Readings: Winter Chapter 6 Binary Systems Readings: Winter Chapter 6

Types of Relationships Solid Solution Ab-An Fo-Fa Eutectic Di-An Reaction relation Fo-Q

Makaopuhi Lava Lake Magma samples recovered from various depths beneath solid crust From Wright and Okamura, (1977) USGS Prof. Paper, 1004.

Makaopuhi Lava Lake Thermocouple attached to sampler to determine temperature Olivine decreases Color of glass changes- change composition From Wright and Okamura, (1977) USGS Prof. Paper, 1004.

Temperature of sample vs. Percent Glass Makaopuhi Lava Lake Temperature of sample vs. Percent Glass 100 90 70 60 50 40 30 20 10 Percent Glass 900 950 1000 1050 1100 1150 1200 1250 Temperature oc 80 > 200 oC range for liquid -> solid Fig. 6-1. From Wright and Okamura, (1977) USGS Prof. Paper, 1004.

Crystallization Behavior of Melts Melts crystallize over a range of temperatures Several minerals crystallize together The number of minerals increases as T decreases The minerals form in sequence with overlap

Melt/Liquid Crystallization Minerals in solid solution change composition as cooling progresses The melt composition also changes during crystallization The minerals that crystallize depend on T and X of the melt Pressure also affects the types of minerals that form and the sequence 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 for us geologists

Two Component Systems Systems with Complete Solid Solution Plagioclase (Ab-An, NaAlSi3O8 - CaAl2Si2O8) 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 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 phi = ? (1) F = ? = C - phi + 1 = 2 - 1 + 1 = 2

Two Degrees of Freedom Must specify 2 independent intensive variables in order to completely determine the system This is a divariant situation Two intensive variables can vary independently without changing f, the number of phases Intensive variables can be any ones (P, T, X, density, molar G-V-S, etc. as far as the Phase Rule is concerned Geologically, it’s best to choose T and X (P is constant) Thus F = T and X(An)Liq is a good choice Because X(Ab)Liq = 1 - X(An)Liq they are not independent, so may pick either but not both

X Must specify T and or can vary these without liq Must specify T and or can vary these without changing the number of phases Now cool to 1475oC (point b) ... what happens?

X Get new phase joining liquid: first crystals of plagioclase: = 0.87 (point c) X An plag F now = 1

X X X X X X F = 2 - 2 + 1 = 1 (“univariant”) Must specify only one variable from among: T X An liq X Ab liq X An plag X Ab plag (P constant) and are dependent upon T The slope of the solidus and liquidus are the expressions of this relationship X An liq X An plag 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

At 1450oC, liquid d and plagioclase f coexist at equilibrium A continuous reaction of the type: liquidA + solidB = liquidC + solidD 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 ef = 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 to form is i when = 0.60 An plag Final plagioclase to form is i when = 0.60 Now f = 1 so F = 2 - 1 + 1 = 2

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

Remove first melt as it forms Partial Melting: Remove first melt as it forms Melt Xbulk = 0.60 and the 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 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

The Olivine System Fo - Fa (Mg2SiO4 - Fe2SiO4) also a solid-solution series Fig. 6-10. Isobaric T-X phase diagram at atmospheric pressure After Bowen and Shairer (1932), Amer. J. Sci. 5th Ser., 24, 177-213.