Evidence for long-range repulsive atomic interactions in metals from bond energy calculations
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T h e f i r s t a n d s e c o n d n e a r e s t n e i g h b o r b o n d e n e r g i e s a r e c a l c u l a t e d f o r a v a r i e t y o f Liquid m e t a l s f r o m h e a t of v a p o r i z a t i o n , d e n s i t y , a n d s u r f a c e t e n s i o n d a t a u s i n g a s i m p l e p a i r - w i s e i n t e r a c t i o n m o d e l o f c o h e s i v e f o r c e s . T h e f i r s t n e a r e s t n e i g h b o r i n t e r a c t i o n i s f o u n d t o be a t t r a c t i v e , w h i l e t h e s e c o n d n e a r e s t n e i g h b o r i n t e r a c t i o n is repulsive. T h i s l o n g e r r a n g e r e p u l s i v e i n t e r a c t i o n is n o t s u r p r i s i n g , in v i e w o f t h e F r i e d e l o s c i l l a t i o n s k n o w n t o e x i s t in t h e p o t e n t i a l f u n c t i o n f o r i o n - i o n i n t e r a c t i o n s i n a m e t a l . It i s s u g g e s t e d t h a t y - p l o t c a l c u lations for s o l i d m e t a l s take this repulsion into account.
/ H E p o t e n t i a l e n e r g y of a p a i r o f a t o m s w h i c h e x p e r i e n c e a van d e r W a a l s i n t e r a c t i o n i s q u i t e f a m i l i a r i n i t s q u a l i t a t i v e f e a t u r e s . A s t h e i n t e r a t o m i c distance i n c r e a s e s , the potential e n e r g y d e c r e a s e s , p a s s e s through a m i n i m u m , and then i n c r e a s e s a s y m p t o t i c a l l y to z e r o . T h e i n t e r a c t i o n is r e p u l s i v e o n l y a t the v e r y s m a l l i n t e r a t o m i c d i s t a n c e s w h e r e e l e c t r o n o v e r l a p is c o n s t r a i n e d a c c o r d i n g to t h e P a u l i exclusion principle. A t all l a r g e r separations, t h e i n t e r a c t i o n is a t t r a c t i v e , r e s u l t i n g f r o m t h e i n d u c e d or permanent dipoles of t h e a t o m s . T h e s i t u a t i o n f o r a c r y s t a l l i n e o r a l i q u i d m e t a l is q u i t e d i f f e r e n t . T h e p o t e n t i a l e n e r g y f o r a p a i r of i o n s i m m e r s e d i n t h e s e a of c o n d u c t i o n e l e c t r o n s d o e s not a s y m p t o t i c a l l y a p p r o a c h z e r o a t t h e l a r g e r i n t e r i o n i c d i s t a n c e s , but e x h i b i t s i n s t e a d a d a m p e d o s c i l l a t i o n a b o u t z e r o . T h u s , i n s t e a d of b e i n g a t t r a c t i v e at all t h e l a r g e r s e p a r a t i o n s , t h e i n t e r a c t i o n is alternately attractive and r e p u l s i v e a s distance inc r e a s e s . T h i s long-range o s c i l l a t o r y b e h a v i o r is a consequence of t h e dielectric screening of t h e ionic c o r e by t h e s u r r o u n d i n g c o n d u c t i o n e l e c t r o n s . A p o t e n t i a l o f t h i s f o r m w a s f i r s t s u g g e s t e d by F r i e d e l 1 a n d t h i s b e h a v i o r is o f t e n c a l l e d F r i e d e l o s c i l l a t i o n s . S i n c e that t i m e , q u a n t u m m e c h a n i c a l d e v e l o p m e n t s , known as p s e u d o p o t e n t i a l t h e o r y , 2 h a v e also y i
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