Freeman, A.J.

Koelling, D.D.

D D Koelling

A J Freeman

Crossref

RELATIVISTIC ELECTRONIC BAND STRUCTURE AND PROPERTIES OF THE HEAVIER ACTINIDES: A SECOND RARE-EARTH SERIES.

UNT (University of North Texas) Digital Library

N O T I C E This report was prepared as an account of work sponsored by the United States Government . Neither the United States nor the United States Atomic Energy Commission, nor any of their employees, nor any of their contractors, subcontractors, or their employees, makes any warranty, express or implied, or assumes any legal liability or responsibility for the accuracy, com-pleteness or usefulness of any information, apparatus, product or process disclosed, or represents that its use would not infringe privately owned rights. RELA.TIVISTIC ELECTRONIC BAUD STRUCTURE AND PROPERTIES ^ / QP THE HEAVIER ACTINIDES: A SECOND RARE-EARTH SERIES* L ^ / " - A * / / / 7 ~ D. D. K o e l l i n g a n d A . J . F r e e m a n P h y s i c s D e p a r t m e n t , N o r t h w e s t e r n U n i v e r s i t y -E v a n s t o n , I l l i n o i s 60201 a n d A r g o n n e N a t i o n a l L a b o r a t o r y , A r g o n n e , I l l i n o i s 60 3̂9 ABSTRACT -The h e a v i e r a c t i n i d e s i . e . , Am a n d "beyond, h a v e "been s t u d i e d "by m e a n s of RA.PW c a l c u l a t i o n s a n d a r e f o u n d t o d i f f e r d r a m a t i c a l l y f r o m t h e l i g h t e r m e t a l s : t h e . 5 f e l e c t r o n s a p p e a r t o b e more l o c a l i z e d s p a t i a l l y , o v e r l a p o n l y w e a k l y w i t h t h e i r 5f n e i g h b o r s a n d show b a n d w i d t h s w h i c h a r e s m a l l r e l a t i v e t o t h e Coulomb c o r r e l a t i o n e n e r g y . H e n c e , j u s t a s i n t h e c a s e o f t h e r a r e - e a r t h m e t a l s , t h e 5f e l e c -t r o n s may n o t b e d e s c r i b e d b y t h e b a n d m o d e l . I n s t e a d , a l o c a l i z e d d e s c r i p t i o n i s r e q u i r e d i n w h i c h , a s i n t h e r a r e - e a r t h s , H u n d ' s r u l e i n t r a - a t o m i c e x c h a n g e c o u p l i n g p r o d u c e s l o c a l i z e d 5f m a g n e t i c moments w h i c h c a n b e o r d e r e d m a g n e t i c a l l y b y i n d i r e c t e x c h a n g e i n t e r a c t i o n . • • U n t i l v e r y r e c e n t l y , l i t t l e was known a b o u t t h e e l e c t r o n i c b a n d s t r u c t u r e of t h e a c t i n i d e *no+«.i*j r r i t h w h i c h t o i n t e r p r e t t h e i r m a g n e t i c p r o p e r t i e s . Q u i t e a s i d e f rom t h e e x p e c t e d t h e o r e t i c a l c o m p l i c a t i o n s o f t r e a t i n g r e l a t i v i s t i c a l l y t h e c o m p l e x c r y s t a l l o -g r a p h i c s t r u c t u r e s f o r m e d b y t h e s e m e t a l s , t h e i r c o n d u c t i o n b a n d s t r u c t u r e s a r e e x p e c t e d t o b e more c o m p l i c a t e d t h a n t h a t of e i t h e r t h e t r a n s i t i o n m e t a l s o r t h e r a r e - e a r t h m e t a l s . He re we r e p o r t on t h e f e e p h a s e s of - these m e t a l s . I n t h e l i g h t e r a c t i n i d e s , d e t a i l e d SSymmetrized R e l a t i v i s t i c APW (SRAFW) s t u d i e s - 1 - h a v e shown t h a t t h e 5f e l e c t r o n s a r e n o t w e l l l o c a l i z e d ( u n l i k e t h e k£ o r b i t a l s I n t h e r a r e - e a r t h m e t a l s ) s o t h e i r i t i n e r a n t n a t u r e makes t h e m h y b r i d i z e s t r o n g l y w i t h b o t h t h e 6d a n d 7s b a n d s . T h i s s t r o n g h y b r i d i z a t i o n o f t h e b r o a d . 5f i t i n e r a n t s t a t e s w i t h t h e v e r y b r o a d 6d-7s b a n d s shown i n F i g . 1 f o r f e e p l u t o n i u m m e t a l r e s u l t s i n a b a n d s t r u c t u r e w h i c h h a s a n o v e r a l l l a r g e e f f e c t i v e b a n d w i d t h f o r t h e ( p o s s i b l e ) m a g n e t i c c a r r i e r s . (The p l a n e wave s t a t e c a n b e s e e n s t a r t i n g a t w i t L t h e p a r a b o l i c s h a p e . The d s t a t e s a t T a r e t h e s p i n - o r b i t s p l i t t g g (r8+ a n d Tj+) a n d ifoe h i g h e r c g(r3 +). A l l s t a t e s s h o v n w i t h n e g a t i v e p a r i t y a t r a r e f - s t a t e s . ) T h i s l a r g e f b a n d w i d t h makes i t e n e r g e t i c a l l y t o o c o s t l y t o p r o d u c e a n y m a g n e t i z a t i o n ( f l i p p i n g of s p i n s ) ; i . e . , i n t h e b a n d p i c t u r e 2 t h e k i n e t i c e n e r g y p e n a l t y o f p r o m o t i n g a n e l e c t r o n of one s p i n b a n d i n t o t h e o p p o s i t e s p i n b a n d e x c e e d s t h e l o w e r i n g of e n e r g y due t o e x c h a n g e i n t e r -a c t i o n s ( b e c a u s e t h e e f f e c t i v e w i d t h . i s j u s t t o o g r e a t ) . T h i s same S u p p o r t e d b y t h e A t o m i c E n e r g y Commiss ion , t h e A i r F o r c e O f f i c e of S c i e n t i f i c R e s e a r c h a n d t h e N a t i o n a l S c i e n c e F o u n d a t i o n . DiSYfttfiUftOti OF THIS WJCtfMOfT f$ KHLWHTfiFJ 2 q u a l i t a t i v e p i c t u r e a p p e a r s t o h o l d f o r a l l . t h e l i g h t e r a c t i n i d e m e t a l s w h i c h show n o m a g n e t i c o r d e r i n g . I n t h e l i g h t e r a c t i n i d e s , t h e i t i n e r a n t o r h a n d p o i n t of v i e w i s a p p l i c a b l e b e c a u s e of t h e l a r g e o v e r l a p b e t w e e n n e i g h b o r i n g 5f e l e c t r o n s r e s u l t i n g i n t h e i r b a n d w i d t h s e x c e e d i n g t h e Coulomb c o r -r e l a t i o n e n e r g y . By c o n t r a s t , t h e hf e l e c t r o n s i n t h e r a r e - e a r t h s a r e h i g h l y l o c a l i z e d , do n o t o v e r l a p n e i g h b o r s a p p r e c i a b l y a n d f o r m a v e r y n a r r o w e n e r g y b a n d i n t h e s o l i d whose e f f e c t i v e w i d t h i s much s m a l l e r t h a n t h e Coulomb c o r r e l a t i o n e n e r g y . 3 Thus u n l i k e t h e c a s e o f t h e 5f e l e c t r o n s i n t h e s e a c t i n i d e s t h e hf e l e c t r o n s may n o t b e t r e a t e d a s b a n d e l e c t r o n s b e c a u s e o f t h e l a r g e e r r o r s ( ~ 10-15 eV) i n t r o d u c e d b y n e g l e c t o f t h e i n t r a - a t o m i c Coulomb c o r r e l a t i o n t e r m s . "We h a v e i n v e s t i g a t e d t h e h e a v i e r a c t i n i d e m e t a l s Am, Cm a n d Bk b y means o f t h e SRAFW m e t h o d . The e f f e c t s of v a r y i n g a , t h e . p a r a m e t e r m u l t i p l y i n g t h e f r e e e l e c t r o n e x c h a n g e p o t e n t i a l a n d a t o m i c s t a r t i n g c o n f i g u r a t i o n s ( r e l a t i v e number o f o c c u p i e d 5f9 6d a n d 7s e l e c t r o n s ) on t h e r e s u l t i n g b a n d s t r u c t u r e was s t u d i e d — ? n i n t h e " w a r p e d " m u f f i n t i n a p p r o x i m a t i o n . S i n c e s p a c e d o e s n o t p e r m i t a d e t a i l e d p r e s e n t a t i o n o f o u r r e s u l t s , a summary w i l l b e g i v e n . F i g . 1 i n c l u d e s t h e b a n d s t r u c t u r e of t h e s e h e a v i e r m e t a l s o b t a i n e d w i t h a = 2/3 ( t h e Kohn-Sham G a s p l r e x c h a n g e a p p r o x i m a -t i o n ) . We h a v e f o u n d t h a t t h e r e i s a s h a r p l y i n c r e a s e d l o c a l i z a t i o n o f t h e 5f e l e c t r o n s i n t h e s e tie t e l e . , 1 th i n c r e a s i n g a t o m i c n u m b e r , i . e . , g r e a t l y d e c r e a s e d o v e r l a p a n d r a p i d n a r r o w i n g o f t h e i r b a n d w i d t h s . ( T h i s l o c a l i z a t i o n i s f o u n d t o b e much g r e a t e r i n t h e a- = 1 c a l c u l a t i o n s , w h i c h we f e e l , h o w e v e r , a r e n o t a s p h y s i c a l l y m e a n i n g -f u l . ) T h e s e much n a r r o w e r b a n d s d o n o t h y b r i d i z e g r e a t l y w i t h t h e 6d a n d Js i t i n e r a n t b a n d s . F u r t h e r , s i n c e t h e Coulomb c o r r e l a t i o n i s l a r g e r e l a t i v e t o t h e e f f e c t i v e b a n d w i d t h , t h e i t i n e r a n t ( to : b a n d ) d e s c r i p t i o n i s n o l o n g e r v a l i d . I n s t e a d t h e l o c a l i z e d d e s c r i p t i o n of t h e i o n i c 5f e l e c t r o n s ( i . e . , l a r g e s p i n - o r b i t a n d B u n d ' s r u l e c o u p l i n g o f L , S a n d J — a l l m a x i m i z e d — i n t e r a c t i n g w i t h t h e i r e n v i r o n m e n t t h r o u g h t h e c r y s t a l l i n e e l e c t r i c f i e l d a n d t h e e x c h a n g e i n t e r a c t i o n s v i a t h e c o n d u c t i o n e l e c t r o n s ) a p p e a r s now more a p p r o p r i a t e , a s i n t h e c a s e o f t h e r a r e e a r t h m e t a l s . I n d e e d , a n a p t d e s c r i p t i o n of t h e s e m e t a l s i s t h a t t h e y a p p e a r t o f o r m a s e c o n d r a r e - e a r t h s e r i e s w i t h a l l t h a t i m p l i e s . F o r m a g n e t i s m we may w e l l e x p e c t f o r t h e h e a v i e r a c t i n i d e m e t a l s t h e d i v e r s i t y ( a n d c o m p l e x i t y ) o f m a g n e t i c o r d e r i n g phenomena f o u n d f o r t h e r a r e - e a r t h m e t a l s . ^ I t t h u s a p p e a r s t o b e a new f r u i t f u l ( b u t d i f f i c u l t ) a r e a f o r magnetr iq r e s e a r c h . One f i n a l r e m a r k s h o u l d b e made a b o u t t h e Cm b a n d s t r u c t u r e w h e r e t h e f - l o c a l i z a t i o n i s n o t n e a r l y a s p r o n o u n c e d a s f o r e i t h e r Am o r B k . T h i s i s due t o . t h e a n o m a l o u s l y s m a l l l a t t i c e c o n s t a n t r e p o r t e d f o r Cm. Had we d e r i v e d a n e f f e c t i v e l a t t i c e c o n s t a n t f r o m t h e a p h a s e ( d h e p ) n e a r n e i g h b o r , d i s t a n c e s , t h e r e s u l t i n g f - b a n d , w i d t h s w o u l d h a v e b e e n a s s m a l l a s far t h e Am a n d B k . 3 REFERENCES 1 . D . D. K o e l l i n g , A . J . F r e e m a n , F . M. M u e l l e r , R h y s , R e v . I B , 1318 (1970); A , J , F r e e m a n a n d D. D. K o e l l i n g , B u l l . Am. P a y s . S o c . Ik, 360 (1969); G. O, Arbman, D. D. K o e l l l n g , A . J . F r e e m a n , BAPS 1^, jjjkh (1970); D. D. K o e l l i n g , A . J . F r e e m a n , G. 0 . Arbman , P l u t o n i u m 1970 a n d O t h e r A c t i n i d e s , e d . W. N . M i n e r , N u c l . Ma t . 17, 19̂ - (1970); A . J . F r e e m a n , D. D. K o e l l i n g J", de P h y s i q u e ( i n p r e s s ) . 2. J . C . S l a t e r , P b y s . R e v . 537, 931 (1936); 52, 198 (1937). 3. S e e t h e r e v i e w c h a p t e r b y A . J . F r e e m a n i n M a g n e t i c P r o p e r t i e s o f t h e R a r e - E a r t h M s t a l s , ( R . J . E l l i o t , e d . P lenum P r e s s , L o n d o n ) 1972, p . 2k$. \ Fig. 1 Energy Bands in (100) direction for fee Pu, Am, Qpat? and Bk 

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RELATIVISTIC ELECTRONIC BAND STRUCTURE AND PROPERTIES OF THE HEAVIER ACTINIDES: A SECOND RARE-EARTH SERIES.

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