Lecture notes and other materials for MSE 5034 & 6034
Notes are developed based on the original version from Prof. Anil Virkar.
Three reference textbooks for this class:
"Phase Transformations in Metals and Alloys", by D. A. Porter, K. E. Easterling and M. Y. Sherif, CRC Press, third edition
"Kinetics of Materials", by Robert W. Balluffi, Samuel M. Allen and W. Craig Carter, Wiley-Interscience, 1st Edition.
"Kinetics in Materials Science and Engineering", by Dennis W. Readey, Taylor and Francis, 1st Edition.
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.
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Lecture |
Additional Readings and Information |
Homework |
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Kinetics vs. Thermodynamics: different but related |
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Kinetics: as described as transformation rate between two equilibrium states |
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Diffusion: Fick's first law |
An animation showing the inter-atomic diffusion across a 4-coordinated lattice. As per Fick's law, the net flux (or movement of atoms) is always in the opposite direction of the concentration gradient. |
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Diffusion: Fick's second law |
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Diffusion Coefficient (Diffusivity) |
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Diffusion in binary substitutional materials (alloys) |
Historic Insight: The Discovery and
Acceptance of the Kirkendall Effect: The Result of a Short
Research Career, https://www.tms.org/pubs/journals/jom/9706/nakajima-9706.html
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How to determine the binary interdiffusion coefficient in real experiments |
additional reading: experimental measurement of interdiffusion co-efficient |
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Surface tension, internal pressure and energy of a spherical particle or droplet
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Particle Coarsening: Ostwald Ripening
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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 |
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Homogeneous Nucleation
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additional
reading: about nucleation
A movie clip: http://www.eng.utah.edu/~lzang/images/supercooled-water.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. |
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Homogeneous Nucleation: solid-solid phase transformation
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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 |
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Heterogeneous Nucleation: Effects of Grain Boundaries and Surface Defects |
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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. |
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Kinetics of Phase Growth: single-component or composition-invariant transformation |
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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.
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Kinetics of Phase Growth in a Two-component System: description of diffusion flux across the alpha/beta interface |
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Kinetics of Phase Growth in a Two-component System: general kinetics analysis based on the dilute-solution approximation |
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HW for lecture 16-18 |
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Eutectoid Transformation in Steels: a typical case of Cellular Precipitation |
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: http://www.eng.utah.edu/~lzang/images/eutectoid-pearlite.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 |
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Eutectoid Transformation in Steels: kinetics of phase growth |
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HW for lecture 19-20 |
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Types of Interfaces: coherent, semi-coherent, and incoherent |
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HW for lecture 21 |
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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 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: http://www.eng.utah.edu/~lzang/images/cahn-hilliard-anim.gif |
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Spinodal Decomposition: Part 2: regarding free energy change and interdiffusion coefficient inside the spinodal |
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Spinodal Decomposition: Part 3: kinetics of the composition fluctuation |
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HW for lecture 22-24 |
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Ordering Transformation |
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Diffusion of Ions: Part 1: basic understanding and the derivation of diffusion flux |
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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 |
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Kinetics of Oxidation of Metals: Part 1: rusting, corrosion, and the surface protection, all about chemistry |
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Kinetics of Oxidation of Metals: Part 2: Wagner Parabolic Model |
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HW for lecture 28-29 |
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Kinetics of Epitaxial Growth: Surface Diffusion and Nucleation |
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