Are these two sentences correct? Do they sound natrular?
I set the timer for 10 minutes. When it had expired the alarm set off.

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'the alarm went off'. Apart from that, and your typo of 'natural', they are fine.

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Thank you! So , there is no need of using past perfect.

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I would say "I set the timer for 10 minutes, and when it expired, the alarm went off."

As they are though, "had expired" sounds a little odd, especially for just colloquial speech.  You'd also need a comma following "expired," as it's the end of a clause.

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