; AND HE INITIATED THE EMER AT XA07Z. I WAS ON THE CTY 285 DEG RADIAL/42 DME. AFTER CIRCUMVENTING THE LINE OF TSTMS; I TURNED TO 015 DEGS AS INSTRUCTED; AND EVENTUALLY TOLD TO PROCEED DIRECT TO VHP; ON A 355 DEG HDG. THE EMER WAS TERMINATED AT XB24Z 5 MI SE OF PFN. BOTH MY COPLT AND JUMP SEAT OBSERVER 'ANOTHER PLT;' AGREED WITH MY DECISION.