Phase Equilibria

Olivine and Clinopyroxene (Augite) follow Bowen’s Reaction Series, Discontinuous Side. Olivine appears first, then decreases as pyroxenes start. Olivine becomes embayed. Note also that, in this case, plagioclases start at cooler temperatures than pyroxenes. Olivine and Clinopyroxene (Augite) follow Bowen’s Reaction Series, Discontinuous Side. Olivine appears first, then decreases as pyroxenes start. Olivine becomes embayed. Note also that, in this case, plagioclases start at cooler temperatures than pyroxenes.

Mineral Stability Phase Stability The stability of a phase is determined by the Gibbs free energy, G. A Mineral of constant composition is considered a solid phase Mineral stability is commonly portrayed on a Phase Diagram

Components and Phases Components are the chemical entities necessary to define all the potential phases in a system of interest Here one Component, Al2SiO5 Phases: number of mineral species plus fluids Here three Phases: Kyanite, Sillimanite, and Andalucite And

Degrees of Freedom f by Examples p + f = c + 2 If T and P can change without changing the mineral assemblage, the system has two degrees of freedom f = 2 If neither T or P can change without changing the mineral assemblage, the system has zero degrees of freedom f = 0 If T and P must change together to maintain the same mineral, the system has one degree of freedom f = 1 The number of things you can change before everything is determined Sill. Ky. On a phase diagram f=0 corresponds to a point, f = 1 to a reaction line, f = 2 to a 1 phase area. And.

The Phase Rule The number of minerals (phases) that may stably coexist is limited by the number of chemical components p + f = c + 2 OR f = c – p +2 where P is the number of mineral phases, c the number of chemical components, and f is the number of degrees of freedom.

Simple System: H20 In a one component system, for example H2O, phase changes occur at constant temperature until one phase is used up. We can use this, for example, to measure the true temperature of crystallization, seen here as the level 2, where liquid water turns to ice. Note: Temperature versus Time plot, Pressure = 0.1 MPa (1 bar, atmospheric pressure)

Crystallization Behavior of Melts 1. Cooling melts crystallize from a liquid to a solid over a range of temperatures (and pressures) 2. Several minerals crystallize over this T range, and the number of minerals increases as T decreases 3. The minerals that form do so sequentially, with considerable overlap 4. Minerals that involve solid solution change composition as cooling progresses 5. The melt composition also changes during crystallization 6. The minerals that crystallize (as well as the sequence) depend on T and X of the melt 7. Pressure can affect the types of minerals that form and the sequence 8. The nature and pressure of the volatiles can also affect the minerals and their sequence

The Phase Rule F = C - f + 2 F = # degrees of freedom f = # of phases The number of intensive parameters that must be specified in order to completely determine the system f = # of phases phases are mechanically separable constituents C = minimum # of components (chemical constituents that must be specified in order to define all phases) 2 = 2 intensive parameters Usually = temperature and pressure, or temperature and composition, for geologists

Here is an internally heated pressure vessel at the AMNH With these you can study, for example: 1. the temperature and pressure conditions at which polymorphs change from one form to another. 2. The reactions of minerals with fluids (for example salty or alkaline water) at high temperatures and pressures. Dangerous, why? 3. The conditions necessary to change one assemblage of minerals to another Called BOMBS http://research.amnh.org/earthplan/research/Equipment/Petrology

High Pressure Experimental Furnace Cross section: sample in red Carbide Pressure Vessle 1 cm Furnace Assembly Talc SAMPLE Graphite Furnace 800 Ton Ram the sample! Fig. 6-5. After Boyd and England (1960), J. Geophys. Res., 65, 741-748. AGU

1 - Component Systems 1. The system SiO2 Fig. 6-6. After Swamy and Saxena (1994), J. Geophys. Res., 99, 11,787-11,794. AGU

1 - C Systems 2. The system H2O Fig. 6-7. After Bridgman (1911) Proc. Amer. Acad. Arts and Sci., 5, 441-513; (1936) J. Chem. Phys., 3, 597-605; (1937) J. Chem. Phys., 5, 964-966.

2 - C Systems A. Systems with Complete Solid Solution 1. Plagioclase 2 components (Ab-An, i.e. NaSiAlSi2O8 - CaAlAlSi2O8) A solid solution is a mixture of one or more solutes in a solvent, where the crystal structure of the solvent remains unchanged by addition of the solutes. Typically the solutes are metal ions of similar ionic radii and having the same charge. Fig. 6-8. Isobaric T-X phase diagram at atmospheric pressure. After Bowen (1913) Amer. J. Sci., 35, 577-599. T - X diagram at constant P = 0.1 MPa F = C - phi + 1 since Pressure is constant: lose 1 degree of Freedom T - X diagram at constant P = 0.1 MPa F = C - phi + 1 since P is constant: lose 1 F

Bulk composition a = An60 Point a: at 1560oC = 60 g An + 40 g Ab XAn = 60/(60+40) = 0.60 Example of cooling with a specific bulk composition Point a: at 1560oC Phases = 1 (liquid, X= An60) 2 components An and Ab Fixed pressure so Deg F = C – phases + 1 F = 2 - 1 + 1 = 2 Example of cooling with a specific bulk composition Point a: at 1560oC phi = ? (1) F = ? = C - phi + 1 = 2 - 1 + 1 = 2

X X At b –c: F = 2 - 2 + 1 = 1 (“univariant”) Must specify only one variable from among: T X An liq Ab plag (P constant) When the temperature drops to b, about 1475C, crystals of plagioclase form at composition c, about 87%An 2 Components An and Ab 2 phases liquid and solid a “tie-line” connects coexisting phases b and c Considering an isobarically cooling magma, (constant pressure) and are dependent upon T X An liq plag liquidus solidus a “tie-line” connects coexisting phases b and c As long as have two phases coexisting at equilibrium, specifying any one intensive variable is sufficient to determine the system The slope of the solidus and liquidus are the expressions of this relationship

At 1450oC, liquid d and plagioclase f coexist at equilibrium As the system cools, Xliq follows the liquidus and Xsolid follows the solidus, in accordance with F = 1 At any T, X(An)Liq and X(An)Plag are dependent upon T We can use the lever principle to determine the proportions of liquid and solid at any T As cool, Xliq follows the liquidus and Xsolid follows the solidus, in accordance with F = 1 At any T, X(An)Liq and X(An)Plag are dependent upon T We can use the lever principle to determine the proportions of liquid and solid at any T

The lever principle: = D Amount of liquid Amount of solid We can use the lever principle to determine the proportions of liquid and solid at any T The lever principle: The bulk composition is the pivot. Amount of liquid ef = Notice these are reversed Solid distance det. Liq. amt. Amount of solid de where d = the liquid composition, f = the solid composition and e = the bulk composition d e f D liquidus de ef solidus

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

X Final plagioclase (solid) to form is i when = 0.60 An pla g Final plagioclase (solid) to form is i when = 0.60 Now phases f = 1 (all solid) so deg F = 2 - 1 + 1 = 2

1. The melt crystallized over a T range of 135oC * Note the following: 1. The melt crystallized over a T range of 135oC * 4. The composition of the liquid changed from b to g 5. 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

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

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 Thus liquid and solid continue to follow liquidus and solidus toward low-T (Albite) end of the system Get quite different final liquid (and hence mineral) composition Thus liquid and solid continue to follow liquidus and solidus toward low-T (albite) end of the system Get quite different final liquid (and hence mineral) composition

Remove first melt as forms Melt Xbulk = 0.60 first liquid = g Partial Melting: Remove first melt as forms Melt Xbulk = 0.60 first liquid = g remove and cool bulk = g ® final plagioclase = i Fractional crystallization and partial melting are important processes in that they can cause significant changes in the final rock that crystallizes beginning with the same source. Fractional crystallization and partial melting are important processes in that they can cause significant changes in the final rock that crystallizes beginning with the same source rock.

Note the difference between the two types of fields The blue fields are one phase fields Any point in these fields represents a true phase composition 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 Plagioclase Liquid plus

2. The Olivine System Fo - Fa (Mg2SiO4 - Fe2SiO4) Is also a solid-solution series Mg+2 to Fe+2 Fig. 6-10. Isobaric T-X phase diagram at atmospheric pressure After Bowen and Shairer (1932), Amer. J. Sci. 5th Ser., 24, 177-213. Are Mg+2 and Fe+2 about the same size? Early Olivines react with the melt much more than early Ca++ Plagioclases. Why?

2-Comp. Eutectic Systems Example: Diopside - Anorthite No solid solution Diopside is a pyroxene MgCaSi2O6 Fig. 6-11. Isobaric T-X phase diagram at atmospheric pressure. After Bowen (1915), Amer. J. Sci. 40, 161-185.

Good choice is T and X(An)Liq Cool composition a: bulk composition = An70 At a: phi = phases = 1 (all liquid) F = C - phi + 1 = 2 - 1 + 1 = 2 Good choice for axes is T and X(An)Liq At a: phi = 1 F = C - phi + 1 = 2 - 1 + 1 = 2 Good choice is T and X(An)Liq

What happens at b? Pure anorthite forms (point c) phi = 2 Cool to 1455oC (point b) What happens at b? Pure Anorthite forms (point c) phi = 2 liquid at b plus solid An at c F = 2 - 2 + 1 = 1 composition of all phases determined by T Xliq is really the only compositional variable in this particular system What happens at b? Pure anorthite forms (point c) phi = 2 F = 2 - 2 + 1 = 1 composition of all phases determined by T Xliq is really the only compositional variable in this particular system

Continue cooling as Xliq varies along the liquidus Continuous reaction: liqa ® anorthite + liqb Lever rule shows less liquid and more anorthite as cooling progresses Lever rule shows less liquid and more Anorthite as cooling progresses

so F = 2 - 3 + 1 = 0 invariant At d, 1274oC f = 3: Di, An, Liquid Pressure, Temp., and the composition of all phases is fixed Must remain at 1274oC until a phase is lost What happens at 1274oC? get new phase Pure diopside g joins liquid d and anorthite h d is called the eutectic point: MUST reach it in all cases

Discontinuous Reaction: at d all at a single T d between g and h, so reaction must be: Liquid = Diopside + Anorthite must run right toward low entropy of solids therefore first phase lost is liquid Below 1274oC have pure Diopside + pure Anorthite phi = 2 and F = 2 - 2 + 1 = 1 Only logical variable in this case is T (since the composition of both solids is fixed) d between g and h, so reaction must be: diopside + anorthite = liquid must run right -> left as cool (toward low entropy) therefore first phase lost is liquid Below 1274oC have diopside + anorthite phi = 2 and F = 2 - 2 + 1 = 1 Only logical variable in this case is T (since the composition of both solids is fixed)

Left of the eutectic get a similar situation Cool An20 1350oC (e) and diopside forms first at f Continue cooling: continuous reaction with F = 1 as liqA -> liqB + diopside At 1274oC anorthite (h) joins diopside (g) + liquid (d) Stay at 1274oC until liquid consumed by discontinuous reaction: liquid -> diopside + anorthite

1. The melt crystallizes over a T range up to ~280oC 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 text

Pyroxene forms before plagioclase Gabbro of the Stillwater Complex, Montana This forms on the left side of the eutectic

Plagioclase forms before Pyroxene Ophitic texture Diabase dike This forms on the right side of the eutectic

Also note: The last melt to crystallize in any binary eutectic mixture is the eutectic composition The final rock composition for no solid solution is the bulk composition

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

Fractional crystallization: If fractional crystallization is efficient, and earlier xtals are removed, the last layer to crystallize will be the eutectic composition, because the last liquid composition is the eutectic composition Since solids are not reactants in eutectic-type continuous reactions, the liquid path is not changed Only the final rock will differ: = eutectic X, and not bulk X Fig. 6-11. Isobaric T-X phase diagram at atmospheric pressure. After Bowen (1915), Amer. J. Sci. 40, 161-185.

Partial Melting: if remove liquid perfectly as soon as it forms: if remove liquid perfectly as soon as it forms (must be rare) First melts of Di + An would be eutectic liquid composition d at 1274oC consume either Di or An first depending on bulk X The melting solid would be either pure Di or An dep on bulk X After one solid consumed, the Temp would rise, with no further melting,until the melting point of the remainiing solid. New melt temp and composition would jump from 1274oC f to either 1392o for pure Diopside or to 1553 for pure Anorthite. Thus heat 118oC or 279oC before next melt if remove liquid perfectly as soon as it forms: melt Di + An to 1274oC discontinuous reaction: Di + An -> eutectic liquid d consume either Di or An first depending on bulk X then melting solid = pure Di or An and jump to 1- C system Thus heat 118 or 279oC before next melt

Binary Peritectic System Crystallization of a mantle partial melt It is possible to combine Forsterite, a Mg Olivine, with Cristobalite SiO2 to get the intermediate Mg-orthopyroxene Enstatite in the Fo-SiO2 system. Fo + Cr = En Mg2SiO4 +SiO2 = 2MgSiO3 Notice the is an extra inflection point, the Peritectic P There are still only two components, Fo and Cr, but an intermediate phase, Enstatite, forms during cooling at and below 1557oC This is called a Peritectic System

Binary Partial Melt Isopleth (the vertical blue line) a line of constant composition Our original Isopleth (composition) is from the mantle composition field on the left. As the partial melt is cooled, the first Olivine crystals are formed at 1890°C. These crystals are 100% Forsterite and are removed from the system, driving the bulk composition to a more SiO2-rich or continental nature. Forsterite continues to be the only crystals formed until the temperature reaches that of the Peritectic. At the Peritectic, Enstatite begins to crystalize. Between the Peritectic and the Eutectic the crystals forming are 100% Enstatite. At the Eutectic the three phases of Enstatite, melt, and Silica co-exist. The melt continues to cool, resulting in two solid phases, Enstatite and silica.

Binary Partial Melt Isopleth (the vertical blue line) a line of constant composition It shows the original bulk composition Our original Isopleth (composition) is from the mantle composition field on the left. As the partial melt is cooled, the first Olivine crystals are formed at 1890°C. These crystals are 100% Forsterite and are removed from the system, driving the bulk composition to a more SiO2-rich or continental nature. Forsterite continues to be the only crystals formed until the temperature reaches that of the Peritectic. At the Peritectic, Enstatite begins to crystalize. Between the Peritectic and the Eutectic the crystals forming are 100% Enstatite. At the Eutectic the three phases of Enstatite, melt, and Silica co-exist. The melt continues to cool, resulting in two solid phases, Enstatite and silica.

Fractional crystallization of a mantle partial melt Initially only Olivine freezes, settles, & is removed. Bulk composition in liquid becomes more silica-rich. Melt composition (Liquidus) approaches Enstatite as Magnesium ions are removed Our original Isopleth (composition) is from the mantle composition field on the left. As the partial melt is cooled, the first Olivine crystals are formed at 1890°C. These crystals are 100% Forsterite and are removed from the system, driving the bulk composition to a more SiO2-rich or continental nature. Forsterite continues to be the only crystals formed until the temperature reaches that of the Peritectic. At the Peritectic, Enstatite begins to crystalize. Between the Peritectic and the Eutectic the crystals forming are 100% Enstatite. At the Eutectic the three phases of Enstatite, melt, and Silica co-exist. The melt continues to cool, resulting in two solid phases, Enstatite and silica.

Fractional crystallization of a mantle partial melt Peritectic - a low temperature inflection point on the liquidus at which a liquid of specified composition is in equilibrium with two or more crystalline phases. Our original Isopleth (composition) is from the mantle composition field on the left. As the partial melt is cooled, the first Olivine crystals are formed at 1890°C. These crystals are 100% Forsterite and are removed from the system, driving the bulk composition to a more SiO2-rich or continental nature. Forsterite continues to be the only crystals formed until the temperature reaches that of the Peritectic. At the Peritectic, Enstatite begins to crystalize. Between the Peritectic and the Eutectic the crystals forming are 100% Enstatite. At the Eutectic the three phases of Enstatite, melt, and Silica co-exist. The melt continues to cool, resulting in two solid phases, Enstatite and silica. Melt changes composition past En , Temp lowers to Peritectic P, then solids X changes at constant T get Enstatite + Fo +L at the Peritectic temperature

Fractional crystallization of a mantle partial melt Eutectic - the T on a T-X diagram where a mixture of elements of a single chemical composition X solidifies at a lower temperature than any other composition made up of the same ingredients. Our original Isopleth (composition) is from the mantle composition field on the left. As the partial melt is cooled, the first Olivine crystals are formed at 1890°C. These crystals are 100% Forsterite and are removed from the system, driving the bulk composition to a more SiO2-rich or continental nature. Forsterite continues to be the only crystals formed until the temperature reaches that of the Peritectic. At the Peritectic, Enstatite begins to crystalize. Between the Peritectic and the Eutectic the crystals forming are 100% Enstatite. At the Eutectic the three phases of Enstatite, melt, and Silica co-exist. The melt continues to cool, resulting in two solid phases, Enstatite and silica. Between the Peritectic and Eutectic E, the crystals forming are 100% Enstatite

Fractional crystallization of a mantle partial melt At Eutectic, Enstatite and SiO2 crystallize at same time. New composition is much more silica rich. Below Eutectic, solids are Enstatite and Silica. At 100 MPa, the Silica mineral is Cristobalite Our original Isopleth (composition) is from the mantle composition field on the left. As the partial melt is cooled, the first Olivine crystals are formed at 1890°C. These crystals are 100% Forsterite and are removed from the system, driving the bulk composition to a more SiO2-rich or continental nature. Forsterite continues to be the only crystals formed until the temperature reaches that of the Peritectic. At the Peritectic, Enstatite begins to crystalize. Between the Peritectic and the Eutectic the crystals forming are 100% Enstatite. At the Eutectic the three phases of Enstatite, melt, and Silica co-exist. The melt continues to cool, resulting in two solid phases, Enstatite and silica. Mantle Crust

Fractional crystallization of a mantle partial melt Notice what happened, Initially, a partial melt of the mantle made of Forsterite olivine, and below 1557C Forsterite plus the pyroxene Enstatite. This is an upper mantle composition. These early crystals are removed. From the Peritectic 1557C to the Eutectic 1543C and below, the composition shifts to Enstatite plus silica, a crust composition Our original Isopleth (composition) is from the mantle composition field on the left. As the partial melt is cooled, the first Olivine crystals are formed at 1890°C. These crystals are 100% Forsterite and are removed from the system, driving the bulk composition to a more SiO2-rich or continental nature. Forsterite continues to be the only crystals formed until the temperature reaches that of the Peritectic. At the Peritectic, Enstatite begins to crystalize. Between the Peritectic and the Eutectic the crystals forming are 100% Enstatite. At the Eutectic the three phases of Enstatite, melt, and Silica co-exist. The melt continues to cool, resulting in two solid phases, Enstatite and silica. Mantle Crust Fractionation of a Mantle partial melt yields a silica rich crust composition

Fractional crystallization of a mantle partial melt Notice what happened, Initially, a partial melt of the mantle made of Forsterite olivine, and below 1557C Forsterite plus the pyroxene Enstatite. This is an upper mantle composition. These early crystals are removed. From the Peritectic 1557C to the Eutectic 1543C and below, the composition shifts to Enstatite plus silica, a crust composition Our original Isopleth (composition) is from the mantle composition field on the left. As the partial melt is cooled, the first Olivine crystals are formed at 1890°C. These crystals are 100% Forsterite and are removed from the system, driving the bulk composition to a more SiO2-rich or continental nature. Forsterite continues to be the only crystals formed until the temperature reaches that of the Peritectic. At the Peritectic, Enstatite begins to crystalize. Between the Peritectic and the Eutectic the crystals forming are 100% Enstatite. At the Eutectic the three phases of Enstatite, melt, and Silica co-exist. The melt continues to cool, resulting in two solid phases, Enstatite and silica. Mantle Crust Fractionation of a Mantle partial melt yields a silica rich crust composition

Fractional crystallization of a mantle partial melt Original isopleth is mantle composition field. For 100 MPa, as the partial melt is cooled, the first Olivine crystals are formed at 1890°C. These crystals are 100% Forsterite and are removed from the system, driving the bulk composition to a more SiO2-rich or continental nature. Forsterite continues to be the only crystals formed until the temperature reaches that of the Peritectic. At the Peritectic, Enstatite begins to crystallize. Between the Peritectic and the Eutectic the crystals forming are 100% Enstatite. At the Eutectic the three phases of Enstatite, melt, and Silica co-exist. The melt continues to cool, resulting in two solid phases, Enstatite and silica. Our original Isopleth (composition) is from the mantle composition field on the left. As the partial melt is cooled, the first Olivine crystals are formed at 1890°C. These crystals are 100% Forsterite and are removed from the system, driving the bulk composition to a more SiO2-rich or continental nature. Forsterite continues to be the only crystals formed until the temperature reaches that of the Peritectic. At the Peritectic, Enstatite begins to crystalize. Between the Peritectic and the Eutectic the crystals forming are 100% Enstatite. At the Eutectic the three phases of Enstatite, melt, and Silica co-exist. The melt continues to cool, resulting in two solid phases, Enstatite and silica. Mantle Crust Fractionation of a Mantle partial melt yields a silica rich crust composition