Silikatlar ikili sistem F F = C = C - - f f + 2 + 2 F = # degrees of freedom F = # degrees of freedom The number of The number of intensive intensive parameters that must be specified in parameters that must be specified in order to completely determine the system order to completely determine the system The Phase Rule The Phase RuleF = C F = C - - f f + 2 + 2 F = # degrees of freedom F = # degrees of freedom The number of intensive parameters that must be specified in The number of intensive parameters that must be specified in order to completely determine the system order to completely determine the system f f = # of phases = # of phases phases are phases are mechanically separable mechanically separable constituents constituents The Phase Rule The Phase RuleF = F = C C - - f f + 2 + 2 F = # degrees of freedom F = # degrees of freedom The number of intensive parameters that must be specified in The number of intensive parameters that must be specified in order to completely determine the system order to completely determine the system f f = # of phases = # of phases phases are mechanically separable constituents phases are mechanically separable constituents C = C = minimum # minimum # of of components components (chemical constituents that must (chemical constituents that must be specified in order to define all phases) be specified in order to define all phases) The Phase Rule The Phase RuleThe Phase Rule The Phase Rule F = C F = C - - f f + + 2 2 F = # degrees of freedom F = # degrees of freedom The number of intensive parameters that must be specified in The number of intensive parameters that must be specified in order to completely determine the system order to completely determine the system f f = # of phases = # of phases phases are mechanically separable constituents phases are mechanically separable constituents C = minimum # of components (chemical constituents C = minimum # of components (chemical constituents that must that must be specified in order to define all phases) be specified in order to define all phases) 2 = 2 2 = 2 intensive intensive parameters parameters Usually = Usually = temperature temperature and and pressure pressure for us geologists for us geologists1 1 - - C Systems C Systems 1. The system SiO 1. The system SiO 2 2 Fig. 6-6. After Swamy and Saxena (1994), J. Geophys. Res., 99, 11,787-11,794. AGU1 1 - - C Systems C Systems 2. The system H 2. The system H 2 2 O O 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 2 - - C Systems C Systems 1. 1. Plagioclase Plagioclase (Ab (Ab- -An, NaAlSi An, NaAlSi 3 3 O O 8 8 - - CaAl CaAl 2 2 Si Si 2 2 O O 8 8 ) ) A. Systems with A. Systems with Complete Solid Solution Complete Solid Solution Fig. 6-8. Isobaric T-X phase diagram at atmospheric pressure. After Bowen (1913) Amer. J. Sci., 35, 577-599.Bulk composition Bulk composition a a = An = An 60 60 = 60 g An + 40 g Ab = 60 g An + 40 g Ab X X An An = 60/(60+40) = 0.60 = 60/(60+40) = 0.60Must specify Must specify T T and or can vary these without and or can vary these without changing the number of phases changing the number of phases X X An An liq liqGet Get new phase new phase joining liquid: joining liquid: first crystals of first crystals of plagioclase: plagioclase: = 0.87 (point = 0.87 (point c c) ) F = ? F = ? X X An An plag plagF = 2 F = 2 - - 2 2 + 1 = + 1 = 1 (“univariant”) 1 (“univariant”) Must specify only Must specify only one one variable from among: variable from among: T T X X An An liq liq X X Ab Ab liq liq X X An An plag plag X X Ab Ab plag plag and and are are dependent upon T dependent upon T The The slope slope of the solidus of the solidus and liquidus are the and liquidus are the expressions of this expressions of this relationship relationship X X An An liq liq X X An An plag plag (P constant) (P constant)At 1450 At 1450 o o C, liquid C, liquid d d and plagioclase and plagioclase f f coexist at equilibrium coexist at equilibrium A A continuous reaction continuous reaction of the type: of the type: liquid liquid A A + solid + solid B B = = liquid liquid C C + solid + solid D DWhen X When X plag plag ? ? h h, then X , then X plag plag = X = X bulk bulk and, according to the and, according to the lever principle, the amount of liquid lever principle, the amount of liquid ? ? 0 0 Thus Thus g g is the composition of the last liquid to crystallize at is the composition of the last liquid to crystallize at 1340 1340 o o C for bulk X = 0.60 C for bulk X = 0.60Final plagioclase to form is Final plagioclase to form is i i when = 0.60 when = 0.60 Now Now f f = 1 = 1 so F = 2 so F = 2 - - 1 + 1 = 2 1 + 1 = 2 X X An An plag plagNote the following: Note the following: 1. 1. The melt crystallized over a T range of 135 The melt crystallized over a T range of 135 o o C * C * 4. 4. The composition of the liquid changed from The composition of the liquid changed from b b to to g g 5. 5. The composition of the solid changed from The composition of the solid changed from c c to to h h Numbers refer Numbers refer to the “behavior to the “behavior of melts” observations of melts” observations * The actual temperatures * The actual temperatures and the range depend on the and the range depend on the bulk composition bulk compositionEquilibrium Equilibrium melting melting is exactly the opposite is exactly the opposite ? ? Heat An Heat An 60 60 and the first melt is and the first melt is g at An g at An 20 20 and 1340 and 1340 o o C C ? ? Continue heating: both melt and plagioclase change X Continue heating: both melt and plagioclase change X ? ? Last plagioclase to melt is Last plagioclase to melt is c (An c (An 87 87 ) at 1475 ) at 1475 o o C CFractional crystallization: Fractional crystallization: Remove crystals as they form so they can’t Remove crystals as they form so they can’t undergo a continuous reaction with the melt undergo a continuous reaction with the melt At any T At any T X X bulk bulk = X = X liq liq due to the removal of the crystals due to the removal of the crystalsPartial Melting: Partial Melting: Remove first melt Remove first melt as forms as forms Melt X Melt X bulk bulk = 0.60 first liquid = = 0.60 first liquid = g g remove and cool bulk = g remove and cool bulk = g ? ? final plagioclase = final plagioclase = i iPlagioclase Plagioclase Liquid Liquid Liquid plus Plagioclase Note the difference between the two types of fields Note the difference between the two types of fields The The blue blue fields are fields are one one phase fields phase fields Any point in these fields represents a true Any point in these fields represents a true phase composition phase composition The blank field is a The blank field is a two two phase field phase field Any point in this field Any point in this field represents a bulk represents a bulk composition composed of two phases composition composed of two phases at the at the edge of the blue fields and connected by a edge of the blue fields and connected by a horizontal tie horizontal tie- -line line2. The Olivine System 2. The Olivine System Fo Fo - - Fa Fa (Mg (Mg 2 2 SiO SiO 4 4 - - Fe Fe 2 2 SiO SiO 4 4 ) ) also a solid also a solid- -solution series solution series Fig. 6-10. Isobaric T-X phase diagram at atmospheric pressure After Bowen and Shairer (1932), Amer. J. Sci. 5th Ser., 24, 177-213.2 2- -C Eutectic Systems C Eutectic Systems Example: Diopside Example: Diopside - - Anorthite Anorthite No solid solution No solid solution Fig. 6-11. Isobaric T-X phase diagram at atmospheric pressure. After Bowen (1915), Amer. J. Sci. 40, 161-185.Cool composition Cool composition a a: : bulk composition = bulk composition = An An 70 70Cool to 1455 Cool to 1455 o o C (point C (point b b) )? ? Continue cooling as X Continue cooling as X liq liq varies along the liquidus varies along the liquidus ? ? Continuous reaction Continuous reaction: liq : liq A A ? ? anorthite + liq anorthite + liq B Bat 1274 at 1274 o o C C f f = 3 = 3 so F = 2 so F = 2 - - 3 + 1 = 3 + 1 = 0 invariant 0 invariant ? ? (P) T and the composition of all phases is fixed (P) T and the composition of all phases is fixed ? ? Must remain at 1274 Must remain at 1274 o o C as a C as a discontinuous discontinuous reaction reaction proceeds until a phase is lost proceeds until a phase is lostDiscontinuous Reaction: Discontinuous Reaction: all at a single T all at a single T ? ? Use Use geometry geometry to determine to determineLeft of the eutectic Left of the eutectic get a similar situation get a similar situationNote the following: Note the following: 1. 1. The melt crystallizes over a T range up to ~280 The melt crystallizes over a T range up to ~280 o o C C 2. 2. A sequence of minerals forms over this interval A sequence of minerals forms over this interval - - And the number of minerals increases as T drops And the number of minerals increases as T drops 6. 6. The minerals that crystallize depend upon T The minerals that crystallize depend upon T - - The sequence changes with the bulk composition The sequence changes with the bulk composition #s are listed #s are listed points in text points in textAugite forms before plagioclase Augite forms before plagioclase This forms on the This forms on the left left side of the eutectic side of the eutectic Gabbro of Gabbro of the the Stillwater Stillwater Complex, Complex, Montana MontanaPlagioclase forms before augite Plagioclase forms before augite This forms on the This forms on the right right side of the eutectic side of the eutectic Ophitic Ophitic texture texture Diabase dike Diabase dikeAlso note: Also note: • • The last melt to crystallize in any binary eutectic The last melt to crystallize in any binary eutectic mixture is the mixture is the eutectic eutectic composition composition • • Equilibrium Equilibrium melting melting is the opposite of equilibrium is the opposite of equilibrium crystallization crystallization • • Thus the Thus the first melt first melt of any mixture of Di and An of any mixture of Di and An must be the eutectic composition as well must be the eutectic composition as wellFractional crystallization: Fractional crystallization: Fig. 6-11. Isobaric T-X phase diagram at atmospheric pressure. After Bowen (1915), Amer. J. Sci. 40, 161-185.Partial Melting: Partial Melting:C. Binary Peritectic Systems Three phases enstatite = forsterite + SiO 2 Figure 6-12. Isobaric T-X phase diagram of the system Fo-Silica at 0.1 MPa. After Bowen and Anderson (1914) and Grieg (1927). Amer. J. Sci.C. Binary Peritectic Systems Figure 6-12. Isobaric T-X phase diagram of the system Fo-Silica at 0.1 MPa. After Bowen and Anderson (1914) and Grieg (1927). Amer. J. Sci.Figure 6-12. Isobaric T-X phase diagram of the system Fo-Silica at 0.1 MPa. After Bowen and Anderson (1914) and Grieg (1927). Amer. J. Sci.i i = = “peritectic” “peritectic” point point 1557 1557 o o C have C have colinear colinear Fo Fo- -En En- -liq liq ? ? geometry indicates a reaction: Fo + liq = En geometry indicates a reaction: Fo + liq = En ? ? consumes consumes olivine (and liquid) olivine (and liquid) ? ? resorbed textures resorbed textures When is the reaction finished? When is the reaction finished? c c d d i i k k m m Fo Fo En En 1557 1557 Bulk X1543 1543 c c d d i i k k m m Fo Fo En En 1557 1557 bulk X bulk X x x y y Cr CrIncongruent Melting of Enstatite Incongruent Melting of Enstatite ? ? Melt of En does not Melt of En does not ? ? melt of same composition melt of same composition ? ? Rather Rather En En ? ? Fo + Liq Fo + Liq i i at the peritectic at the peritectic Partial Melting of Fo + En (harzburgite) mantle Partial Melting of Fo + En (harzburgite) mantle ? ? En + Fo also En + Fo also ? ? firsl liq = firsl liq = i i ? ? Remove Remove i i and cool and cool ? ? Result = Result = ? ? 1543 1543 c c d d i i Fo Fo En En 1557 1557 bulk X bulk X Cr CrImmiscible Liquids Cool X = n Cool X = n ? ? At 1960 At 1960 o o C hit C hit solvus solvus exsolution exsolution ? ? 2 liquids 2 liquids o o and and p p f f = 2 F = 1 = 2 F = 1 both liquids follow solvus both liquids follow solvus Mafic Mafic- -rich rich liquid liquid Silica Silica- -rich rich liquid liquid Crst Crst 1695 1695 Reaction? Reaction? At 1695 o C get Crst alsoPressure Effects Different phases have different compressibilities Thus P will change Gibbs Free Energy differentially ? Raises melting point ? Shift eutectic position (and thus X of first melt, etc.) Figure 6-15. The system Fo- SiO 2 at atmospheric pressure and 1.2 GPa. After Bowen and Schairer (1935), Am. J. Sci., Chen and Presnall (1975) Am. Min.D. Solid Solution with Eutectic: Ab-Or (the alkali feldspars) Eutectic liquidus minimum Figure 6-16. T-X phase diagram of the system albite- orthoclase at 0.2 GPa H 2 O pressure. After Bowen and Tuttle (1950). J. Geology.Effect of P H O on Ab-Or 2 2 Figure 6-17. The Albite-K-feldspar system at various H 2 O pressures. (a) and (b) after Bowen and Tuttle (1950), J. Geol, (c) after Morse (1970) J. Petrol.