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Abstract/Syllabus:

Irvine, Darrell, and Nicola Marzari, 3.012 Fundamentals of Materials Science, Fall 2005. (Massachusetts Institute of Technology: MIT OpenCourseWare), http://ocw.mit.edu  (Accessed 07 Jul, 2010). License: Creative Commons BY-NC-SA

Fundamentals of Materials Science

Fall 2005

Diagram of two crystal structures.
Charge density in paraelectric and ferroelectric PbTiO3. See lecture notes for Lec #16, Structure and Bonding. (Figure by Prof. Nicola Marzari.)

Course Highlights

This course features complete lecture notes, assignments, and exams.

Course Description

This course focuses on the fundamentals of structure, energetics, and bonding that underpin materials science. It is the introductory lecture class for sophomore students in Materials Science and Engineering, taken with 3.014 and 3.016 to create a unified introduction to the subject. Topics include: an introduction to thermodynamic functions and laws governing equilibrium properties, relating macroscopic behavior to atomistic and molecular models of materials; the role of electronic bonding in determining the energy, structure, and stability of materials; quantum mechanical descriptions of interacting electrons and atoms; materials phenomena, such as heat capacities, phase transformations, and multiphase equilibria to chemical reactions and magnetism; symmetry properties of molecules and solids; structure of complex, disordered, and amorphous materials; tensors and constraints on physical properties imposed by symmetry; and determination of structure through diffraction. Real-world applications include engineered alloys, electronic and magnetic materials, ionic and network solids, polymers, and biomaterials.

Technical Requirements

Special software is required to use some of the files in this course: .cif, .mov, and .zip.

Syllabus

In addition to a thorough overview of 3.012, this page presents background information on the Department of Materials Science and Engineering (DMSE) undergraduate curriculum.
The DMSE Undergraduate Curriculum

Overview of DMSE Undergraduate Curriculum (PDF)

3.012 is the introductory lecture class for sophomore students in Materials Science and Engineering, taken with 3.014 and 3.016 to create a unified introduction to the subject.
3.012 Course Information
Philosophy of the Course

3.012 is an introduction to three topics fundamental to materials science and engineering: structure, bonding, and thermodynamics. These topics are not traditionally taught in tandem, though a structure course and thermodynamics course are usually part of the first core courses taken in a Materials Science and Engineering curriculum. The motivation for bringing these subjects together in 3.012 is to aid in teaching you the conceptual ties between these subjects. Bonding dictates structure, and structure in turn provides constraints on the thermodynamic properties of materials. These topics are intimately related and a full understanding of materials' synthesis, fabrication, and processing relies on bringing out these interconnections. In addition, it is enlightening to learn about the same materials from different viewpoints, to better appreciate the diverse perspectives we take when looking at materials science: What is the crystal structure of diamond? How does it affect its thermodynamics properties? How is it related to the nature of the bonding between carbon atoms? One then begins to see how these fundamental properties of materials are connected.

Many fascinating materials phenomena will become clear in the course of the class - Why are some materials easily polarized in one direction and not in another? Why are the heat capacities of very different crystals nearly equal at high temperatures? How do electrons "tunnel" through high barriers, and how can we exploit this to image atoms and molecules in real time? What prevents certain processes from occurring, while others proceed spontaneously? In addition, structure, bonding, and thermodynamic behavior underlie nearly every application of materials to a greater or lesser extent, and these topics play significant roles in the properties of materials that you will learn about in the coming 3 years.
Explanation of Course Units

The units reported in the course catalog: (5) (0) (10) appear confusing, given the course schedule (6 hours lecture per week, 2 hours recitation per week) - recall the units system is (hours lecture/recitation) (hours lab) (hours outside class). This is due to the integration of 3.012 with the laboratory course 3.014 - which runs 4 weeks of the term, and takes over the lecture time for 3.012 during lab weeks. Thus the course catalog units reflect an 'average' value measured over the entire term. In practice, you will have 2 hours lecture Monday Wednesday Friday, along with 2 recitations of 1 hour each on Tuesday and Thursday - during '3.012' weeks. During '3.014' lab weeks, 3.012 will not be in session. The schedule of the lecture/lab sessions is shown in the calendar section.
Prerequisites or Corequisites

One of the following: 18.03, 18.034, 3.016
Textbooks

Two textbooks are required for this class.

    *
      Engel, T., and P. Reid. Physical Chemistry. San Francisco, CA: Benjamin Cummings, 2005. ISBN: 9780805338423. [Note: this is the single-volume edition.]
    *
      Allen, S. M., and E. L. Thomas. The Structure of Materials. New York, NY: J. Wiley & Sons, 1999. ISBN: 9780471000822.

The following supplemental textbooks are suggested, as alternative sources of background reading or practice problem-solving.

Structure and Bonding:

    *
      Rohrer, G. Structure and Bonding in Crystalline Materials. New York, NY: Cambridge University Press, 2001. ISBN: 9780521663793.
    *
      Atkins, P. W., and J. de Paula. Physical Chemistry. 7th ed. New York, NY: Oxford University Press, 2002. ISBN: 9780198792857.
    *
      Nye, J. F. Physical Properties of Crystals: Their Representation by Tensors and Matrices. New York, NY: Oxford University Press, 1985. ISBN: 9780198511656.
    *
      Mortimer, R. G. Physical Chemistry. 2nd ed. San Diego, CA: Elsevier, 2000. ISBN: 9780125083461.
    *
      Thaller, B. Visual Quantum Mechanics. New York, NY: Springer-Verlag/TELOS, 2002. ISBN: 9780387989297.
    *
      Bransden, B. H., and C. J. Joachain. Quantum Mechanics. 2nd ed. Upper Saddle River, NJ: Prentice Hall, 2000. ISBN: 9780582356917.
    *
      Bransden, B. H., and C. J. Joachain. Physics of Atoms and Molecules. 2nd ed. Upper Saddle River, NJ: Prentice Hall, 2003. ISBN: 9780582356924.
    *
      Petrucci, R. H., W. S. Harwood, and F. G. Herring. General Chemistry: Principles and Modern Applications. 8th ed. Upper Saddle River, NJ: Prentice Hall, 2001. ISBN: 9780130143297.

Thermodynamics and Statistical Mechanics:

    *
      Dill, K. A., and S. Bromberg. Molecular Driving Forces . New York, NY: Routledge, 2002. ISBN: 9780815320517.
    *
      Bent, H. A. The Second Law. New York, NY: Oxford University Press, 1965. ISBN: 9780195008296.
    *
      Callen, H. B. Thermodynamics. New York, NY: John Wiley & Sons, 1960. ISBN: 9780471130352.
    *
      Denbigh, K. G. The Principles of Chemical Equilibrium. 4th ed. New York, NY: Cambridge University Press, 1981. ISBN: 9780521281508.
    *
      Mortimer, R. G. Physical Chemistry. 2nd ed. San Diego, CA: Elsevier, 2000. ISBN: 9780125083461.

Recitations

Recitations are scheduled in two sections, held Tuesdays and Thursdays during lecture weeks (but not during 3.014 lab weeks). Recitations on Tuesdays will reinforce thermodynamics material, and Thursday recitations will cover bonding/structure material.
Evaluation

Evaluation

1. Composition of Final Grades:

Activities Percentages
Problem Sets (~5 Graded Homeworks Over the Course of the Term) 20%
3 Exams 80%

Two of the exams are 2 hour quizzes given during lecture sessions, the last exam will fall during finals' week. The final exam is not cumulative.

2. Final Letter Grades:

Final letter grades will be determined by total weighted scores from the problems sets and 3 exams. The approximate score breakdown will be:

Weighted Scores Grades
80 and Above A
70-79 B
55-69 C
Less than 55 Failing

Note that these are the approximate score assignments: if your score falls at the border (e.g., between an A and B), we will look more carefully at your effort in the term to determine the final grade: did you improve over the course of the term? Were you diligent in doing the problem sets? The purpose of giving you these score assignments is to give you some indication of how you are doing as the term progresses.

3. Problem Sets:

Each problem set will contain 2-3 problems from structure/bonding and 2-3 problems from thermodynamics that will be graded. Problem sets can be turned in at recitation/lecture on the due date, or you may leave them in the drop box outside Prof. Irvine's office no later than 5 pm on the due date.

Important: Problem Set Turn-in Policy - The problems sets are a critical part of learning the material in this course. Generally, the problem set solutions will be provided immediately after the turn-in deadline. Late problem sets will not be accepted (they will be scored as zero points).

4. Exams:

Each exam will contain approximately half thermodynamics problems, and half structure/bonding questions. Two of the three exams will be given during lecture periods; see the calendar section for the detailed schedule. The last exam, though scheduled in finals week, will not be cumulative - it will only cover the lectures from Exam 2 onward.

Additional Syllabus information on the Thermodynamics Component

Calendar

SES # Key

L = Lecture
Rb = Recitation: Structure and Bonding
Rt = Recitation: Thermodynamics
Lab = 3.014 Lab Week

Instructor for Structure and Bonding: Prof. Nicola Marzari
Instructor for Thermodynamics: Prof. Darrell Irvine

Ses # Structure and Bonding TOPICS Thermodynamics TOPICS Key Dates
Orientation: Research and Careers in Materials Science and Engineering
L1 Classical or Quantum: Electrons as Waves, Wave Mechanics Fundamental Concepts Problem set 1 out
L2 Schrödinger's Equation and Discrete Energy States of a Confined Electron Fundamental Concepts (cont.)  
Rt1   Recitation  
L3 Free Electrons, Electrons in a Metal, and the Scanning Tunneling Microscope First Law of Thermodynamics  
Rb1 Recitation    
L4 Curiosity Killed the Cat: General Principles of Quantum Mechanics Temperature, Heat, and Entropy  
Rt2   Recitation  
L5 The Hydrogen Atom Heat Storage and Release in Phase Transitions Problem set 1 due

Problem set 2 out
Rb2 Recitation    
L6 The Hydrogen Atom (cont.) Examples of Work Important in Materials Science and Engineering: Polarization, Magnetic, Chemical  
Labs 1 3.014 Lab Week 1 Problem set 2 due
L7 Alphabet Soup: The Periodic Table Thermal Properties of Materials; Fundamental Equations Problem set 3 out
Rt3   Recitation  
L8 The Periodic Table (cont.) Fundamental Equations (cont.); Equilibrium and the Second Law  
Rb3 Recitation    
L9 The Variational Principle; Application to Hydrogen Atom Free Energy; Applying the Second Law in Laboratory Conditions  
Rt4   Recitation  
  Exam 1  
Rb4 Recitation    
L10 Molecules from Atoms: Energy Minimization, Hybridization of Atomic Orbitals Chemical Potentials and the Gibbs Free Energy  
L11 Bonding in Molecules: Hartree and Hartree-Fock Equations, Symmetries, Bond Order Models of the Chemical Potential Problem set 4 out
Rt5   Recitation  
L12 Polymers Part 1: Diagonalization on a Basis, Huckel Model Chemical Reaction Equilibria  
Rb5 Recitation    
L13 Quantum Oscillation Electrochemical Equilibria  
Labs 2 3.014 Lab Week 2 Problem set 3 due

Problem set 4 due
L14 Point Groups and Bravais Lattices Batteries; Thermodynamic Stability Problem set 5 out
Rt6   Recitation  
L15 Symmetry Operations Phase Changes and Phase Diagrams of Single-Component Materials  
Rb6 Recitation    
L16 Structure of Solids Single-Component Phase Diagrams (cont.); Thermodynamics of Solutions  
L17 X-ray Diffraction Free Energy of Multi-phase Solutions at Equilibrium  
Rt7   Recitation  
L18 X-rays at Work: Laue Condition, Ewald Construction, Bragg's Law, Powder Diffraction Binary Phase Diagrams: Miscibility Gaps and Eutectics Problem set 5 due
Rb7 Recitation    
  Exam 2  
Labs 3 3.014 Lab Week 3  
L19 From Diffraction to Structure Binary Phase Diagrams (cont.)  
L20 Symmetries and Tensors Spinodals and Binodals; Continuous Phase Transitions; Introduction to Statistical Mechanics Problem set 6 out
Rt8   Recitation  
L21 Non-crystalline Materials Connecting Events at the Atomic/Molecular Level to Macroscopic Thermodynamic Behavior: Two Postulates of Statistical Mechanics; Microscopic Definition of Entropy  
L22 Polymers Part 2 Connecting Events at the Atomic/Molecular Level to Macroscopic Thermodynamic Behavior (cont.): The Boltzman Factor and Partition Function; Thermal Behavior of the Einstein Solid  
L23 Glasses Lattice Models of Materials; Modeling Polymer Solutions  
Rb8 Recitation    
L24 Liquid Crystals Flory-Huggins Theory  
Labs 4 3.014 Lab Week 4 Problem set 6 due
Rt9   Recitation: Final Review  
Rb9 Recitation: Final Review    
  Final Exam



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