Tricritical point: Difference between revisions

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In condensed matter physics, dealing with the macroscopic physical properties of matter, a tricritical point is a point in the phase diagram of a system at which three-phase coexistence terminates^[1]. This definition is clearly parallel to the definition of an ordinary critical point as the point at which two-phase coexistence terminates.

A line of three-phase coexistence is termed a triple point for a one-component system, since, from Gibbs' phase rule, this condition is only achieved for a single point in the phase diagram (F=2-3+1=0). For tricritical points to be observed, one need a mixture with more components. It can be shown^[2] that three is the minimum number of components for which these points can appear. In this case, one may have a two-dimensional region of three-phase coexistence (F=2-3+3=2) (thus, each point in this region corresponds to a triple point). This region will terminate in two critical lines of phase coexistence; these two critical lines may then terminate at a single tricritical point. This point is therefore "twice critical", since it belong to two critical branches. Indeed, its critical behavior is different from critical points: the critical dimension is lowered so the classical exponents turn out to apply for real systems.

It seems more convenient ^{[citation needed]} experimentally to consider mixtures with four components for which one thermodynamic variable (usually the pressure or the volume) is kept fixed. The situation then reduces to the one described for mixtures of three components.

References

^ B. Widom, Theory of Phase Equilibrium, J. Phys. Chem 1996, 100, 13190-13199
^ ibid.

[1] B. Widom, Theory of Phase Equilibrium, J. Phys. Chem 1996, 100, 13190-13199

[2] ibid.

[1]

[2]

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 A line of three-phase coexistence is termed a [[triple point]] for a one-component system, since, from [[Gibbs' phase rule]], this condition is only achieved for a single point in the phase diagram
-(''F''=2-3+1=0). For tricritical points to be observed, one need a mixture with more components. It can be shown<ref>''ibid''.</ref> that '''three''' is the minimum number of components for which thcoexistence; these two critical lines may then terminate at a single tricritical point. This point is therefore "twice critical", since it belong to two critical branches. Indeed, its [[critical behavior]] is different from critical points: the [[critical dimension]] is lowered so the [[landau theory|classical exponents]] turn out to apply for real systems.
+(''F''=2-3+1=0). For tricritical points to be observed, one need a mixture with more components. It can be shown<ref>''ibid''.</ref> that '''three''' is the minimum number of components for which these points can appear. In this case, one may have a two-dimensional region of three-phase coexistence
+(''F''=2-3+3=2) (thus, each point in this region corresponds to a [[triple point]]). This region will terminate in two critical lines of phase coexistence; these two critical lines may then terminate at a single tricritical point. This point is therefore "twice critical", since it belong to two critical branches. Indeed, its [[critical behavior]] is different from critical points: the [[critical dimension]] is lowered so the [[landau theory|classical exponents]] turn out to apply for real systems.
 It seems more convenient {{Fact|date=April 2009}} experimentally to consider mixtures with four components for which one thermodynamic variable (usually the pressure or the volume) is kept fixed. The situation then reduces to the one described for mixtures of three components.