Does a divorce occur with the statement, "After four months, if you do not bring me your graduation certificate, I will send the divorce paper," and when does it occur, or is an expiation for breaking an oath required?

Your statement to your wife: "If you do not bring me the graduation certificate after four months, I will send the divorce paper" is merely a promise of divorce, and fulfilling it is not recommended. You are not obligated to divorce now or in the future, whether she brings the certificate or not, unless you fulfill the promise and divorce her. We advise you to stay away from uttering words of divorce.