Ternary phase diagrams PDF

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Unary phase diagrams Gibbs’ phase rule: f = c − p + 2 = 1 − p + 2 = 3 − p • Thus, p = 1, 2, 3 • Phase diagram is two-dimensional • Coexistence curves coincide in (a) • Coexistence curves joined by horizontal tie lines in (b): coexistence region

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• In panel (a), three-phase equilibrium corresponds to a single point • In panel (b), such a point becomes a set of three points on a specific tie line • In panel (c), the tie lines are no longer horizontal; a three-phase equilibrium corresponds to a tie triangle • Note: any number of phases can exist in a unary system, just not simultaneously!

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Binary phase diagrams • Gibbs’ phase rule: f = c − p + 2 = 2 − p + 2 = 4 − p • Phase diagram is three-dimensional • Simplest structure arises for three thermodynamic potentials • Two-phase coexistence: surfaces • Three-phase coexistence: lines • Four-phase coexistence: points • Quantitative information is obtained from sections, preferably taken at a constant value for a thermodynamic potential

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Isobaric sections have a similar topology as unary phase diagrams (since they have the same number of degrees of freedom):

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Ternary phase diagrams Here, f = 5 − p, and so two variables must be fixed in order to have a two-dimensional representation. Typically, isothermal isobaric sections are used:

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Gibbs triangle Representation (c) turns out to be a useful format, but is often shown in a modified (symmetric) form:

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• Each apex corresponds to a pure system • The sides of the triangle correspond to binary mixtures • A line parallel to a side of the triangle corresponds to a system in which the mole fraction of the component corresponding to the apex facing that side is kept constant

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Example

Light: three-phase coexistence Dark: two-phase coexistence (metastable region)

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Lever rule in tie triangles In phase diagrams in which neither of the axes represents are thermodynamic potential, three-phase regions are represented by tie triangles. The lever rule is now immediately generalized, and the mole fractions of the coexisting phases are as follows:

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fα =

PD AD

PE fβ = BE

PF C fǫ = F...