Ezek. 24:1-2, "Again in the ninth year, in the tenth month, in the tenth day of the month, the word of the Lord came unto me, saying, 2 Son of man, write thee the name of the day, even of this same day: the king of Babylon set himself against Jerusalem this same day." (KJV)
The traditional date observed for the both the first and second destruction of the temple is said to be the 9th of Av. However, Josephus recorded only the burning of the temple on the 10th of AV in AD 70. (Josephus Book of Wars 6.244-271) The Romans did not tear down the walls and stones of the temple until the first of Tishrei. (1)
The scriptures in Ezekiel recorded the destruction of the first temple on the tenth (10th) day of the tenth month. That places doubt on the traditional teaching for the 9th of Av, and upholds Josephus' record for the burning of the temple on the 10th of Av.
But, the month of Av by the Jewish calendar is the 7th month, not the tenth month.
Which month was the tenth month in Ezekiel's time of the Babylonian captivity? Is it possible the tenth month was a Babylonian month on a Babylonian calendar?
Note 1) The Scientific Date for the Destruction of Herod's Temple in AD 70 - here