C = 3: Ternary Systems: Example 1: Ternary Eutectic Anorthite Note three binary eutectics No solid solution Ternary eutectic = E As add components, becomes increasingly difficult to dipict. 1-C: P - T diagrams easy 2-C: isobaric T-X, isothermal P-X… 3-C: ?? Still need T or P variable Project? Hard to use as shown E T Forsterite Diopside

An-Ab-Kfsp Ternary - Flattened An-Kfsp Binary Ab-Kfsp Binary An-Ab Binary Nekvasil & Lindsley, 1990; Brown, 1993

Intersection of Liquidus Surfaces Temperature falls from E toward M in Thermal Valley

T - X Projection of Di - An - Fo Figure 7.2. Isobaric diagram illustrating the liquidus temperatures in the Di-An-Fo system at atmospheric pressure (0.1 MPa). After Bowen (1915), A. J. Sci., and Morse (1994), Basalts and Phase Diagrams. Krieger Publishers. X-X diagram with T contours (P constant) Liquidus surface works like topographic map Red lines are ternary cotectic troughs Run from binary eutectics down T to ternary eutectic M Separate fields labeled for liquidus phase in that field

Crystallization Relationships Cool composition a from 2000oC At 2000oC: phi = ? (1 (liquid) F = ? F = C - f + 1 = 3 - 1 + 1 = 3 = T, X(An)Liq, X(Di)Liq, and X(Fo)Liq only 2 of 3 X’s are independent Next cool to 1700oC Intersect liquidus surface What happens??

Pure Fo forms Just as in binary f = ? F = ? a Liquid An An + Liq Di + Liq Di + An a An Pure Fo forms Just as in binary f = ? F = ?

f = 2 (Fo + Liq) F = 3 - 2 + 1 = 2 If on liquidus, need to specify only 2 intensive variables to determine the system T and or and X of pure Fo is fixed X An liq X An liq X Fo liq

Continue to cool; Fo crystallizes and liquid loses Fo component Xliq moves directly away from Fo corner “Liquid line of descent” is a -> b Along this line liquid cools from 1700oC to about 1350oC with a continuous reaction: LiqA -> LiqB + Fo

Lever principle ® relative proportions of liquid & Fo At 1500oC Liq x + Fo = bulk a x/Fo = a-Fo/x-a At any point can use the lever principle to determine the relative proportions of liquid and Fo

Pure diopside joins olivine + liquid What happens next at 1350oC ? Pure diopside joins olivine + liquid phi = 3 F = 3 - 3 + 1 = 1 (univariant at constant P) Xliq = F(T) only Liquid line of descent follows cotectic -> M

New continuous reaction as liquid follows cotectic: Bulk solid extract LiqA ® LiqB + Fo + Di Bulk solid extract Di/Fo in bulk solid extract using lever principle 1400 1300 1500 1274 1270 1392 Diopside Di + Liq M b c Fo + Liq 1387 Bulk solid extract crystallizing from the liquid at any point (T): draw tangent back to the Di-Fo join At 1350oC that is point c Use c and the lever principle to get the Di-Fo ratio crystallizing at that instant (not the total solid mass crystallized)

Liq/total solids = a-m/Liq-a total Di/Fo = m-Fo/Di-m At 1300oC liquid = X Imagine triangular plane X - Di - Fo balanced on bulk a Liq x a Di m Fo Liq/total solids = a-m/Liq-a total Di/Fo = m-Fo/Di-m Total amounts of three phases at any T can be determined by a modified lever principle:

At 1270oC reach M the ternary eutectic anorthite joins liquid + forsterite + diopside phi = 4 F = 3 - 4 + 1 = 0 (invariant) discontinuous reaction: Liq = Di + An + Fo stay at 1270oC until consume liq Below 1270oC have all solid Fo + Di + An phi = 3 F = 3 - 3 + 1 = 1

Partial Melting (remove melt): Try bulk = a First melt at M (1270oC) Stay at M until consume one phase (An) Why An? Only Di and Fo left Jump to Di-Fo binary No further melt until N at 1387oC Stay at N until consume one phase (Di) Only Fo left No further melt until 1890oC

Ternary Peritectic Systems: (at 0.1 MPa) 3 binary systems: Fo-An eutectic An-SiO2 eutectic Fo-SiO2 peritectic Figure 7.4. Isobaric diagram illustrating the cotectic and peritectic curves in the system forsterite-anorthite-silica at 0.1 MPa. After Anderson (1915) A. J. Sci., and Irvine (1975) CIW Yearb. 74. Shown without liquidus contours to reduce clutter Binary peritectic behavior extends into the ternary system c = ternary peritectic d = ternary eutectic Liquid immiscibility extends slightly into ternary, then becomes miscible Final mineral assemblage determined by sub-triangle (Fo-En-An) or (En-An-Qtz)

Begin with composition a Fo crystallizes first phi = 2 F = 3 - 2 + 1 = 2 Xliq -> b as cool En now forms and F = 1 Xliq then follows peritectic curve toward c

Fo En Forsterite + Liq Enstatite + Liq a b y x As Xliq follows peritectic can get bulk solid extract at any T by tangent method example at point x the tangent -> y as bulk solid We know Fo, En, and Liq are the three phases since y = solids, it must be comprised of Fo and En but y falls outside the Fo-En join y = En + (-Fo) the reaction must be: Liq + Fo -> En which is a peritectic continuous reaction If y fell between En and Fo it would be L = En + Fo 1890

Xliq -> g where An joins En + Liq As before get continuous reaction Liq = An + En Xliq -> d where Tridymite also forms Again stay at d with discontinuous reaction: Liq = An + En + S until last liq gone Since e lies in the triangle En - An - SiO2, that is the final mineral assemblage

Other areas are relatively simple Liq h Fo first and Xliq ® i An joins and Xliq ® c F = 0 and stay at c until liquid consumed never leave c You pick others?

4 - Component Diagrams Add Fo to Ab - An - Di Plag - Diopside cotectic curve becomes a surface As do Di - An - Fo cotectics Surfaces meet in 4-C univariant curves, which meet in 4-C invariant points. Cannot visualize depth in diagram (is point y in the Di-An-Fo face, the Di-Ab-Fo face, or between?) Reaching the point where lose the advantage of model systems Figure 7.12. The system diopside-anorthite-albite-forsterite. After Yoder and Tilley (1962). J. Petrol.

> 4 Components May as well melt real rocks On right is a P-T diagram for the melting of a Snake River basalt. Each curve represents the loss of a phase as heat system. - Compare to simpler systems Note pressure effects Ol - Plag - Cpx at low P Garnet at high P (eclogite) Figure 7.13. Pressure-temperature phase diagram for the melting of a Snake River (Idaho, USA) tholeiitic basalt under anhydrous conditions. After Thompson (1972). Carnegie Inst. Wash Yb. 71