Dislocations – Linear Defects– Two-dimensional or line defect – Line around which atoms are misaligned – related to slip

• Edge dislocation:– extra half-plane of atoms inserted in a crystal structure– Or – think of it as a partially slipped crystal– b to dislocation line

• Screw dislocation:– spiral planar ramp resulting from shear deformation– b to dislocation line

Burger’s vector, b: measure of lattice distortion or the amount of displacement. Burger’s vector is equal in magnitude to interatomic spacing.

Edge Dislocation

Source: G. Dieter, Mechanical Metallurgy, McGraw Hill, 1986.

• This is a crystal that is slipping• Slip has occurred in the direction of

slip vector over the area ABCD• Boundary between portion that has

slipped and not slipped is AD• AD is the edge dislocation• The Burger’s vector b is

= magnitude to the amount of slip Is acting in the direction of slip Note that b is ┴ dislocation line

Dislocations – Linear Defects

Fig. 4.3, Callister 7e.

Edge Dislocation

• Dislocation motion requires the successive bumping of a half plane of atoms (from left to right here).

• Bonds across the slipping planes are broken and remade in succession.

Atomic view of edgedislocation motion fromleft to right as a crystalis sheared.

(Courtesy P.M. Anderson)

Motion of Edge Dislocation

Dislocations – Linear Defects

Adapted from Fig. 4.4, Callister 7e.

Burgers vector b

Dislocationline

b

(a)(b)

Screw Dislocation

Edge, Screw, and Mixed Dislocations

Adapted from Fig. 4.5, Callister 7e.

Edge

Screw

Mixed

Dislocations – Linear DefectsDislocations are visible in electron micrographs

Adapted from Fig. 4.6, Callister 7e.

Transmission Electron Micrograph of Titanium Alloy. Dark lines are dislocations. 51450X

Interfacial - Planar Defects

Surfaces – Atoms do not have the same coordination number – Therefore are in higher energy state– Surface energy, [=] J/m2

– Materials always try to reduce surface energy – tendency towards spherical shapes

Solidification- result of casting of molten material– 2 steps

• Nuclei form

• Nuclei grow to form crystals – grain structure

• Start with a molten material – all liquid

Grain Boundaries – Interfacial Defects

• Crystals grow until they meet each other

nuclei crystals growing grain structureliquid

Grain Boundaries

Grain Boundaries• regions between crystals• transition from lattice of one

region to that of the other• slightly disordered• low density in grain

boundaries– high mobility– high diffusivity– high chemical reactivity

High energy locations where impurities tend to segregate to

Planar Defects in Solids• One case is a twin boundary (plane)

– Special kind of grain boundary– Mirror lattice symmetry– Essentially a reflection of atom positions across the twin plane.

• Stacking faults– For FCC metals an error in ABCABC packing sequence– Ex: ABCABABC

Adapted from Fig. 4.9, Callister 7e.

Brass at 60XFigure4.13c

Diffusion

Diffusion - Mass transport by atomic motion

Mechanisms• Gases & Liquids – random (Brownian) motion• Solids – vacancy diffusion or interstitial diffusion

• Interdiffusion: In an alloy, atoms tend to migrate from regions of high conc. to regions of low conc.

Initially

Adapted from Figs. 5.1 and 5.2, Callister 7e.

Diffusion

After some time

• Self-diffusion: In an elemental solid, atoms also migrate.

Label some atoms After some time

Diffusion

A

B

C

DA

B

C

D

Diffusion MechanismsVacancy Diffusion:

• atoms exchange with vacancies • applies to substitutional impurity atoms • rate depends on: --number of vacancies --activation energy to exchange.

increasing elapsed time

• Simulation of interdiffusion across an interface:

• Rate of substitutional diffusion depends on: --vacancy concentration --frequency of jumping.

(Courtesy P.M. Anderson)

Diffusion Simulation

Diffusion MechanismsInterstitial diffusion – smaller atoms can diffuse between atoms

in lattice positions.

Which will be faster – vacancy diffusion or interstitial diffusion?

Adapted from Fig. 5.3 (b), Callister 7e.

Case Hardening:

• Diffuse carbon atoms into the host iron atoms at the surface.

• Use a controlled atmosphere with a specific carbon potential (effective concentration)

• Elevated Temperature

• Example of interstitial diffusion is a case hardened gear.

Result: The higher concentration of C atoms near the surface increases the local hardness of steel.

Processing Using Diffusion