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C = 3: Ternary C = 3: Ternary Systems: Systems: Example 1: Ternary Eutectic Example 1: Ternary Eutectic Di - An - Fo Di - An - Fo T M M Anorthite Anorthite Forsterite Forsterite Diopside Diopside Note three binary Note three binary eutectics eutectics No solid solution No solid solution Ternary eutectic Ternary eutectic = M = M

Ch 07 Ternary Phase.ppt

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  • C = 3: Ternary Systems:Example 1: Ternary EutecticDi - An - FoTMAnorthiteForsteriteDiopsideNote three binary eutecticsNo solid solutionTernary eutectic = M

  • T - X Projection of Di - An - FoFigure 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.

  • Crystallization Relationships

  • Pure Fo formsJust as in binaryf = ?F = ?

  • f = 2 (Fo + Liq)F = 3 - 2 + 1 = 2If on liquidus, need to specifyonly 2 intensive variablesto determine the systemT and or and

    X of pure Fo is fixed

  • Lever principle relative proportions of liquid & FoAt 1500oC Liq x + Fo = bulk ax/Fo = a-Fo/x-a

  • New continuous reaction as liquid follows cotectic:LiqA LiqB + Fo + DiBulk solid extractDi/Fo in bulk solid extract using lever principle

  • At 1300oC liquid = XImagine triangular plane X - Di - Fo balanced on bulk aLiq/total solids = a-m/Liq-atotal Di/Fo = m-Fo/Di-maDiLiq xFom

  • Partial Melting (remove melt):

  • Ternary Peritectic Systems:(at 0.1 MPa)

    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. 3 binary systems:Fo-An eutecticAn-SiO2 eutecticFo-SiO2 peritectic

  • 1890

  • Works the same way as the Fo - En - SiO2 binary

  • Diopside-Albite-AnorthiteDi - An EutecticDi - Ab EutecticAb - An solid solutionFigure 7-5. Isobaric diagram illustrating the liquidus temperatures in the system diopside-anorthite-albite at atmospheric pressure (0.1 MPa). After Morse (1994), Basalts and Phase Diagrams. Krieger Publushers

  • Isobaric polythermal projectionFigure 7-5. Isobaric diagram illustrating the liquidus temperatures in the system diopside-anorthite-albite at atmospheric pressure (0.1 MPa). After Morse (1994), Basalts and Phase Diagrams. Krieger Publishers.

  • Note:Binary character is usually maintainedwhen a new component is added Eutectic behavior remains eutectic Peritectic behavior remains peritectic Solid solutions remain so as well

  • ObliqueViewIsothermalSectionFigure 7-8. Oblique view illustrating an isothermal section through the diopside-albite-anorthite system. Figure 7-9. Isothermal section at 1250oC (and 0.1 MPa) in the system Di-An-Ab. Both from Morse (1994), Basalts and Phase Diagrams. Krieger Publishers.

  • Ternary FeldsparsFigure 7-10. After Carmichael et al. (1974), Igneous Petrology. McGraw Hill.

  • Ternary FeldsparsTrace of solvus at three temperature intervals

    Triangle shows coexisting feldspars and liquid at 900oCFigure 7-11. Winter (2001) An Introduction to Igneous and Metamorphic Petrology. Prentice Hall.

  • 4 - Component DiagramsFigure 7-12. The system diopside-anorthite-albite-forsterite. After Yoder and Tilley (1962). J. Petrol.

  • > 4 ComponentsFigure 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

  • olivineCalcic plagioclaseMg pyroxeneMg-Ca pyroxeneamphibolebiotite(Spinel)Temperaturepotash feldspar muscovite quartzalkalic plagioclaseCalci-alkalic plagioclasealkali-calcic plagioclaseBowens Reaction SeriesDiscontinuousSeriesContinuousSeries

  • The Effect of Pressure

  • Eutectic systemFigure 7-16. Effect of lithostatic pressure on the liquidus and eutectic composition in the diopside-anorthite system. 1 GPa data from Presnall et al. (1978). Contr. Min. Pet., 66, 203-220.

  • The Effect of Water on MeltingDry melting: solid liquidAdd water- water enters the melt Reaction becomes: solid + water = liq(aq)Figure 7-19. The effect of H2O saturation on the melting of albite, from the experiments by Burnham and Davis (1974). A J Sci 274, 902-940. The dry melting curve is from Boyd and England (1963). JGR 68, 311-323.

  • Figure 7-20. Experimentally determined melting intervals of gabbro under H2O-free (dry), and H2O-saturated conditions. After Lambert and Wyllie (1972). J. Geol., 80, 693-708.

  • Dry and water-saturated solidi for some common rock typesThe more mafic the rockthe higher the meltingpoint

    All solidi are greatlylowered by water

    Figure 7-21. H2O-saturated (solid) and H2O-free (dashed) solidi (beginning of melting) for granodiorite (Robertson and Wyllie, 1971), gabbro (Lambert and Wyllie, 1972) and peridotite (H2O-saturated: Kushiro et al., 1968; dry: Ito and Kennedy, 1967).

  • We know the behavior of water-free and water-saturatedmelting by experiments, which are easy to control by performing them in dry and wet sealed vessles

    What about real rocks?

    Some may be dry, some saturated, but most are morelikely to be in between these extremes a fixed water content < saturation levels a fixed water activity

  • The Albite-Water SystemRed curves = melting for a fixed mol % water in the melt (Xw)

    Blue curves tell the water content of a water- saturated melt mFigure 7-22. From Burnham and Davis (1974). A J Sci., 274, 902-940.

  • Raise a melt with a ratioof albite:water = 1:1 (Xwater = 0.5)from point a at 925oC and1 GPa pressure, toward the Earths surface under isothermal conditions.meltFigure 7-22. From Burnham and Davis (1974). A J Sci., 274, 902-940.

  • Conclusions:A rising magma witha fixed % water willprogressively melt

    At shallower levels itwill become saturated,and expel water intoits surroundingsFigure 7-22. From Burnham and Davis (1974). A J Sci., 274, 902-940.

  • Another example: isobaric heating of albite with10 mol % water at 0.6 GPa.Figure 7-22. From Burnham and Davis (1974). A J Sci., 274, 902-940.

  • Conclusion:Although the addition of water can drastically reduce the melting point of rocks, the amount of melt produced at the lower temperature may be quite limited, depending on the amount of water available15% 20% 50% 100%Figure 7-22. From Burnham and Davis (1974). A J Sci., 274, 902-940.

  • Melting of Albite with a fixed activity of H2OFluid may be a CO2-H2O mixture with Pf = PTotalFigure 7-23. From Burnham and Davis (1974). A J Sci., 274, 902-940.

  • Melting of Albite with a fixed activity of H2OFluid may be a CO2-H2O mixture with Pf = PTotalFigure 7-26. From Millhollen et al. (1974). J. Geol., 82, 575-587.

  • The solubility of water in a melt depends on the structure ofthe melt (which reflects the structure of the mineralogicalequivalent)Figure 7-25. The effect of H2O on the diopside-anorthite liquidus. Dry and 1 atm from Figure 7-16, PH2O = Ptotal curve for 1 GPa from Yoder (1965). CIW Yb 64.

  • Effect of Pressure, Water, and CO2 on the positionof the eutectic in the basalt systemIncreased pressure moves theternary eutectic (first melt) fromsilica-saturated to highly undersat.alkaline basaltsWater moves the (2 Gpa) eutectictoward higher silica, while CO2 moves it to more alkaline types

    As add components, becomes increasingly difficult to dipict.1-C: P - T diagrams easy2-C: isobaric T-X, isothermal P-X3-C: ??Still need T or P variableProject? Hard to use as shownX-X diagram with T contours (P constant)Liquidus surface works like topographic mapRed lines are ternary cotectic troughsRun from binary eutectics down T to ternary eutectic MSeparate fields labeled for liquidus phase in that field

    Cool composition a from 2000oCAt 2000oC: phi = ? (1 (liquid)F = ? F = C - f + 1 = 3 - 1 + 1 = 3 = T, X(An)Liq, X(Di)Liq, and X(Fo)Liqonly 2 of 3 Xs are independent

    Next cool to 1700oCIntersect liquidus surfaceWhat happens??Continue to cool;Fo crystallizes and liquid loses Fo componentXliq moves directly away from Fo corner Liquid line of descent is a -> bAlong this line liquid cools from 1700oC to about 1350oC with a continuous reaction:LiqA -> LiqB + Fo

    At any point can use the lever principle to determine the relative proportions of liquid and Fo

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

    Bulk solid extract crystallizing from the liquid at any point (T): draw tangent back to the Di-Fo joinAt 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)Total amounts of three phases at any T can be determined by a modified lever principle:

    At 1270oC reach M the ternary eutecticanorthite joins liquid + forsterite + diopsidephi = 4F = 3 - 4 + 1 = 0 (invariant)discontinuous reaction:Liq = Di + An + Fostay at 1270oC until consume liqBelow 1270oC have all solid Fo + Di + Anphi = 3F = 3 - 3 + 1 = 1Similar process with bulk X in any other fieldCool d to 1400oC and anorthite forms firstXliq -> directly away from An and reaches cotectic at point e at 1290oC when forsterite joins An + LiqNow univariant and Xliq followsthe cotectic where Di forms at 1270oC and the last liquid is consumedCan get any sequence of Di-An-Fo depending on bulk X Eutectic is always the last liquid and first meltEquilibrium Melting: the opposite of equilibrium crystallizationFractional crystallization (remove crystals):Same liquid line of descent (since no solid solution)only difference is final rock = M not a

    Try bulk = aFirst melt at M (1270oC)Stay at M until consume one phase (An) Why An?Only Di and Fo leftJump to Di-Fo binaryNo further melt until N at 1387oCStay at N until consume one phase (Di)Only Fo leftNo further melt until 1890oC

    Shown without liquidus contours to reduce clutterBinary peritectic behavior extends into the ternary systemc = ternary peritecticd = ternary eutectic

    Liquid immiscibility extends slightly into ternary, then becomes miscibleFinal mineral assemblage determined by sub-triangle (Fo-En-An) or (En-An-Qtz)Begin with composition aFo crystallizes first phi = 2 F = 3 - 2 + 1 = 2Xliq -> b as coolEn now forms and F = 1Xliq then follows peritectic curve toward c

    As Xliq follows peritectic can get bulk solid extract at any T by tangent methodexample at point x the tangent -> y as bulk solidWe know Fo, En, and Liq are the three phasessince y = solids, it must be comprised of Fo and Enbut y falls outside the Fo-En joiny = En + (-Fo)the reaction must be: Liq + Fo -> En which is a peritectic continuous reactionIf y fell between En and Fo it would be L = En + FoContinue cooling with continuous reaction until Xliq reaches c at 1270oCNow get An + En + Fo + Liqphi = 4 F = 3 - 4 + 1 = 0stay here with discontinuous reaction: Liq + Fo = En + Anuntil Liquid used upSince a plots in the Fo - En - An triangle these must be the final phases

    If the bulk X is between Fo and En the liquid disappears first at theperitectic temperature and Fo + En remain as the final solids

    If, on the other hand, the bulk X lies to the right of En, then Fo is consumed first and the liduid continues to evolve toward the eutectic

    As a variation on this sequence: begin with eFo is first phase to crystallize. As it does so,Xliq -> b where En also formsAs before get continuous reaction Liq + Fo = EnBut, when Xliq reaches f the Xbulk (e) lies directly between En and Xliq

    Whenever Xbulk lies directly between two phases, these two phases alone add to comprise the system: En + f = eThus En and liquid are all it takes, so the olivine must be consumed by the reaction at this pointphi = 2 and F = 3 - 2 + 1 = 2Xliq then leaves the peritectic curve -> En + Liq field (directly away from En)

    Xliq -> g where An joins En + LiqAs before get continuous reaction Liq = An + EnXliq -> d where Tridymite also formsAgain stay at d with discontinuous reaction:Liq = An + En + Suntil last liq goneSince e lies in the triangle En - An - SiO2, that is the final mineral assemblageOther areas are relatively simpleLiq hFo first and Xliq i An joins and Xliq cF = 0 and stay at c until liquid consumednever leave cYou pick others?

    Fractional crystallizationOnly real difference on liq path is in the Fo fieldSince lose Fo, it cant react with the liquid to -> En So cross peritectic curve at b where En begins to crystallize and head straight -> eHere An forms and follow cotectic -> d Tridymite formsFinal rock = d

    Oblique View

    Cotectic trough slopes down continuously from Di - An (1274oC) to Di - Ab (1133oC)Isothermal contours on the liquidus only. None on the solidus (so Xplag indefinite).Cotectic in red.Some tie-lines connecting plagioclase compositions with cotectic liquids shown in greenLets begin by cooling composition a

    Above 1300oC phi = 1 so F = C - phi + 1 = 3 - 1 + 1 = 3At 1300oC diopside forms at the liquidus temperatureF = 3 - 2 + 1 = 2 (liquid is restricted to the liquidus surface)As cool further get continuous reaction liqA -> Di + liqB and Xliq moves directly away from Di

    At 1230oC plagioclase joins diopside and liquid bF = 3 - 3 + 1 = 1So Xliq now restricted to the cotectic curveXplag can now be found from tie-lines (since they apply to cotectic liquids)Xplag = An80

    Xliq follows cotectic as continuous reaction: liqA -> Di + Plag + liqB proceedsAt any point the bulk composition a must be within the triangle Di - Plag - Liq which comprise itWhen Xliq reaches c Xplag reaches An50Now Di-a-Plag are colinearThus c is the last drop of liquid

    Now we cool a liquid of composition dFirst solid to form will be plagioclase BUT, we cannot tell what composition it will bePlag forms at about 1420oCXplag is about An87Must be higher than An75Why?

    Now follow continuous reaction of type: liqA + plagB liqC + plagDPlagioclase follows path at baseLiquid follows curved path (since moves away from a moving plagioclase comp.)At 1230oC liquid reaches e and diopside forms along with cotectic liquid and plag An75 (tie-line works now)

    Continuous reaction: liqA + plagB -> Di + liqC + plagDAs liquid moves e -> f and plag moves -> An65When Xplag An65 then Di - d - plag are colinearThus the last liquid = f

    Figure 7-10. Schematic oblique view of the ternary feldspar system vs. temperatureThe ternary liquidus and solvus surfaces have the hatch patternThe solidus is shadedPurple line e-c is the cotectic minimumThe yellow curve from a to b is the trace of solids that coexist with the cotectic liquidsx-y-z = coexisting plag-Afs-liq at constant TSolvus gets larger as T loweredAdd Fo to Ab - An - DiPlag - Diopside cotectic curve becomes a surfaceAs do Di - An - Fo cotecticsSurfaces 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

    May as well melt real rocksOn 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 effectsOl - Plag - Cpx at low PGarnet at high P (eclogite)

    ~All solid - liquid (melting) reactions have a positive slope

    Increasing pressure (P1 -> P2) thus raises the melting point (T1 -> T2) of a solid

    In a eutectic system increasing pressure will raise the melting point (as predicted)

    The magnitude of the effect will vary for different minerals Anorthite compresses less than DiopsideThus the elevation of the m. p. is less for An than DiThe eutectic thus shifts toward An

    Dry melt reaction: solid -> liquidAdd water- water enters the meltSo the reaction becomes:solid + water = liq(aq)Thus adding water drives the reaction to the right.Liquid is stabilized at the expense of the solid.The result is to lower the melting point.Pressure is required to hold the water in the melt, so increased pressure allows more water to enter the melt and this increases the melting point depression

    Note the difference in the dry melting temperature andthe melting interval of a basalt as compared to the water-saturated equivalentsThe melting pointdepression is quitedramatic

    Especially at lowto intermediatepressures

    Granite is only a crustal rock (not found deeper than 1 GPa)

    Return to a simpler system that we knowGreen curves = dry and water-saturated melting Red curves = melting for a fixed mol % water in the melt (Xw)Blue curves tell the water content of a water-saturated meltNote that any curve for a fixed % water and a curve that is saturated with that same % intersect at the green saturated curve

    At a it is above the water-sat. solidus, so it is at least partially melted.

    If it had 0.52% water it would be completely molten (red curves).With only 50% water it is nearly molten, but not entirely so.When the melt rises to b it does become completely molten (liquidus for 50% water)From b to c the melt becomes progressively more superheatedAt c the melt reaches the point where it is now saturated with 50% water (blue curve) so free water phase releasedFrom c to d the melt is saturated with progressively less waterBetween c and d the water content of the saturated melt will be reduced from 50% to 30% (nearly halved)

    At e it is solid albite.At f it would all melt if it had enough water (65%), but it has only 10% waterThus only 10/65 or 15% will melt.At g it would be completely molten if it were 50% water, but with 10% it will be 10/50 or 20% molten.At h it will be 10/20 or 50% molten and at i it will finally be 100% molten.Melting starts out very slowly, and accelerates near the appropriate liquidus curve (see blue % at top)

    The solubility of water in a melt depends on the structure of the melt (which reflects the structure of the mineralogical equivalent)

    Water dissolves more in polymerized melts (An > Di)

    Thus the melting point depression effect is greater for An than Di

    The eutectic moves toward An

    Left: Effect of pressure on the ternary eutectic (minimum melt composition) in the system Fo-Ne-SiO2 (base of the basalt tetrahedron). From Kushiro (1968). JGR 73, 619-634.Right: Figure 7-27. Effect of volatiles on the ternary eutectic (minimum melt composition) in the system Fo-Ne-SiO2 (base of the basalt tetrahedron) at 2 GPa. Volatile-free from Kushiro (1968) JGR 73, 619-634, H2O-saturated curve from Kushiro (1972), J. Petrol., 13, 311-334, CO2saturated curve from Eggler (1974) CIW Yb 74.