University of Virginia, Department of Materials Science and EngineeringMSE 3050: Thermodynamics and Kinetics of MaterialsSpring 2016, Monday and Wednesday, 3:30 - 4:45 pm Mechanical Engineering Building 339 | |

Instructor: Leonid V. ZhigileiOffice: Wilsdorf Hall 303DOffice Hours: 11:00 am to noon Monday & openTelephone: (434) 243 3582E-mail:
lz2n@virginia.eduTeaching Assistant: Miao HeOffice: Wilsdorf Hall 303Office Hours: 5-6pm Wednesday, 2-3 pm FridayE-mail:
e-mailWeb: http://www.people.virginia.edu/~lz2n/mse305/Class e-mail:
e-mail |

Homework #1 was due Wednesday, February 3Homework #2 was due Wednesday, February 17Homework #3 was due Wednesday, March 2Mid-Term Exam #1 - Wednesday, March 16Homework #4 was due Wednesday, March 30Homework #5 was due Monday, April 11Computer Laboratory (Homework #6) was due Monday, April 20Mid-Term Exam #2 - Monday, April 18Homework #7 is due Wednesday, April 27Final Exam - Thursday, May 5, 2-5 pm, Mechanical Engineering Building 339 |

**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, 2^{nd} edition, Chapman & Hall, London, UK, 1992 (TN690 .P597 - placed on reserve circulate, Science and Engineering Library).
This textbook (2^{nd} edition) was reprinted by CRC Press in 2003; 3^{rd} edition was published by CRC Press in 2009.

D. R. Gaskell, Introduction to the Thermodynamics of Materials, 4^{th} 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.

**Topics that are covered include:**

**Introduction**
Notes

Questionnaire

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 (
*extracurricular - not tested*) Notes - Thermodynamic relations

- One-component systems
Notes

paper on ice skating new insights into the origin of liquid layer on ice- 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
- 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

- 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 (
*extracurricular - not tested*) Notes- Driving force for diffusion
- Diffusion in ideal and real solutions
- Thermodynamic factor
- Diffusion against the concentration gradient: Spinodal decomposition

- Solutions to the diffusion equation
Notes
- Numerical integration (
*extracurricular - not tested*) - Analytical solution
- Applications
- Chemical homogenization
- Carburization of steel

- Numerical integration (
- 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 two-step nucleation in solid-solid phase transitions

comment on the above paper

paper on square 2D water ice

paper on Mpemba effect

entropic contributions to ordering transitions

paper on open colloidal lattices stabilized by entropy

comment on the above paper

paper on generation of one-component metallic glass

another paper on generation of one-component metallic glass

paper on melting of the Earth’s inner core

comment on the above paper

paper on surface wetting

comment on ice formation in the atmosphere

paper on the out-of-plane component of the liquid-vapor surface tension

**
**