1. LECTURE 3 M. I. Baskes Mississippi State University
University of California, San Diego
and
Los Alamos National Laboratory

2. COURSE OUTLINE Some Concepts Dislocation Motion Bond energy CREATOR
Many body effects
DYNAMO
Transferability
XATOMS
Reference state
Common Neighbor Analysis (CNA)
Screening
Models
Pair potentials
Embedded Atom Method (EAM)
theory
examples
Modified Embedded Atom Method (MEAM)

3. DISLOCATION MOTION DEPENDS ON IT’S CHARACTER
When a dislocation moves under an applied shear stress:
individual atoms move in directions parallel to the Burgers vector
the dislocation moves in a direction perpendicular to the dislocation line
An edge dislocation moves in the direction of the Burgers vector
A screw dislocation moves in a direction perpendicular to the Burgers vector

4. DISLOCATIONS MOTION DEPENDS ON CORE SIZE
The ease of dislocation glide is partly determined by the degree of distortion (with respect to the perfect lattice) around the dislocation core. When the distortion is spread over a large area, the dislocation is easy to move. Such dislocations are known as wide dislocations, and exist in ductile metals.
The Peierls stress is the stress necessary to move a dislocation

5. A DISLOCATION CREATES A DISPLACEMENT FIELD
Edge dislocation at origin
Isotropic elasticity
Burgers vector b
Poisson ratio ν
Displacement (ux,uy) at point (x,y)
r2=x2+y2
Implemented in CREATOR using anisotropic elasticity

6. CREATOR IS A COMPUTER CODE USED TO CREATE INITIAL POSITIONS OF ATOMS
We will use it to create a lattice with a dislocation
Material: EAM Cu
Dislocation character: edge
Dislocation position: between 2 slip planes
Use CREATOR menus from top to bottom only
Sometimes you need a return to continue
Data may be delimited by returns, tabs, spaces, or commas
CREATOR is not forgiving – type carefully!

7. USE CREATOR TO INSERT THE DISLOCATION
are you an expert? (1=yes,0=no)
2 generate or modify lattice
4 rotate axes 2 4
lattice maker menu
enter rotated crystallographic axes in terms of old
***********************************
1 -1 0
1 define primitive lattice vectors
1 1 1 1
0 0 0
select lattice type
*********************
1 fcc
5 define region and/or periodicity 5
enter lattice constant
region definition
3.615
*****************************
origin for region:
2 x,y,z coordinates of origin
2 define types
enter origin for region
2 redefine old type
1 define cubic region
which type?
periodic in x? y? z?
enter z for element and mass in amu
0 0 1

8. USE CREATOR TO INSERT THE DISLOCATION (CONT’D)
enter x boundaries of cell
1 -1 0
-50 50
1 1 1
enter y boundaries of cell
7 return
-14 15 7
length of periodic unit= how many to include?
7 generate atom positions 3
select cutoff distance of like pairs
lattice maker menu
***********************************
enter the maximum number of self consistent iterations for displacements? 0=not self consistent
6 define dislocations 6
dislocation definition 10
**********************
14 return to main menu 14
0 dislocations defined so far
3 write lattice to file
modifications
(you may change elastic constants)
name of file for output? header?
3 add a dislocation
disloc.atm
Edge dislocation in Cu y=0.5
position on slip plane (hlc, rotated),burgers vector (hlc, unrotated)slip plane normal (unrotated)
6 stop
0 .5 0

9. MODIFY THE TOP OF THE FILE TO REDUCE CELL SIZE
Edge dislocation in Cu y=0.5
E E E+01
E E E+01 E
E E E+01
E E E+00 1
E E E+01
E E E+01
E E E+01
This is necessary to get CNA to work!

10. XATOMS IS A COMPUTER CODE USED TO VISUALIZE ATOMS
We will use it to visualize a lattice with a dislocation before and after application of strain
xatoms < disloc.atm &

11. IN AN FCC MATERIAL AN EDGE DISLOCATION HAS 2 PLANES INSERTED
Use style to view by depth

12. A BURGERS CIRCUIT MAY BE DRAWN TO DETERMINE THE BURGERS VECTOR15
Burgers vector a/2{110} in fcc
Use view to limit region shown 3 3 14

13. COMMON NEIGHBOR ANALYSIS (CNA) PROVIDES THE LOCAL STRUCTURE
Decomposition of the radial distribution function (RDF) according to environment of the pairs
All atom pairs separated at r < rc , where rc is position of first minimum of the RDF, are called bonded-pairs.
The bonded-pairs are classified by a set of three indices ‘jkl’:
j = number of shared (common) nearest-neighbors
k= number of bonds between these common neighbors
l= number of bonds in the longest continuous chain formed by the k bonds between common neighbors.
For example: FCC has 12 (421) bonded-pairs
HCP has 6 (421) and 6 (422) bonded-pairs.

14. CNA DISTINGUISHES FCC AND HCP
Blue = Atoms in Bonded-Pair.
Black = Common-Neighbors.
Red = Longest Continuous Chain
of Bonds.
FCC: 421 Pair
HCP: 422 Pair

15. CNA IS A COMPUTER CODE TO PERFORM COMMON NEIGHBOR ANALYSIS
Use rc=3 for Cu (-R)
Atom positions: *.atm file (-I)
File format: baskes (-F)
Identified atoms *.CNA file (–O)
ID the dislocation in the file created with CREATOR
CNA -R 3.0 -I disloc.atm -F baskes -O disloc.CNA

16. IT IS EASY TO LOCATE THE DISLOCATION USING CNA
xatoms < disloc.CNA &

17. DYNAMO IS A COMPUTER CODE TO PERFORM (M)EAM MD OR MS SIMULATIONS
Instructions *.i file
Initial atom positions *.atm file
Final atom positions *.r file
EAM parameters *.fcn file

18. INPUT FILE FOR MINIMIZATION
disloc.i
$latcard /
$velcard /
$prntcard
$bndcard ibdtyp=1,idynper=-1,-1,-1 /
printf='disloc.p'
$neicard nmeth=-2 /
rstrtf='disloc.r'
$defcard /
conff='none'
$fixcard ymin=11,ymax=1000,mode=3 /
ipatoms= 2
$fixcard ymin=-1000,ymax=-10,mode=3 /
ipitera=-1
$fixcard /
iconst=0
$tmpcard /
ipinter=0
$regcard / /
$avecard /
$headcard header=' Cu dislocation' /
$intcard inte=-1,nfmax=1000,tol=1e-6 /
$funccard funcfl='cuu3.fcn’ /
$continue contin=.f. /
$initcard
initf='disloc.atm'
genvel=.f.,gendis=.f.,
scale=1.0
Hold top and bottom atoms fixed

19. EAM PARAMETERS
We will use parameters from the 1986 EAM paper (Universal functions)
Foiles, S.M., Baskes, M.I., and Daw, M.S., PRB, 33, p (1986)
cuu3.fcn

20. RELAX AND VIEW THE DISLOCATION USING DYNAMO, CNA, AND XATOMS
eam88 < disloc.i &
CNA -R 3.0 -I disloc.r -F baskes -O relaxed_disloc.CNA
xatoms < relaxed_disloc.CNA &
In style, change atom size
Stacking fault
Core

21. USING XATOMS TO IMAGE THE CNA FILE
atom type
2 fcc
3 hcp
5 other
Average x of the hcp (SF) atoms
Draw rectangle around dislocation
Right click (PC)
Command click (Mac)

22. INPUT FILE FOR SHEAR
disloc_shear.i
$latcard /
$prntcard
$velcard /
printf='disloc_00001.p'
$bndcard ibdtyp=1,idynper=-1,-1,-1 /
rstrtf='disloc_00001.r'
$neicard nmeth=-2 /
conff='none'
$defcard /
ipatoms= 2
$fixcard ymin=11,ymax=1000, mode=4,vector= ,0,0 /
ipitera=-1
iconst=0
$fixcard ymin=-1000,ymax=-10, mode=3 /
ipinter=0
$fixcard num=3063,mode=3 /
meamf='meamf'
$fixcard num=477,mode=3 / /
$fixcard /
$headcard header=' Cu dislocation' /
$tmpcard /
$funccard funcfl='cuu3.fcn’ /
$regcard /
$initcard
$avecard /
initf='disloc.r'
$intcard inte=-1,nfmax=10000,tol=1e-6 /
genvel=.f.,gendis=.f.,
$continue contin=.f. /
scale=1.0
Hold bottom atoms fixed and apply force to top atoms

23. VARY SHEAR FORCE UNTIL DISLOCATION MOVES
force (eV/Å/atom)
Hold bottom atoms fixed and apply force to top atoms

24. CALCULATION OF PEIERLS STRESS
Stress = ( eV/Å/atom) (249 atoms) / (50 Å x 13.3 Å) (160 GPa / (eV/Å3))= 0.45 MPa
c44=76.8 GPa
Peierls stress = 5.8x!0-6 c44 as expected very small for an fcc material