1. Phase Equilibria in Silicate Systems Intro. Petrol. EPSC-212, Francis-13

2. Fundamentals: Units Types of units commonly used: Weight units: = gms species/ 100gms (X-Ray analytical techniques determine weight fraction element) Molar Units: = gms species / (molecular wt. of species), normalized to 100 (most chemical phenomena are proportional to molecular proportions) Atomic units: = (no. moles species) x (no. atoms per species), normalized to 100 atoms Cation units: = (no. moles species) x (no. cations per species), typically normalized to some total number of cations (or anions). Oxygen units: = (no. moles species) x (no. oxygens per species), commonly normalized to some total number of anions (closest to volume proportions) Example: Coordinates of Enstatite (MgSiO 3 ) in: Mg 2 SiO 4 - SiO 2 space Weight units: 70 30 Molecular units: 50 50 Cations units: 75 25 Oxygen units 66.7 33.3 Winter, J.D.; 2001: An Introduction to Igneous and Metamorphic Petrology. Prentice Hall, Chapter 5-7, 2001.

3. F Degrees of Freedom = C omponents - P hases + 2 The Mineralogical Phase Rule In any chemical system at equilibrium, the following relationship holds: F equals the minimum number of variables that must be specified in order to completely define the state of a system. F is thus the variance of the system, the number of unknowns. C equals the number of independent chemical components needed to define the composition of the system. P equals the number of physical phases present in the system, which include the number of solid minerals, plus liquid and gas phases, if present. 2 represents the variables pressure and temperature.

4. Single Component Systems: SiO 2 When a solid consist of 2 coexisting minerals (phases): F = C – P + 2 = 1 - 2 + 2 = 1 Such a system is invariant at any given pressure, and thus a single component solid phase will melt at 1 unique temperature at any specified pressure. The boundary between the 2 phases in P - T space will be a univariant line with a slope approximated by: d  G = -  SdT +  VdP = 0 dP/dT =  S/  V This is also true for solid - liquid phase boundaries because, to a first approximation,  H o and  S o are constant for small changes in temperature (true for all reactions not involving a relatively compressible vapour phase).

5. Two Component Systems: Mg 2 SiO 4 – SiO 2 Pure forsterite melts at 2163 o C at 1 atm. If extra SiO 2 is added to the system, SiO 2 will be present only in the melt phase, while forsterite will remain a pure phase. The temperature at which forsterite crystallizes is now an inverse function of SiO 2 content: at equilibrium: G FoOl = G FoLiq and  G Fo = 0 G o Fo + R × T × Ln(a FoOl ) = G o FoLiq + R × T × Ln(a FoLiq )  G o Fo = - R × T × Ln(a FoLiq /a FoOl ) or  G o Fo = - R × T × Ln(1-XSiO 2 ), a FoOl = 1.0, assume activity (a) = mole fraction X) and  G o Fo =  H o Fo – T ×  S o Fo =  H o Fo – T ×  H o Fo / T Fo If  Ho and  So are insensitive to small changes in T & P, then:  H o Fo – T ×  H o Fo / T Fo = - R × T × Ln(1-XSiO 2 ) or Ln(1-XSiO 2 ) =  H o Fo / R × (T - T Fo ) / (T×T Fo ) van't Hoff equation for melting point depression

6. Binary Phase Diagrams No solid-solution Between end-members If a system is comprised of 2 components, then where a solid and liquid phase coexist: F = 2 - 2 + 2 = 2 Such a system is univariant at any given pressure, and thus the melting point of a solid will depend on the proportions of the two components. In the absence of extensive solid solution, the presence of an additional component will reduce the melting temperature of single component solid phases because the additional component typically dissolves preferentially in the liquid phase. The Eutectic point “e” of a two component system is invariant (F = 0, if pressure fixed) and is defined by the intersection of two univariant (F = 1) liquidus curves, originating from the melting temperatures of the two pure end-member phases. e Two Component Systems:

7. Peritectic versus Eutectic Invariant points p - oliv + liq opx e - liq opx + qtz e 2 - liq neph + albite e 1 - liq albite + qtz e1e1 e2e2

8. The Lever Rule T 1 : Forst / Enst : d / a; Forst / whole = d /(a+d) T 2 : Forst / liquid : c / a; Forst / whole = c /(a+c) T 3 : Forst / liquid : b / a; Forst / whole = b /(a+b) X For bulk Composition X

9. Liquids vs Cumulates Fractional Crystallization vs Partial Melting Upon cooling to 1557 o C, early crystallized olivine exhibits a reaction relationship with the residual liquid of composition “p” to form orthopyroxene. Either olivine or melt must disappear before cooling can continue. During partial melting, orthopyroxene begins to melt incongruently at 1557 o C to form olivine plus a liquid of composition “p”. Orthopyroxene must be consumed before the temperature can increase. Equilibrium vs Fractional Cumulate Rocks versus Rocks that represent liquids 1557

10. The presence of other components in solid solution at levels that are insufficient to stabilize a separate phase destroys the invariant nature of melting. The temperature and composition of the first melt are determined by the amount of the additional component. During partial melting, these additional components are typically the first to be refined out into the melt.

11. Bianary Systems with extensive Solid Solution: Olivine exhibits complete solid solution between the forsterite (Mg 2 SiO 4 ) and fayalite (Fe 2 SiO 4 ) end-members. In Fe and Mg bearing systems, neither the olivine solid nor the olivine liquid are pure end-member components: We now have two van't Hoff equations: Ln(X FoLiq / X FoOl ) =  H o Fo / R × (T - T Fo ) / (T × T Fo ) Ln(X FaLiq / X FaOl ) =  H o Fa /R × (T - T Fa ) /(T × T Fa ) Because: X FaLig = 1-X FoLiq and X FaOl = 1-X FoOl Then: Ln(X FoLiq / X FoOl ) =  H o Fo / R × (T - T Fo ) / (T × T Fo ) Ln(1-X FoLiq / (1-X FoOl )) =  H o Fa /R × (T - T Fa ) / (T × T Fa ) The choice of any T between T Fo and T Fa will enable the calculation of the compositions of the coexisting olivine and liquid for that T, and thus the solidus and liquidus at any T. Exactly analogous solid solution relationships can be developed for the plagioclase series feldspars: anorthite CaAl 2 Si 2 O 8 - albite NaAlSi 3 O 8

12. P = 1 atm Ternary Systems: Forsterite – Diopside – Anorthite Liquidus Projection In order to portray the magmatic phase relations of systems with more than two chemical components, we need to develop specialized projection schemes. Three component systems can be represented on a two dimensional sheet of paper, if we project only those phase relationships for which a magmatic liquid is present.

13. X P = 1 atm A Liquid of bulk composition X cools to the olivine liquidus surface at 1600°C, at which point Forsterite begins to crystalize The liquid composition moves directly away from Fo, producing a dunite cumulate, until it reaches the cotectic, at which point Diopside begins to crystallize with Forsterite. Ternary Systems: Forsterite – Diopside - Anorthite

14. X P = 1 atm Co-precipitation of Forsterite + Diopside causes liquid composition to move down cotectic curve, producing a wehrlite cumulate. Forsterite – Diopside - Anorthite

15. X P = 1 atm The liquid composition reaches the ternary eutectic at 1270°C, at which point Anorthite begins to crystallize with Diopside and Forsterite, producing a gabbroic cumulate. The composition of the liquid remains at the eutectic point until all the liquid is consumed. Forsterite – Diopside - Anorthite

16. The composition of the first melt of an assemblage ABD is that of invariant eutectic point e ABD, while the composition of the first melt of assemblage DBC is that of invariant eutectic point e DBC. The intersection of a univariant curve with the Alkemade line joining the compositions of the coexisting solid phases defines a thermal maximum along the univariant curve. Ternary Systems

17. with Solid Solution:

18. The invariant point “ p”, at which olivine, clinopyroxene and orthopyroxene coexist with a liquid, is a peritectic point because it lies outside of the compositional volume of the solid phases. It represents the first melt of any assemblage consisting of olivine, opx, and cpx (mantle peridotite) at 1 atm., and is analogous in composition to a quartz-normative basalt. Similarly, the univariant curve along which olivine and orthopyroxene coexist with a liquid is a reaction curve because the tangent to the curve at any point cuts the olivine - orthopyroxene Alkemade line with a negative olivine intercept. The invariant point “ e” is a eutectic and represents the composition of the first melt of an assemblage of quartz- diopside-orthopyroxene. The composition of “ e ” approximates that of the Earth’s continental crust. Oliv - Cpx - Qtz Liquidus Projection:

19. SiO 2 45.2 49.4 60.3 TiO 2 0.7 1.4 1.0 Al 2 O 3 3.5 15.4 15.6 MgO 37.5 7.6 3.9 FeO 8.5 10.1 7.2 CaO 3.1 12.5 5.8 Na 2 O 0.6 2.6 3.2 K 2 O 0.1 0.3 2.5 Total 99.2 99.3 99.5 Cations normalized to 100 cations Si 38.5 46.156.4 Ti 0.5 1.0 0.7 Al 3.6 16.9 17.2 Mg 47.6 10.6 5.4 Fe 6.0 7.9 5.6 Ca 2.8 12.5 5.8 Na 0.9 4.7 5.8 K 0.1 0.5 3.0 O 140.2 153.0 161.3 Mineralogy (oxygen units, XFe 3+ = 0.10) Quartz 0.0 0.0 13.0 Feldspar 13.2 57.3 64.3 Clinopyroxene 6.7 25.7 5.9 Orthopyroxene 18.3 4.1 14.7 Olivine 59.9 9.9 0.0 Oxides 1.8 3.0 2.0 Mantle Ocean Continent crust crust Oceanic crust - MORB basalt e 1 Continental crust - granite e 2

20. Liquidus Projections for haplo-basalts The Basalt Tetrahedron at 1 atm: The olivine - clinopyroxene - plagioclase plane is a thermal divide in the haplo-basalt system at low pressures and separates natural magmas into two fundamentally different magmatic series. Sub-alkaline basaltic magmas with compositions to the Qtz-rich side of the plane fractionate towards Qtz-saturated residual liquids, such as rhyolite. Alkaline basaltic magmas with compositions to the Qtz-poor side of the plane fractionate towards residual liquids saturated in a feldspathoid, such as nepheline phonolite.

21. Since the dominant mineral in the mantle source of basaltic magmas is olivine, we can achieve a further simplification by projecting the liquidus of basaltic systems from the perspective of olivine:

22. Alkaline basaltic lavas are volumetrically insignificant (~1%), but strongly enriched in highly incompatible trace elements profiles compared to sub-alkaline lavas, and low in HREE, Y, & Sc. These characteristics are generally ascribed to small degrees of partial melting at elevated pressures, leaving garnet as a phase in the refractory residue. Alkaline basalts fall to the Foid-side of the olivine- clinopyroxene-plagioclase plane (1 atm thermal divide) and fractionate to foid-saturated residual liquids. Sub-alkaline basalts fall to the Quartz-side and fractionate towards quartz-saturated residual liquids.

23. The Effect of Pressure Increasing pressure shifts the oliv- cpx-opx peritectic point towards less Si-rich compositions. At approximately 10 kbs this invariant point moves into the oliv - cpx- opx compositional volume, and the first melt of the mantle has an olivine basalt composition. The invariant point is still a peritectic point, however, because of the extensive solid solution of cpx towards opx. At pressures exceeding 15-20 kbs, this invariant point moves outside the simple olivine - cpx - qtz system, into the Neph-normative volume of the basalt tetrahedron. The first melt of mantle peridotite is an alkaline olivine basalt at these high pressures. 1 atm

24. Since the dominant mineral in the mantle source of basaltic magmas is olivine, we can achieve a further simplification by projecting the liquidus of basaltic systems from the perspective of olivine: Movement of the invariant point determining the composition of the first melt with increasing pressure.