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Lecture 6 Phase Equilibria II

# Lecture 6 Phase Equilibria II - x Liquid Phase Equilibria...

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Unformatted text preview: x Liquid Phase Equilibria II Forsterite + liquid Silica mineral + liquid 1557 GEOL 320 -- Petrology Enstatite+ liquid 1543 Enstatite + silica mineral Forsterite + Enstatite Two Component Systems A. Systems with Complete Solid Solution 1. Plagioclase Albite (Ab), NaAlSi3O8 to Anorthite (An) CaAl2Si2O8 CRYSTALLIZATION Fig. 6-8. Isobaric T-X phase diagram at atmospheric pressure. After Bowen (1913) Amer. J. Sci., 35, 577-599. Starting Composition of the Melt Bulk composition a = An60 = 60 g An + 40 g Ab XAn = 60/(60+40) = 0.60 F = 2 -- Φ + 1 F =c 1 + 1 2 What are the minimum # of What are the number of components (c)? phases? So the degrees of freedom (F) = 2. CRYSTALLIZATION F =2 Must specify 2 independent variables in order to completely determine the system (divariant situation) Can vary 2 intensive variables independently without changing the number of phases CRYSTALLIZATION Must specify T and X liq An Melt cools to 1475˚C . . . What happens (point b)? A new phase joins the liquid. Ca-rich plagioclase An87 F=? CRYSTALLIZATION b c F = 2 - 2 + 1 = 1 (“univariant”) Must specify only one variable from among: plag liq liq plag T X An X Ab X An X Ab (P constant) Considering an isobarically cooling magma, liq X An X plag An and are dependent upon T The slope of the solidus and liquidus are the expressions of this relationship CRYSTALLIZATION At 1450oC, liquid d and plagioclase f coexist at equilibrium b c d A continuous reaction of the type: liquidb + solidc = liquidD + solidF CRYSTALLIZATION e f The lever principle: Amount of liquid Amount of solid ef = de where d = the liquid composition, f = the solid composition and e = the bulk composition d f e ∆ liquidus de ef solidus CRYSTALLIZATION When Xplag → h, then Xplag = Xbulk and, according to the lever principle, the amount of liquid → 0 Thus g is the composition of the last liquid to crystallize at 1340oC for bulk X = 0.60 CRYSTALLIZATION plag plag Final plagioclase to form is i when X An = 0.60 Now Φ = 1 so F = 2 - 1 + 1 = 2 CRYSTALLIZATION Note the following: 1. The melt crystallized over a T range of 135oC * 2. The composition of the liquid changed from b to g 3. The composition of the solid changed from c to h Numbers refer to the “behavior of melts” observations *The actual temperatures and the range depend on the bulk composition What type of texture(s) might we see? CRYSTALLIZATION Equilibrium melting is exactly the opposite Heat An60 and the first melt is g at An20 and 1340oC Continue heating: both melt and plagioclase change X Last plagioclase to melt is c (An87) at 1475oC q q q MELTING Fractional Crystallization Remove crystals as they form so they can’t undergo a continuous reaction with the melt At any T, Xbulk = Xliq due to the removal of the crystals CRYSTALLIZATION Partial Melting Remove first melt as it forms Melt Xbulk = 0.60 first liquid = g remove and cool bulk = g → final plagioclase = i MELTING Note the difference between the two types of fields . . . The blue fields are one phase fields Liquid Any point in these fields represents a true phase composition Plagioclase plus The blank field is a two phase field Any point in this field represents a bulk composition composed of two phases at the edge of the blue fields and connected by a horizontal tie-line Liquid Plagioclase 2-C Eutectic Systems Ex: Diopside – Anorthite (no solid solution) CRYSTALLIZATION Eutectic system – system consisting of 2 or more solid phases and a liquid whose composition can be expressed in terms of positive quantities of the solid phases, all coexisting at the min. melting T of the assemblage of solids Fig. 6-11. Isobaric T-X phase diagram at atmospheric pressure. After Bowen (1915), Amer. J. Sci. 40, 161-185. Starting Melt Composition Starting composition a: bulk composition = An70 F = c –Φ +1 2 –1 So we can specify T or liq liq XAn or XDi CRYSTALLIZATION Crystallization of solid (An100) Cool to 1455 C (point b) o CRYSTALLIZATION Liquid of composition b (An70 – Di30) q Continue cooling as Xliq varies along the liquidus q Continuous reaction: liquidA → anorthite + liquidB CRYSTALLIZATION at 1274oC f = 3 so F = 2 - 3 + 1 = 0 invariant 3 (P) T and the composition of all phases is fixed 3 Must remain at 1274oC as a discontinuous reaction proceeds until a phase is lost At the eutectic: Ratio of 3 co-existing diopside to anorthite: 58/42 phases CRYSTALLIZATION Discontinuous Reaction: all at a single T 3 Liquid = diopside + anorthite When all any bulk composition that’sanot a pure1 = 1 For composition of the rock is 58/42 + The final of the liquid is consumed, F = 2 – 2mixture endmember,so T final be lowered. the can and anorthite of diopside liquid to crystallize must always be at the eutectic composition and temperature. CRYSTALLIZATION Left of the eutectic get a similar situation CRYSTALLIZATION Note the following: 1. The melt crystallizes over a T range up to ~280oC 2. A sequence of minerals forms over this interval - And the number of minerals increases as T drops 6. The minerals that crystallize depend upon T - The sequence changes with the bulk composition #s are listed points in the previous lecture CRYSTALLIZATION Augite forms before plagioclase Gabbro of the Stillwater Complex, Montana This forms on the left side of the eutectic CRYSTALLIZATION Plagioclase forms before augite Ophitic texture Diabase dike This forms on the right side of the eutectic CRYSTALLIZATION Equilibrium Melting Equilibrium melting is the opposite of equilibrium crystallization • Thus the first melt of any mixture of Di and An must be the eutectic composition as well MELTING Fractional Crystallization Final rock composition will match the path or In systems w/o solid solution, neither the eutectic the compositions of the final solids or melt is affected. CRYSTALLIZATION Fig. 6-11. Isobaric T-X phase diagram at atmospheric pressure. After Bowen (1915), Amer. J. Sci. 40, 161-185. Partial Melting • • • • first melt to form of composition d, melt removed one of the solid phases consumed by melting becomes a one-component system comp. and T of melt would “jump” discontinuously from d to pure Di or An depending on initial bulk composition Binary Peritectic Systems How many components are in this system? Two: Mg2SiO4 and SiO2 Mg2SiO4 + SiO2 → 2MgSiO3 If together, oliv and qtz would react to form opx, so Mg-rich oliv and qtz don’t co-exist in equilibrium Figure 6-12. Isobaric T-X phase diagram of the system FoSilica at 0.1 MPa. After Bowen and Anderson (1914) and Grieg (1927). Amer. J. Sci. Binary Peritectic Systems On the right side of the eutectic and away from the 2liquid field, we can treat the system as a eutectic system Liquid → SiO2 + 2MgSiO3 Figure 6-12. Isobaric T-X phase diagram of the system Fo-Silica at 0.1 MPa. After Bowen and Anderson (1914) and Grieg (1927). Amer. J. Sci. Binary Peritectic Systems Figure 6-12. Isobaric T-X phase diagram of the system Fo-Silica at 0.1 MPa. After Bowen and Anderson (1914) and Grieg (1927). Amer. J. Sci. i = “peritectic” point 1557oC have colinear Fo-En-liq 3 geometry indicates a reaction: Fo + liq = En 3 consumes olivine (and liquid) → resorbed textures When is the reaction finished? 1557 im k d Fo Bulk X En c y x i m k 1557 1543 d c bulk X Fo En Cr Incongruent Melting of Enstatite Melt of En does not → melt of same composition 3 Rather En → Fo + Liq i at the peritectic 3 Partial Melting of Fo + En (harzburgite) mantle En + Fo also → firsl liq = i 3 Remove i and cool 3 Result = ? 3 i 1557 d 1543 c bulk X Fo En Cr Immiscible Liquids Cool X = n q At 1960oC hit solvus exsolution → 2 liquids o and p φ=2 F=1 both liquids follow solvus At 1695oC get Crst also Reaction? 1695 Mafic-rich liquid Crst Silica-rich liquid D. Solid Solution with Eutectic: Ab-Or (the alkali feldspars) Eutectic liquidus minimum Figure 6-16. T-X phase diagram of the system albiteorthoclase at 0.2 GPa H2O pressure. After Bowen and Tuttle (1950). J. Geology. Effect of PH O on Ab-Or 2 Figure 6-17. The Albite-K-feldspar system at various H2O pressures. (a) and (b) after Bowen and Tuttle (1950), J. Geol, (c) after Morse (1970) J. Petrol. ...
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