A320 CAPTAIN REPORTS ENGINE FAILURE AT FL340 WITH ATTEMPTED RESTART THAT ALSO FAILS. AN EMERGENCY IS DECLARED WITH A DIVERT TO THE NEAREST SUITABLE ARPT.

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ACCORDING TO PRELIMINARY MAINT FINDINGS; I HEARD THE HOT SECTION OF THE TURBINE CAME APART. I CANNOT CONFIRM THIS. ENRTE AT FL340 HEARD A LOUD BOOM; FOLLOWED BY LOSS OF #1 ENG. DECLARED AN EMER AND REQUESTED LOWER ALT. REQUESTED DIRECT ZZZ; BEING THE NEAREST ARPT. WE FOLLOWED ECAM AND QRH PROCS. I BRIEFED THE PAX AND RAN THROUGH PROCS WITH THE FLT ATTENDANTS. NOTIFIED OPS. ENG HAD RESTART PARAMETERS; SO WE ELECTED TO ATTEMPT A RESTART. ENG STARTED OK UNTIL I BROUGHT THE THRUST LEVER OUT OF IDLE; THEN IDENTICAL LOUD BOOM AND FAILURE. WE HELD OVER THE ARPT REVIEWING ENG OUT AND GAR PROCS. AFTER COMPLETING ALL CHKLISTS AND REVIEWING ZZZ APCH PLATES; WE WERE GIVEN VECTORS FOR THE LONGEST RWY; WITH THE EQUIP STANDING BY. A SUBSEQUENT UNEVENTFUL PRECAUTIONARY LNDG OCCURRED. AFTER EXITING THE RWY; WE STOPPED SO THE FIRE TRUCKS COULD CHK OUT OUR #1 ENG. AFTER VISUAL AND VERBAL CONFIRMATION OF NO FIRE; FROM CFR; WE TAXIED TO THE GATE. SUPPLEMENTAL INFO FROM ACN 741363: THE ENG RESTART WITH NO DAMAGE SHOULD HAVE NOT BEEN ATTEMPTED KNOWING WHAT WE KNOW NOW THAT THE ENG WAS BROKE HARD. WE HAD A VISUAL INSPECTION FROM THE CABIN CREW AND THE ECAM SUGGESTED NO DAMAGE; BUT THE ENG WAS BROKEN BEYOND FLT IDLE PWR SETTINGS.