
Phase Diagrams with More Than Two Components  
Add 3rd dimension: temperature. Add 3rd dimension: temperature

System nephelinealbitesodium silicate

System nephelinesilicadiopside  congruent melting  binary compound

System forsteritesilicaanorthite  binary compound  incongruent melting

System diopsideanorthitealbite

System albiteanorthitediopsideforsterite

See http://platetectonic.narod.ru/petrographyigneouslinks.html
C http://ijolite.geology.uiuc.edu/08SprgClass/geo436/lectures.html
http://ijolite.geology.uiuc.edu/08SprgClass/geo436/436%20lectures/L8Phase4.html
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 nephelinealbitesodium silicate
Components NeAbSs
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 nephelinesilicadiopside  congruent melting  binary compound.
Components NeTrDi: albite forms between Ne and Tr; line joining Ab and Di separates equilateral triangle into 2 separate triangular diagrams.
AbDi represents a thermal divide
C. System forsteritesilicaanorthite  binary compound  incongruent melting
Components FoTrAn
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 diopsideanorthitealbite
Components DiAnAb
DiAn and DiAb sides represent binary eutectic systems  generates cotectic line in ternary diagram
AbAn side is solid solution loop  no minimum.
Thus there is no ternary eutectic. One cotectic line descends continuously from DiAn eutectic temperature to DiAb 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 albiteanorthitediopsideforsterite
Figure represents system as a tetrahedron
FoDiAn and AbFoDi sides are simple ternary eutectics.
AbAnDi and AbAnF 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
