HAL Id: jpa-00227262
https://hal.archives-ouvertes.fr/jpa-00227262
Submitted on 1 Jan 1987
HAL is a multi-disciplinary open access archive for the deposit and dissemination of sci- entific research documents, whether they are pub- lished or not. The documents may come from teaching and research institutions in France or abroad, or from public or private research centers.
L’archive ouverte pluridisciplinaire HAL, est destinée au dépôt et à la diffusion de documents scientifiques de niveau recherche, publiés ou non, émanant des établissements d’enseignement et de recherche français ou étrangers, des laboratoires publics ou privés.
ANOMALOUS X-RAY RAMAN SPECTRUM OF POLYCRYSTALLINE BORON
A. Zdetsis, D. Papademitriou
To cite this version:
A. Zdetsis, D. Papademitriou. ANOMALOUS X-RAY RAMAN SPECTRUM OF POLY- CRYSTALLINE BORON. Journal de Physique Colloques, 1987, 48 (C9), pp.C9-843-C9-846.
�10.1051/jphyscol:19879150�. �jpa-00227262�
JOURNAL DE PHYSIQUE
Colloque C9, suppl6ment au n012, Tome 48, dbcembre 1987
ANOMALOUS X-RAY RAMAN SPECTRUM OF POLYCRYSTALLINE BORON
A.D. ZDETSIS and D.K. PAPADEMITRIOU*
Department of Physics, University of Crete and Research Center of Crete, PO Box 1527, 711 10 Heraklio, Crete, Greece
'Department of Physics, University of Ioannina, Ioannina, Greece
k b s c r a c t
-
The anomalous peaks i n t h e x - r a y Raman spectrum o f p o l y c r y s t a l l i n e b o r o n have been examined e x p e r i m e n t a l l y and t h e o r e t i c a l l y . These peaks a r e a s s o c i a t e d w i t h d - l i k e a t o m i c s t a t e s h i g h i n t h e c o n d u c t i o n bands, The "anomalous" n a t u r e o f these peaks i s a l s o m a n i f e s t e d i n t h e i r a n g u l a r dependence.The e x i s t e n c e o f anomalous peaks i n t h e x - r a y energy l o s s spectrum o f Be i n t h e r e g i o n o f t h e x - r a y Raman band [1,2 has m o t i v a t e d t h e search f o r such "anomalous"
d
peaks i n m a t e r i a l s o t h e r t h a n Be. ese anomalous peaks a r e n o t h i n g more, b u t complex m a n i f e s t a t i o n s o f t h e bonding c h a r a c t e r o f t h e s t a t e s n e a r and above t h e Fermi l e v e l
[2]
.
,The anomalous peaks, t h e r e f o r e , correspond t o s i m i l a r peaks i n t h e e l e c t r o n i c d e n s ~ t y o f s t a t e s (DOS),
around and above t h e Fermi 1 e v e l . I n a n t i c i p a t i o n o f d i s - c o v e r i n g s i m i l a r anomalous peaks i n b o r o n and t h u s p r o b i n g i t s e l e c t r o n i c s t r u c t u r e i n t h e unoccupied c o n d u c t i o n bands, we u n d e r t o o k t h e p r e s e n t t h e o r e t i c a l and e x p e r i - mental i n v e s t i g a t i o n f o r t h e x - r a y Raman spectrum o f boron.Due t o t h e c o m p l i c a t e d c r y s t a l s t r u c t u r e o f boron, i t s e l e c t r o n i c s t r u c t u r e i s n o t known q u i t e a c c u r a t e l y . The c r y s t a l s t r u c t u r e o f boron, w i t h s e v e r a l atoms p e r u n i t c e l l o c c u r s i n two d i f f e r e n t c r y s t a l forms, t e t r a g o n a l and rhombohedral, b o t h based on t h e icosahedron geometry. The s i m p l e s t form, which i s rhombohedral w i t h 12 atoms p e r u n i t c e l l , i s shown i n f i g u r e 1 i n a p r o j e c t i o n on t h e (001) p l a n e o f t h e
F i g u r e I
The s t r u c t u r e o f rhombohedral b o r o n p r o j e c t e d o n t o t h e (001) p l a n e o f t h e r e l a t e d hexagonal u n i t c e l l . The d i s t a n c e s a r e : a=2.03i, b=1.78A, c=1.73a and d=4.91i ( r e f . 131
1.
Article published online by EDP Sciences and available at http://dx.doi.org/10.1051/jphyscol:19879150
C9-844 JOURNAL DE PHYSIQUE
r e l a t e d hexagonal c e l l [3]. S i n c e t h e b a s i c u n i t f o r b o t h o f t h e s e c o m p l i c a t e d s t r u c t u r e s i s t h e icosahedron, i t i s reasonable t o model p o l y c r y s t a l l i n e boron w i t h a small c l u s t e r o f 12 b o r o n atoms i n i c o s a h e d r a l geometry. Small c l u s t e r have been v e r y u s e f u l and adequate i n d e s c r i b i n g t h e anomalous peaks i n t h e r e g i o n o f t h e x - r a y Raman band o f Be 121. Needless t o say t h a t s m a l l c l u s t e r t e c h n i q u e s can p r o v i d e n o t o n l y bonding i n f o r m a t i o n b u t a l s o i n n e r c o r e b i n d i n g e n e r g i e s [4] as w e l l as s t r u c t u r a l and phonon p r o p e r t i e s [4,5]. The s m a l l a t o m i c c l u s t e r used h e r e t o d e s c r i b e t h e e l e c t r o n i c s t r u c t u r e o f boron c o n s i s t s o f t h e t w e l v e atoms p l a c e d i n t h e c o r n e r s o f one o f t h e f o u r i c o s a h e d r a shown i n f i g . 1 . The gaussian b a s i s f u n c t i o n s f o r B have been c o n t r a c t e d o u t o f t h e Huzinaga s e t (S.Huzinaga:Approximate wave f u n c t i o n s I , 1971, u n p u b l i s h e d ) and have been enhanced w i t h v i r t u a l d - o r b i t a l s . The c l u s t e r h a m i l t o n i a n i s formed and d i a g o n a l i z e d u s i n g t h e u n r e s t r i c t e d H a r t r e e - Fock (UHF) method. I n t h e UHF, c o n t r a r y t o t h e usual r e s t r i c t e d Hartree-Fock (RHF) method, t h e s p i n - u p spin-down p a i r s a r e n o t r e s t r i c t r e d t o have t h e same s p a t i a l w a v e f u n c t i o n and t h e o r b i t a l s a r e n o t r e q u i r e d e x p l i c i t l y t o have t h e symmetry p r o p e r t i e s o f t h e p o i n t group o f t h e c r y s t a l . The s t a n d a r d POLYATOM computer code was used t o compute t h e i n t e g r a l s and t h e program UHFABK o f A. B a r r y Kunz was employ- ed t o p e r f o r m t h e UHF c a l c u l a t i o n s .
The e x p e r i m e n t a l s e t up f o r t h e energy l o s s x - r a y spectroscopy under1 i n g t h e x - r a y Raman measurements, i s s i m i l a r t o t h e one d e s c r i b e d b e f o r e f o r Be
[I!.
I t c o n s i s t s m a i n l y o f a Rigaku-Denki ( t y p e RU-200PL) 12KW r o t a t i n g anode x - r a y gene- r a t o r , w i t h a Cu t a r g e t and a f l a t s i n g l e c r y s t a l spectrometer. The x - r a y t u b e was o p e r a t e d a t 5 5 KV and 180mA and t h e s p e c t r o m e t e r r e s o l u t i o n was E/AE
"
1100. The s c a t t e r e r was oowder o f p o l y c r y s t a l l i n e boron. To a c h i e v e a good accuracy t h e s p e c t r a were o b t a i n e d by step-scanning, u s i n g a f i x e d - t i m e c o u n t i n g method and t h e Cu KB l i n e . The s p e c t r a were scanned f i v e t i m e s f o r e v e r y s c a t t e r i n g a n g l e and t h e s t a t i - s t i c a l e r r o r was 1.3%. The s t e p o f t h e scanner was 0.01 and t h e t i m e d u r a t i o n o f each s t e p was 400 sec.The r e s u l t s o f o u r t h e o r e t i c a l and e x p e r i m e n t a l i n v e s t i g a t i o n s a r e summarized i n a condensed f o r m i n f i g . 2 , which shows t h e x - r a y Raman spectrum and t h e "anomalous
Energy
Fig.2. The measured x - r a y Raman spectrum and t h e c a l c u l a t e d energy l e v e l diagram and s i m u l a t e d DOS. The energy r e g i o n shown, i n c l u d e s t h e Raman band and t h e anomalous peaks. The l a r g e d o t s i n t h e spectrum r e p r e s e n t t h e a c t u a l measurements. The smooth l i n e i s t h e r e s u l t o f a s p l i n e s f i t .
peaks". The Raman band i s l o c a t e d around 200eV and t h e "anomalous peaks" i n t h e r e g i o n o f 380eV q u i t e f a r f r o m t h e Raman band. I n t h e same f i g u r e t h e r e s u l t s o f t h e c a l c u l a t i o n i n t h e r e g i o n o f t h e Fermi l e v e l and t h e r e g i o n o f 300eV above t h e I s l e v e l a r e shown i n t h e f o r m o f an energy l e v e l diagram superimposed w i t h t h e "simu- l a t e d " DOS i n t h e same energy r e g i o n . T h i s s i m u l a t e d DOS, as e x p l a i n e d b e f o r e [1,63 i s c o n s t r u c t e d f r o m t h e energy l e v e l diagram b y a s u i t a b l e Gaussian broadening.
I t becomes i m m e d i a t e l y c l e a r t h a t b o t h t h e Raman band and t h e "anomalous" peak s t r u c t u r e around 280eV a r e w e l l reproduced i n t h e c a l c u l a t e d energy l e v e l diagram and DOS o f f i g u r e 2. The s t a t e s around t h e Fermi l e v e l ( i . e . t h e h i g h e s t occupied o r b i t a l ) p r o d u c i n g t h e Raman band a r e o f a t o m i c p t y p e w i t h a s m a l l a d m i x t u r e o f s t y p e o r b i t a l s . The s t a t e s r e s p o n s i b l e f o r t h e "anomalous" peak s t r u c t u r e i n f i g . 2 a r e o f d - c h a r a c t e r w i t h a s m a l l a d m i x t u r e o f s and p t y p e s t a t e s . The energy s p l i t - t i n g between d - o r b i t a l s o f d i f f e r e n t symmetry and o f d i f f e r e n t percentage o f s and p a d m i x t u r e r e s u l t s i n a r a t h e r l a r g e w i d t h f o r t h e c o r r e s p o n d i n g "anomalous" peak.
R e l a t i v e l y t o t h e Raman peak, t h e h i g h t o f t h e anomalous peak seems t o be l a r q e r due perhaps t o t h e more compact n a t u r e o f t h e d o r b i t a l s , compared t o t h e sp o r b i t a l s r e s p o n s i b l e f o r t h e Raman peak.
The spectrum o f f i g . 2 was t a k e n a t a s c a t t e r i n g a n g l e o f 55O, b u t t h e p o s i t i o n s o f t h e anomalous peaks remain p r a c t i c a l l y t h e same f o r a l a r g e v a r i e t y o f angles.
The s c a t t e r i n g a n g l e v a r i a t i o n used i n o u r x - r a y Raman s c a t t e r i n g measurements ranges f r o m 45" t o 105" w i t h a s t e p o f 10". The a n g u l a r dependence o f t h e i n t e n s i t y , o n l v ' f o r
e
u i t e l o w s c a t t e r i n g a n g l e s f o l l o w s t h e t h e o r e t i c a l e x p r e s s i o n o f Mizuno and Ohmura 71. T h i s e x p r e s s i o n based on t h e d i p o l e a p p r o x i m a t i o n g i v e s t h e s c a t t e r i n g i n t e n s i t y I as a f u n c t i o n o f t h e s c a t t e r i n g a n g l e4na cP 2
I ( @ ) = K ( l + c o s 2 @ ) ( - s i n - )
A0 2
where K i s a c o n s t a n t and a i s t h e mean r a d i u s o f t h e charge d i s t r i b u t i o n o f t h e K - e l e c t r o n s o f t h e p o l y c r y s t a l l i n e s c a t t e r e r . E q u a t i o n ( 1 ) t o g e t h e r w i t h t h e c o n d i - t i o n f o r t h e occurence o f t h e x - r a y Raman process s e t s t h e t h e o r e t i c a l framework f o r the dependence o f I on 9. The mathematical c o n d i t i o n f o r t h e occurence o f t h e x - r d y Raman s c a t t e r i n g i s w r i t t e n :
w i t h A t h e wavelenqth o f t h e i n c i d e n t r a d i a t i o n . E q u a t i o n ( 2 s i m p l y t t e s t h a t t h e magnitude of t h e mamentun t r a n s f e r s h o u l d be s m a l l e r o r equal t o l / o
171.
The observed d i s c r e p a n c y i n t h e a n g u l a r dependence of t h e spectrum f o r moderate and h i g h s c a t t e r i n g angles, based on t h e p r e v i o u s d i s c u s s i o n ( e q u a t i o n s ( 1 ) and (211, c o u l d be a s s o c i a t e d w i t h a v i o l a t i o n o f t h e d i p o l e a p p r o x i m a t i o n on w h i c h ( I ) i s based. T h i s a s s e r t i o n , i s c e r t a i n l y i n a c c o r d w i t h o u r UHF c l u s t e r t h e o r e t i c a l r e s u l t s which a t t r i b u t e t h e anomalous peaks t o d - l i k e a t o m i c s t a t e s . T h i s seems t o v i o l a t e d i p o l e s t t j e c t i o n r u l e s . C e r t a i n l y f o r a s o l i d and i n t h i s deep i n t h e c o n t i - nuum energy r e g i o n , i t i s d i f f i c u l t t o access t h e v a l i d i t y of d i p o l e s e l e c t i o n r u l e s based on t h e a t o m i s t i c a n g u l a r m o m e n t u m ~ o t i o n . l h i s s i t u a t i o n c a l l s f o r a f u r t h e r and deeper t h e o r e t i c a l i n v e s t i g a t i o n .
References
[I]
D.K. Papademitriou and D.fI. f l i l i o t i s , J. Phvs. Soc. Janan. 51 (1982) 2966 [2] A.D. Z d e t s i s and D. f l i l i o t i s . S o l i d S t a t e Commun. 42 (1982) 227: A.D. Z d e t s i s .t o be n u b l i s h e d i n Phvs. Rev. B.
[3] P.J. Brown and J.B. F o r s y t h , t h e c r y s t a l s t r u c t u r e o f s o l i d s , (Edward A r n o l d , London and Cran Russal:, flew York, t973j
C9-846 JOURNAL DE PHYSIQUE
14)
A.D. Z d e t s i s , Phys. Rev. B34 (1986) 7666 [5] A.D. Z d e t s i s , Phys. Rev. 835 (1987) 5868[6] A,.D.Zdetsis and A.B. Kunz, Phys. Rev. 832 (1985) 6358 Y. Muzuno and Y. Ohmura, J. Phys. Soc. Japan, 22 (1967) 445
