Session Overview
| Modules | Crystalline Materials |
| Concepts | defects in crystals: point defects, line defects |
| Keywords | point defect, line defect, substitutional impurity, interstitial impurity, vacancy, self interstitial, ionic defect, Hope Diamond, Schottky defect, Frenkel defect, F-center, charge neutrality, edge dislocation, screw dislocation, dislocation motion, bubble raft model, chemical imperfection, structural imperfection, formation energy, entropy factor, stoichiometric unit, effective charge, Kröger-Vink notation |
| Chemical Substances | aluminum (Al), steel, diamond, doped silicon, LaNi5, copper (Cu), rock salt (NaCl), zirconia (ZrO2) |
| Applications | aluminum alloys for soda cans, n-and p-type semiconductors, steel, hydrogen embrittlement of steel, Hope diamond, colored gold, hydrogen storage |
Prerequisites
Before starting this session, you should be familiar with:
- Ionic crystal lattices (Session 8)
- Cubic crystal structures (Session 15)
- Distribution of energies as described by Maxwell-Boltzmann statistics (Session 14)
Looking Ahead
Compare the expression for the energy required to produce a vacancy, derived in this lecture, with the expression for the rate of a chemical reaction (the Arrhenius equation), presented in Session 22: Introduction to Kinetics.
Learning Objectives
After completing this session, you should be able to:
- Sketch a crystal containing any of the following defects: substitutional impurity, interstitial impurity, vacancy, Schottky, Frenkel.
- Calculate the vacancy concentration in a crystal at a given temperature.
- Write expressions for defects in a given ionic crystal, and explain why they have higher energies of formation than similar defects in metallic crystals.
- Explain why a given crystal has either substitutional or interstitial impurity atoms.
- Give 3 examples of additives that have a detrimental effect on the surrounding crystal, and 3 examples that improve the material properties.
Reading
Archived Lecture Notes #6 (PDF), Sections 1-2
| Book Chapters | Topics |
|---|---|
| [Saylor] 12.4, “Defects in Crystals.” | Defects in metals, memory metal, defects in ionic and molecular crystals, nonstoichiometric compounds |
| [JS] 4.1, “The Solid Solution – Chemical Imperfection.” | Random and ordered solid solutions, Hume-Rothery rules, interstitial and substitutional solutes, charge neutrality |
| [JS] 4.2, “Point Defects – Zero-Dimensional Imperfections.” | Vacancies and interstitial defects, Schottky and Frenkel defects |
| [JS] 4.3, “Linear Defects, or Dislocations – One-Dimensional Imperfections.” | Burgers vector; edge, screw, mixed, and partial dislocations |
| [JS] 5.1, “Thermally-Activated Processes.” | Arrhenius equation, activation energy, Maxwell-Boltzmann distribution, process mechanisms and rate-limiting steps |
| [JS] 5.2, “Thermal Production of Point Defects.” | Activation energy of vacancies vs. interstitials, Arrhenius plot, thermal expansion |
Lecture Video
Resources
Lecture Summary
Prof. Michael Demkowicz (homepage) lectures today, introducing the next topic: imperfections in crystal lattices. In the real world, materials rarely consist of single, perfect crystals; defects in crystals occur naturally, or are introduced during processing. While unwanted defects can weaken or contaminate materials (e.g. Li+ in saline solution (NaCl(aq)), others can create enhanced properties (e.g. alloys, dopants). Creating an empty crystal lattice site (vacancy) requires overcoming bonds with nearest-neighbor atoms, typically with thermal energy. Vacancies in a regular lattice of A atoms may be filled by an atom of B (substitutional, e.g. P in Si, B in C), while interstitial sites can host atoms of A (self interstitial) or B (interstitial impurity, e.g. C in Fe, H in LaNi5, H in Fe). In ionic crystals, overall charge neutrality must be preserved, so a whole stoichiometric unit may be removed to create two or more vacancies (Schottky); one ion may move to an interstitial site (Frenkel); or one or more electrons may fill an anionic vacancy (F-center). Line defects occur when a lattice mismatch runs through the crystal.
Homework
Textbook Problems
[JS] Chapter 5, Sample Problem 2, Practice Problem 2
| [Saylor] Sections | Conceptual | Numerical |
|---|---|---|
| [Saylor] 12.4, “Defects in Crystals.” | 6, 7, 8, 9, 10 | 1, 2, 4, 5 |
For Further Study
Supplemental Readings
Hull, Derek, and David J. Bacon. Introduction to Dislocations. Boston, MA: Butterworth-Heinemann, 2001. ISBN: 9780750646819.
People
Culture
Other OCW and OER Content
| Content | Provider | Level | Notes |
|---|---|---|---|
| Introduction to Dislocations | DoITPoMS | Undergraduate | |
| 3.14/3.40J/22.71J Physical Metallurgy | MIT OpenCourseWare | Undergraduate (elective) / Graduate | |
| Crystal Structure | Connexions | Undergraduate |
