Grading: Homework 25%; Mid-Term Exams 30%; Final 45%
Homework #1 was due Wednesday, February 1
Homework #2 was due Wednesday, February 15
Homework #3 was due Monday, February 27
Review Session - Monday, February 27, 6:30 pm, Mechanical Engineering Building 339
Mid-Term Exam - Wednesday, February 29
Homework #4 was due Monday, March 26
Homework #5 was due Monday, April 2
Computer Laboratory (and homework #6) - Wednesday, April 4 (homework #6 was due on Monday, April 9)
Mid-Term Exam - Wednesday, April 11
Homework #7 is due Monday, April 30
Review session - Sunday, May 6, 2:00 pm, Mechanical Engineering Building 339
Final Exam - Thursday, May 10, 2-5 pm, Mechanical Engineering Building 339
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Abstract:
In this course we start from a brief review of classical thermodynamics necessary for understanding of phase diagrams. We will then apply the thermodynamic concepts to the analysis of phase equilibria and phase transformations in one-component and multi-component systems. We will learn how to read and analyze phase diagrams of real materials and how to construct phase diagrams from thermodynamic data. In the last part of the course we will consider the basic concepts of kinetic phenomena in materials. Most kinetic phenomena in condensed matter involve diffusion and we will focus on the mechanisms of diffusion in materials as well as on the analytical and numerical methods to describe diffusion. By the end of the course we will see how the interplay of thermodynamic driving forces and kinetics of mass transfer is defining the formation of complex microstructure of real materials.
Main (optional) textbooks:
D. A. Porter and K. E. Easterling, Phase Transformations in Metals and Alloys, 2nd edition, Chapman & Hall, London, UK, 1992 (TN690 .P597 - placed on reserve circulate, Science and Engineering Library).
This textbook (2nd edition) was reprinted by CRC Press in 2003; 3rd edition was published by CRC Press in 2009.
D. R. Gaskell, Introduction to the Thermodynamics of Materials, 4th edition, New York: Taylor & Francis, 2003 (TN673 .G33 2003 - placed on reserve circulate, Science and Engineering Library).
In the first part of this course, when we review the fundamentals of thermodynamics, it would be useful for you to read sections of Gaskell's book suggested in the lecture notes. You may also want to look for more compact and sometimes more clear explanations given in Porter and Easterling. Please keep in mind that notation varies from textbook to textbook; nevertheless, looking into different textbooks may help to clarify complicated topics and provide additional examples.
Kinetics is not covered in Gaskell. In the second part of the course the main source of material will come from the lecture notes and from Porter and Easterling.
Lecture notes: will appear at this Web page as course progresses.
Syllabus in pdf
Topics that are covered include:
Introduction
Notes
Short review of mathematical methods in thermodynamics by S. M. Blinder
Review of classical thermodynamics
- First Law - Energy Balance
Notes
- Thermodynamic functions of state
- Internal energy, heat and work
- Types of paths (isobaric, isochoric, isothermal, adiabatic)
- Enthalpy, heat capacity, heat of formation, phase transformations
- Calculation of enthalpy as a function of temperature
- Heats of reactions and the Hess’s law
- Theoretical Calculation of the Heat Capacity
Notes
paper on heat capacity and the equipartition theorem
- Principle of equipartition of energy
- Heat capacity of ideal and real gases
- Heat capacity of solids: Dulong-Petit, Einstein, Debye models
- Heat capacity of metals - electronic contribution
- Entropy and the Second Law
Notes
- Concept of equilibrium
- Reversible and irreversible processes
- The direction of spontaneous change
- Entropy and spontaneous/irreversible processes
- Calculation of entropy in isochoric and isobaric processes
- Calculation of entropy in reversible and irreversible processes
- The Statistical Interpretation of Entropy
Notes
- Physical meaning of entropy
- Microstates and macrostates
- Statistical interpretation of entropy and Boltzmann equation
- Configurational entropy and thermal entropy
- Calculation of the equilibrium vacancy concentration
- Fundamental equations
Notes
- The Helmholtz Free Energy
- The Gibbs Free energy
- Changes in composition
- Chemical potential
- Thermodynamic relations
Phase Transitions and Phase Diagrams
- One-component systems
Notes
paper on ice skating
- Enthalpy and entropy dependence on P and T
- Gibbs free energy dependence on P and T
- Clapeyron equation
- Understanding phase diagrams for one-component systems
- Polymorphic phase transitions
- Driving force for a phase transition
- First order and second-order phase transitions
- Introduction to Solution Thermodynamics
Notes
- Ideal solution: Entropy of formation and Gibbs free energy
- Chemical potential of an ideal solution
- Regular solutions: Heat of formation of a solution
- Activity of a component
- Real solutions: interstitial solid solutions, ordered phases, intermediate phases, compounds
- Equilibrium in heterogeneous systems
- Binary phase diagrams
Notes
paper on reconstruction of historical pipe organs
- Binary phase diagrams and Gibbs free energy curves
- Binary solutions with unlimited solubility
- Relative proportion of phases (tie lines and the lever principle)
- Development of microstructure in isomorphous alloys
- Binary eutectic systems (limited solid solubility)
- Solid state reactions (eutectoid, peritectoid reactions)
- Binary systems with intermediate phases/compounds
- The iron-carbon system (steel and cast iron)
- Gibbs phase rule
- Temperature dependence of solubility
- Multi-component (ternary) phase diagrams
Kinetics
Notes
- Basic concepts in kinetics
- Kinetics of phase transformations
- Activation free energy barrier
- Arrhenius rate equation
- Atomic mechanisms of diffusion
- Substitutional diffusion
- Interstitial diffusion
- Temperature dependence
- High diffusivity paths (grain boundaries, free surfaces, dislocations)
- Diffusion in solids - phenomenological description
- Driving force for diffusion in ideal and regular solutions
- Flux, steady-state diffusion, Fick’s first law
- Diffusion coefficient, Einstein relation
- Nonsteady-state diffusion, Fick’s second law
- Thermodynamics of diffusion
- Driving force for diffusion
- Diffusion in ideal and real solutions
- Thermodynamic factor
- Diffusion against the concentration gradient: Spinodal decomposition
- Solutions to the diffusion equation
- Numerical integration
- Analytical solution
- Applications
- Chemical homogenization
- Carburization of steel
- Nucleation and growth
Notes
- Supercooling and superheating
- Driving force for phase transformation
- Homogeneous nucleation
- Critical radius, nucleation rate
- Heterogeneous nucleation
- Nucleation in melting and boiling
- Growth mechanisms
- Rate of phase transformations
- Solidification and growth morphologies
Papers for extracurricular reading:
paper on surface wetting
paper on the out-of-plane component of the liquid-vapor surface tension
lz2n@virginia.edu
Computational Materials Group
Materials Science & Engineering
