Dislocations—Linear Defects

Dislocations are abrupt changes in the regular ordering of atoms,

along a line (dislocation line) in the solid. They occur in high density

and are very important in mechanical properties of material.

They are characterized by the Burgers vector, found by doing a loop

around the dislocation line and noticing the extra interatomic spacing

needed to close the loop. The Burgers vector in metals points in a

close packed direction.

Edge dislocations occur when an extra plane is inserted. The

dislocation line is at the end of the plane. In an edge dislocation, the

Burgers vector is perpendicular to the dislocation line.

Screw dislocations result when displacing planes relative to each

other through shear. In this case, the Burgers vector is parallel to the

dislocation line.

Burgers vector b. It help us to describe the size and the direction

of the main lattice distortion caused by a dislocation.

Dislocations shown above have Burgers vector directed

perpendicular to the dislocation line. These dislocations are called

edge dislocations.

There is a second

basic type of

dislocation, called

screw dislocation.

The screw dislocation

is parallel to the

direction in which the

crystal is being

displaced (Burgers

vector is parallel to the

dislocation line).

DislocationsDislocations

Edge dislocation

Screw dislocation

Burgers vector b

Dislocation

line ζζζζ

bζζζζb//

ζζζζ⊥b

Mixed/partial dislocations: The

exact structure of dislocations in

real crystals is usually more

complicated than the ones shown.

Edge and screw dislocations are

just extreme forms of the possible

dislocation structures. Most

dislocations have mixed edge/screw

character. To add to the complexity

of real defect structures, dislocation

are often split in "partial“

dislocations that have their cores

spread out over a larger area.

Interfacial Defects

External Surfaces :

The environment of an atom at a surface differs from that of an atom

in the bulk, in that the number of neighbors (coordination) decreases.

This introduces unbalanced forces which result in relaxation (the

lattice spacing is decreased) or reconstruction (the crystal structure

changes).

Surface atoms have unsatisfied atomic bonds, and higher energies

than the bulk atoms ⇒ Surface energy, γ (J/m2)

• Surface areas tend to minimize (e.g. liquid drop)

• Solid surfaces can “reconstruct” to satisfy atomic bonds at

surfaces.

External SurfaceExternal Surface

Free surface can be modeled as a simple termination of the bulk

crystal on low-index planes (those having the lowest energy). The

resultant picture is the so-called terrace-ledge-kink (TLK) model.

Surfaces and interfaces are very

reactive and it is usual that impurities

segregate there. Since energy is

required to form a surface, grains tend

to grow in size at the expense of

smaller grains to minimize energy.

This occurs by diffusion, which is

accelerated at high temperatures.

Grain Boundaries :

Polycrystalline material comprised of many small crystals or

grains. The grains have different crystallographic orientation.

There exist atomic mismatch within the regions where grains

meet. These regions are called grain boundaries.

Surfaces and interfaces are reactive and impurities tend to

segregate there. Since energy is associated with interfaces,

grains tend to grow in size at the expense of smaller grains to

minimize energy. This is accelerated at high temperatures.

The density of atoms in the region including the grain boundary

is smaller than the bulk value, since void space occurs in the

interface.

Interfacial defects

• Interfacial defects form either between different phases, or

between different crystals.

Interfaces between

crystals are grain

boundaries, as

discussed earlier.

Microscopy

Visible light: 0.4~0.7m

Resolution limit ~ 0.5λλλλ~ 0.3µµµµ

Brass (annealing twins)

FCC - Cu/Zn alloy

Bronze (Cu/Sn alloy)

Examined by the

optical properties

of the surface: need etching

Depth of field is important:

needs a flat surface

(polishing) Up to 2000x

Grain Size

100x

3.5”

ASTM (American Society for Testing

And Materials)

grain size number n

12 −= nN

N = no. of grains/in2

46 grains + 22 on circumference

= 46 + 22/2 =57 grains

N=57 / π (3.5/2)2 = 6 grains/in2

6=2n-1, n=3.6 n N

With

Scanning Electron Microscope

Electron gun

Condenser

lens

Scan coils

Objective

lens

Specimen Detector

Display &

storage

Display &

storage

Scan generator

High depth of

field !!!

2000x

Modes: Emissive, reflective,

absorptive, X-ray, etc..

10~50,000x

Transmission Electron Microscope - TEM

Electron gun

Condenser

lens

Objective

lens

Specimen

Camera

Magnifying

lenses

In TEM, sample thickness < 1000A for electron transmission

Diffraction, Microscopy, Spectroscopy are all possible

in the same column. Applications: determine

dislocation, defects, micro-precipitates, etc..

Up to

1,000,000x