Is it obligatory to pay expiation for an oath or a vow made to oneself without uttering it aloud, and then not fulfilling it?

Merely updating one's intention with a vow or an oath does not entail a legal ruling, because the validity of a vow and an oath depends on uttering them verbally. The Prophet, peace and blessings be upon him, said: "Indeed, Allah has forgiven my Ummah for whatever evil thoughts or suggestions occur to their minds, as long as they do not act upon them or speak about them." Therefore, mental existence has no effect, and consideration is given to verbal existence in matters of speech.