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AN EVALUATION OF X-RAY LOSS DUE TO ELECTRON BACKSCATTER
R. Myklebust
To cite this version:
R. Myklebust. AN EVALUATION OF X-RAY LOSS DUE TO ELECTRON BACKSCATTER. Jour- nal de Physique Colloques, 1984, 45 (C2), pp.C2-41-C2-42. �10.1051/jphyscol:1984210�. �jpa-00223766�
JOURNAL DE PHYSIQUE
Colloque C2, suppl6ment au n02, Tome 45, f6vrier 1984 page C2-41
AN E V A L U A T I O N OF X-RAY LOSS DUE TO ELECTRON BACKSCATTER
R.L. Myklebust
National Bureau o f Standards, Washington, DC 20234, U.S.A.
sum& - Nous a v o n s c a l c u l i une n o u v e l l e f o r m u l e p o u r l a p e r t e , d e r a y o n s x p a r r 6 t r o d i f f u s i o n d ' g l e c t r o n s . Nous a v o n s u t i l i s e un c a l c u l Monte C a r l o p o u r l a d i f f u s i o n d 1 6 l e c t r o n s d a n s l e s s o l i d e s . A b s t r a c t - A new f o r m u l a t i o n o f t h e x - r a y l o s s d u e t o e l e c t r o n b a c k s c a t t e r i n g h a s b e e n computed from Monte C a r l o s i m u l a t i o n f o r e l e c t r o n s c a t t e r i n g i n s o l i d s .
One o f t h e m a j o r c o r r e c t i o n s w h i c h f o r m s t h e b a s i s o f t h e a t o m i c number - a b s o r p t i o n - f l u o r e s c e n c e m a t r i x c o r r e c t i o n p r o c e d u r e ( Z A F ) t e c h n i q u e i n q u a n t i t a t i v e e l e c t r o n p r o b e m i c r o a n a l y s i s is t h e s o - c a l l e d " R - f a c t o r " . The R - f a c t o r is a m e a s u r e o f t h e r a t i o of t h e t o t a l i n n e r s h e l l i o n i z a t i o n w h i c h is a c t u a l l y p r o d u c e d i n t h e s p e c i m e n o v e r t h a t which would o c c u r i n t h e a b s e n c e o f e l e c t r o n b a c k s c a t t e r i n g . The f o r m u l a t i o n o f t h e R - f a c t o r which is c u r r e n t l y i n u s e is b a s e d o n e m p i r i c a l f i t s of e x p e r i m e n t a l d a t a on e l e c t r o n b a c k s c a t t e r i n g and b a c k s c a t t e r e d e l e c t r o n e n e r g y d i s t r i b u t i o n s [ l ] . W h i l e t h i s f o r m u l a t i o n is o f g r e a t v a l u e i n q u a n t i t a t i v e m i c r o a n a l y s i s , t h e r e e x i s t s some u n c e r t a i n t y i n i t s a c c u r a c y d u e t o t h e l i m i t e d a n g u l a r i n t e g r a t i o n o f t h e b a c k s c a t t e r e d e l e c t r o n e n e r g y d i s t r i b u t i o n i n t h e e x p e r i m e n t a l m e a s u r e m e n t s . M o r e o v e r , t h e e x p r e s s i o n f o r R is i n t h e form o f a f i f t h d e g r e e p o l y n o m i a l i n two s e p a r a t e v a r i a b l e s which is i n c o n v e n i e n t t o c a l c u l a t e .
The l o s s o f x - r a y i n t e n s i t y d u e t o b a c k s c a t t e r e d e l e c t r o n s h a s been r e - e v a l u a t e d w i t h t h e a i d o f a Monte C a r l o s i m u l a t i o n f o r e l e c t r o n s c a t t e r i n g i n s o l i d s [ 2 ] . The a d v a n t a g e of t h e Monte C a r l o s i m u l a t i o n i s t h e c a p a b i l i t y o f e f f e c t i v e l y i n t e g r a t i n g t h e e n e r g y d i s t r i b u t i o n o f b a c k s c a t t e r e d e l e c t r o n s o v e r a l l p o s s i b l e a n g l e s o f e m i s s i o n . A d d i t i o n a l l y , t h e Monte C a r l o s i m u l a t i o n c a n b e a p p l i e d t o t h e c a l c u l a t i o n o f t i l t e d s p e c i m e n s f o r w h i c h v i r t u a l l y no e x p e r i m e n t a l d a t a e x i s t . The Monte C a r l o s i m u l a t i o n we h a v e employed is a s i n g l e s c a t t e r i n g model u s i n g a R u t h e r f o r d e l a s t i c s c a t t e r i n g c r o s s - s e c t i o n , t h e B e t h e c o n t i n u o u s e n e r g y l o s s e x p r e s s i o n , and t h e B e t h e i n n e r s h e l l i o n i z a t i o n c r o s s - s e c t i o n a s m o d i f i e d b y Mott and Massey. I n i t i a l e l e c t r o n e n e r g i e s i n t h e r a n g e 4 - 50 keV w e r e c o n s i d e r e d i n t h i s s t u d y . The r e s u l t s a r e p r e s e n t e d a s R , t h e r a t i o o f x - r a y s g e n e r a t e d w i t h i n t h e s o l i d t o t h e t o t a l x - r a y s t h a t would h a v e b e e n g e n e r a t e d had none of t h e e l e c t r o n s b a c k s c a t t e r e d .
The R v a l u e s f o r K x - r a y l i n e s a g r e e d r e a s o n a b l y w e l l w i t h t h o s e o f Duncumb; h o w e v e r , t h e R v a l u e s f o r L and M x - r a y l i n e s a r e d i f f e r e n t . T a b l e 1 l i s t s a few o f t h e v a l u e s o b t a i n e d t o g e t h e r w i t h v a l u e s computed w i t h a n e x p r e s s i o n d u e t o Duncumb. A t h i r d v a l u e , R ( c a l c l ) , i s l i s t e d w h i c h was computed w i t h t h e e x p r e s s i o n :
Article published online by EDP Sciences and available at http://dx.doi.org/10.1051/jphyscol:1984210
JOURNAL DE PHYSIQUE
w h e r e Z is t h e a t o m i c number a n d U is t h e o v e r v o l t a g e ( i n i t i a l e l e c t r o n e n e r g y ( E O ) / e x c i t a t i o n p o t e n t i a l ) . The c o e f f i c i e n t s a , b , a n d c h a v e d i f f e r e n t v a l u e s f o r e a c h s e r i e s o f x - r a y l i n e s . R , h o w e v e r , s h o u l d n o t b e a f u n c t i o n o f t h e x - r a y l i n e s e r i e s . A d d i t i o n a l Monte C a r l o c a l c u l a t i o n s w e r e made h o l d i n g t h e a t o m i c number Z c o n s t a n t w h i l e v a r y i n g t h e beam v o l t a g e t o g e t h e r w i t h t h e c h a r a c t e r i s t i c x - r a y l i n e t o g i v e a c o n s t a n t o v e r v o l t a g e . A s e r i e s o f L - l i n e s was s e l e c t e d r a n g i n g i n a t o m i c number f r o m 40 t o 9 2 a n d beam v o l t a g e s f r o m 8.89 t o 68.66 keV. The c o m p u t e d R - v a l u e s v a r i e d a p p r o x i m a t e l y l i n e a r l y w i t h v o l t a g e f r o m . 6 1 t o .69.
E l e m e n t A1 S b Pb Au
I r A1 S b AU A1 S b Au
TABLE 1
L i n e 2 R(MC) R(Duncumb) R ( c a l c 1 ) R ( c a l c 2 )
TK 46.24-2 - 9 3 9 . 9 1 8 . 9 1 0
SiK 4 7 . 3 5 . 6 8 5 . 7 5 2 . 7 1 2 .696
A1K 4 6.24 . 5 7 9 . 6 7 4 - 5 8 2 . 5 9 6
CuK 4 3 5 . 9 - 6 5 5 .68 1 . 5 9 3 . 6 3 6
I r L 2 22.4 . 7 0 9 . 7 5 7 . 7 1 2 . 7 1 2
NdL 4 2 4 . 8 . 9 1 9 - 9 3 9 .909 - 9 3 1
SbL 4 1 6 . 5 . 7 0 5 - 7 5 2 . 7 1 2 - 7 0 6
NbL 4 9.48 . 6 1 7 - 6 8 1 . 6 3 3 . 6 0 6
AuM 4 8 . 8 2 - 9 1 8 . 9 3 9 . 9 0 7 , 9 1 3
AuM 4 8 . 8 2 .696 , 7 5 2 .697 .697
AuM 4 8 . 8 2 . 6 0 8 - 6 8 1 . 6 0 4 . 6 0 5
By a d d i n g a t e r m l i n e a r i n EO t o t h e a b o v e e x p r e s s i o n , a b e t t e r f i t t o t h e d a t a was o b t a i n e d . The m o d i f i e d e x p r e s s i o n , v a l i d i r r e s p e c t i v e o f t h e x - r a y l i n e s e r i e s , b e c o m e s :
The f o u r t h R - v a l u e l i s t e d , R ( c a l c 2 ) , i n T a b l e 1 i s c o m p u t e d u s i n g e x p r e s s i o n ( 2 ) w i t h t h e f o l l o w i n g c o e f f i c i e n t s : a = -.0081517, b =
. 0 0 0 0 3 6 1 3 , c = . 0 0 9 5 8 3 , a n d d = . 0 0 1 1 4 1 .
The p r i n c i p a l d i f f e r e n c e s i n q u a n t i t a t i v e a n a l y s e s c a l c u l a t e d w i t h t h e f o r m u l a t i o n s f o r R a r e e v i d e n t f o r h i g h a t o m i c number e l e m e n t s . T h r e e l e a d s i l i c a t e g l a s s e s w e r e a n a l y z e d u s i n g two d i f f e r e n t l e a d s t a n d a r d s . The r e s u l t s of t h e a n a l y s e s a r e shown i n T a b l e 2. W h i l e t h e r e is n o t a g r e a t d e a l o f d i f f e r e n c e among t h e r e s u l t s , t h e c a l c u l a t i o n s made w i t h t h e new e x p r e s s i o n f o r R y i e l d v a l u e s c l o s e r t o t h e r e f e r e n c e v a l u e s i n a l l c a s e s .
TABLE 2
Lead a n a l y s e s a t 1 5 keV a n d Pb M-alpha x - r a y l i n e f o r s t a n d a r d s G l a s s C o m p o s i t i o n New R ( c a l c 1 ) Duncumb R - f a c t o r
Pb ~ b T e K-227 PbTe K-227
R e f e r e n c e s
1. DUNCUMB, P. a n d REED, S.J.B., NBS S p e c . Pub. 2 9 8 , K.F.J.
H e i n r i c h , e d . , ( 1 9 6 8 ) 1 3 3 .
2. MYKLEBUST, R.L., NEWBURY, D.E. a n d YAKOWITZ, H . , NBS S p e c .
Pub. 4 6 0 , H e i n r i c h , K.F.J., Newbury, D.E. and Y a k o w i t z , H . , e d s . , ( 1 9 7 5 ) 1 0 5 .
