M. J. Demkowicz Financial Support: Center for Materials at Irradiation and Mechanical Extremes (CMIME) at LANL, an Energy Frontier Research Center (EFRC) funded by U.S. Department of Energy, Office of Science, Office of Basic Energy Sciences Acknowledgments: A. Kashinath, A. Vattré, B. Uberuaga, X.-Y. Liu, A. Caro, and A. Misra
the “bad” patch • Coherent region experiences strain emanated by the “bad” patch • Interface with well separated “bad” patches may be described within the same theory as that of dislocations: misfit dislocations simplified side view Semi-coherent interfaces (2D defects) can be represented as arrays of dislocations (1D defects)
core (linear elasticity is inapplicable) • has a line vector (1-d defects) • described by a vector that displaces atoms when it moves Defects in Crystals, H. Foell. http://www.tf.uni-kiel.de/matwis/amat/def_en
MDI • Two sets of misfit dislocations with Burgers vectors • Misfit dislocation intersections (MDI) where different sets of dislocations meet General features of semicoherent fcc-bcc interfaces
2.1 nm 0.9 nm Side-views by themselves often tell wrong things! • Misfit dislocations in this case are not perpendicular to the sideview • The spacing obtained from sideview is not dislocation spacing!
i Compute vectors R'i-Ri where the vectors are the lines joining the closest fcc and bcc atoms to their corresponding nearest neighbors 1 1 1 2 2 3 3 4 4 5 5 6 6 Cu-Fe NW R0 • Pick an atom in 1 grain. Find the closest 2nd grain atom to that atom • Take nearest in-grain neighbors around each atom • Find one-to-one correspondence so that closest atoms are paired!
between center atoms • Ri -vector between a center and ith in-grain atom for 1st grain • R’i -vector between a center and ith in-grain atom for 2nd grain R i R' i Compute vectors R'i-Ri where the vectors are the lines joining the closest fcc and bcc atoms to their corresponding nearest neighbors 1 1 1 2 2 3 3 4 4 5 5 6 6 Cu-Fe NW R0
i R' i Compute vectors R'i-Ri where the vectors are the lines joining the closest fcc and bcc atoms to their corresponding nearest neighbors 1 1 1 2 2 3 3 4 4 5 5 6 6 Cu-Fe NW R0 R0 i , Ri • R and R’ are matrices containing all vectors Ri and R’i • Solve for R = DR’; D is identify when the locality is coherent • |D-I| is an intensity indicator - higher the value, lesser the coherency ||R0 i R 1 i 1||
identify dislocation line and Burgers vectors • Assumption: A coherent patch exists at the interface • Advantage: Reference structure not required • Limitations: Dislocation core thickness cannot be determined (yet)
the origin of this vector to the center atom of one grain (any grain) R i R' i Compute vectors R'i-Ri where the vectors are the lines joining the closest fcc and bcc atoms to their corresponding nearest neighbors 1 1 1 2 2 3 3 4 4 5 5 6 6 Cu-Fe NW R0
Discontinuity in vectors directions (Mean of these vectors are taken as first approximations) fcc<110> fcc<112> First, take Ri-R’i and place it about the center atom CuFe NW
Discontinuity in vectors directions (Mean of these vectors are taken as first approximations) fcc<110> fcc<112> First, take Ri-R’i and place it about the center atom • Take the mean of all the vectors about a single center CuFe NW
of the Burgers vector with X-axis Yellow and light blue: BV is 180 or 0 degrees with +x-axis Purple : BV is 60 degrees with +x-axis Orange : BV is 120 degrees with +x-axis CuFe NW
of the Burgers vector with X-axis Yellow and light blue: BV is 180 or 0 degrees with +x-axis Purple : BV is 60 degrees with +x-axis Orange : BV is 120 degrees with +x-axis • We assumed that the coherent patch is where central atoms overlap • That assumption may be incorrect. • We sample other places in the interface and compare with |D-I| plot CuFe NW