Geol 2312 Igneous and Metamorphic Petrology Lecture 6 Phase Diagrams for One- and Two-Component Systems February 4, 2009

Makaopuhi Lava Lake, Hawaii Watching a Magma Crystallize TEMPERATURE TIME From Wright and Okamura, (1977) USGS Prof. Paper, 1004.

Makaopuhi Lava Lake, Hawaii 1250 1200 1150 1100 1050 1000 950 0 10 20 30 40 0 10 10 20 30 40 Liquidus Melt Crust Solidus Olivine Clinopyroxene Plagioclase Opaque 100 90 70 60 50 40 30 20 10 Percent Glass 900 950 1000 1050 1100 1150 1200 1250 Temperature oc 80 Winter (2001), Figs. 6-1 & 6-2. From Wright and Okamura (1977) USGS Prof. Paper, 1004.

Makaopuhi Lava Lake, Hawaii Compositional Changes in Solid Solution Minerals 100 Olivine Augite Plagioclase 90 80 Weight % Glass 70 60 50 .9 .8 .7 .9 .8 .7 .6 80 70 60 Mg / (Mg + Fe) Mg / (Mg + Fe) An Winter (2001), Fig. 6-3. From Wright and Okamura, (1977) USGS Prof. Paper, 1004.

Crystallization Behavior of Magmas from natural and experimental observations and thermodymanic predictions Cooling melts crystallize from a liquid to a solid over a range of temperatures (and pressures) Several minerals crystallize over this T range, and the number of minerals increases as T decreases The minerals that form do so sequentially, generally with considerable overlap Minerals that involve solid solution change composition as cooling progresses The melt composition also changes during crystallization The minerals that crystallize (as well as the sequence) depend on T and X of the melt Pressure can affect the temperature range at which a melt crystallizes and the types of minerals that form The nature and pressure of volatiles can also affect the temperature range of xtallization and the mineral sequence

Why do Magmas Crystallize This Way? Predicted by Phase Diagrams Although magmas (melts + crystals) are some of the most complex systems in nature, we can evaluate how they form and crystallize by simplifying them into their basic chemical constituent parts and empirically determine (observe) how these simple systems react to geologically important variables – temperature and pressure. We portray this behavior through the construction of PHASE DIAGRAMS

Phase Diagrams Terminology PHASE of a System A physically distinct part of a system that may be mechanically separated from other distinct parts. (e.g., in a glass of ice water (the system), ice and water are two phases mechanically distinct phases) COMPONENTS of a System The minimum number of chemical constituents that are necessary to define the complete composition of a system (e.g. for the plagioclase system, components are NaAlSi3O8 – albite and CaAl2Si2O8 - anorthite) VARIABLES that define the STATE of a System Extensive – dependent on the quantity of the system – volume, mass, moles, ... Intensive – properties of the phases of a system that are independent of quantities (temperature, pressure, density, molecular proportions, elemental ratios, ...) Note that ratios of extensive variables become intensive (V/m = density, V/moles=molar volume)

F = C - f + 2 Gibbs Phase Rule F = # degrees of freedom The number of intensive parameters that must be specified in order to completely determine the system, or the number of variables that can be changed independently and still maintain equilibrium 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 = Two intensive parameters Usually = temperature and pressure ONLY APPLIES TO SYSTEMS IN CHEMICAL EQUILIBRIUM!!

PHASE RULE IN A ONE-COMPONENT SYSTEM SiO2 F = C - f + 2 Divariant Field F = 1 – 1 + 2 = 2 Univariant Line F = 1 – 2 + 2 = 1 Invariant Point F = 1 – 3 + 2 = 0

PHASE RULE IN A ONE-COMPONENT SYSTEM H2O Fluid PHASE RULE IN A ONE-COMPONENT SYSTEM H2O Note that HEAT is different than TEMPERATURE. A boiling pot of water must be continuously heated to completely turn to steam, all the while sitting at 100oC This heat is called the latent heat of vaporization The heat require to turn solid into liquid is the latent heat of fusion Sublimation

Two-Component System with Solid Solution compare X and T at a constant P System – Plagioclase Phases – Liquid and Plagioclase mineral Components – Ab (NaAlSi3O8) An (CaAl2Si2O8) coupled substitution! An content = An / (Ab + An) F = C - f + 1 (only 1 variable since P is constant) Divariant Field F = 2 – 1 + 1 = 2 Univariant Field F = 2 – 2 + 1 = 1 Phase Relationships determined by Experimental Data

Two-Component System with Solid Solution Equilibrium Crystallization a – Starting bulk composition of melt = An60 b – Beginning of crystallization T= 1475oC c – Composition of first plagioclase to crystallize = An87

Two-Component System with Solid Solution Equilibrium Crystallization a – Starting bulk composition of melt = An60 b – Beginning of crystallization T= 1475oC c – Composition of first plagioclase to crystallize at 1475oC = An87 d – Melt composition at 1450oC = An48 e – Bulk composition of Magma (Melt + Crystals = An60) f – Composition of Plagioclase at 1450oC = An81

Two-Component System with Solid Solution Equilibrium Crystallization Using the Lever Rule to determine Crystal:Melt Ratio %Plag %Melt %Melt 40% 60%

Two-Component System with Solid Solution Equilibrium Crystallization a – Starting bulk composition of melt = An60 b – Beginning of crystallization T= 1475oC c – Composition of first plagioclase to crystallize at 1475oC = An87 d – Melt composition at 1450oC = An48 e – Bulk composition of Magma (Melt + Crystals = An60) f – Composition of Plagioclase at 1450oC = An81 g – Last melt composition at 1340oC = An18 h – Final composition of plagioclase at 1450oC = An60 i – Subsolidus cooling of plagioclase

Two-Component System with Solid Solution Fractional Crystallization As crystals form, they are removed (fractionated) from the system and thus are not allowed to reequilibrate with the cooling melt. This has the effect of incrementally resetting the bulk composition of the liquid to a lower An content with each crystallization step. Consequently, the final melt may have a composition of An0 (pure Ab end member)

Two-Component System with Solid Solution Fractional Crystallization Because of coupled substitution of Ca-Na and Al-Si in plagioclase, reequilibration is difficult with T decrease, leading to chemically zoned crystals like this one. Avg. An=60 uts.cc.utexas.edu/~rmr/CLweb/volcanic.htm

Two-Component System with Solid Solution Olivine Sonju Lake Intrusion Fayalite Fe2SiO4 Fosterite Fe2SiO4