Phase Diagrams with More Than Two Components 

Add 3rd dimension: temperature. Add 3rd dimension: temperature

System nepheline-albite-sodium silicate

System nepheline-silica-diopside - congruent melting - binary compound

System forsterite-silica-anorthite - binary compound - incongruent melting

System diopside-anorthite-albite

System albite-anorthite-diopside-forsterite


I. Ternary systems: 3 components

A. Representation by an equilateral triangle

-Vertex A = 100% A, 0% B and C

-A ranges from 0% along BC to 100% at A

-Any point on AB = mixture of A and B, no C

-Any point in the interior of the triangle = mixture of all 3

-Note: this holds even if the triangle is not equilateral.

B. Lever rule applies

-Along side BC, A=0: let X be along side BC. Then %B = XC/BC ; %C = BX/BC

-If A is added, ratio B and C doesn''t change => composition lies along line XA

-At Y along XA, composition is: %A = XY/XA; %(B+C) = YA/XA (but B/C = XC/BX, so %B = (XC/BC)*(YA/XA)/%C = (BX/BC)*(YA/XA)

-Diagram this out on paper to confirm!

C. Add 3rd dimension: temperature

-Simplest ternary diagram: each side represents a binary eutectic system: liquidus lines become surfaces ; eutectic points become cotectic lines; a ternary eutectic forms where the 3 liquidus surfaces intersect; arrows show direction of decreasing temperature

II. Ternary systems without solid solution

A. System nepheline-albite-sodium silicate

-Components Ne-Ab-Ss

-Binary eutectics along each side => 3 cotectic lines.

-Adding the 3rd component to each side lowers the temperature below the binary eutectic. 3 cotectic lines intersect at ternary eutectic point = lowest melting temperature

B. System nepheline-silica-diopside - congruent melting - binary compound.

-Components Ne-Tr-Di: albite forms between Ne and Tr; line joining Ab and Di separates equilateral triangle into 2 separate triangular diagrams.

-Ab-Di represents a thermal divide

C. System forsterite-silica-anorthite - binary compound - incongruent melting

-Components Fo-Tr-An

-Recall enstatite melts incongruently to Fo + liquid

-Peritectic point in binary diagram becomes a reaction curve in ternary: in 3D diagram, cotectic lines ~ valleys; reaction curve ~ inflection point (change in slope)

III. Ternary systems with solid solution

A. One or more sides represent solid solution binary systems (no binary eutectic)

B. System diopside-anorthite-albite

-Components Di-An-Ab

-Di-An and Di-Ab sides represent binary eutectic systems - generates cotectic line in ternary diagram

-Ab-An side is solid solution loop - no minimum.

-Thus there is no ternary eutectic. One cotectic line descends continuously from Di-An eutectic temperature to Di-Ab eutectic temperature.

-At any point along cotectic, Di crystallizes along with plagioclase of intermediate composition.
IV. Quaternary systems

A. Models real systems very well, but graphical representation becomes difficult (4D)

B. System albite-anorthite-diopside-forsterite

-Figure represents system as a tetrahedron

-Fo-Di-An and Ab-Fo-Di sides are simple ternary eutectics.

-Ab-An-Di and Ab-An-F o sides have no eutectic because of solid solution between Ab and An.

-Note: since 3 dimensions represent 4 components, T and P can''t be shown. Tetrahedral diagrams are isobaric and isothermal

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