D:\2009\LectureNotes\Part2PhaseDiagrams.wpdEPSc 352: Lecture Overview for Part 2, Phase Diagrams(( Read chapters 1 and 2 in Ehlers’ Interpretation of Geological Phase Diagrams,which is on reserve (book itself on reserve in the EPSc library; chapters sent toyou as a PDF “EhlersCh1and2".) K Phase Diagrams: Ways of Exploring Compositional Aspects of the Stability ofa SystemConsider: We know 1) there is plenty of Mg, Si, and O available in a particular volume ofmaterial; 2) those three elements are energetically favored to bond together; 3) both forsterite(Mg2SiO4) and enstatite (Mg2Si2O6) are minerals containing those 3 components. So, which ofthose minerals is THE STABLE compound of Mg, Si, O? Can they both be stable; if so, underwhat conditions? If those minerals can be co-stable, are there other Mg, Si, O minerals that canbe stable together with forsterite and enstatite? How do we figure out these answers? Yes,there are some “laws” that govern (limit) what can occur.P + F = C + 2 F = C + 2 - PP = # of phases C = # of components F = # of degrees of freedomP-T diagram for system H2O: 1 component; assemblage can have 1, 2, or 3 phasesGraphical representation: be aware that composition can be recorded as wt. % or mole %Why care about exact mineral compositions?Reflect bulk composition of the parent systemSpecific compositions of coexisting minerals (equilibrium) reflect T and P at which theyformed or last equilibratedFe2+/Mg ratio in coexisting mica and garnetPhase diagrams represent:which mineral(s) form from a certain composition (ratio of elements) held at P, T, etc.what happens if you change the T, P, etc. of a particular mineralwhat happens if you cool a melt of a specific compositionwhat happens if, at a fixed T, you add compositional components to a melthow the melting behavior of one mineral is affected by the presence of other mineralsT-X diagrams: changes in mineral assemblage and mineral chemistry upon cooling of a liquidisopleth: line of constant compositionisotherm: line of constant temperatureDifferent kinds of compounds with respect to melting behavior:fixed composition vs. solid solutioncongruently melting vs. incongruently meltingcompatible vs. incompatible mineral pairs, e.g., Fo + SiO2 = En2K Anorthite-diopside system: both end members are congruently melting andcompatible; system has a eutectic. End product of cooling is individual crystals of diopside and anorthite, in the same wt. %proportions as the original melt.liquidus soliduseutecticfluxing effect of adding one compound to anothersaturation: through decrease in temperature or change in composition (concentration)Lever rule: (concentration of component A in a phase) x (proportion of that phase)Mass balance: what you get out = what you began with (just a re-distribution of the elements among the phases present at each set of conditions)For the cooling liquid of composition C1 (75 wt.% A + 25 wt.% D), here are two examples of howto carry out the mass-balance calculations by application of the phase rule:1) At 1400°C: total length of the tie line is 48mm. Use lever rule to determine % crystals &liquid.31mm/48mm = 0.65 (or 65 wt.%) liquid 17mm/48mm = 0.35 (or 35 wt. %) solid65 wt.% liquid + 35 wt.% solid0.65(62 wt.% A + 38 wt.% D) + 0.35(100 wt.% A)= 40 wt.% A + 25 wt.% D + 35 wt.% A = 75 wt.% A + 25 wt.% D Proper bulk composition 2) At 1270°C: total length of tie line is 72 mm. Using lever rule,31mm/72mm = 0.43 liquid (essentially eutectic liquid) 41mm/72mm = 0.57 solid (anorthite xls) 0.43 (42 wt.% A + 58 wt% D) + 0.57(100 wt.% A)Now, consider removing sufficient heat such that the above mixture of crystals and eutecticliquid fully crystallizes, i.e., such that the existing anorthite crystals remain stable and theeutectic liquid fully crystallizes into a mixture of crystals with a total composition equal to that ofitself.(18 wt.% An xls + 25 wt.% Diop xls) + 57 wt.% An xls = 75 wt.% An xls + 25 wt.% Diop xls From eutectic liquid Original xlsWeb reference on phase diagrams and their petrologic usefulnesshttp://www.brocku.ca/earthsciences/people/gfinn/petrology/phase.htmKeep clicking forward arrow to get more information and examples about phase diagrams;3repeatedly click on back arrow to learn more about geologic processes surroundingmelting and crystallization of silicates; click blue-coded terms in text for more information.K Leucite-Tridymite Binary T-X Phase Diagram: An intermediate compound isstable; it is incongruently meltingDue to incongruently melting intermediate compound, there is a peritectic as well as a eutectic.Because there is a stable, intermediate compound, the two end-member compounds areincompatible.A phase transition is shown for the SiO2 phases – seen as a horizontal phase boundary. Boundary separates two fields that contain different polymorphs of SiO2.Peritectic is a reaction point: some or all of one solid phase is resorbed during peritecticreaction.Geologic implications of such systems: huge decrease in the temperature of initial melting ofeach end-member mineral when the second mineral/component is added; formation of a largetemperature interval over which both crystals and liquid co-exist (possibility of mechanicallyseparating crystals from liquid: density segregation, tectonic movement).Fractionation can occur in such a system: separating the liquid/melt from the crystals with whichit is in equilibrium. Can drive the remaining melt to form a solid assemblage that would not bestable from equilibrium crystallization of the original melt.--Read summary of this diagram by Channon Visscher. Note the level of detail in hisdiscussion. This is the level of detail expected of you for questions on homework set #3.K Nepheline-Tridymite Binary T-X Phase Diagram: Intermediate, congruentlymelting compound is stable. Due to intermediate, congruently melting compound, there are two eutectics.Can view this whole binary as the piecing together of two binaries with eutectics.See temperature-shifts in solidus between two parts of diagram. The difference in temperaturebetween the solidi reflects the different eutectics (between different pairs of phases).Two pairs of polymorphs.Look at melting, as well as crystallization, behavior.(( Begin working on Homework Set #3 (phase diagrams). Refer to chapters 14and 2 in the Ehlers’ book (required reading). An additional excellent section onphase