Crystalline Materials

19. Point & Line Defects

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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


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.


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


Lecture Slides (PDF - 3.0MB)

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.


Problems (PDF)

Solutions (PDF)

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.


Yakov Frenkel

Walter Schottky

Jan Burgers


Francois Dallegret

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  

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Course Info

Learning Resource Types

groups Course Introduction
grading Exams with Solutions
notes Lecture Notes
theaters Lecture Videos
assignment_turned_in Problem Sets with Solutions
theaters Recitation Videos