What is the shape factor f() = (2 + cos)(1 cos)²/4, also known as geometry factor, what it depends on, and what is its meaning?

a) It participates in the expression for nucleation rate. The shape factor depends on , the wetting angle between the melt and the solid in contact. Complete wetting indicates continued growth on the already nucleated solid, i.e. no nucleation barrier (the same chemical composition). Partial wetting happens between the melt and the heterogeneous solid (foreign solid with the chemical composition different from the melt). Higher wetting angle indicates better wetting, which increases the nucleation rate by lowering the nucleation energy. Particles that are not wet by the melt do not contribute to increased nucleation rate by heterogeneous nucleation.

b) It participates in the expression for nucleation rate, and depends on , the wetting angle between the melt and the solid in contact. The shape factor depends on , the wetting angle between the melt and the solid in contact. The higher value of f(), the higher nucleation rate.

c) It participates in the expression for nucleation rate, and depends on , the wetting angle between the melt and the solid in contact. The shape factor depends on , the wetting angle between the melt and the solid in contact. No wetting indicated homogeneous nucleation, which has the maximum nucleation rate.

d) It describes real geometry with geometric correction factor , and correlates experimental and theoretical values of the nucleation rate.

e) This factor does not exist.

According to a similar posting of this question, answer choice (b) is not correct as the cross-posting of that question has been downvoted for that answer choice.