Chapter 6: The Phase Rule and One and Two-Component Systems aka Phase Equilibria
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1 Chapter 6: The Phase Rule and One and Two-Component Systems aka Phase Equilibria
2 Makaopuhi Lava Lake Magma samples recovered from various depths beneath solid crust From Wright and Okamura, (1977) USGS Prof. Paper, 1004.
3 Makaopuhi Lava Lake Thermocouple attached to sampler to determine temperature From Wright and Okamura, (1977) USGS Prof. Paper, 1004.
4 Temperature of sample vs. Percent Glass 1250 Makaopuhi Lava Lake Temperature o c Percent Glass Fig From Wright and Okamura, (1977) USGS Prof. Paper, 1004.
5 Makaopuhi Lava Lake Minerals that form during crystallization Olivine Clinopyroxene Plagioclase Opaque Liquidus olivine decreases below 1175 o C Temperature o C Melt Crust 1000 Solidus Fig From Wright and Okamura, (1977) USGS Prof. Paper, 1004.
6 Makaopuhi Lava Lake Mineral composition during crystallization 100 Olivine Augite Plagioclase 90 Weight % Glass Mg / (Mg + Fe) Mg / (Mg + Fe) An Fig From Wright and Okamura, (1977) USGS Prof. Paper, 1004.
7 Crystallization Behavior of Melts 1. Cooling melts crystallize from a liquid to a solid over a range of temperatures (and pressures)
8 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 generally increases as T decreases
9 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. Minerals that form do so sequentially, with considerable overlap
10 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. Minerals that form do so sequentially, with considerable overlap 4. Minerals that involve solid solution change composition as cooling progresses
11 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 consideral overlap 4. Minerals that involve solid solution change composition as cooling progresses 5. The melt composition also changes during crystallization
12 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 consideral 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
13 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 consideral 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
14 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 consideral 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 composition (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
15 Phase equilibrium and Gibbs Phase Rule Capable of analyzing systems in a way that allows us to grasp the dynamics of each and to account for the contribution of each chemical constituent to the variations Understand how the introduction of additional constituents affects a system helps us better comprehend new systems and more complex systems in nature
16 The Gibbs Phase Rule F = # degrees of freedom F = C - φ + 2 The number of independently intensive parameters that must be specified in order to completely determine the system at equilibrium conditions Consist of properties of the substances that compose a system (e.g., mineral assemblage) Examples: Pressure, Temperature, density, molar volume
17 F = # degrees of freedom F = C - φ + 2 The number of intensive parameters that must be specified in order to completely determine the system φ = # of phases The Phase Rule phases are mechanically separable constituents
18 F = # degrees of freedom F = C - φ + 2 The number of intensive parameters that must be specified in order to completely determine the system φ = # of phases The Phase Rule phases are mechanically separable constituents C = minimum # of components (chemical constituents that must be specified in order to define all phases)
19 F = # degrees of freedom The Phase Rule F = C - φ + 2 The number of intensive parameters that must be specified in order to completely determine the system φ = # 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
20 High Pressure Experimental Furnace Cross section: sample in red 800 Ton Ram the sample! Carbide Pressure Vessle SAMPLE Graphite Furnace 1 cm Furnace Assembly Fig After Boyd and England (1960), J. Geophys. Res., 65, AGU
21 1 - C Systems 1. The system SiO 2 Fig After Swamy and Saxena (1994), J. Geophys. Res., 99, 11,787-11,794. AGU
22 1 - C Systems 2. The system H 2 O Fig After Bridgman (1911) Proc. Amer. Acad. Arts and Sci., 5, ; (1936) J. Chem. Phys., 3, ; (1937) J. Chem. Phys., 5,
23 2 - C Systems A. Systems with Complete Solid Solution 1. Plagioclase (Ab-An, NaAlSi 3 O 8 - CaAl 2 Si 2 O 8 ) Fig Isobaric T-X phase diagram at atmospheric pressure. After Bowen (1913) Amer. J. Sci., 35,
24 Bulk composition a = An 60 = 60 g An + 40 g Ab X An = 60/(60+40) = 0.60
25 F = 2 1. Must specify 2 independent intensive variables in order to completely determine the system = a divariant situation same as: 2. Can vary 2 intensive variables independently without changing φ, the number of phases
26 Get new phase joining liquid: Must specify T and X liq An or can vary these without Now cool to 1475 o plag first crystals of plagioclase: C (point X b) = what (point happens? c) changing the number An of phases F =?
27 Considering an isobarically cooling magma, liq X An plag X An and are dependent upon T F = = 1 ( univariant ) Must specify only one variable from among: liq liq plag plag T (P constant) X An X Ab X An X Ab The slope of the solidus and liquidus are the expressions of this relationship
28 At 1450 o C, liquid d and plagioclase f coexist at equilibrium A continuous reaction of the type: liquid B + solid C = liquid D + solid F
29 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 liquidus d de e ef f solidus
30 When X plag h, then X plag = X bulk and, according to the lever principle, the amount of liquid 0 Thus g is the composition of the last liquid to crystallize at 1340 o C for bulk X = 0.60
31 Final plagioclase to form is i when = 0.60 Now φ = 1 so F = = 2 plag X An
32 Note the following: 1. The melt crystallized over a T range of 135 o C * 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
33 Equilibrium melting is exactly the opposite Heat An 60 and the first melt is g at An 20 and 1340 o C Continue heating: both melt and plagioclase change X Last plagioclase to melt is c (An 87 ) at 1475 o C
34 Fractional crystallization: Remove crystals as they form so they can t undergo a continuous reaction with the melt At any T X bulk = X liq due to the removal of the crystals
35 Partial Melting: Remove first melt as forms Melt X bulk = 0.60 first liquid = g remove and cool bulk = g final plagioclase = i
36 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 Liquid 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 plus Plagioclase
37 2. The Olivine System Fo - Fa (Mg 2 SiO 4 - Fe 2 SiO 4 ) also a solid-solution series Fig Isobaric T-X phase diagram at atmospheric pressure After Bowen and Shairer (1932), Amer. J. Sci. 5th Ser., 24,
38 2-C Eutectic Systems Example: Diopside - Anorthite No solid solution Fig Isobaric T-X phase diagram at atmospheric pressure. After Bowen (1915), Amer. J. Sci. 40,
39 Cool composition a: bulk composition = An 70
40 Cool to 1455 o C (point b)
41 Continue cooling as X liq varies along the liquidus Continuous reaction: liq A anorthite + liq B
42 at 1274 o C φ = 3 so F = = 0 invariant (P) T and the composition of all phases is fixed Must remain at 1274 o C as a discontinuous reaction proceeds until a phase is lost
43 Discontinuous Reaction: all at a single T Use geometry to determine
44 Left of the eutectic get a similar situation
45 #s are listed points in text Note the following: 1. The melt crystallizes over a T range up to ~280 o C 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
46 Augite forms before plagioclase Gabbro of the Stillwater Complex, Montana This forms on the left side of the eutectic
47 Plagioclase forms before augite Ophitic texture Diabase dike This forms on the right side of the eutectic
48 Also note: The last melt to crystallize in any binary eutectic mixture is the eutectic 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
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