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' prestudy. 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 wellround understanding of Kinetics. To correlate the "abstract" Kinetics theory to the real practices of materials science engineering, we provide various such realworld examples that help understand the beauty and powerful application of the theories.
Lecture 
Additional Readings and Information 
Homework 
Kinetics vs. Thermodynamics: different but related 


Kinetics: as described as transformation rate between two equilibrium states 


Diffusion: Fick's first law 
An animation showing the interatomic diffusion across a 4coordinated lattice. As per Fick¡¯s law, the net flux (or movement of atoms) is always in the opposite direction of the concentration gradient. 

Diffusion: Fick's second law 


Diffusion Coefficient (Diffusivity) 


Diffusion in binary substitutional materials (alloys) 

How to determine the binary interdiffusion coefficient in real experiments 
additional reading: experimental measurement of interdiffusion coefficient 

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



Particle Coarsening: Ostwald Ripening

additional reading: about Ostwaldripeningparticlecoarsening A movie clip showing crystals growth through Ostwald ripening under constant temperature: http://www.eng.utah.edu/~lzang/images/ostwaldripening.avi 

Homogeneous Nucleation

additional
reading: about nucleation A movie clip: http://www.eng.utah.edu/~lzang/images/supercooledwater.avi 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. 

Homogeneous Nucleation: solidsolid phase transformation



Heterogeneous Nucleation: a surface catalyzed process 
a movie clip demonstrates a example of heterogeneous nucleation: formation of carbondioxide bubbles from a carbonated water, and facilitated by a piece of chalk  an ideal nucleation sites for bubbles. 
HW for lecture 1012 
Heterogeneous Nucleation: Effects of Grain Boundaries and Surface Defects 


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/platinumnanocrystal.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. 

Kinetics of Phase Growth: singlecomponent or compositioninvariant transformation 


Kinetics of Phase Growth in a Twocomponent System: dilutesolution 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. X_{B}) 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. X_{B}) curve.
3. Understand the
relationship between the molar free energy curve (G vs. X_{B})
and the binary phase diagram, and how to deduce the phase system from
the (G vs. X_{B}) curve at different temperatures.
4. Understand the
relationship between the molar free energy curve (G vs. X_{B})
and the multiple phase diagram, and how to deduce the phase system from
the (G vs. X_{B}) curve at different temperatures.


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


Kinetics of Phase Growth in a Twocomponent System: general kinetics analysis based on the dilutesolution approximation 

HW for lecture 1618 
Eutectoid Transformation in Steels: a typical case of Cellular Precipitation 
showing the coherent, onedimensional 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: http://www.eng.utah.edu/~lzang/images/eutectoidpearlite.wmv 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: http://www.eng.utah.edu/~lzang/images/pearlite.jpg 

Eutectoid Transformation in Steels: kinetics of phase growth 

HW for lecture 1920 
Types of Interfaces: coherent, semicoherent, and incoherent 

HW for lecture 21 
Spinodal Decomposition: Part 1: general description and practical implications 
About John W. Cahn: see Wikipedia page https://en.wikipedia.org/wiki/John_W._Cahn 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 uniformsized, periodic fine microstructure in macroscopic scale (as we will learn in details in Lectures 2224).
an animation for the microstructural evolution under the CahnHilliard equation, demonstrating distinctive coarsening and phase separation through spinodal decomposition: http://www.eng.utah.edu/~lzang/images/cahnhilliardanim.gif 

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


Spinodal Decomposition: Part 3: kinetics of the composition fluctuation 

HW for lecture 2224 
Ordering Transformation 


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


Diffusion of Ions: Part 2: coupled diffusion of cations and anions as described by NernstPlanck Equation 
additional reading 1: literature1960SelfDiffusion of the Chloride Ion in Sodium Chloride
additional reading 2: literature1950SelfDiffusion of Sodium in Sodium Chloride and Sodium Bromide 

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


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

HW for lecture 2829 
Kinetics of Epitaxial Growth: Surface Diffusion and Nucleation 

