Title: COMPUTATIONAL MODELING OF MATERIALS: THREE HIERARCHICAL LEVELS
1COMPUTATIONAL MODELING OF MATERIALS THREE
HIERARCHICAL LEVELS
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3Embedded Atom Method Energy Functions (D.J.Oh and
R.A.Johnson, 1989 ,Atomic Simulation of
Materials, EdtsV Vitek and D.J.Srolovitz,p 233)
The total internal energy of the crystal
where
and
Internal energy associated with atom i Embedded
Energy of atom i. Contribution to electron
density of ith atom and jth atom. Â Two
body central potential between ith atom and jth
atom. Â
4 Embedded energy is of the form
where
are equilibrium and cut off interatomic
separations
5The constants required in the above equation are
listed for Al, Cu and Mg atoms below
Al Cu Mg
? 5 5 6
? 10.5 8.5 10.5
? 20 20 20
rc 1.9 1.9 1.7
?e 0.12538 0.36952 0.14720
a -4.8144 -4.0956 -1.1049
b 0.47685 -1.6979 -1.3122
?e 12.793 12.793 12.316
6CONSTRUCTION OF COMPUTATIONAL CRYSTAL
CONSTRUCTION OF COMPUTATIONAL CRYSTAL
7BOUNDARY CONDITIONS FOR GB SLIDING
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103 GB Sliding and Migration at 500K (Applied Shear)
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14Mg
Al
y
GB
15Energy distribution at grain boundaries
16Note
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21Radius Distribution Function (RDF)
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