defects or imperfections in solidsimperfections crystal defects are imperfections in crystals caused...
TRANSCRIPT
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