dislocation structures: grain boundaries and cell walls
DESCRIPTION
Dislocation Structures: Grain Boundaries and Cell Walls. Polycrystal rotations expelled into sharp grain boundaries. Copper crystal http:// www.minsocam.org/msa/coll - ectors_corner/vft/mi4a.htm. Dislocations organize into patterns. Cell Wall Structures. Plasticity Work Hardening - PowerPoint PPT PresentationTRANSCRIPT
Dislocation Structures: Grain Boundaries and Cell WallsDislocations organize into patterns
Copper crystalhttp://www.minsocam.org/msa/
coll-ectors_corner/vft/mi4a.htm
Polycrystalrotations expelled into sharp grain boundaries
PlasticityWork Hardening
Dislocation Tangles
Cell Wall Structures
Crystals are weirdNo elegant, continuum explanation for wall formation
Crystals have broken translational, orientational symmetries• Translational wave: phonon, defect: dislocation• Orientational wave, defect? Grain boundaries
Continuous broken symmetries: magnets, superconductors, superfluids, dozens of liquid crystals, spin glasses, quantum Hall states, early universe vacuum states… Only crystals form walls*
Why? *Smectic A focal conics, quasicrystals
Plasticity in Crystals1Plas-tic: adj [… fr. Gk. plastikos, fr. plassein to mold, form] … 2 a: capable of being molded or modeled (Webster’s) Bent Fork
• Metals are Polycrystals• Crystals have Atoms in Rows• How do Crystals Bend?
Crystal Axis Orientation Varies between Grains
CrystalsBroken Symmetry and Order Parameters
Order Parameter Space is a Torus:U(x) maps physical space into order
parameter space
• Crystals Break Translational Symmetry• Order Parameter Labels Local Ground State: Displacement Field U(x)• Residual lattice symmetry U(x) U(x) + n v1 + m v2
Unit cell with periodic boundary
micro
DislocationsTopology, Burger’s vector, tangling
Burger’s vector: loop around defect, registry on lattice shifts (extra columns on top). Topological charge.
Dislocation line: tangent t, Burger’s vector b
Screw
Edge
Plastic Deformation: mediated by dislocation line motion, limited by dislocation entanglement
climbglide
Crystals and Dislocations
Missing Half-Plane of Atoms
Dislocations in 3D are Lines(Screw, edge, junctions, tangles)
Broken Symmetry, Order Parameters, Topological Defects
At Dislocation,Order Parameter Winds Around TorusWinding Number =Topological Charge =Burgers Vector
Work hardening and dislocations3D dislocations tangle up
During plastic deformation under external stress, new dislocations form, tangle up. Harder to push through tangle – increases yield stress. Tangle ‘remembers’ previous maximum stress.
Grain boundaries and dislocationsDislocations form walls
Low angle grain boundary • wall of aligned dislocations, strength b, separated by d• favored by dislocation interaction energy• mediates rotation of crystal (q=b/d)• strain field ~exp(-y/d) expelled from bulk• energy~(b2/d)log(d/b) ~-bq logq
Cell Wall StructuresMatt Bierbaum, Yong Chen, Woosong Choi, Stefanos
Papanikolaou, Surachate Limkumnerd, JPS
Dislocation tangles eventually organize also into ‘cell structures’ – fractal walls?
Cellular structures (Glide only)Plastic deformation, relaxing from random
“dented” initial strain field
DOE BES
(Climb & Glide qualitatively sharper in 2D, but rather similar in 3D)
Avalanches when bending forks
Small avalanches in Metal Micropillars
Dislocation Tangle Structure
Dislocation motion happens in bursts of all sizes
Ice crackles when it is squeezedSo, surprisingly, do other metalsAvalanches at microscaleAnalogies to earthquakesPlasticity fractal in time and space?
Kraft
Stretch
Avalanches in Ice
Num
ber
Size
105
1091010-10
1/1000 cm
Dislocation Structures: Grain Boundaries and Cell WallsDislocations organize into patterns
Copper crystalhttp://www.minsocam.org/msa/
coll-ectors_corner/vft/mi4a.htm
Polycrystalrotations expelled into sharp grain boundaries
PlasticityWork Hardening
Dislocation Tangles
Cell Wall Structures
Power laws and scalingRenormalization-group predictions
qs <r(
x) r
(x+R
)> R -s
Power law <r r>~R-h correlationscut off by initial random length scale
<L L> correlations ~ R2-h
q2-s <
(L(x
)-L(x
+R))2 >
Climb & Glide
Glide Only 2D
Emergent scale invarianceSelf-similar in space; correlation functions
Real-space rescaling
Power law dependence of mean misorientations
DOE BES
Glide OnlyClim
b & Glid
e
3D
RefinementCell sizes decrease and misorientations increase
Relaxed Strained
Boundaries above qc
Self-similar implies no characteristic scale! Size goes down as cutoff qc goes to zero.
DOE BES
Compare with previous methodsFractal and non-fractal scaling analysis both realistic
Fractal dimension
df~1.50.1 (Hähner
expt 1.64-1.79)
Refinement scaling collapses
qav ~ 1/Dav ~ e0.260.14
(Hughes expt e0.5, 0.66
different function)
DOE BES