Possessive adjectives are special adjectives or determiners used to express possession of a noun; they precede all other elements in a noun phrase. If you use possessive adjectives, you do not need articles.
My mass spectrometer has a vacuum leak.
[Compare The mass spectrometer has a vacuum leak.] Choose a possessive adjective that agrees in person, number, and gender with the possessor noun, not the noun being possessed.
Dorothy Mary Crowfoot, winner of the 1964 Nobel Prize in Chemistry, was born on May 12, 1910 in Cairo, Egypt. His father had studied ancient history at Oxford University.
[The possessive adjective, his, should agree with the gender of the possessor, Dorothy Crowfoot (feminine), not the possessed noun, father (masculine).]
Dorothy Mary Crowfoot, winner of the 1964 Nobel Prize in Chemistry, was born on May 12, 1910 in Cairo, Egypt. Her father had studied ancient history at Oxford University.