Thermodynamics of Materials

Calendar

The schedule below is intended to give independent learners an idea of the timings of readings, lectures, and assignments in order to plan a course of study. Please refer to the readings section for full text citations.

Session	Topics	Text	Due Dates
Class 1	Introduction to thermodynamics Entropy and spontaneous processes Molecular interactions and enthalpy Scope of thermodynamics, matter at equilibrium Use of thermodynamics, phase diagrams and other maps CALPHAD and Thermo-Calc	Ferrie: Statistical Physics for Babies	-
Class 2	Scope and use of thermodynamics Systems, phases, states, and state functions Equations of state Compressibility and thermal expansion Extensive vs intensive properties	DeHoff: ch. 1, 2.1–2.2	-
Class 3	Process variables and the First Law Conceptual introduction to work and heat Classifying processes: Adiabatic, isobaric, isochronic Heat capacity First law	DeHoff: ch. 2, 3.1	-
Class 4	Heat engines and energy conversion efficiency Heat engines Carnot cycle with ideal gas Carnot efficiency Clausius’ theorem	DeHoff: App. H	-
Lab 1 (Virtual)	Phase diagrams for materials selection: Fe-C: Understanding phase diagrams and their role in materials selection and design	-	CI-M presentation topic
Class 5	Second Law and entropy maximization Combined statement of first and second laws Equilibrium in an isolated system	DeHoff: ch. 3.2–3.5, 5.1-5.2	Pset 1
Class 6	Thermodynamic potentials Chemical potential General strategy	DeHoff: ch. 4	-
Class 7	Ideal gas processes Adiabatic Isothermal Free expansion	DeHoff: ch. 4	-
Class 8	Mathematical implications of equilibrium and spontaneous processes Mathematical formulation of entropy max Equilibrium conditions for a unary, heterogeneous system Partial thermodynamic equilibrium Spontaneous processes and entropy generation	DeHoff: ch. 5	Pset 2
Class 9	Case studies: Specific heats and phase transformations	-	-
Exam 1	-	-	Lab 1 write-up CI-M presentation rough draft (ungraded)
Class 10	Introduction to unary phase transformations Unary phase transformations Gibbs surfaces Reaction/transformation quantities	DeHoff: ch. 7.1–7.2	-
Class 11	Phase coexistence in unary systems Clausius-Clapeyron equation Vapor pressure Gibbs phase rule	DeHoff: ch. 7	-
Class 12	Case studies: Saturation vapor pressure	-	-
Class 13	Introduction to ideal (gas) mixtures Dalton’s rule Gibbs free energy of an ideal gas mixture Balancing chemical reactions	Denbigh: ch. 4.1–4.5	Pset 3
Class 14	Reacting gas mixtures at equilibrium Minimum Gibbs free energy for an ideal gas chemical reaction Reaction equilibrium constant and LeChatelier’s principle van’t Hoff equation	Denbigh: ch. 4.1–4.9	-
-	-	-	CI-M Presentation slide deck
Class 15	Introduction to solutions, general case Solubility and solubility limits The process of making solutions Difference between reactions and solutions Introduction to solution modeling	Callister: ch. 9.–9.6                     DeHoff: ch. 8.1	Pset 4
Class 16	Partial molar properties PMP definition Gibbs-Duhem equation Calculating PMPs from solution models, including graphical solution	DeHoff: ch. 8.1–8.4	-
Class 17	Solution models: Ideal, dilute, and regular Ideal gas mixtures and the ideal solution model Non-ideal solutions, activity, and activity coefficients Dilute solution model, Henry’s and Raoult’s laws Regular solution models	DeHoff: ch. 8	-
Lab 2 (Virtual)	Thermal energy storage: Phase change materials Understand binary phase diagrams: Solidus, liquidus, eutectics Understand and quantify thermodynamic quantities, e.g., heat capacity, latent heat of fusion	-	Annotated bibliography due
Class 18	Case study in reacting gas mixtures; introducing the Nernst equation	-	Pset 5
Exam 2	-	-	-
Class SP1*	Social and personal 1 Discuss social and personal aspects of working in the field of materials science	See readings section for options	-
Class 19	Regular solutions models and stability Quasi-chemical model Temperature-dependence of the simple regular model Stability and spontaneous unmixing	DeHoff: ch. 8	-
Class 20	Introduction to binary phase diagrams Chemical potential in multicomponent systems Equilibrium conditions in multi-component, multi-phase systems Gibbs phase rule for multicomponent, heterogeneous systems	Callister: ch. 9.7, 9.8   DeHoff: ch. 9, 10.1	-
Class 21	Phase coexistence and separation Condition for 2-phase coexistence Common tangent construction Spinodal phase diagram	DeHoff: ch. 9, 10.1	-
Class 22	Free energy-composition diagrams, general case Reference states Drawing free energy-composition diagrams	DeHoff: ch. 10.1	Pset 6
Class 23	Building binary phase diagrams, part I Taut rope construction Lens diagrams Eutectic systems	DeHoff: ch. 10	-
Class 24	Building binary phase diagrams, part II Peritectic systems Intermediate phases Exploring Thermo-Calc Line compounds (if time allows)	DeHoff: ch. 10	Pset 7
Class 25	Building binary phase diagrams, part III Case study: Modeling the Cr-Fe system	DeHoff: ch. 10	-
Class 26	CALPHAD: Case studies and Prof. Olson guest lecture	DeHoff: ch. 10	-
Class 27	Introduction to statistical thermodynamics Macrostates and microstates Counting microstates Ensembles and ergodicity	DeHoff ch. 6	Pset 8
Lab 3  (Virtual)	Computational statistical thermodynamics Understand probability distributions and the Boltzmann distribution Understand origin of temperature from microscopic degrees of freedom  Understand fluctuations and thermalization	-	-
Class 28	Boltzmann hypothesis Boltzmann hypothesis Configurational entropy Setting up maximum entropy for isolated system	DeHoff ch. 6, Chandler ch. 3	-
-	-	-	Literature review full draft (ungraded)
Class 29	Boltzmann distribution Boltzmann distribution as equilibrium condition Microcanonical and canonical ensembles Partition functions	DeHoff ch. 6 Chandler ch. 3	-
-	-	-	Pset 9 Literature review final draft due
Class 30	Intermediate phases and reactions	DeHoff: ch. 10, 11.1–11.2   Callister: ch. 9.13   Denbigh: ch. 4.8	-
-	-	-	Lab 3 write-up
Class 31	Reacting multi-phase systems Solid-vapor equilibrium Oxidation and Richardson-Ellingham diagrams	DeHoff: ch. 11	-
Class 32	Case study: Reacting, multi-component, multi-phase systems	-	Pset 10
Class SP2*	Social and personal 2 Discuss social and personal aspects of working in the field of materials science	See readings section	-
Class 33	Gameshow (in-class exam review)	-	-
Final Exam	-	-	-

*Novel for the course this year, two class sessions were devoted to discussing the social and personal aspects of working in the field of materials science. The intention was to have students explore their individual purpose and motivation for pursuing careers in science and engineering, and to have them think about the impact of their work on the wider world.

Please note that the information on this page was intended for students enrolled in the residential MIT course and is included to provide insight into how the course was conducted in Spring 2021. OCW is not a distance education program, and we do not offer instructor interactions, grading, or certification of completion.