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LECTURE 3 M. I. Baskes Mississippi State University
University of California, San Diego and Los Alamos National Laboratory
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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)
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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
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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
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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
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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!
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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
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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
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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!
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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 &
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IN AN FCC MATERIAL AN EDGE DISLOCATION HAS 2 PLANES INSERTED
Use style to view by depth
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A BURGERS CIRCUIT MAY BE DRAWN TO DETERMINE THE BURGERS VECTOR
15 Burgers vector a/2{110} in fcc Use view to limit region shown 3 3 14
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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.
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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
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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
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IT IS EASY TO LOCATE THE DISLOCATION USING CNA
xatoms < disloc.CNA &
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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
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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
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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
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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
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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)
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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
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VARY SHEAR FORCE UNTIL DISLOCATION MOVES
force (eV/Å/atom) Hold bottom atoms fixed and apply force to top atoms
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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
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