Segregation of Alloying Elements Near a Grain Boundary

(a) How to investigate segregation of alloying elements (or impurities) near grain boundaries?
(b) What is a stress pattern near a grain boundary in Aluminum?
(c) How does the segregation affect the stress pattern near the grain boundary in Aluminum?

adesh.zip :Click HERE to Download a DEMO version of ADESH
(ADESH works on PC-DOS. You will need the pkunzip.exe utility for this zipped file.)

Answer

(a) We will use Aluminum cell with a grain boundary for this purpose. Simple steps to take are: (1) Make an Aluminum cell, (2) Input a grain boundary in the cell, (3) Input aloying elements randomly, (4) Use the Swapping erlaxation technique to rearrange the atoms in a minimum energy configuration, (5) Examine the resulting configuration.

ADESH users: You can take following steps with ADESH . Create an aluminum cell by choosing: (1) FCC Unit Cell, (2) Aluminum Atom, (3) Miller Indices: X(1 1 0), Y(0 0 1), Z(-1 1 0).
Make a two dimensional cell with a size of +20 to -20 Angstroms along X and Y directions and from -2 to 1 Angstroms along Z. Make the boundary by specifying grain boundary angle, width of the core you wish to reconstruct (in Compute menu). Extend the cell along Z (to make it 3D) by using the option in the Compute menu. Use the translational displacement options to move the two grains against each other while monitoring the energy of the system. Choose the minimum energy configuration. Further relax individual atoms at the boundary plane by using Relax option in Compute menu. Resulting configuration is the starting cell for this project.
Insert alloying elements (Copper) randomly with 'Alloy' option. Resulting configuration can be seen with File-View (Figure B). Figure B shows a central slice of the 3D cell. The grain boundary is vertical coming out of the screen. Hence it is seen as a vertical line in Figure B. Yellow circles represent Aluminum atoms and red circles are copper atoms.




Relax the cell with 'Swap' technique in Compute-Relax option. It took about five hours for a cell with 1500 atoms to relax on a 486DX2 computer. Final configuration shows copper atoms segregated near the grain boundary (Figure C).

(b) & (c) The energy contours for the grain boundary configurations are plotted in 'Figure D'. Figure D-a shows maximum energy for a grain boundary with the starting cell with no alloying elements. The strain energy pattern reflects the stress pattern. Hence the strain elergy drops to the ideal or bulk level within about ten angstroms from the grain boundary.
"The Strain In The Grain Stays Mainly In The Plane".
The relaxed cell with the copper atoms segregated near the grain bundary plane shows lowest energy contour (Figure D-c). The lowering of energy is the driving force for the segregation.

Figure Captions:

Questions? Comments? Suggestions?
Send a note to Anjali Nandedkar at CASA Engineering
info@casaengineering.com

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