Thermodynamics - Geochemistry - Lecture Slides, Slides of Geochemistry

Download Thermodynamics - Geochemistry - Lecture Slides and more Slides Geochemistry in PDF only on Docsity! Thermodynamics Docsity.com Mineral Physics Program Fundamentals of mineralogy, petrology, phase equilibria • Lecture 1. Composition and Structure of Earth’s Interior (Lars) • Lecture 2. Mineralogy and Crystal Chemistry (Abby) • Lecture 3. Introduction to Thermodynamics (Lars) Fundamentals of physical properties of earth materials • Lecture 4. Elasticity and Equations of State (Abby) • Lecture 5. Lattice dynamics and Statistical Mechanics (Lars) • Lecture 6. Transport Properties (Abby) Frontiers • Lecture 7. Electronic Structure and Ab Initio Theory (Lars) • Lecture 8. Experimental Methods and Challenges (Abby) • Lecture 9. Building a Terrestrial Planet (Lars/Abby) Tutorials • Constructing Earth Models (Lars) • Constructing and Interpreting Phase Diagrams (Abby) • Interpreting Lateral Heterogeneity (Abby) • First principles theory (Lars) Docsity.com Macroscopic Properties • Volume (Density) • Entropy • Energy • Proportions of Phases • Composition of Phases • … • Not – Crystal size – Crystal shape – Details of arrangement Docsity.com Thermodynamic Variables • Second Order – Heat capacity – Thermal expansivity – Bulk modulus – Grüneisen parameter • First Order – V: Volume, – S: Entropy – Ni: Amount of components – P: Pressure – T: Temperature I : Chemical Potential CP  T S T       P ,Ni   1 V V T       P ,Ni KS  V P V       S,Ni   V T T V       S,Ni Docsity.com Foundations 1 • What defines the equilibrium state of our system? – Three quantities • Ni (Composition) • V (Geometry) • U (“thermal effects”) • Ideal Gas – Energy is all kinetic so – U = i mivi2  ways to redistribute KE among particles while leaving U unchanged Docsity.com Fundamental Relation • U = U(S,V,Ni) • Complete information of all properties of all equilibrium states • S,V,Ni are natural variables of U • U = U(T,V,Ni) not fundamental In te rn al E ne rg y, U Temperature, T=(dU/dS)V,Ni In te rn al E ne rg y, U Entropy, S Docsity.com Legendre Transformations • Two equivalent representations – y=f(x) =y-px – i.e. =g(p) • Identify – yU, xV,S, pP,T, G • G = U - dU/dV V - dU/dS S or • G(P,T,Ni) = U(V,S,Ni) + PV - TS • G(P,T,Ni) is also fundamental! y x   Docsity.com Thermodynamic Square • Thermodynamic Potentials – F = Helmholtz free energy – G = Gibbs free energy – H = Enthalpy – U = Internal energy • Surrounded by natural variables • First derivatives • Second derivatives (Maxwell Relations) V F T U G S H P Docsity.com One Component Phase Equilibria dG = VdP - SdT G T Ttr G P Ptr A B T P B A Phase Diagram dTdP  V S Slope=V Slope=-S Docsity.com Two Component Phase Equilibria • Phase: Homogeneous in chemical composition and physical state • Component: Chemically independent constituent • Example: (Mg,Fe)2SiO4 • Phases: olivine, wadsleyite, ringwoodite, … • Components: Mg2SiO4,Fe2SiO4 • Why not Mg,Fe,Si,O? Docsity.com Phase Rule • p phases, c components • Equilibrium: uniformity of intensive variables across coexisting phases: • P(a),T(a),i(a) • Equations – 2(p-1)+c(p-1) • Unknowns – 2p+p(c-1) • Degrees of Freedom – f=c-p+2 c≈5,p≈4 f≈3 Docsity.com P re ss ur e 10 Composition, xB    G ib bs F re e E ne rg y, G 10 Composition, xB   G ib bs F re e E ne rg y, G 10 Composition, xB   G ib bs F re e E ne rg y, G 10 Composition, xB   Docsity.com Non-ideal solutions • Internal Energy a non-linear function of composition – Compare A-B bond energy to average of A-A, B-B – Tendency towards dispersal, clustering. • Exsolution – cpx-opx,Mg-pv,Ca-pv • Formally: I = Gi + RTlnai – ai is the activity and may differ from the mole fraction Docsity.com Example: Phase Equilibria • Mg2SiO4-Fe2SiO4 System • Olivine to wadsleyite phase transformation Katsura et al. (2004) GRL Docsity.com