Is expiation for an oath obligatory when swearing by divorce and by what is unlawful?

The majority of scholars hold that a conditional divorce oath takes effect. If a person breaks their oath of divorce regarding not accessing the internet, the divorce takes effect according to the majority. However, Sheikh al-Islam Ibn Taymiyyah is of the opinion that an expiation for a broken oath (kaffarat yamin) is required if the intention was not to divorce. As for conditioning the prohibition on accessing the internet again, it depends on the intention: if the intention was divorce, it becomes a second divorce; if the intention was ẓihār (a form of injurious divorce by likening one's wife to an unmarriageable relative), it is ẓihār, and its expiation is obligatory before having intercourse with the wife; and if the intention was an oath by Allah or if there was no specific intention, an expiation for a broken oath is required. This prohibition is binding if the wife is still under the husband's marital authority. If the prohibition occurs after the idda (waiting period) has expired, it is null and void, unless the intention was ẓihār, in which case it transforms into ẓihār.