Length Scale of Imperfections Dislocations and their Scale

point, line, planar, and volumetric defects

Vacancies, impurities dislocations Grain and twin boundaries Voids Inclusions precipitates From Chawla and Meyers, Mechanical Behavior of Materials 1

Line Defects: Dislocations

Dislocations : • are line defects, • cause slip between crystal plane when they move, • produce permanent (plastic) deformation.

Schematic of a Zinc (HCP): • before deformation • after tensile elongation slip steps Adapted from Fig. 7.9, Callister 6e.

Actual strained hcp Zn

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Incremental Slip and Bond Breaking

• Dislocations slip planes • 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.

incrementally

...

Atomic view of edge dislocation motion from left to right as a crystal is sheared.

Shear stress QuickTime™ and a Cinepak decompressor are needed to see this picture.

(Courtesy P.M. Anderson) Snapshot midway in shear

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Edge Dislocations Exiting Crystal Form Steps

Burger’s Vector = b Shear stress

The caterpillar or rug-moving analogy

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• Dislocations are line defects that separate Slipped vs Not Slipped.

• They form loops inside crystal, having

screw, edge and mixed

character.

• Dislocation moves perpendicular to line direction along each segment.

• Top of crystal moves in direction of

b

(Burger’s vector).

• Same surface steps created.

Hayden, Moffatt, Wulff, “The Structure and Properties of Materials,” Vol III (1965) 5

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Formation of Steps from Screw and Edge Dislocations

Shear stress Edge Shear stress Screw

Both screw and edge motion create same steps!

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The Edge Dislocations and Burger’s Vector

Looking along line direction of edge Burger’s vector = extra step Stress fields at an Edge dislocation

• • •

Edge looks like extra plane of atoms.

Burger’s vector is perpendicular to line.

Positive Edge (upper half plane)

• • •

Is there a Negative Edge?

Where is it?

What happens when edge gets to surface of crystal?

•

What are the stresses near edge?

Like trying to zip up those old jeans.

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Burger’s vectors mostly on the most close-packed planes in the most closed-packed direction What are the most close-packed PLANES AND DIRECTIONS fcc, bcc, and sc?

b

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Dislocations Can Create Vacancies and Interstitials

•

All defects cost energy (J/m 2 or erg/cm 2 ) But getting rid of defects, like large dislocations, does lower energy (but not to perfect crystal).

• •

Dislocations can annihilate one another! Non-overlapping edges create vacancies.

Overlapping edges create interstitials.

Almost complete plane of atoms   Slip plane  vacancies Slip plane  Slip plane Overalapping  Slip plane  Non-overlapping Extra atoms go into interstitial 10

Planar Defects: Surfaces

All defects cost energy (energy is higher than perfect crystal) Surfaces, grain, interphase and twin boundaries, stacking faults Planar Defect Energy is Energy per Unit Area (J/m 2 or erg/cm 2 )

•

Surfaces: missing or fewer number of optimal or preferred bonds.

surface

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Planar Defects: Grain Boundary

All defects cost Energy per Unit Area (J/m 2 or erg/cm 2 )

•

Grain boundary: fewer and/or missing optimal bonds.

- low-angle GB and high-angle GB.

high-angle Grain boundaries surface low-angle

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Relative Energies of Grain Boundaries

•

The grains affect properties

•

mechanical,

•

electrical, …

•

Recall they affect diffraction so you know they’re there.

•

What should happen to grains as temperature increases?

Hint: surfaces (interfaces) cost energy .

high-angle Grain I Grain 2 low-angle Grain 3

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Dislocation Interactions Can Create Planar Defects!

Small-Angle Grain Boundaries: a tilt and a twist

b

Tilt

•

All defects cost energy (J/m 2 Tilt Grain boundary: or erg/cm 2 ) - from array of edge dislocations - misorientation of crystal planes =

 C •

Twist Grain boundary - when



is parallel to boundary Should energy of GB depend on



?

T

If dislocation cost energy, how are they there?

Twist

 Bi-crystals are made by twist boundaries  sin  ~  =b/d 14 d

Twin Boundaries: an atomic mirror plane

original atomic positions before twinning •

There has to be another opposite twin nearby to get back to perfect crystal, because all defects cost energy (J/m 2 or erg/cm 2 ) and to much defect costly.

•

Stress twins can be created (e.g., Tin) in which case the atoms must move at the speed of sound.

What happens when something moves at speed of sound?

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Twin Boundaries: Load drop in F vs %EL

Stress twins are created and work to create them lead to load drop.

f 

Cu-8.0at.%Al

Sudden load drop accompanies twinning normal twinning direction twin plane F m  cos  cos f Schmid factor

M. S. Szczerba, T. Bajor, T. Tokarski Phil. Mag. 84 (2004) 481-502.

fcc fcc twin

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Stacking Faults: Messed up stacking

FCC HCP

slip • • •

All defects cost energy (J/m 2 or erg/cm 2 ).

Stress, dislocation motion can create Stacking Faults.

What is stacking of FCC and HCP in terms of A,B, and C positions in (111) planes?

…ABCABCABC…

hcp

...ABCACABABCABC...

…….fcc

fcc ………..

17 or C or C

Optical Microscopy

• Useful up to 2000X magnification.

• Polishing removes surface features (e.g., scratches) • Etching changes reflectance, depending on crystal orientation.

Adapted from Fig. 4.11(b) and (c), Callister 6e. (Fig. 4.11(c) is courtesy of J.E. Burke, General Electric Co.

close-packed planes 0.75mm

micrograph of Brass (Cu and Zn)

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Optical Microscopy

Grain boundaries...

• are imperfections, • are more susceptible to etching, • may be revealed as dark lines, • change direction in a polycrystal.

Adapted from Fig. 4.12(a) and (b), Callister 6e.

(Fig. 4.12(b) is courtesy of L.C. Smith and C. Brady, the National Bureau of Standards, Washington, DC [now the National Institute of Standards and Technology, Gaithersburg, MD].)

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Polymer, too: Colloidal Epitaxy via Focused Ion Beam Lithography SEM of patterned cover slip

Silica ( f =1.18

m m, 0.5vol%) Zirconia ( f ~ 3nm, 0.03vol%)

From Prof. Braun’s group.

On cover of Langmuir (2004)

Objective lens Sedimented growth: dislocations and SF In 37th layer: GB and SF

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Use Microscopy to see defects: contrast using optical, electron, scanning probe Poly-xtal Pb ~1x Poly-xtal Cu-Zn 60x

• • • •

Optical ~ 2x10 3 x Scanning EM ~ 5x10 4 x High-resolution TEM ~10 6 x Scanning probe ~10 9 x topo-map) Fe-Cr GB 100x Dislocation in Ti alloy ~50,000 x

Old brass door knobs have been etched by acid in your sweat and you can see with your eyes the grains and their different orientations.

Move w/  change w/ T and 23

TEM Image of Dislocations in Ti Alloy

•

Why are dislocations not loops?

•

Dislocations are formed -solidification - plastic deformation - thermal stresses from cooling

In focus

51,450 x

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SUMMARY

• Defect materials responsible for most desired properties useful to engineering, e.g., mechanical, thermal, and electrical.

• They occur in metals, ceramics, polymers, and semiconductors.

• Defect can be categorized in terms of domain, tilt … ), stacking faults, … Point, Line, or Planar defects.

• Point: vacancies, interstitials, substitutional, … • Line: dislocations (mostly for metals, but not exclusively).

• Planar: surfaces, grain boundaries, boundaries (twin, antiphase, • Defects can be observed by eye or various microscopies.

• Defects can be created or affected by temperature, stress, etc., requiring or leading to other defects, as with dislocations.

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