MSE 103 – Phase Transformations and Kinetics

Course Number:  MSE 103
Course Units:  3
 
INSTRUCTOR: Professor Andreas M. Glaeser
 
CATALOG DESCRIPTION:
The nature, mechanisms and kinetics of phase transformations and microstructural changes in the solid state. Atom diffusion in solids. Phase transformations through the nucleation and growth of new matrix or precipitate phases. Martensitic transformations, spinodal decomposition. The use of phase transformations to control microstructure. 
 
COURSE PREREQUISITES:

MSE 102, E45; Undergraduate thermodynamics course recommended.

PREREQUISITE KNOWLEDGE AND/OR SKILLS TEXTBOOK(S) AND/OR OTHER REQUIRED MATERIAL:

Required text: Porter and Easterling, Phase Transformations in Metals and Alloys, CRC Press

Supplementary texts: Books that provide additional background on topics of thermodynamics, phase diagrams, diffusion, and phase transformations are on reserve and available at the Engineering Library.

COURSE OBJECTIVES:

The overall goals of the course are to: 1) develop an understanding of why materials and microstructures undergo changes by reinforcing and significantly extending concepts introduced in chemical thermodynamics courses, 2) provide an understanding of how diffusion enables changes in the chemical distribution and microstructure of materials by discussing mechanisms and rates of diffusion and the role of driving force on diffusional processes, and 3) to formulate and discuss a variety of phase transformations and the effects of temperature and driving force on the nature of the transformation and its impact on the resulting microstructure. In summary, the tools required to understand how and why phase transformations occur, and how and why microstructures can be controlled are developed.

DESIRED COURSE OUTCOMES:

The course seeks to develop an understanding of the thermodynamic driving force for phase transformations and the role that chemical driving forces, strain energy and interfacial energy play in producing or modifying these driving forces. The course attempts to indicate the important role that the unique structure and characteristics of surfaces and interfaces can have. Diffusion processes and mechanisms are introduced, and common solutions to Fick’s laws are presented to acquaint students with the key characteristics of such solutions and to provide an understanding of spatiotemporal-scaling behavior. Limitations of the solutions are also discussed. The importance of the relationship between concentration gradients and chemical potential gradients is emphasized, with spinodal decomposition serving a key role. Diffusion and the importance of the phase diagram and underlying solution thermodynamics on diffusion processes is emphasized. A number of phase transformations are described, and treatments developed with a template framework so that students can extend the considerations of model systems to more complex cases. This is done to focus attention on fundamentals and not on the details and peculiarities of specific systems. Homogeneous and heterogeneous nucleation as well as growth processes are covered to provide an understanding of the underlying factors that dictate final microstructures.

Specific outcomes of the course are:

  • Understanding of thermodynamics of single and multiple component systems, solution models, activities, etc., and their relationship to the equilibrium phase diagram.
  • Ability to calculate single-component and multiple-component phase diagrams from thermodynamic data or solution models.
  • An appreciation of the importance and energy characteristics of surfaces and interfaces, and their impact on equilibrium microstructures and capillarity-driven processes.
  • Ability to address/solve problems involving steady-state and nonsteady-state diffusion of varying degrees of complexity, and to understanding the spatiotemporal scaling behavior of solutions to such diffusion problems.
  • Understanding of the fundamental mechanisms of diffusion and the importance of processing conditions, notably temperature, and microstructural features such as grain boundaries, dislocations, and surfaces on the total transport in a material.
  • A deeper understanding of the role of the thermodynamic driving force for diffusion, and an alternative treatment of diffusion in terms of an appropriate gradient in potential.
  • Knowledge of how driving forces of varying types and barriers due to surface energy effects interact to dictate the rate of phase transformation and microstructural change.
  • An understanding of how through manipulation of temperature, driving force, and initial microstructure, a wide range of final microstructures can be produced through an appreciation of the competing processes that determine the overall path of microstructural evolution.
 
TOPICS COVERED:
  • Fundamental principles of thermodynamics relevant to a description of phase equilibrium. Application to single-component systems, single-component phase diagrams. Solution thermodynamics, ideal and regular solution models, calculation of binary phase diagrams from solution models and free energy curves. Activity-composition diagrams. Quantitative assessments of driving forces for mixing and phase transformations. Phase separation in binary alloys; features of the spinodal region. Ordering reactions and the Bragg-Williams formulation. Introduction to ternary and quaternary systems and associated phase diagrams. The Gibbs triangle and construction rules for ternary phase diagrams. The use of phase diagrams and solution thermodynamics in assessing viable materials combinations and as a guide to materials design.
  • Introduction to surfaces and interfaces. Estimation of surface energies for solids and liquids. Effect of particle size on chemical potential, and driving forces for mass exchange during coarsening and Rayleigh instabilities. Effect of crystallographic orientation on surface energy. Singular and vicinal surfaces. The Wulff plot, the Wulff-Herring construction, the Wulff theorem and the equilibrium shape. Twist and tilt grain boundaries, low-angle and high-angle boundaries. General and special boundaries. 
  • Material transport by diffusion. The laws of diffusion as presented by Fick. Fick’s first law, and application to steady-state diffusion problems. Derivation of Fick’s second law. Effect of diffusion geometry on forms of solutions and concentration profiles. Important solutions to the diffusion equation. Homogenization solutions and separation of variables methods. Thin film and error function solutions. Sievert’s Law. Carburization of steel. Removal of dissolved gases in metals. Distance-time-diffusivity scaling characteristics of solutions to diffusion problems. Superposition methods of treating more complex problems. Mechanisms and processes of diffusion: self-diffusion, interstitial diffusion, interdiffusion, short-circuit diffusion. Role of temperature, crystal structure, atomic size ratios, grain boundary structure, melting point on rates of diffusion. Microstructural effects. Self-diffusion coefficients and the role of homologous temperature. Interdiffusion, the Kirkendall effect, and Kirkendall porosity. Microstructural implications. Relationships between concentration gradients and chemical potential gradients. The formulation of diffusion in terms of chemical potential gradients. Uphill diffusion within the chemical spinodal. 
  • Phase transformations. Homogeneous nucleation of solidification. The Turnbull experiments. Heterogeneous nucleation of solidification. Force-based and energy-based descriptions of the equilibrium geometry of the critical nucleus. Role of heterogeneities on modifying the rate of solidification and microstructure, and their impact on glass formation, and processing of glass ceramics. Examples from the literature. TTT diagrams. Nucleation of precipitates from a supersaturated solid solution, with and without strain. The development of nonequilibrium transition phases due to interfacial energy effects. Coherent, semi-coherent, and incoherent interfaces and energetics. Heterogeneous nucleation of precipitates and effects of matrix microstructure (grain size and dislocation density) on the resulting phase distribution. Spinodal decomposition of alloys. Strain energy as a driving force for recrystallization. Excess surface energy and coarsening; implication to nanostructures. Introduction to martensitic transformations.

 

COURSE FORMAT:

Three hours of lecture and one hour of discussion per week.

CONTRIBUTION OF THE COURSE TO MEETING THE PROFESSIONAL COMPONENT:

An understanding of phase equilibrium, the thermodynamic basis of phase equilibrium and phase transformations, the processes by which diffusion occurs, the properties of surfaces and interfaces, and their confluence in dictating the course of phase transformations are essential elements of a materials scientist’s educational repertoire. This course seeks to provide these essentials. The course emphasizes the interrelationships between thermodynamics, kinetics and phase transformations. An extensive and challenging set of homework assignments is designed to help the students understand and appreciate these components and their interrelationships. Use of the computer and lower-division computer skills are frequently required to solve problems in an efficient manner.

RELATIONSHIP OF THE COURSE TO UNDERGRADUATE DEGREE PROGRAM OBJECTIVES:

The course is intended to provide the necessary background in thermodynamics, phase equilibrium, diffusion and phase transformations to upper-division undergraduates in the Department and students pursuing a joint major between the Department and other engineering departments (mechanical engineering, chemical engineering, nuclear engineering, and electrical engineering). For some double majors it provides their most significant coverage of chemical thermodynamics. For all students, it is intended to provide the materials-independent basics that prepare them for other upper-division courses within the department that focus on processing or production of specific types of materials (metals, ceramics, semiconductors) or materials in specific configurations (thin films).

ASSESSMENT OF STUDENT PROGRESS TOWARD COURSE OBJECTIVES:

  • Approximately twenty-five to thirty problem sets each semester designed to provide immediate reinforcement and utilization of concepts presented in lecture.
  • Two 80-minute mid-term examinations
  • Final examination
 
PERSON(S) WHO PREPARED THIS DESCRIPTION:

Professor Andreas M. Glaeser