MATE 664 Lecture 01

Thermodynamics and Kinetics

Author

Dr. Tian Tian

Published

January 5, 2026

Note

Slides 👉 Open presentation🗒️
PDF version of course note 👉 Open in pdf
Handwritten notes 👉 Open in pdf

Land Acknowledgement

The University of Alberta acknowledges that we are located on Treaty 6 territory, and respects the histories, languages, and cultures of the First Nations, Métis, Inuit, and all First Peoples of Canada, whose presence continues to enrich our vibrant community.

Learning Outcomes

After today’s lecture, you will be able to:

Identify the key components of the course syllabus, content and grading schemes.
Recall common interaction methods and resources available in the course.
Recall basic concepts in thermodynamics and kinetics
State assumptions of equilibrium
Describe the influence of entropy in kinetic systems

Course Information

Course: MAT E 664 – Kinetics of Materials
Term: Winter 2026
Lectures: Mon & Wed
Time: 14:00 – 15:20
Location: HC 2-14

Meet the Instructor

Office: DICE 12-245
Email: tian.tian@ualberta.ca
Office hour: by appointment
I joined CME in 2025 as assistant professor.
Research fields: machine learning, multiscale materials simulations, computational tools
Let’s enjoy learning together!

TAs & Seminar Sessions

Teaching Assistant
- Hanlin Wang — hanlin7@ualberta.ca
Course & Assignment Questions
- No formal seminar or lab sessions
- Questions related to course content or assignments
- Please book an appointment with the TA (and instructor) as needed
Support Format
- One-on-one or small-group discussions
- Concept clarification and guidance

Course Grading

Assignments: 25%
- 4 assignments (best 3 counted)
- Submission via Canvas
Final Project: 30%
- Research-related topic
- In-class oral presentation
Final Exam: 45%
- In person, open book
- Apr 20, 2026 · 1:00 p.m.

Details please see the course syllabus

Textbook and References

Our primary textbooks for this course are:

Kinetics of Materials by R.W. Balluffi, S.M. Allen, and W.C. Carter.

Materials Kinetics: Transport and Rate Phenomena by John C. Mauro.

What Will We Learn in MAT E 664 (1)?

Theory: irreversible thermodynamics & driving forces

\[ \text{Flux} = \text{Kinetic coefficients} \times \text{Driving Force} \]

What Will We Learn in MAT E 664 (2)?

Mass transport on solid material interfaces: $v_{step} = \beta (c - c_{eq})$

## What Will We Learn in MAT E 664 (3)?

Nucleation theory: $r_{c} = -\dfrac{2\gamma}{\Delta G_v}$

What Will We Learn in MAT E 664 (4)?

Spinodal Decomposition (Pattern Formation) \[ \dfrac{\partial c}{\partial t} = \nabla \cdot \left( M \nabla \left[ \dfrac{\partial f(c)}{\partial c} - \kappa \nabla^{2} c \right] \right) \]

Interaction Time!

We will use Wooclap in this course for real-time interactions.

Participation link 👉 https://app.wooclap.com/664L01?from=instruction-slide

Results to be published after the class

Thermodynamics vs. Kinetics

Feature	Thermodynamics	Kinetics
Greek Name	Therme (heat) + dynamis (power)	Kinetikos (of motion)
Focus	Eventually: Predicts the final state	Rate: How fast a process occurs
General Form	Free energy change ($\Delta G$)	Reaction rates, flux, activation energy
Condition	Equilibrium	Non-equilibrium

The True Meaning of Equilibrium

Equilibrium is a balance of time scales: \[ \tau_{\text{observation}} \gg \tau_{\text{process}} \]

Thermodynamic descriptions are relevant when the observation time scale is much larger than the time scale of the processes reaching equilibrium.
It’s about specific processes reaching a steady state, not necessarily the entire system.

Coffee reaching equilibrium

⁴

Kinetic Processes

Kinetic processes are distinct from thermodynamic equilibrium:

Conditions: Occur away from equilibrium.
Cause Require a thermodynamic driving force.
Rate: Coupled with a rate parameter or coefficient.

Irreversible Thermodynamics is key to understanding these processes (Lecture 2).

Classical Thermodynamics Revisited

thermodynamics memory card

⁵

## Thermodynamic Interplay Between $H$ and $S$

Whether a process from A → B is spontaneous or non-spontaneous depends on the sign of free energy difference, $\Delta G = G_{B} - G_{A}$.

H vs S

⁶

What is $\Delta G$ for a reversible process at equilibrium?: $\Delta G = 0$,
How can we check the stability of a certain material at $P, T$?: Use the phase diagram!

How Stable Is Diamond?

Which phase is the most stable at r.t. & 1 atm?
Should we worry our diamond rings turn into pencil?

diamond

Two-State model of Thermodynamics vs Kinetics

$\Delta G^0$: Free energy of reaction → will reaction happen? (Thermodynamics)
$\Delta G^*$: Free energy of activation → how likely / fast? (Kinetics)

2 state system

Arrhenius Plot Demo

Where Does Entropy $S$ Come From?

Claussius (1865) Classical thermodynamics.
- Entropy is a state variable of internal energy.
- $dU(S, V) = TdS - pdV$
Boltzmann (1877) Statistical mechanics.
- Entropy is a measure of accessible microstates (atoms + probability!)
- $S = k_B \log(\Omega)$

Why The Logarithm?

$S$ as an extensive quantity → Additive $S_T = S_1 + S_2$
$\Omega$ as microstates is multiplicative → $\Omega_T = \Omega_1 \cdot \Omega_2$
If $S = f(\Omega)$, then $S_T = f(\Omega_T) = f(\Omega_1 \cdot \Omega_2)$ → $f(\Omega_1 \cdot \Omega_2) = f(\Omega_1) + f(\Omega_2)$
$f(x) = C \log(x)$ is the unique solution using Cauchy’s functional equation results

Entropy IS NOT Disorder!

Common statement of entropy is measure of disorder
Boltzmann equation measures how many possibilities of arrangement
Disorder is not uniquely linked to number of microstates!

messy-book

Entropy IS NOT Disorder – II!

High entropy alloys (HEAs): Example of high configurational entropy material
Many HEAs have much more ordered lattice than binary alloys

hea

⁷

What Should We Really Think of Entropy

Arrow of time: mixed cream and coffee cannot be demixed
- Newtonian dynamics is time-reversible
- We cannot rewind to low entropy state from Newtonian dynamics!
Loss of information:
- Shannon entropy: $S_{info} = -k_B \sum_i p_i \log(p_i)$
- Shannon entropy can be measured on the exact state!
Uncertainty:
- Link to Heisenberg’s principle $\Delta x \Delta p \leq \hbar/2$
- See Hirschman Am. J. Math., 1957 79, 152

Where Can We Go From Here?

Irreversible thermodynamics

Real processes occur away from equilibrium, where entropy is produced.
Entropy generation as a driving force

Gradients in temperature, concentration, and chemical potential drive fluxes by increasing total entropy.
From equilibrium to dynamics

Entropy provides the unifying language for diffusion, heat flow, chemical reactions, and transport phenomena.

Stay Tuned!

Brief Introduction to Course AI Helper

A Socratic Gemini chatbot aiming to help course learning and key concepts
Access the AI helper here: 👉 https://gemini.google.com/gem/1c118102b2d1

Summary

What we learned today:

Syllabus / course contents of MATE 664
Kinetic rate and equilibrium
Concept of entropy revisited
Laws of thermodynamics revisited

See you next time!

Footnotes

Image credit: A.R. Verma↩︎
Image credit: crystalverse.com↩︎
Image credit: Mathis Plapp, École Polytechnique (FR)↩︎
Image credit: John C. Mauro↩︎
Image credit: John C. Mauro↩︎
Image credit: John C. Mauro↩︎
Small 2024, 20, 2311929↩︎

--- title: "MATE 664 Lecture 01" subtitle: "Thermodynamics and Kinetics" author: "Dr. Tian Tian" date: "2026-01-05" format: html: {} revealjs: output-file: slides.html pdf: output-file: L01.pdf --- ::: {.content-visible when-format="html" unless-format="revealjs"} ::: {.callout-note} - Slides 👉 [Open presentation🗒️](./slides.html) - PDF version of course note 👉 [Open in pdf](./L01.pdf) - Handwritten notes 👉 [Open in pdf](./public/L01_annotated.pdf) ::: ::: ## Land Acknowledgement {.center} #### The University of Alberta acknowledges that we are located on Treaty 6 territory, and respects the histories, languages, and cultures of the First Nations, Métis, Inuit, and all First Peoples of Canada, whose presence continues to enrich our vibrant community. ## Learning Outcomes After today's lecture, you will be able to: - **Identify** the key components of the course syllabus, content and grading schemes. - **Recall** common interaction methods and resources available in the course. - **Recall** basic concepts in thermodynamics and kinetics - **State** assumptions of equilibrium - **Describe** the influence of entropy in kinetic systems ## Course Information - **Course:** MAT E 664 – Kinetics of Materials - **Term:** Winter 2026 - **Lectures:** Mon & Wed - **Time:** 14:00 – 15:20 - **Location:** HC 2-14 ## Meet the Instructor - **Office**: DICE 12-245 - **Email**: tian.tian@ualberta.ca - **Office hour**: by appointment - I joined CME in 2025 as assistant professor. - Research fields: machine learning, multiscale materials simulations, computational tools - Let’s enjoy learning together! ## TAs & Seminar Sessions - **Teaching Assistant** - Hanlin Wang — hanlin7@ualberta.ca - **Course & Assignment Questions** - No formal seminar or lab sessions - Questions related to course content or assignments - Please book an appointment with the TA (and instructor) as needed - **Support Format** - One-on-one or small-group discussions - Concept clarification and guidance ## Course Grading - **Assignments:** 25% - 4 assignments (best 3 counted) - Submission via Canvas - **Final Project:** 30% - Research-related topic - In-class oral presentation - **Final Exam:** 45% - In person, open book - **Apr 20, 2026 · 1:00 p.m.** _Details please see the [course syllabus](../../syllabus/assets/MATE664-winter-2026-course-syllabus.pdf)_ ## Textbook and References Our primary textbooks for this course are: :::{.columns} :::{.column width="50%"} - **Kinetics of Materials** by R.W. Balluffi, S.M. Allen, and W.C. Carter. <div style="width: 60%;"> <img src="public/balluffi.jpg" style=" width: 100%; max-height: 80vh; object-fit: cover; display: block; " /> </div> ::: :::{.column width="50%"} - **Materials Kinetics: Transport and Rate Phenomena** by John C. Mauro. <div style="width: 60%;"> <img src="public/mauro.jpg" style=" width: 100%; max-height: 80vh; object-fit: cover; display: block; " /> </div> ::: ::: --- ## What Will We Learn in MAT E 664 (1)? Theory: irreversible thermodynamics & driving forces $$ \text{Flux} = \text{Kinetic coefficients} \times \text{Driving Force} $$ <div style="width: 100%;"> <img src="https://www.ntnu.edu/documents/1412485/1277516986/Onsager_heading.jpg" style=" width: 100%; max-height: 80vh; object-fit: cover; display: block;" /> </div> --- ## What Will We Learn in MAT E 664 (2)? Mass transport on solid material interfaces: $v_{step} = \beta (c - c_{eq})$ <div style="width: 100%;"> <img src="public/SiC-spiral.png" style=" width: 100%; max-height: 80vh; object-fit: cover; display: block;" /> </div> ^[_Image credit: A.R. Verma_] --- ## What Will We Learn in MAT E 664 (3)? Nucleation theory: $r_{c} = -\dfrac{2\gamma}{\Delta G_v}$ <div style="width: 100%;"> <img src="public/copper-sulfate-impurities-header.jpg" style=" width: 100%; max-height: 80vh; object-fit: cover; display: block; " /> </div> ^[_Image credit: crystalverse.com_] --- ## What Will We Learn in MAT E 664 (4)? Spinodal Decomposition (Pattern Formation) $$ \dfrac{\partial c}{\partial t} = \nabla \cdot \left( M \nabla \left[ \dfrac{\partial f(c)}{\partial c} - \kappa \nabla^{2} c \right] \right) $$ <div style="width: 100%;"> <img src="https://pmc.polytechnique.fr/~mp/spide.GIF" style=" width: 100%; max-height: 80vh; object-fit: cover; display: block; " /> </div> ^[_Image credit: Mathis Plapp, École Polytechnique (FR)_] --- ## Interaction Time! We will use Wooclap in this course for real-time interactions. Participation link 👉 [https://app.wooclap.com/664L01?from=instruction-slide](https://app.wooclap.com/664L01?from=instruction-slide) *Results to be published after the class* --- ## Thermodynamics vs. Kinetics | Feature | Thermodynamics | Kinetics | |:-----------------|:-----------------------------------------|:----------------------------------------| | **Greek Name** | *Therme* (heat) + *dynamis* (power) | *Kinetikos* (of motion) | | **Focus** | **Eventually**: Predicts the final state | **Rate**: How fast a process occurs | | **General Form** | Free energy change ($\Delta G$) | Reaction rates, flux, activation energy | | **Condition** | Equilibrium | Non-equilibrium | --- ## The True Meaning of Equilibrium Equilibrium is a balance of time scales: $$ \tau_{\text{observation}} \gg \tau_{\text{process}} $$ - **Thermodynamic descriptions** are relevant when the observation time scale is much larger than the time scale of the processes reaching equilibrium. - It's about **specific processes** reaching a steady state, not necessarily the entire system. <div style="width: 100%; text-align: center;"> <img src="public/mauro-coffee-eq.png" alt="Coffee reaching equilibrium" style=" width: 100%; max-height: 80vh; object-fit: cover; display: block; margin: 0 auto;" /> </div> ^[_Image credit: John C. Mauro_] --- ## Kinetic Processes Kinetic processes are distinct from thermodynamic equilibrium: 1. **Conditions:** Occur away from equilibrium. 2. **Cause** Require a thermodynamic **driving force**. 3. **Rate:** Coupled with a **rate parameter** or **coefficient**. **Irreversible Thermodynamics** is key to understanding these processes ([Lecture 2](../L02/)). --- ## Classical Thermodynamics Revisited <div style="width: 80%; text-align: center;"> <img src="public/mauro-thermo-card.png" alt="thermodynamics memory card" style=" width: 80%; max-height: 80vh; object-fit: cover; display: block; margin: 0 auto;" /> </div> ^[_Image credit: John C. Mauro_] --- ## ## Thermodynamic Interplay Between $H$ and $S$ Whether a process from A → B is **spontaneous** or **non-spontaneous** depends on the sign of free energy difference, $\Delta G = G_{B} - G_{A}$. <div style="width: 80%; text-align: center;"> <img src="public/mauro-spontaneous-vs.png" alt="H vs S" style=" width: 80%; max-height: 80vh; object-fit: cover; display: block; margin: 0 auto;" /> </div> ^[_Image credit: John C. Mauro_] - What is $\Delta G$ for a reversible process at equilibrium?: $\Delta G = 0$, - How can we check the stability of a certain material at $P, T$?: Use the phase diagram! ## How Stable Is Diamond? - Which phase is the most stable at r.t. & 1 atm? - Should we worry our diamond rings turn into pencil? <div style="width: 100%; text-align: center;"> <img src="public/diamond-phase.png" alt="diamond" style=" width: 100%; max-height: 80vh; object-fit: cover; display: block; margin: 0 auto;" /> </div> ## Two-State model of Thermodynamics vs Kinetics - $\Delta G^0$: Free energy of **reaction** → will reaction happen? (**Thermodynamics**) - $\Delta G^*$: Free energy of **activation** → how likely / fast? (**Kinetics**) <div style="width: 100%; text-align: center;"> <img src="public/mauro-2state.png" alt="2 state system" style=" width: 100%; max-height: 80vh; object-fit: cover; display: block; margin: 0 auto;" /> </div> ## Arrhenius Plot Demo <iframe width="100%" height="800px" src="../../scripts/L01_ea.html" > </iframe> ## Where Does Entropy $S$ Come From? - Claussius (1865) **Classical thermodynamics**. - Entropy is a state variable of internal energy. - $dU(S, V) = TdS - pdV$ - Boltzmann (1877) **Statistical mechanics**. - Entropy is a measure of accessible microstates (atoms + probability!) - $S = k_B \log(\Omega)$ <div style="width: 100%; text-align: center;"> <img src="https://upload.wikimedia.org/wikipedia/commons/thumb/6/63/Zentralfriedhof_Vienna_-_Boltzmann.JPG/960px-Zentralfriedhof_Vienna_-_Boltzmann.JPG" alt="2 state system" style=" width: 50%; max-height: 80vh; object-fit: cover; display: block; margin: 0 auto;" /> </div> ## Why The Logarithm? - $S$ as an **extensive** quantity → **Additive** $S_T = S_1 + S_2$ - $\Omega$ as microstates is **multiplicative** → $\Omega_T = \Omega_1 \cdot \Omega_2$ - If $S = f(\Omega)$, then $S_T = f(\Omega_T) = f(\Omega_1 \cdot \Omega_2)$ → $f(\Omega_1 \cdot \Omega_2) = f(\Omega_1) + f(\Omega_2)$ - $f(x) = C \log(x)$ is the unique solution using Cauchy's functional equation results ## Entropy *IS NOT* Disorder! - Common statement of entropy is measure of *disorder* - Boltzmann equation measures **how many possibilities** of arrangement - Disorder is not uniquely linked to number of microstates! <div style="width: 100%; text-align: center;"> <img src="public/disorder-compare.png" alt="messy-book" style=" width: 100%; max-height: 80vh; object-fit: cover; display: block; margin: 0 auto;" /> </div> ## Entropy *IS NOT* Disorder -- II! - **High entropy alloys** (**HEAs**): Example of high configurational entropy material - Many HEAs have much more ordered lattice than binary alloys <div style="width: 100%; text-align: center;"> <img src="public/smll202311929-fig-0002-m.jpg" alt="hea" style=" width: 100%; max-height: 80vh; object-fit: cover; display: block; margin: 0 auto;" /> </div> ^[_Small_ **2024**, 20, 2311929] ## What Should We Really Think of Entropy - **Arrow of time**: mixed cream and coffee cannot be demixed - Newtonian dynamics is time-reversible - We cannot rewind to low entropy state from Newtonian dynamics! - **Loss of information**: - **Shannon entropy**: $S_{info} = -k_B \sum_i p_i \log(p_i)$ - Shannon entropy **can be measured** on the exact state! - **Uncertainty**: - Link to Heisenberg's principle $\Delta x \Delta p \leq \hbar/2$ - See Hirschman *Am. J. Math.*, **1957** 79, 152 ## Where Can We Go From Here? - **Irreversible thermodynamics** Real processes occur away from equilibrium, where entropy is **produced**. - **Entropy generation as a driving force** **Gradients** in temperature, concentration, and chemical potential drive fluxes by increasing total entropy. - **From equilibrium to dynamics** Entropy provides the unifying language for diffusion, heat flow, chemical reactions, and transport phenomena. **Stay Tuned!** ## Brief Introduction to Course AI Helper - A Socratic Gemini chatbot aiming to help course learning and key concepts - **Access the AI helper here:** 👉 [https://gemini.google.com/gem/1c118102b2d1](https://gemini.google.com/gem/1c118102b2d1) <div style="width: 100%; text-align: center;"> <img src="https://quickchart.io/qr?text=https://gemini.google.com/gem/1c118102b2d1&size=150" alt="QR Code for AI Helper" style="width: 150px; height: 150px; display: block; margin: 0 auto;" /> </div> ## Summary What we learned today: - Syllabus / course contents of MATE 664 - Kinetic rate and equilibrium - Concept of entropy revisited - Laws of thermodynamics revisited **See you next time!**