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Phase Rule and Binary Phase Diagram
Transcript of Phase Rule and Binary Phase Diagram
Mgo 0.05*50% MgO = 2.5% 5% Olivine 8% Augite 0.08*14% MgO
= 1.1% = Daughter Basalt = (10-2.5-1.1)/.87 = 7.33% MgO Solidus:
Solid only below, liquid + solid below Components:
Minimum number of chemically distinct species needed to describe system Liquidus:
In P-T space, represents maximum solubility of solid in liquid
Liquid only above, solid + liquid below Eutectic:
Mixture of phases with lowest possible melting point for those components.
Refers both to the Eutectic Composition and to the Eutectic Temperature. F = c - p + 2
Closed system at equilibrium Phase rule of j. willard gibbs F =
Variance or degrees of freedom
Equals number of intensive variables needed to constrain system (T, P, or composition X) c = Components p = Phases 2 = Temperature and Pressures Condensed phase rule =
isobaric or isothermal F = c - p + 1 (P or T fixed) c = 1; p = 1
F = 1 - 1 + 2 = 2 Unary systems
= 1 component T and P both can vary,
Divariant c = 1; p = 2
F = 1 - 2 + 2 = 1 T or P can vary
Univariant c = 1; p =3
F = 1 - 3 + 2 = 0 T and P both fixed
Invariant Olivine (Forsterite-Fayalite) BINARY SOLID SOLUTIONS ISOPLETH = Constant Composition PROPORTIONS Calculated from LEVER RULE Plagioclase (Anorthite-Albite) COMPOSITIONS read DIRECTLY off the BOTTOM scale on Diagram (%An) Equilibrium Crystallization:
Final Plagioclase = Bulk Composition Fractional Crystallization:
Liquid and Plagioclase both evolve to compositions more sodic (Na-rich) than bulk composition of system. % crystals = (100 * ab)/ac (cc) photo by medhead on Flickr % liq = (100 * bc)/ac Diopside-Anorthite system (A = Diopside, B = Anorthite) SIMPLE BINARY EUTECTIC WITH NO Solid Solution Compositions from bottom of diagram
%A or %B (Both Crystals and Liquid) PROPORTIONS FROM LEVER RULE: % xtls = (100 * a)/(a+b)% liquid = (100 * b)/(a+b) Equilibrium crystallization = Fractional crystallization >> Liquid Follows Continuous Path >> Crystal Compositions “Jump” But Equilibrium melting NOT = Fractional melting Equilibrium melting:
>> Liquid, Crystals Follows Continuous Path Fractional melting:
>> Crystals Follows Continuous Path
>> Liquid Compositions “Jump” Example: System Forsterite-SiO2 (A=Forsterite, B=SiO2, AB=Enstatite) PERITECTIC SYSTEMS R = Reaction Point or “Peritectic” Phase Rule at Peritectic: F= 2-3+1= 0 Invariant EQUILIBRIUM CRYSTALLIZATION: BC X : Ol+L, Ol+En+L (at Peritectic), Stop at Peritectic (Final= Ol+En) BC Y : Ol+L, Ol+En+L (at Peritectic), En+L, En+SiO2 (at Eutectic) How do we know which final assemblage? >> If Bulk Comp to Left of AB, Final Assemblage Must = A + AB.
>> If Bulk Comp to Right of AB, Final Assemblage Must = AB + B. FRACTIONAL CRYSTALLIZATION: BOTH BC X & BC Y: OL+L --> EN+L (at Peritectic) --> En+SiO2+L (Eutectic) WHY ?? NO olivine to react with liquid during fractional crystallization. System:
Isolated part of Universe
Open to energy exchange
(usually) Closed to matter exchange