Phase diagram Need to represent how mineral reactions at equilibrium vary with P and T.

Slides:



Advertisements
Similar presentations
The thermodynamics of phase transformations
Advertisements

Thermodynamics l l a system: Some portion of the universe that you wish to study l The surroundings: The adjacent part of the universe outside the system.
Learning Objectives and Fundamental Questions What is thermodynamics and how are its concepts used in petrology? How can heat and mass flux be predicted.
Essential Questions How do igneous rocks form?
1 Binary Phase Diagrams GLY 4200 Fall, Binary Diagrams Binary diagrams have two components We therefore usually choose to plot both T (temperature)
Mineral Stability Diagrams and Chemical Weathering of Feldspars
Lecture 19 Overview Ch. 4-5 List of topics Heat engines
Phase Equilibria.
Crystal-Melt Equilibria in Magmatic Systems Learning Objectives: –How are crystal-melt equilibria displayed graphically as phase diagrams? –What are the.
Kinetics and Equilibrium Chapter 15. I: Definitions Activation Energy: the minimum amount of energy needed to produce an activated complex Heat of Reaction:
Chapter 6 Interpretation of Phase Diagrams Phase diagrams summarize in graphical form the ranges of temperature (or pressure) and composition over which.
Lecture 7 (9/27/2006) Crystal Chemistry Part 6: Phase Diagrams.
Distillation l l Start with a partially fermented product (containing some EtOH) l l Through a process of heating, vapor production, and condensation,
Phase Diagrams Best, Chapter 14.
Readings: Winter Chapter 6
Gibbs Free Energy Gibbs free energy is a measure of chemical energy All chemical systems tend naturally toward states of minimum Gibbs free energy G =
Gibbs Phase Rule The number of variables which are required to describe the state of a system: p+f=c+2 f=c-p+2 –Where p=# of phases, c= # of components,
Phase Equilibrium At a constant pressure simple compounds (like ice) melt at a single temperature More complex compounds (like silicate magmas) have very.
GOLDSCHMIDT’S RULES 1. The ions of one element can extensively replace those of another in ionic crystals if their radii differ by less than approximately.
Isograds for a single shale unit in southern Vermont
Eutectic and Peritectic Systems
Phase Equilibrium. Makaopuhi Lava Lake Magma samples recovered from various depths beneath solid crust From Wright and Okamura, (1977) USGS Prof. Paper,
GOLDSCHMIDT’S RULES 1. The ions of one element can extensively replace those of another in ionic crystals if their radii differ by less than approximately.
Volume Changes (Equation of State) Volume is related to energy changes: Mineral volume changes as a function of T: , coefficient of thermal expansion.
Predicting Equilibrium and Phases, Components, Species Lecture 5.
Chapter 5.1 – Igneous Rocks Magma – molten rock below Earth’s surface Lava – magma that flows out onto the surface Igneous rocks – rocks that form when.
Intro to Igneous Rocks.
Mineral Stability What controls when and where a particular mineral forms? Commonly referred to as “Rock cycle” Rock cycle: Mineralogical changes that.
Chemistry of Igneous Rocks Characterization of different types (having different chemistries): –Ultramafic  Mafic  Intermediate  Felsic Composition.
Thermochemistry First law of thermochemistry: Internal energy of an isolated system is constant; energy cannot be created or destroyed; however, energy.
Reaction Rate How Fast Does the Reaction Go Collision Theory l In order to react molecules and atoms must touch each other. l They must hit each other.
THERMODYNAMICS Internal Energy Enthalpy Entropy Free Energy Chapter 17 (McM) Chapter 20 Silberberg.
Solid solutions Example: Olivine: (Mg,Fe) 2 SiO 4 two endmembers of similar crystal form and structure: Forsterite: Mg 2 SiO 4 and Fayalite: Fe 2 SiO 4.
(Earth Science Teachers’ Association)
Microstructure and Phase Transformations in Multicomponent Systems
The Phase Rule and its application. Thermodynamics A system: Some portion of the universe that you wish to study The surroundings: The adjacent part of.
What are igneous rocks? SWBAT compare and contrast intrusive and extrusive igneous rocks; describe the composition of magma; discuss the factors that affect.
Lab 3. Binary Phase Diagrams. Binary Peritectic System Peritectic point - The point on a phase diagram where a reaction takes place between a previously.
Chapter 17 Spontaneity, entropy and free energy. Spontaneous l A reaction that will occur without outside intervention. l We need both thermodynamics.
Copyright©2004 by Houghton Mifflin Company. All rights reserved. 1 Introductory Chemistry: A Foundation FIFTH EDITION by Steven S. Zumdahl University of.
Byeong-Joo Lee Byeong-Joo Lee POSTECH - MSE Phase Equilibria in a Single- Component System.
Geol 2312 Igneous and Metamorphic Petrology
The Phase Rule and its application
Kinetics, Thermodynamics and Equilibrium Regents Chemistry.
Calculating Equilibrium Composition  Example  Cl 2 (g) → 2Cl (g)
Chemical Equilibrium By Doba Jackson, Ph.D.. Outline of Chpt 5 Gibbs Energy and Helmholtz Energy Gibbs energy of a reaction mixture (Chemical Potential)
1 Reaction Rate How Fast Does the Reaction Go 2 Collision Theory l In order to react molecules and atoms must collide with each other. l They must hit.
Reaction Series and Melting Behavior GLY Spring, 2016
Thermodynamics and the Phase Rule
Magma Differentiate magma based on it’s chemical composition  felsic vs. mafic.
General Phase Equilibrium
G EOL 2312 I GNEOUS AND M ETAMORPHIC P ETROLOGY Lecture 4 Introduction to Thermodynamics Jan. 27, 2016.
Hot Under the Collar (part III) Phase Diagrams
Crater Lake Jena Hershkowitz and Ethan Farina-Henry.
Chapter 17 Stability of minerals. Introduction Kinetics (the rate of reactions): Kinetics (the rate of reactions): –Reaction rates slow down on cooling.
And now, THERMODYNAMICS!. Thermodynamics need not be so hard if you think of it as heat and chemical “flow” between “phases”.
Exsolution and Phase Diagrams Lecture 11. Alkali Feldspar Exsolution ‘Microcline’ - an alkali feldspar in which Na- and K-rich bands have formed perpendicular.
Kinetics, Thermodynamics and Equilibrium Regents Chemistry.
1 Thermodynamic Equations (a)Heat, Work and the 1 st Law PV=nRT equation of state for ideal (perfect) gas work done against external pressure work done.
Chapter 19 Spontaneity, entropy and free energy (rev. 11/09/08)
Thermodynamics and the Phase Rule
Geol 2312 Igneous and Metamorphic Petrology
Thermodynamics and the Phase Rule
Your Guide to Stability and Occurrence of Minerals
Classical description of a single component system
Phase Diagrams Liquid a b Anorthite + Liquid T C Diopside + Anorthite
Eutectic and Peritectic Systems
The Phase Rule.
Igneous Rocks Chapter 5.
Reaction Kinetics and Equilibrium
Presentation transcript:

Phase diagram Need to represent how mineral reactions at equilibrium vary with P and T

P-X stability and mixing

Gibbs Phase Rule The number of variables which are required to describe the state of a system: p+f=c+2 f=c-p+2 –Where p=# of phases, c= # of components, f= degrees of freedom –The degrees of freedom correspond to the number of intensive variables that can be changed without changing the number of phases in the system

Variance and f f=c-p+2 Consider a one component (unary) diagram If considering presence of 1 phase (the liquid, solid, OR gas) it is divariant 2 phases = univariant 3 phases = invariant

Melts Liquid composed of predominantly silica and oxygen. Like water, other ions impart greater conductivity to the solution Si and O is polymerized in the liquid to differing degrees – how ‘rigid’ this network may be is uncertain… Viscosity of the liquid  increases with increased silica content, i.e. it has less resistance to flow with more SiO 2 … related to polymerization?? There is H 2 O is magma  2-6% typically – H 2 O decreases the overall melting T of a magma, what does that mean for mineral crystallization?

Thermodynamic definitions G i(solid) = G i(melt) Ultimately the relationships between these is related to the entropy of fusion (  S 0 fus ), which is the entropy change associated with the change in state from liquid to crystal These entropies are the basis for the order associated with Bowen’s reaction series  greater bonding changes in networks, greater entropy change  lower T equilibrium

Melt-crystal equilibrium Precipitated crystals react with cooling liquid, eventually will re-equilibrate back, totally cooled magma xstals show same composition UNLESS it cools so quickly the xstal becomes zoned or the early precipitates are segregated and removed from contact with the bulk of the melt

Why aren’t all feldspars zoned? Kinetics, segregation IF there is sufficient time, the crystals will re-equilibrate with the magma they are in – and reflect the total Na-Ca content of the magma IF not, then different minerals of different composition will be present in zoned plagioclase or segregated from each other physically

Exsolution P-X stability and mixing

More than 1 crystal can precipitate from a melt – different crystals, different stabilities… –2+ minerals that do not share equilibrium in a melt are immiscible (opposite of a solid solution) –Liquidus  Line describing equilibrium between melt and one mineral at equilibrium –Solidus  Line describing equilibrium with melt and solid –Eutectic  point of composition where melt and solid can coexist at equilibrium Diopside is a pyroxene Anorthite is a feldspar Solidus Liquidus Eutectic

Melt at composition X cools to point Y where anorthite (NOT diopside at all) crystallizes, the melt becomes more diopside rich to point C, precipitating more anorthite with the melt becoming more diopside-rich This continues and the melt continues to cool and shift composition until it reaches the eutectic when diopside can start forming A B S1S1 Z C S2S2 At eutectic, diopside AND anorhtite crystals precipitate Lever Rule  diopside/anorthite (42%/58%) crystallize until last of melt precipitates and the rock composition is Z

Melting  when heated to eutectic, the rock would melt such that all the heat goes towards heat of fusion of diopside and anorthite, melts so that 42% diopside / 58% anorthite… When diopside gone, temperature can increase and rest of anorthite can melt (along liquidus)

How does free energy change with T and P? From  G=  H-T  S: T and P changes affect free energy and can drive reactions!!

Volume Changes (Equation of State) Volume is related to energy changes: Mineral volume changes as a function of T: , coefficient of thermal expansion Mineral volume changes as a function of P: , coefficient of isothermal expansion For Minerals:

Volume Changes (Equation of State) Gases and liquids undergo significant volume changes with T and P changes Number of empirically based EOS solns.. For metamorphic environments: –Redlich and Kwong equation: V-bar denotes a molar quatity, a Rw and b RK are constants

Phase Relations Rule: At equilibrium, reactants and products have the same Gibbs Energy –For 2+ things at equilibrium, can investigate the P-T relationships  different minerals change with T-P differently… For  G R =  S R dT +  V R dP, at equilibrium,  G  rearranging: Clausius-Clapeyron equation Remember that a line on a phase diagram describes equilibrium,  G R =0!!

 V for solids stays nearly constant as P, T change,  V for liquids and gases DOES NOT Solid-solid reactions linear  S and V nearly constant,  S/  V constant  + slope in diagram For metamorphic reactions involving liquids or gases, volume changes are significant,  V terms large and a function of T and P (and often complex functions) – slope is not linear and can change sign (change slope + to –)  S R change with T or P? V = Vº(1-  P)

Example – Diamond-graphite To get C from graphite to diamond at 25ºC requires 1600 MPa of pressure, let’s calculate what P it requires at 1000ºC: graphitediamond  (K -1 ) 1.05E E-06  (MPa -1 ) 3.08E E-06 Sº (J/mol K) Vº (cm3/mol)

Clausius-Clapyron Example