Real crystals, crystal defects · POINT DEFECTS Real crystals, crystal defects 4/34. VACANCY Real...

Real crystals, crystal defects

Real crystals, crystal defects 1/34

• The strength of real metals is less than 1% than

that of calculated from ideal crystal models

• Doping Si with 10-8 weight percent Boron increases its conductivity by two-times

• CRYSTAL DEFECTS

REAL CRYSTALS

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• Point defects (0 dim.)

• Line defects (1 dim.) dislocations

• Surface defects (2 dim.)

• Volume defects (3 dim.)

CRYSTAL DEFECTS

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• Vacancy (empty lattice space)

• Self interstitial atoms

• Foreign atoms (interstitial or substitutional

places)

POINT DEFECTS

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VACANCY

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The vacancy is the

absence of an atom from

the lattice. The attractive

and repulsive forces

acting on the neighboring

atoms are changed, so

lattice distortion is

produced in the

environment of the

vacancy.

SUBSTITUTIONAL ATOM

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The substitutional atom is

a foreign atom in the

lattice. The attractive and

repulsive forces acting on

the neighboring atoms are

changed, so lattice

distortion is produced in

the environment of the

atom.

INTERSTITIAL ATOM

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The interstitial atom is a

foreign atom between the

regular lattice positions.

The attractive and

repulsive forces acting on

the neighboring atoms are

changed, so lattice

distortion is produced in the

environment of the atom.

FRENKEL-MECHANISM

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Due to high energy

interaction (e.g. particle

irradiation) an atom left the

lattice site leaving a

vacancy behind and mode

into an interstitial position.

It causes extreme lattice

distortion.

WAGNER-SCHOTTKY MECHANISM

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Atoms leaving the free surface, and atoms jump from the

interior to their place. In this way a vacancy diffuses trough

the lattice into the materials interior.

• Radiation– Atoms are moved out of the regular lattice position (e.g.

Frenkel-pair)

• Heat

nü: number of empty lattice sites

N: number of lattice sites

Qü: activation energy

k: Boltzmann constant

T: temperature

POINT DEFECTS

Point defect density

Exponential

curve

slope

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POINT DEFECTS IN ALLOYS

Solid solution: base metal (A) + solved atom (B)

Substitutional alloy

e.g. Cu + Ni

interstitial alloy

e.g. Fe + C

Second phase in solid solution

or

Second phase particle

different chemical composition

different structure

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EFFECT OF POINT DEFECTS

Aluminium Copper

Strain (%) Strain (%)

Str

ess (

MP

a)

Str

ess (

MP

a)

softSlow cooling

quenchingNeutron irradiated

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• Large difference between theoretical and

measured flow stress of metals.

• Dislocation theory: plastic deformation does not

happen in one step → dislocation motion

DISLOCATIONS (1 D)

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2 (1 )

merőleges

párhuzamos

E

G

E G

Poisson coefficient

(ε - strain)

Tensile stress

Shear stress

MECHANICAL PROPERTIES

perpendicular

parallel

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• Assumption: during the deformation the crystal planes slip in one step relative to each other by simultaneous motion of the atoms.

• The stress what is necessary to start the plastic deformation calculated this way is 1-2 order of magnitude higher than the measured values.

• Conclusion: during the plastic deformation the slip of crystal planes don’t occur in one step, but through a continuous motion; that is, there are regions where the slip already occurred, and others where didn’t.

• The lines separating this regions are called dislocations.

THEORETICAL YIELD STRESS

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DISLOCATIONS MOTION

The analogy between

the dislocations and

the caterpillar

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BURGERS-CIRCLE

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In a defect-free lattice starting from a lattice position and

stepping the same distance to right, down, left and upward,

we return to the starting point.

If the crystal contains a dislocation, the starting and end

point will be different. The vector connecting them is the

Burgers-vector.

Dislocation line: l

Slip plane.

→fixed

Burgers vector: b

b l,

The line of the

dislocation and the

elemental deformation

caused are

perpendicular.

EDGE DISLOCATION

Extra half plane

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Dislocation line: l

Burgers vector: b

Slip plane is not fixed

→glissile

No extra half plane!

b II l, The line of the

dislocation and the

elemental deformation

caused are parallel.

SCREW DISLOCATION

The axis of the screw dislocation

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Partial slip

A line in the space

0-90°

The angle between the line of the

dislocation and the elemental

deformation it causes is between 0

and 90°.

COMPOSITE DISLOCATION

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• Dislocation: border of slipped and non-slipped regions

• Linear defect

• Starts and ends on a crystal surface, ore forms a

closed loop

• Plastic deformation along the whole dislocation is

constant

• Burgers vector is in the closest packed plane and

direction, and b = d

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BASIC PROPERTIES OF DISLOCATIONS

• Macroscopic surface

• Small angle grain boundary

• High angle grain boundary

• Phase boundary

• Coherent phase boundary

• Twin boundary

• Stacking fault

PLANAR DEFECTS

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• Atoms on the surface are at higher energetic state than in

the crystal interior, because there are no atomic bondings

at every directions.

• Surface energy decreases if additional atoms join the

surface.

• Oxide layer formation.

• Chemical reactions.

MACROSCOPIC SURFACE

surface

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Dislocations are arranged

below each others

SMALL ANGLE GRAIN BOUNDARY

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The angle difference of the

orientation of the regions separated

by small angle grain boundaries:

< 5°

During solidification the

randomly oriented grains

touch each other. Grains

differ from each other

only in orientation.

HIGH ANGLE GRAIN BOUNDARIES

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SMALL AND HIGH ANGLE GRAIN BOUNDARIES

Surface

energy

Small angle grain boundary High angle grain boundary

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PHASE BOUNDARY

Coherent

Low energy surface defectSemicoherent

Incoherent

High energy

surface defect

phase boundary

Phase

boundary

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• Atoms on the two sides of the boundary are similar

• There can be found a plane in both phases where the

atomic arrangement is similar

• Orientation difference is fixed on the phase boundary

COHERENT PHASE BOUNDARY

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• Coherent boundary, separates

similar phases

• The two sides of the boundary

are mirror images

• It can be formed during

crystallization or plastic

deformation in FCC or HCP

materials

TWIN BOUNDARY

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Parallel lines in a

microscopic image

TWIN BOUNDARY

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Due to missing

atoms (internal

stacking fault)

the stacking order of

atomic layers is

locally changed.

STACKING FAULT

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Due to included extra

atoms (external stacking

fault)

the stacking order of

atomic layers is locally

changed.

STACKING FAULT

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• Cavities

• Inclusions

• Precipitations

• Gas bubbles

VOLUME (3 DIM.) DEFECTS

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CAVITIES

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Cavities along grain boundaries.

Scanning electron microscope image.