3.012 | Fall 2005 | Undergraduate

Fundamentals of Materials Science


Many assigned readings are from the course textbooks:

E&R: Engel, T., and P. Reid. Physical Chemistry. San Francisco, CA: Benjamin Cummings, 2005. ISBN: 9780805338423. [Note: this is the single-volume edition.]

A&T: Allen, S. M., and E. L. Thomas. The Structure of Materials. New York, NY: J. Wiley & Sons, 1999. ISBN: 9780471000822.

  Structure and Bonding Thermodynamics
Ses # Topics Readings Topics Readings
Orientation: Research and Careers in Materials Science and Engineering
L1 Classical or Quantum: Electrons as Waves, Wave Mechanics E&R: Read 12.1, 12.2, 12.4; Study 12.5, 13.2, 13.3 and problem P12.10; Review A.1 (complex numbers). Fundamental Concepts E&R: 1.1 and 1.2


Bent, The Second Law, pp. 1-5

L2 Schrödinger’s Equation and Discrete Energy States of a Confined Electron E&R: Review 12.5, 13.2, and 13.3; Study 13.4 and 13.5.

Mortimer, R. G. “Principles of Quantum Mechanics: Classical Mechanics.” Section 14.1 in Physical Chemistry. 2nd ed. San Diego, CA: Elsevier, 2000. ISBN: 9780125083461.

Dill, D. “Analytic solution of the Schrödinger equation: Particle in a box.” (PDF)

Smith, D. Y. “Spin-Orbit Effects in the F and K Bands of Colored Alkali Halides.” Physical Review B 6, no. 2 (July 15, 1972): 565-581.

Fundamental Concepts (cont.) E&R: 1.4, 2.1, 2.2, and 2.3.
L3 Free Electrons, Electrons in a Metal, and the Scanning Tunneling Microscope E&R: Study 15.1 and 15.2; Read 14.1-14.4. First Law of Thermodynamics E&R: 2.5, 2.6, 2.7, 2.9, and 3.1.
L4 Curiosity Killed the Cat: General Principles of Quantum Mechanics E&R: Study 15.3 (2-,3-dim box), 16.3 (?-electrons in conjugated molecules), and 16.5-6 (Scanning Tunnelling Microscope).


Binning, G., and H. Rohrer. “Scanning tunneling microscopy - from birth to adolescence.” Reviews of Modern Physics 59, no. 3 (1987): 615-625. (1986 Nobel Lecture)

Temperature, Heat, and Entropy E&R: 1.3, 2.4, and 3.2.
L5 The Hydrogen Atom E&R: Study 14.1, 14.2, and 14.3; Read 14.4. Heat Storage and Release in Phase Transitions E&R: 2.8, 3.4, and 4.6.
L6 The Hydrogen Atom (cont.) E&R: Study 14.1, 14.2, and 14.3; Read 14.4, also read 22.6 (XPS and Auger) for 3.014 Week 1. Examples of Work Important in Materials Science and Engineering: Polarization, Magnetic, Chemical Zemansky, M. W., and R. H. Dittman. “Work” In Heat and Thermodynamics. 7th Ed. Burr Ridge, IL: McGraw-Hill, 1996, pp. 49-68. ISBN: 9780070170599.

Callister, W. D., Jr. “Magnetic Properties.” In Fundamentals of Materials Science and Engineering. 2nd ed. New York, NY: John Wiley & Sons, 2004, pp. 730-744. ISBN: 9780471470144.

Labs 1 3.014 Lab Week 1
L7 Alphabet Soup: The Periodic Table E&R: Study 18.4, 18.5, and 20.1 to 20.5. Thermal Properties of Materials; Fundamental Equations E&R: 3.1 and 3.5.
L8 The Periodic Table (cont.) E&R: Study 21.5 and 21.6; Read: 17.2 (Stern-Gerlach). Fundamental Equations (cont.); Equilibrium and the Second Law E&R: Chapters 5.1-5.8.


Dill and Bromberg. “How to Design a Fundamental Equation.” In Molecular Driving Forces. New York, NY: Routledge, 2003, pp. 153-155. ISBN: 9780815320517.

L9 The Variational Principle; Application to Hydrogen Atom E&R: Study 21.4, 23.1, 23.2, and 23.3. Free Energy; Applying the Second Law in Laboratory Conditions E&R: 6.1, 6.2, 6.3 (less important), and 6.4.
  Exam 1
L10 Molecules from Atoms: Energy Minimization, Hybridization of Atomic Orbitals E&R: Study 21.4 and 23.3; Read 23.4, 24.1, and 24.2. Chemical Potentials and the Gibbs Free Energy E&R: 6.4.
L11 Bonding in Molecules: Hartree and Hartree-Fock Equations, Symmetries, Bond Order E&R: Study 25.2, 25.4, 24.4, and 24.6. Models of the Chemical Potential E&R: 6.3, 6.4, 6.5, 9.1, 9.2, and 9.5.
L12 Polymers Part 1: Diagonalization on a Basis, Huckel Model E&R: Study 24.2, 24.4-6; Read math supplement A.7 and A.8, working with determinants and working with matrices. Chemical Reaction Equilibria E&R: 6.7- 6.9, 6.11, 6.12, and 9.11-9.13.
L13 Quantum Oscillation E&R: Study 25.7 (Huckel Model), 18.1 (Quantum Oscillator); Read 18.6 (Classical Harmonic Oscillator). Electrochemical Equilibria E&R: 11.1-11.5, 11.8-11.9, and 11.11-11.13.


E&R: 11.14-11.15.

Labs 2 3.014 Lab Week 2
L14 Point Groups and Bravais Lattices E&R: Study 25.7 (Huckel Model), 18.1 (Quantum Oscillator)Read 18.6 (Classical Harmonic Oscillator). Batteries; Thermodynamic Stability E&R: 6.2 (Maxwell Relations).

Lupis, C. H. P. “Stability of one-component systems.” In Chemical Thermodynamics of Materials. Upper Saddle River, NJ: Prentice Hall, 1983, pp. 34-35. ISBN: 9780444007797.

Callen, H. B. “Stability of Thermodynamic Systems.” In Thermodynamics and an Introduction to Thermostatistics. 2nd ed. New York, NY: John Wiley & Sons, 1985, pp. 202-212. ISBN: 9780471862567.

L15 Symmetry Operations A&T: Study 3.1.1 - 3.1.4, 3.2.1, 3.2.4, and 3.2.5. Phase Changes and Phase Diagrams of Single-Component Materials E&R: 8.1-8.5.

Wang, X., S. Scandolo, and R. Car. “Carbon Phase Diagrams from Ab Initio Molecular Dynamics.” Physical Review Letters 95 (October 28, 2005): 185701.

L16 Structure of Solids A&T: Study 3.1.1-3.1.4 and 3.2.1; Read 3.2.4 and 3.2.5 (only Crystal Systems, Bravais Lattices, Unit Cells). Single-Component Phase Diagrams (cont.); Thermodynamics of Solutions Gaskell. “The free energy of solution.” Chapter 11.5 in Introduction to Metallurgical Thermodynamics. pp. 328-338

E&R: 9.6 and 9.7.

L17 X-ray Diffraction A&T: Study 3.2.2 up to p. 140, and 3.4. Free Energy of Multi-phase Solutions at Equilibrium E&R: 9.6 and 9.7.
L18 X-rays at Work: Laue Condition, Ewald Construction, Bragg’s Law, Powder Diffraction Read: Notes by Prof. B. Wuensch (PDF - 4.3 MB) (Courtesy of Prof. Wuensch. Used with permission.) Binary Phase Diagrams: Miscibility Gaps and Eutectics Lupis. “Binary Phase Diagrams.” Chapter VII in Chemical Thermodynamics of Materials. pp. 204-219
  Exam 2
Labs 3 3.014 Lab Week 3
L19 From Diffraction to Structure X-Ray Diffraction Theory (ChE 386K)
This University of Texas-Austin course Web site by Steve Swinnea at has many details (from Lec #19 on, note different 2? convention).
Binary Phase Diagrams (cont.) Callister, W. D., Jr. “Phase Diagrams.” Chapter 10S in Fundamentals of Materials Science and Engineering. pp. S67-S84.
L20 Symmetries and Tensors A&T: Study 3.3 (Symmetry Constraints)
Read all of Chapter 1.
Spinodals and Binodals; Continuous Phase Transitions; Introduction to Statistical Mechanics E&R: 13.1 and 13.2.


Zallen. “The Glass Transition.” Chapter 1.4 in The Physics of Amorphous Solids. pp. 16-23.

Review E&R Chapter 12 -Basic Probability Concepts.

L21 Non-crystalline Materials A&T: Study 3.3 (Symmetry Constraints)
Read all of Chapter 1.
Connecting Events at the Atomic/Molecular Level to Macroscopic Thermodynamic Behavior: Two Postulates of Statistical Mechanics; Microscopic Definition of Entropy E&R: 31.1-31.4.
L22 Polymers Part 2 A&T: Study 2.1-2.3.1. Connecting Events at the Atomic/Molecular Level to Macroscopic Thermodynamic Behavior (cont.): The Boltzman Factor and Partition Function; Thermal Behavior of the Einstein Solid E&R: 31.5, 32.1-31.2, 33.1-33.3.


E&R: 33.4-33.5.

L23 Glasses A&T: Study 2.1-2.4.3. Lattice Models of Materials; Modeling Polymer Solutions E&R: 32.3-32.4.

Dill and Bromberg. Chapter 15 “Solutions & Mixtures.” pp. 267-273, and Chapter 31 “Polymer Solutions.” pp. 593-605. Supplementary

E&R: 32.5-32.9 (Details of Rotational, Vibrational, and Electronic Partition Functions for Simple Molecules).

L24 Liquid Crystals A&T: Study 2.1-2.4 and 4.1-4.4.3. Flory-Huggins Theory Dill and Bromberg. “Polymer Solutions.” Chapter 31, pp. 593-605.
Labs 4 3.014 Lab Week 4
  Final Exam

Course Info

As Taught In
Fall 2005
Learning Resource Types
Exams with Solutions
Lecture Notes
Problem Sets with Solutions
Written Assignments with Examples