The nucleation theorem is a general relation between the nucleation work, the nucleus size, and the supersaturation or other thermodynamic parameters of the old phase. The theorem appears in different forms, depending not only on the chosen set of independent variables describing the nucleation work but also on which of these variables is changed while the others are held fixed. This paper gives a rigorous, systematic, and comprehensive presentation of various forms of the nucleation theorem and shows how some of them can be applied to concrete cases of nucleation. Both theoretical and experimental applications of the theorem to nucleation in unary, binary, or ternary phases are considered.
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