Unit 4.2: Line Defects (Dislocations)

1. Unit Introduction

Line defects, or dislocations, are one-dimensional imperfections in a crystal lattice. Unlike point defects, they extend along a line through the crystal. Dislocations are critical in understanding plastic deformation, strengthening of metals, and mechanical behavior, making them a high-yield topic in JE/AE exams.

2. Definitions

• Line Defect (Dislocation): A defect in which atoms are misaligned along a line in the crystal lattice.

• Edge Dislocation: Extra half-plane of atoms inserted into the lattice, causing local distortion.

• Screw Dislocation: Lattice planes spiral around a line, resembling a screw.

• Burger’s Vector ($\vec{b}$): A vector representing the magnitude and direction of lattice distortion caused by a dislocation.

• Mixed Dislocation: Combination of edge and screw dislocations.

3. Core Concept Explanation

1. Nature of Dislocations:

   • One-dimensional defects; extend along the length of a crystal.

   • Responsible for plastic deformation in metals at lower stresses than predicted theoretically.

2. Edge Dislocation:

   • Visualized as an extra half-plane of atoms inserted in the lattice.

   • The line defect is at the edge of the extra plane.

   • Stress is concentrated near the dislocation line.

3. Screw Dislocation:

   • Formed by shear stress that causes lattice planes to shift.

   • Atoms around the dislocation line are displaced in a spiral manner.

4. Mixed Dislocations:

   • Real crystals often have dislocations with both edge and screw components.

5. Burger’s Vector:

   • Determines dislocation type: perpendicular to dislocation line → edge; parallel → screw.

   • Magnitude equals the lattice distortion per dislocation.

4. Important Classifications

5. Key Principles / Concepts

1. Slip:

   • Plastic deformation occurs by dislocation motion along slip planes.

   • Slip is easier along planes with highest atomic density.

2. Dislocation Motion:

   • Dislocations move under applied stress, causing permanent deformation.

   • Motion is easier at higher temperatures (enhanced diffusion).

3. Strengthening Mechanisms:

   • Reducing dislocation motion strengthens metals (work hardening, alloying, grain boundary strengthening).

4. Energy of Dislocation:

   • Energy per unit length depends on Burger’s vector and elastic constants:

     $$E \propto Gb^2$$

     where $G$ = shear modulus, $b$ = Burger’s vector magnitude.

6. Important Tables / Comparisons

7. Properties / Characteristics

• One-dimensional defects; extend along a line.

• Cause plastic deformation at lower stress than theoretical predictions.

• Dislocation density (number of dislocations per unit volume) affects strength.

• Can interact, multiply, and be pinned by obstacles.

8. Applications in Engineering

• Explains plastic deformation in metals.

• Basis for work hardening and alloy strengthening.

• Guides heat treatment processes to control dislocation density.

• Important in mechanical design, predicting yield strength and ductility.

9. Exam-Focused Points

• Types of dislocations: edge, screw, mixed.

• Burger’s vector direction defines dislocation type.

• Dislocations are responsible for plastic deformation.

• Strengthening mechanisms involve impeding dislocation motion.

• Slip planes are along densest atomic planes.

10. Common Exam Traps

• Confusing edge vs screw dislocations. Rule: Burger’s vector ⟂ line → edge; ‖ line → screw.

• Forgetting that real crystals usually have mixed dislocations.

• Mixing slip plane and slip direction; slip plane = plane of easiest dislocation motion, slip direction = Burger’s vector.

11. Example Competitive Exam Questions (Q–A Format)

1. Question: What is an edge dislocation?
   Answer: A line defect where an extra half-plane of atoms is inserted into the crystal, causing lattice distortion perpendicular to the dislocation line.

2. Question: What is the direction of the Burger’s vector in a screw dislocation?
   Answer: Parallel to the dislocation line.

3. Question: What causes plastic deformation in metals at lower stress than theoretical prediction?
   Answer: Motion of dislocations along slip planes.

4. Question: How can metals be strengthened using dislocations?
   Answer: By impeding dislocation motion through work hardening, alloying, or grain boundary strengthening.

5. Question: What is a mixed dislocation?
   Answer: A dislocation that has both edge and screw components.

12. Quick Revision Summary

• Line defects (Dislocations): 1D defects extending along a line.

• Edge: Extra half-plane, Burger’s vector ⟂ line.

• Screw: Spiral distortion, Burger’s vector ‖ line.

• Mixed: Combination of edge and screw.

• Responsible for plastic deformation.

• Slip: motion along densest planes.

• Strengthening: restrict dislocation motion.

• Dislocation density affects yield strength and ductility.