Module 4 Imperfections in Solids and Diffusion

Types of Imperfections

Defined in terms of dimensionality: 0D, 1D, 2D

• 0D point defects

• 1D line defects

• 2D interfacial defects

Point defects - 0D

• Vacancies

• interstitials

• Substitutions

Line Defects - 1D

• Dislocations

Interfacial Defects - 2D

• Grain boundaries

How do you determine the number of Vacancies?

N_v/N = exp(-Q_v/kT)

• Nv_ Number of vacancies

• N_ Number of tot. lattice sites

• Q_v_ activation energy

• k_ Boltzmann’s constant

• T_ temperature

*Each lattice site is a potential vacancy *

How is the activation energy determined?

Experimentally

As temperature increases…

So does the number of vacancies withing the lattice

Dislocations

• 1D defects where atoms are misaligned

• Move when stresses are applied

• Can be permanent (plastic results from dislocation motion)

Burger’s Vector (b)

Used as a measure of distortion in the lattice

Edge Dislocation

• Extra half- plane of atoms inserted into a crystalline structure

• b is perpendicular to the dislocation line

Screw Dislocation

• Spiral planar ramp resulting from shear deformation

• b is parallel to the dislocation line

Mixed dislocation

• A dislocation with both edge and screw components

Twin Boundaries

• 2D Planar defect

• Mirror reflections of atom positions of one side

  of twin plane to the other side

Stacking Faults

• 2D Planar defect

• Occur when there is an error in the planar

  stacking sequence

Grain Boundaries

• 2D Planar defect

• Misalignments between (single crystal) regions / grains.

• Critical for ceramics and many metals, the defects promote:

  • High mobility

  • High chemical reactivity

Dopants

Purposeful impurity that turns glass into different colors.

Impurities in metals

• Substitutional Solid Solution

• Interstitial Solid solution

• Solid solution plus particles of a new phase

What makes the second phase in a material unique?

• Different composition

• Different structure

Hume - Rothery Rules (for formation of solid solutions

• Δr (atomic radius) < 15%

• Similar electronegativities (close on periodic table)

• Same crystal structure for pure metals

• Valences: a metal will have a greater tendency to dissolve a metal with a higher valence

Hume Rothery Suggestions Example

Would you predict more Al or Ag to dissolve in Zn?

Solution solubility Example

Given the following information, what can you predict about the solubility of Cr and Fe in nickel?

Diffusion

• Atoms tend to migrate from regions of high concentration to regions of low

  concentration

*Nature abhors a gradient *

Self Diffusion

Migration of host atoms in pure metals

Vacancy Diffusion

• Atoms and vacancies exchange positions

• applies to host and substitutional impurity atom

What does vacancy diffusion rates depend on?

• Number of vacancies

• Temperature

• Activation energy

Interstitial Diffusion

• Small interstitial atoms move from one position to an adjacent one

• Faster than vacancy diffusion b/c there’s always an opening

Diffusion coefficient

D = D₀exp(-Q_d / RT)