Lecture notes and other materials for MSE 5034 & 6034

Notes are developed based on the original version from Prof. Anil Virkar.

Click to download.

These notes are posted here mainly for the convenience of students' pre-study.  But the lecturing materials to be finally delivered by the Instructor in class may be subject to some change, for example by adding new information concerned the "real world" problems and issues of materials science and engineering.  So, keeping regular attendance and taking additional notes in class are strongly suggested.

Since we don't have a primary Textbook, the Lectures notes, together with the additional readings thus provided, are expected to offer sufficient knowledge and information that are needed for well-round  understanding of Kinetics.  To correlate the "abstract" Kinetics theory to the real practices of materials science engineering, we provide various such real-world examples that help understand the beauty and powerful application of the theories.



Additional Readings and Information


Lecture 1

Kinetics vs. Thermodynamics: different but related



Lecture 2

Kinetics: as described as transformation rate between two equilibrium states


HW for lecture 1-2

Lecture 3

Diffusion: Fick's first law

An animation showing the inter-atomic diffusion across a 4-coordinated lattice. As per Ficks law, the net flux (or movement of atoms) is always in the opposite direction of the concentration gradient.

HW for lecture 3

Lecture 4

Diffusion: Fick's second law


HW for lecture 4

Lecture 5

Diffusion Coefficient (Diffusivity)


HW for lecture 5

Lecture 6

Diffusion in binary substitutional materials (alloys)

additional reading: about grain boundary, crystalline defects including point defects and line dislocation, and the examples in real-world materials science and engineering.

HW for lecture 6

Lecture 7

How to determine the binary interdiffusion coefficient in real experiments

additional reading: experimental measurement of interdiffusion co-efficient


Lecture 8

Surface tension, internal pressure and energy of a spherical particle or droplet




Lecture 9

Particle Coarsening: Ostwald Ripening


additional reading: about Ostwald-ripening-particle-coarsening

A movie clip showing crystals growth through Ostwald ripening under constant temperature: http://www.eng.utah.edu/~lzang/images/ostwald-ripening.avi


Lecture 10

Homogeneous Nucleation


additional reading: about nucleation

A movie clip:


Pure water freezes at -42 C, rather than at its freezing temperature of 0 C. So, if cooled slowly below the freezing point, pure water may remain liquid (supercooled) for extended period --- homogeneous nucleation takes time! However, the crystallization into ice may be facilitated by adding some nucleation "seeds": small ice particles, or simply by shaking.


Lecture 11

Homogeneous Nucleation: solid-solid phase transformation




Lecture 12

Heterogeneous Nucleation: a surface catalyzed process


a movie clip demonstrates a example of heterogeneous nucleation: formation of carbon-dioxide bubbles from a carbonated water, and facilitated by a piece of chalk --- an ideal nucleation sites for bubbles.


HW for lecture 10-12

Lecture 13

Heterogeneous Nucleation: Effects of Grain Boundaries and Surface Defects



Lecture 14

Rate of Nucleation

Movie clip 1: nucleation and growth of platinum nanocrystals --- a movie taken in situ during the synthesis, showing that the nuclei form throughout the phase transformation so that a wide range of particles sizes exist before the latter stage of Ostwald ripening that eventually leads to formation of uniform size of particles. images/platinum-nanocrystal.wmv

Movie clip 2: nucleation, growth and fragmentation of bubbles --- an animation of what makes volcanoes work. Here you see all the nuclei form right at the beginning of transformation, the later stage of transformation is dominated by the growth of bubbles, while no new nuclei form.


Lecture 15

Kinetics of Phase Growth: single-component or composition-invariant transformation


Lecture 16

Kinetics of Phase Growth in a Two-component System: dilute-solution approximation

This lecture will require some basics of thermodynamics that you learned before, such as,

1.  How to get chemical potential m from the molar free energy curve (G vs. XB) for a single phase system.

2.  Understand the molar free energy curve (G vs. X) for a binary phase system a/b, how to get chemical potential m of each of the two component A and B in the a and b phase, respectively, from the (G vs. XB) curve.

3.  Understand the relationship between the molar free energy curve (G vs. XB) and the binary phase diagram, and how to deduce the phase system from the (G vs. XB) curve at different temperatures.

4.  Understand the relationship between the molar free energy curve (G vs. XB) and the multiple phase diagram, and how to deduce the phase system from the (G vs. XB) curve at different temperatures.



Lecture 17

Kinetics of Phase Growth in a Two-component System: description of diffusion flux across the alpha/beta interface



Lecture 18

Kinetics of Phase Growth in a Two-component System: general kinetics analysis based on the dilute-solution approximation


HW for lecture 16-18

Lecture 19

Eutectoid Transformation in Steels: a typical case of Cellular Precipitation


A Flash animation (click):

showing the coherent, one-dimensional growth of the ferrite (light color) and cementite (dark) phases, at consumption of the parent austenite phase, leading to formation of lamellar (layered) structures composed of alternating layers of ferrite (88 wt%) and cementite (12wt%).

from Cambridge University Engineering Department


A movie clip:


showing the coherent phase transformation from austenite to pearlite. note: the pearlite phase composes of light ferrite and dark cementite, which coherently grow along one dimenaion.


A photograph showing the microstructure of Pearlite:

The two phases of pearlite are clearly visible in the micrograph above. These phases are ferrite and cementite. The ferrite appears white, and is laminated against the cementite which appears grey.


Lecture 20

Eutectoid Transformation in Steels: kinetics of phase growth


HW for lecture 19-20

Lecture 21

Types of Interfaces: coherent, semi-coherent, and incoherent


HW for lecture 21

Lecture 22

Spinodal Decomposition: Part 1: general description and practical implications

About John W. Cahn: see Wikipedia page


John W. Cahn developed a flexible continuum model (equation) that can interpret the spinodal decomposition, a unique phase transformation process that is characterized by the occurrence of diffusion up against a concentration gradient (see Lecture 5), often referred as "uphill" diffusion, leading to formation of a uniform-sized, periodic fine microstructure in macroscopic scale (as we will learn in details in Lectures 22-24).


an animation for the microstructural evolution under the Cahn-Hilliard equation, demonstrating distinctive coarsening and phase separation through spinodal decomposition:


a movie clip
simulating the 3D spinodal decomposition (from Oono, Y. and Puri, S., Study of phase-separation dynamics by use of cell dynamical systems. I. Modeling, Physical Review A (General Physics), Volume 38, Issue 1, July 1, 1988, pp.434-453): http://www.eng.utah.edu/~lzang/images/3D-spinodal.mpg


Lecture 23

Spinodal Decomposition: Part 2: regarding free energy change and interdiffusion coefficient inside the spinodal



Lecture 24

Spinodal Decomposition: Part 3: kinetics of the composition fluctuation


HW for lecture 22-24

Lecture 25

Ordering Transformation



Lecture 26

Diffusion of Ions: Part 1: basic understanding and the derivation of diffusion flux



Lecture 27

Diffusion of Ions: Part 2: coupled diffusion of cations and anions as described by Nernst-Planck Equation

 additional reading 1: literature-1960-Self-Diffusion of the Chloride Ion in Sodium Chloride

additional reading 2: literature-1950-Self-Diffusion of Sodium in Sodium Chloride and Sodium Bromide

Lecture 28

Kinetics of Oxidation of Metals: Part 1: rusting, corrosion, and the surface protection, all about chemistry



Lecture 29

Kinetics of Oxidation of Metals: Part 2: Wagner Parabolic Model


HW for lecture 28-29

Lecture 30

Kinetics of Epitaxial Growth: Surface Diffusion and Nucleation