A deduction of the multicriticality conditions of mixtures from the Gibbs tangent plane criterion

•We report a systematic deduction of the multicriticality conditions of mixture.•The deduction uses the Gibbs tangent plane criterion for phase stability analysis.•The proof is based on the principle of mathematical induction, being valid for any order.

Here, we follow a classification proposed by Griffiths and Widom [1], where the order of a multicritical point in a mixture is equal to the number of phases which simultaneously become identical, considering m phases and assuming that m − 1 of these phases become identical to a given test phase. Thus, employing Rolle's theorem and basic properties of the so-called tangent-plane distance function, we develop a deduction of the multicriticality conditions of mixture from Gibbs tangent plane criterion, which relies on the principle of mathematical induction, being appropriate for any m ≥ 2.