Defects or Imperfections in Solids

Chapter four

Imperfections

�Crystal defects are imperfections in crystalscaused by deviations from the individuallattice structure

�Actually, all crystals are imperfect�Actually, all crystals are imperfect

� “Crystals are like people, it’s their defects that make them more interesting.”

� Imperfections give properties of crystallinesolids, i.e. they dominate the materialproperties

We can classify defects

by dimensions:

�Point defects

�Line defects�Line defects

�Planar or surface defects

�Volume or bulk defects

Types of Point Defects

�Vacancy

� Interstitial

�Substitutional

� Larger

� Smaller

�Frenkel

�Schottky

Vacancies

�There are naturally occurring vacancies in all crystals

�The number of vacancies goes up as the temperature goes up

You can calculate the number of �You can calculate the number of vacancies

Nv = N exp( -Qv /RT )

� Depending on the units for Q, you may use the

Stephan Boltmann constant instead of R

� N is the total number of sites in a sample

� Nv is the number of vacancies

� Q is the activation energy for the formation of a

vacancy

� R is the gas constant, 1.987 cal/mole.K

or 8.31 J/mol.K

�Nv goes up exponentially with temperature

�What happens to the predicted density if you have a lot of vacancies?

�What is the self interstitial atom?

Interstitial atoms

� An atom must be fairly tiny to fit into the

interstitial holes

� Hydrogen and Helium can diffuse fairly rapidly

through metals by moving through the

interstitial holesinterstitial holes

� Interstitial Carbon is commonly used to

strengthen iron

Substitutional atoms

�Atom replaces the host atom of materials

�What is the solid solution?

�Which factors affected the dissolving of solute in the solvent?solute in the solvent?

�

Surface and Grain Boundaries

� The atoms at the boundary of a grain or on

the surface are not surrounded by other

atoms – they are not held in place as strongly

� Grains don’t line up perfectly where the grain � Grains don’t line up perfectly where the grain

boundaries meet – that’s an imperfection too.

� Dislocations can usually not cross grain

boundaries

ASTM Grain Size

�N = 2n-1

�N is the number of grains per square inch at a magnification of 100

n is the ASTM grain size�n is the ASTM grain size

Strength of a Material

� Based on the bond strength most materials

should be much stronger than they are

� From Chapter one we know that the strength

for an ionic bond should be about 106 psifor an ionic bond should be about 10 psi

� More typical strength is 40*103 psi

� Why?

� Materials must not usually fail by breaking

bonds!!

Dislocations

�Line imperfections in a 3D lattice

�Edge

�Screw

�Mixed

Deformation

�Deformation of materials occurs when a line defect (dislocation) moves through the material

�Be sure to watch the video from the text�Be sure to watch the video from the text

Edge Dislocation

�Extra plane of atoms

�See the animations in the text

�Burgers vector

� Deformation direction

� For edge dislocations it is perpendicular to

the dislocation line

Screw Dislocation

�A ramped step

�Burgers vector

� Direction of the displacement of the atoms

For a screw dislocation it is parallel to the � For a screw dislocation it is parallel to the

line of the dislocation

�Harder to visualize than edge dislocations

Deformation

�When a shear force is applied to a material, the dislocations move

�Do the “paper clip” experiment

�Real materials have lots of dislocations, �Real materials have lots of dislocations, therefore the strength of the material depends on the force required to make the dislocation move, not the bonding energy

What happens when a

dislocation runs into a flaw?

�Takes more energy to move “over the flaw” – See the video

�May stop moving all together

Therefore, introducing flaws into the �Therefore, introducing flaws into the material, actually strengthens it!!

Dislocation Interactions

� Dislocation tangles

� When dislocations run into each other you get the

traffic jam effect

� More dislocations actually increase the strength of

a materiala material

� (Remember – real materials already have a lot of

dislocations – just like SLC already has a lot of

traffic)

� More traffic results in grid lock, not more cars

moving

Frank Read Source

�Produces more dislocations

�Applying a force to the material increases the number of dislocations

Traffic jams are more common�Traffic jams are more common

�Called “strain hardening” or “cold work” and is discussed in Chapter 7

Slip

�When dislocations move slip occurs� Direction of movement – same as the

Burgers vector

�Slip is easiest on close packed planes�Slip is easiest on close packed planes

�Slip is easiest in the close packed direction

�See the table on the “Slip” card in the text

Slip

�Affects

� Ductility

� Material Strength

Schmidt’s Law

� In order for a dislocation to move in its slip system, a shear force acting in the slip direction must be produced by the applied force.applied force.

� Note – Schmidt’s law is not covered by

Russ

Schmidt’s Law

Normal

to slip λφ

σ = F/A

Slip directionto slip

plane

Ao

Ατr = Fr / A - Resolved Shear

Stress

Schmidt’s Law

�Fr = F cos(λ)

�Α = Α0/cos(φ)

� τ = σ cos(φ) cos(λ)

� Where:� Where:� τ = Fr / A = resolved shear stress in the slip

direction

� σ = F/Ao = unidirectional stress applied to the cylinder