Does a divorce occur when the husband writes to his wife: "I swear by divorce that if you utter another word, that will be the last conversation between us," intending to prevent a dispute, and then the wife speaks afterward about a different matter?

If your intention in swearing by divorce was not to speak to your wife about a specific problem, and you did not speak about that problem, but rather the conversation was about reproaching you for the oath and so forth, then you have not broken your oath, and no divorce has occurred. Intention is considered in an oath to particularize the general and generalize the specific. The basis of an oath is the intention of the swearer. So, if he intends by his oath something that the wording can bear, his oath turns to that, whether the wording conforms to its apparent meaning or contradicts it.