Is expiation obligatory upon one who swore by the Qur'an to marry a girl, but her family refused, and she married another man? And what is its amount?

Whoever swears by Allah, or by one of His attributes, or by the Holy Quran, and then breaks their oath, must offer expiation. If there was no intention (for each individual to swear separately) when the oath was taken, then each person owes an expiation for an oath, due to the breaking of the oath by failing to fulfill what was sworn upon, such as the family preventing marriage. The expiation is to feed ten poor people, or clothe them, or free a slave. If one cannot find these, then they must fast for three days, as Allah Almighty says: "So its expiation is the feeding of ten poor people from the average of that which you feed your [own] families or clothing them or freeing a slave. But whoever finds not [the means] - then a fast of three days. That is the expiation for oaths when you have sworn. And guard your oaths. Thus does Allah make clear to you His verses that you may be grateful." (Al-Ma'idah:89). It must be noted that it is not permissible for a Muslim man to establish a friendship with a woman who is a stranger to him, as it is a gateway to evil and temptation.