What is the expiation for someone who vowed not to have intercourse with his wife for a known period, but then had intercourse with her before that period expired?

A vow to abandon something permissible is not binding according to the majority of scholars because it is not a vow of an act of devotion. Some scholars are of the view that the person who makes a vow to abandon something permissible has the choice between fulfilling it or atoning for it with an expiation similar to an oath (kaffarat yamin). Your performing the expiation of an oath is more cautious. There is no expiation for someone compelled to break a vow if the conditions of compulsion are met.