1 Length Scale of Imperfections Vacancies, impurities dislocations Grain and twin boundaries Voids Inclusions precipitates point, line, planar, and volumetric defects Line Defects: Dislocations and their Scale From Chawla and Meyers, Mechanical Behavior of Materials

2 are line defects, cause slip between crystal plane when they move, produce permanent (plastic) deformation. Dislocations: Schematic of a Zinc (HCP): before deformation after tensile elongation slip steps Line Defects: Dislocations Adapted from Fig. 7.9, Callister 6e. Actual strained hcp Zn

3 Dislocations slip planes incrementally... 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. Atomic view of edge dislocation motion from left to right as a crystal is sheared. (Courtesy P.M. Anderson) Incremental Slip and Bond Breaking Snapshot midway in shear Shear stress

4 Edge Dislocations Exiting Crystal Form Steps Shear stress Burger’s Vector = b The caterpillar or rug-moving analogy

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

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7 Formation of Steps from Screw and Edge Dislocations Shear stress Edge Screw Both screw and edge motion create same steps!

8 The Edge Dislocations and Burger’s Vector Looking along line direction of edge Stress fields at an Edge dislocation Burger’s vector = extra step 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.

9 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

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

11 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

12 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. surface low-angle high-angle Grain boundaries

13 Relative Energies of Grain Boundaries low-angle high-angle Grain I Grain 2 Grain 3 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.

14 Dislocation Interactions Can Create Planar Defects! Small-Angle Grain Boundaries: a tilt and a twist All defects cost energy (J/m 2 or erg/cm 2 ) Tilt Grain boundary: - from array of edge dislocations - misorientation of crystal planes =  Twist Grain boundary - when  is parallel to boundary Should energy of GB depend on  ? If dislocation cost energy, how are they there?  Tilt  Twist Bi-crystals are made by twist boundaries d b sin  ~  =b/d T C

15 Twin Boundaries: an atomic mirror plane 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? original atomic positions before twinning

16 Twin Boundaries: Load drop in F vs %EL Stress twins are created and work to create them lead to load drop. M. S. Szczerba, T. Bajor, T. Tokarski Phil. Mag. 84 (2004) Sudden load drop accompanies twinning Cu-8.0at.%Al   normal twin plane twinning direction F Schmid factor fcc twin

17 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? FCC HCP …ABCABCABC… Stacking Faults: Messed up stacking slip...ABCACABABCABC... hcp …….fcc fcc ……….. or C

18 Useful up to 2000X magnification. Polishing removes surface features (e.g., scratches) Etching changes reflectance, depending on crystal orientation. close-packed planes micrograph of Brass (Cu and Zn) Adapted from Fig. 4.11(b) and (c), Callister 6e. (Fig. 4.11(c) is courtesy of J.E. Burke, General Electric Co. 0.75mm Optical Microscopy

19 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].) Optical Microscopy

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22 Polymer, too: Colloidal Epitaxy via Focused Ion Beam Lithography SEM of patterned cover slip Objective lens Silica (  =1.18  m, 0.5vol%) Zirconia (  ~ 3nm, 0.03vol%) In 37th layer: GB and SF Sedimented growth: dislocations and SF From Prof. Braun’s group. On cover of Langmuir (2004)

23 Use Microscopy to see defects: contrast using optical, electron, scanning probe Poly-xtal Pb ~1x Poly-xtal Cu-Zn 60x Fe-Cr GB 100x Optical ~ 2x10 3 x Scanning EM ~ 5x10 4 x High-resolution TEM ~10 6 x Scanning probe ~10 9 x topo-map) Dislocation in Ti alloy ~50,000 x Move w/  and change w/ T 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.

24 TEM Image of Dislocations in Ti Alloy 51,450 x Why are dislocations not loops? Dislocations are formed -solidification - plastic deformation - thermal stresses from cooling In focus

25 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 Point, Line, or Planar defects. Point: vacancies, interstitials, substitutional, … Line: dislocations (mostly for metals, but not exclusively). Planar: surfaces, grain boundaries, boundaries (twin, antiphase, domain, tilt … ), stacking faults, … 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.