Crystallographic Aspects of Dislocations

Outline Slip Systems Cross Slip Partial Dislocations Stacking Faults BCC, FCC, HCP Cross Slip Partial Dislocations Stacking Faults The Thompson Tetrahedron Fancy Stuff Frank rule, Frank loop, Lomer lock, Lomer-Cotrell dislocations, prismatic dislocations 22.71: Physical Metallurgy

Different views of FCC supercell Slip Systems http://ilan.schnell-web.net/physics/fcc/ Systems of planes and directions that make dislocation movement easy Different views of FCC supercell 22.71: Physical Metallurgy

Different views of FCC supercell Slip Systems http://ilan.schnell-web.net/physics/fcc/ Systems of planes and directions that make dislocation movement easy Different views of FCC supercell 22.71: Physical Metallurgy

Different views of FCC supercell Slip Systems http://ilan.schnell-web.net/physics/fcc/ Systems of planes and directions that make dislocation movement easy Different views of FCC supercell 22.71: Physical Metallurgy

Counting Slip Systems Multiply: Number of non-parallel planes Number of close packed directions per plane l k h Same slip planes! 22.71: Physical Metallurgy

Draw primary slip systems for FCC, BCC, and HCP crystal systems In Class Draw primary slip systems for FCC, BCC, and HCP crystal systems 22.71: Physical Metallurgy

Evidence of Slip Systems http://www.doitpoms.ac.uk/tlplib/slip/printall.php 22.71: Physical Metallurgy

Annealing twins in brass Side Note: Twinning http://www.doitpoms.ac.uk/tlplib/miller_indices/printall.php Bands can “flip” to mirror image of surrounding crystal Annealing twins in brass 22.71: Physical Metallurgy

Side Note: Twinning Alternate plastic deformation mechanism http://moisespinedacaf.blogspot.com/ http://dcg.materials.drexel.edu/?page_id=14#nuclear Twinning observed in irradiated reactor pressure vessel steel 22.71: Physical Metallurgy

Twinning http://dcg.materials.drexel.edu/?page_id=14#nuclear Differently oriented dislocations inside/outside twin boundary! MIT Dept. of Nuclear Science & Engineering 22.74: Radiation Damage & Effects in Nuclear Materials Prof. Michael P. Short Page 11 22.71: Physical Metallurgy

Evidence of Slip Systems http://www.doitpoms.ac.uk/tlplib/miller_indices/printall.php A scanning electron micrograph of a single crystal of cadmium deforming by dislocation slip on 100 planes, forming steps on the surface 22.71: Physical Metallurgy

Evidence of Slip Systems N. Friedman et al. Phys. Rev. Lett. 109, 095507 (2012) Nanopillar compression tests using a diamond flat punch Clear 45 degree angles observed Slip systems activated by shear 22.71: Physical Metallurgy

Evidence of Slip Systems S. Brinckmann et al. Phys. Rev. Lett. 100, 155502 (2008) Nanopillar compression tests using a diamond flat punch Clear 45 degree angles observed Slip systems activated by shear 22.71: Physical Metallurgy

Secondary Slip Systems When something blocks a primary slip system, a secondary slip system may activate Only if it is energetically favorable to continue deforming What happens if a secondary system can’t activate? 22.71: Physical Metallurgy

Cross Slip Dislocation switches slip systems if it get stuck Derek Hull and David J. Bacon, Introduction to dislocations, 4th ed. (Butterworth-Heinemann, Oxford, 2001). Dislocation switches slip systems if it get stuck Example: pinned screw dislocation time 22.71: Physical Metallurgy

Cross Slip Allen & Thomas, p. 100 [101] l k h 22.71: Physical Metallurgy

Slip Systems Slip directions partially or fully enclose slip planes Allen & Thomas, “The Structure of Materials,” p. 116 Slip directions partially or fully enclose slip planes 22.71: Physical Metallurgy

HCP Slip Systems { } { } { } Ideal c/a = 1.63299 11 2 4 c 10 1 1 11 2 [0001] { } 10 1 1 { } 11 2 2 a2 { } 11 2 4 a 1   22.71: Physical Metallurgy

Partial Dislocations Look carefully at the (111) plane in FCC How many ways can atom A move to location B? B B A A 22.71: Physical Metallurgy

Partial Dislocations Look carefully at the (111) plane in FCC How many ways can atom A move to location B? B B A A 22.71: Physical Metallurgy

Partial Dislocations Allen & Thomas, p. 119 A “perfect” dislocation can split into two “partials” These move in unison 22.71: Physical Metallurgy

Partial Dislocations Allen & Thomas, p. 117 A “perfect” dislocation can split into two “partials” 22.71: Physical Metallurgy

Partial Dislocation Separation After formation, the two partials repel each other Why? Opposite screw parts attract Parallel edge parts repel 22.71: Physical Metallurgy

Stacking Faults The shifted portion of the partial dislocation is a “stacking fault” Atomic stacking order into the screen has changed Was ABCA / BCABCABC … Now it is ABCA / CABCABC … 22.71: Physical Metallurgy

Stacking Fault Energy (SFE) Energy needed to create a stacking fault High SFE materials deform by full dislocation glide Cross slip is easier Low SFE materials deform by SF creation and glide Cross slip is harder What is the cutoff threshold? Frank’s Rule! If 𝑏 1 2 ≥ 𝑏 1+ 2 + 𝑏 1− 2 , then splitting is energetically favorable 22.71: Physical Metallurgy

The Thompson Tetrahedron http://imechanica.org/files/Partial%20Dislocation%20Tutorial%20for%20FCC%20Metals.pdf 22.71: Physical Metallurgy

Lomer-Cottrell Dislocation http://imechanica.org/files/Partial%20Dislocation%20Tutorial%20for%20FCC%20Metals.pdf Two partials hit at 60 degree angles Each consists of a leading and trailing partial Leading partial intersections will form a new full edge dislocation 22.71: Physical Metallurgy

Lomer-Cottrell Dislocation http://imechanica.org/files/Partial%20Dislocation%20Tutorial%20for%20FCC%20Metals.pdf Lomer-Cottrell Dislocation Determination 22.71: Physical Metallurgy

Lomer Lock Both original dislocations (BC and DB) were in slip planes Is the new dislocation in any slip planes? What happens next? 22.71: Physical Metallurgy

What Happens When Dislocations Get Stuck? When bits get pinned, they can bow out… creating Frank-Read sources http://youtu.be/Db85wOCWJkU 22.71: Physical Metallurgy

Dislocation Loops Loops have mixed edge/screw character May be circular planes of atoms between two planes 22.71: Physical Metallurgy

Frank-Read Loop Sources Come from sessile sections of dislocations Old strain direction 22.71: Physical Metallurgy

Frank-Read Loop Sources http://virtualexplorer.com.au/special/meansvolume/contribs/wilson/Generation.html http://www.numodis.fr/tridis/TEM/recordings/FR_loin_53.mpg 22.71: Physical Metallurgy

Forces Between Dislocations X & Y forces, no Z-force Peach-Kohler Equation Burgers vector of dislocation (2) transposed Line vector of dislocation (2) transposed Force vector on dislocation (2) Stress tensor induced by dislocation (1) 22.71: Physical Metallurgy

Forces Lead to Pileup Dislocations moving & piling up in Inconel 617 (Ni-based alloy) under in-situ straining in the TEM http://youtu.be/r-geDwE8Z5Y 22.71: Physical Metallurgy

Forces Lead to Grain Boundaries http://www.tf.uni-kiel.de/matwis/amat/def_en/kap_7/backbone/r7_2_1.html Tilt grain boundary in Al http://moisespinedacaf.blogspot.com/ 22.71: Physical Metallurgy