Defects in Crystals Overview

Defects or Imperfections in Crystals

• Crystalline materials contain imperfections, which affect material properties like strength, hardness, and ductility.
• Imperfections are classified by their geometry: point, line, surface, and volume.

Point Imperfections

• Point defects disrupt the perfect atomic or ionic arrangements in a crystal structure.
• They can be introduced by atom/ion movement during processing, heating, or intentional/unintentional impurity introduction.
• Types of point imperfections include:
  • Vacancies: An atom/ion missing from its normal site in the crystal structure. This increases the material's randomness and thermodynamic stability.
  • Interstitials: An atom/ion occupying an interstitial site (position between lattice points), distorting the crystal structure.
  • Substitutional defects: One atom/ion is replaced by a different type of atom/ion in the lattice.
  • Impurity Atoms: Foreign atoms occupying regular lattice sites or interstitial positions.

Concentration of Vacancies

• The number of vacancies increases exponentially with temperature.
• This relationship is described by an equation involving the number of vacancies ($n_v$), the number of atoms ($n$), the energy required to create a vacancy ($Q_v$), the gas constant ($R$), and the temperature ($T$).

Example: Vacancy Concentration in Copper

• At 25°C, a specific number of vacancies are present.
• To increase vacancy concentration by a factor of 1000, a higher temperature is needed.

Interstitial Defects

• An extra atom/ion is inserted into an unoccupied position in the crystal structure.

Substitutional Defects

• One atom/ion is replaced by a different type of atom/ion.
• The size of the replacing atom/ion interacts with the host structure.

Schottky Defects

• A positively charged ion and a negatively charged ion are removed from the crystal structure to maintain neutrality.

Frenkel Defects

• An ion moves from its normal position to an interstitial site.

Line Imperfections (Dislocations)

• Line defects occur when atoms are dislocated from their normal lattice sites.
• Types of dislocations include:
  • Edge Dislocation: A plane of atoms is inserted or removed, creating a dislocation. Bond lengths on one side are compressed.
  • Screw Dislocation: A shear deformation displaces atoms along a dislocation line.
• Mixed dislocations have both edge and screw components.

Surface Imperfections

• Surface imperfections include grain boundaries.
• Grains have identical atomic arrangements.
• Grain boundaries are surfaces separating different grains; atoms are not arranged in a regular manner, creating compression and tension zones.

Volume Imperfections

• Volume imperfections like foreign-particle inclusions, voids, or pores, disrupt the crystal structure over a large volume.
• They can include non-crystalline regions of at least a few tens of Ångströms in size.

Grain Size and Yield Strength (Hall-Petch Equation)

• Smaller grain size leads to higher yield strength.
• The Hall-Petch equation quantifies the relationship between average grain diameter and yield strength.
• Higher yield strength results from dislocations encountering grain boundaries.

Optical Microscopy and Metallography

• Optical microscopy is used for grain structure analysis and visualizing grain boundaries.
• Metallography is the process of preparing and studying metallic samples visually.
• The American Society for Testing and Materials (ASTM) grain size numbering system categorizes grain size.