In my department, we are allowed to take "half-day" leave: it could be either for the first half or the second half of the day. Are the following sentences pertaining to "leave application" grammatical and idiomatic?

1. Sir, may I apply for half-day afternoon leave?
2. I am on half-day leave this morning.
3. On Monday, I shall be on half-day morning leave.
4. I am taking urgent half-day afternoon leave tomorrow.
5. May I have your permission to apply for half-day leave for the morning?
Those all sound fine to me, Selvakumar.
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Dear sir/mam

I will drop my ___________ back home and come to the office for the meeting at the earliest.

I hope you will understand my situation and grant me leave for half day. I will come back to the office post lunch.

Thanking you,

Yours sincerely,

Dear Sir,
I would like to request leave for first half (April 15, 2017)

Thank you very much for your consideration of this matter.

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