md2011-08-note_Part_2

md2011-08-note_Part_2 - I Here, V 2 is a pair potential,...

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Unformatted text preview: I Here, V 2 is a pair potential, and V 3 is the three-body part I The f i are f 2 ( r ) = A ( Br- p- 1 ) exp [( r- a )- 1 ] , r < a , r > a (6) f 3 ( r i , r j , r k ) = h ( r ij , r ik , θ jik ) + h ( r ji , r jk , θ ijk ) + h ( r ki , r kj , θ ikj ) (7) I Function h is h ( r ij , r ik , θ jik ) = λ exp [ γ ( r ij- a )- 1 + γ ( r ik- a )- 1 ]( cos θ ijk + 1 3 ) 2 ] , where r ij < a and r ik < a , else (8) I The explicitness of the angle is in the + 1 / 3 term I As mentioned, the explicit angle becomes a problem when different phases or disordered systems are studied I Actually, it’s rather surprising that the SW potential works for liquid silicon because of this I The constants A , B , p , a , λ and γ are all positive and fitted to get the diamond structure as the most stable lattice, as well as to the melting point, cohesive energy and lattice parameter I According to rumors, the authors also tested the potential against elastic constants, although this is not stated in the article I Melting point was fixed by adjusting the cohesive energy to a value 7% off I Despite the explicit angle, SW provides a better description of...
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This note was uploaded on 02/14/2012 for the course CSE 6590 taught by Professor Kotakoski during the Winter '12 term at York University.

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md2011-08-note_Part_2 - I Here, V 2 is a pair potential,...

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