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QUANTITATIVE X-RAY ENERGY DISPERSIVE ANALYSIS OF THIN FOILS
W. Voice, R. Faulkner
To cite this version:
W. Voice, R. Faulkner. QUANTITATIVE X-RAY ENERGY DISPERSIVE ANALYSIS OF THIN FOILS. Journal de Physique Colloques, 1984, 45 (C2), pp.C2-401-C2-405. �10.1051/jphyscol:1984291�.
�jpa-00224006�
JOURNAL DE PHYSIQUE
Colloque C2, supplCment au n02, Tome 45, f6vrier 1984 page C2-401
QUANTITATIVE X-RAY ENERGY DISPERSIVE ANALYSIS OF THIN FOILS
W.E. Voice and R.G. Faulkner
Department of MateriaZs Engineering and Design, Loughborough University of TeechnoZogy, U.K.
Rksumk
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On d k c r i t une mkthode d e microanalyse X q u a n t i t a t i v e d e s lames minces en microscopie Q l e c t r o n i q u e en t r a n s m i s s i o n B balayage (STEM). La mkthode p r 6 d i t d e s f a c t e u r s de c o r r e c t i o n dgpendant de 1 ' k p a i s s e u r de l a lame, de l l a n g l e d ' i n c l i n a i s o n de l l $ c h a n t i l l o n e t de v a r i a b l e s instrumen- t a l e s . On montre que l ' a b s o r p t i o n p e u t Gtre importante dans l e s a l l i a g e s b a s e n i c k e l mGme pour d e s Bpaisseurs v o i s i n e s de 10008.
A b s t r a c t
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A procedure f o r making q u a n t i t a t i v e X-ray a n a l y s i s of t h i n f o i l s i n scanning t r a n s m i s s i o n e l e c t r o n microscopes (STEM) i s d e s c r i b e d . The technique p r e d i c t s c o r r e c t i o n parameters based on t h e t h i c k n e s s of t h e f o i l , t h e specimen geometry and e l e c t r o n microscope i n s t r u m e n t a l v a r i a b l e s . I t i s shown t h a t a b s o r p t i o n can play an important r o l e i n n i c k e l based a l l o y specimens even a t f o i l t h i c k n e s s e s of around 1000X.
I n t r o d u c t i o n
Microanalysis of t h i n f o i l s i n STEM i s becoming i n c r e a s i n g l y important. The reduc- ed beam s p r e a d i n g t h a t o c c u r s i n t h i n f i l m compared t o bulk specimens allows a n a l y s i s of much s m a l l e r r e g i o n s t h a n i s p o s s i b l e i n t h e bulk sample e l e c t r o n probe m i c r o a n a l y s i s technique. Q u a n t i f i c a t i o n of X-ray d a t a from t h i n f i l m s i s n o t well developed. Most c o r r e c t i o n s s o f a r a p p l i e d t o t h i n f i l m d a t a have assumed t h a t minimal a b s o r p t i o n o c c u r s and any c o r r e c t i o n f a c t o r s a p p l i e d have been determined e m p i r i c a l l y ( 1 ) . I t i s apparent from s e v e r a l t h i n f i l m a n a l y t i c a l i n v e s t i g a t i o n s (2) t h a t a b s o r p t i o n and f l u o r e s c e n c e cannot be n e g l e c t e d . Simulations of e l e c t r o n beam i n t e r a c t i o n s with t h i n f i l m specimens u s i n g t h e Monte Carlo method a l s o show t h a t X-rays produced i n t h i n f o i l s undergo c o n s i d e r a b l e i n t e r a c t i o n with t h e analysed m a t e r i a l b e f o r e they emerge from t h e specimen. ( 3 ) .
To q u a n t i f y X-ray d a t a from t h i n f o i l s t h e X-ray g e n e r a t i o n a s a f u n c t i o n of depth must f i r s t be understood. For t h e bulk sample case t h i s h a s been w e l l d e f i n e d through an a n a l y t i c a l e x p r e s s i o n by P h i l i b e r t ( 4 ) . No such e x p r e s s i o n has y e t been developed f o r t h i n f i l m s . The b e s t a t t e m p t s s o f a r have t r i e d t o s i m u l a t e t h e e l e c t r o n s c a t t e r i n g behaviour w i t h i n t h e sample by s i n g l e e l e c t r o n s c a t t e r i n g models ( 5 , 6 , 7 ) . The Monte Carlo t e c h n i q u e has a l s o s u c c e s s f u l l y s i m u l a t e d beam broadening i n bulk specimens ( 8 ) and t h i n f i l m s ( 9 ) . Once t h e X-ray g e n e r a t i o n from t h e e l e c t r o n i n t e r a c t i o n i s q u a n t i f i e d , t h e mean p a t h l e n g t h of X-rays reach- i n g t h e d e t e c t o r must be considered s o t h a t a b s o r p t i o n and f l u o r e s c e n c e can be e s t i m a t e d . This depends upon t h e specimen geometry and o r i e n t a t i o n with r e s p e c t t o t h e d e t e c t o r .
In o r d e r t o q u a n t i f y t h e a n a l y s e s of t h i n f i l m s t o account f o r t h e above-mentioned e f f e c t s , i t i s thought t h a t t h e Monte Carlo approach o f f e r s t h e most chance of s u c c e s s . This paper d e s c r i b e s t h e use of t h e Monte Carlo t e c h n q i u e t o p r e d i c t c o r r e c t i o n f a c t o r s i n t h i n f i l m specimens a s a f u n c t i o n of specimen geometry and microscope i n s t r u m e n t a l v a r i a b l e s .
Choice of I n i t i a l Concentration
In o r d e r t o d e f i n e t h e e l e c t r o n i n t e r a c t i o n with t h e t h i n f i l m specimen an i n i t i a l
Article published online by EDP Sciences and available at http://dx.doi.org/10.1051/jphyscol:1984291
C2-402 JOURNAL DE
PHYSIQUEcomposition must be d e f i n e d . This i s taken from t h e analysed spectrum by summingthe peak i n t e n s i t i e s f o r a l l elements p r e s e n t p l u s any u n d e t e c t e d elements l i k e carbon, which a r e c a l c u l a t e d by s t o i c h i o m e t r i c r a t i o t e c h n i q u e s . The f r a c t i o n a l peak i n t e n - s i t y f o r t h e element A of t h e t o t a l i n t e n s i t i e s i s
CA.
T h i s i s c o r r e c t e d t o a more reasonable value by s t a n d a r d l e s s a n a l y s i s u s i n g t h e f o l l o w i n g e q u a t i o nwhere A i s t h e atomic weight of A
QA i s t h e i o n i s a t i o n c r o s s s e c t i o n (10) w i s t h e f l u o r e s c e n t y i e l d (11)
The c o n c e n t r a t i o n s of a l l o t h e r elements p r e s e n t a r e c o r r e c t e d i n a s i m i l a r way and t h e f i n a l element p r o p o r t i o n s a r e normalised. This composition d e f i n e s t h e d e n s i t y , atomic weight and atomic number of t h e a l l o y i n which t h e e l e c t r o n i n t e r a c t i o n can be d e f i n e d u s i n g t h e Monte Carlo t e c h n i q u e .
Monte Carlo C a l c u l a t i o n of E l e c t r o n I n t e r a c t i o n with Thin Film Specimens
The e l e c t r o n i n t e r a c t i o n with t h e specimen i s c a l c u l a t e d w i t h t h e programme develop- ed by Curgenven and Duncumb (12) and d e s c r i b e d i n r e f e r e n c e ( 9 ) . I t uses 500 e l e c t r o n s whose t r a j e c t o r i e s a r e d i v i d e d i n t o 500 e q u i d i s t a n t s t e p s which add up t o t h e Bethe range. A t each s t e p t h e energy i s r e c a l c u l a t e d and a change i n d i r e c t i o n i s c a l c u l a t e d on a random number-based Rutherford e l a s t i c s c a t t e r i n g model. The e l e c t r o n i n t e r a c t i o n is c a l c u l a t e d assuming t h a t t h e m a t e r i a l has t h e composition e s t i m a t e d i n t h e p r e v i o u s s e c t i o n .
X-ray Generation I n t e n s i t y f o r I n d i v i d u a l Elements
A t t h e energy a p p r o p r i a t e t o t h e p a r t i c u l a r s t e p t h e i o n i s a t i o n c r o s s s e c t i o n Q(E) i s c a l c u l a t e d f o r any element, A , from
Q ( E ) = e 4 s b I n U U where e i s t h e e l e c t r o n charge
s i s t h e number of e l e c t r o n s i n t h e s h e l l of A
b i s a c o n s t a n t (0.25 f o r L s h e l l and 0.35 f o r K s h e l l ) U i s t h e o v e r v o l t a g e : E/EC
EC i s t h e c r i t i c a l e x c i t a t i o n p o t e n t i a l of A.
The number of i o n i s a t i o n s , n , p e r u n i t p a t h l e n g t h , X , i s given a t energy E by
where N i s Avogadro's number and pA i s t h e d e n s i t y .
To g i v e t h e X-ray g e n e r a t i o n i n t e n s i t y t h i s number (n) i s m u l t i p l i e d by t h e f l u o r e s - cent y i e l d w , where
where a = 106 f o r K and 10' f o r L r a d i a t i o n . Hence a number r e l a t e d t o t h e X-ray g e n e r a t i o n can be c a l c u l a t e d f o r each of t h e elements p r e s e n t along e l e c t r o n t r a j e c t o r i e s which have been d e f i n e d by t h e o v e r a l l composition.
X-ray Generation a s a Function of Depth
A s e r i e s of s l i c e s beneath t h e specimen s u r f a c e (1001 t h i c k ) i s considered. I n each s l i c e t h e g e n e r a t i o n of X-rays i s considered i n r i n g s around t h e beam d i r e c t i o n . The X-ray g e n e r a t i o n d e n s i t y , G , a s a f u n c t i o n of r i n g r a d i u s , R , i s determined by summ- i n g a l l t h e c o n t r i b u t i o n s of n X w f o r each t r a j e c t o r y which c r o s s e s t h e r i n g and then d i v i d i n g t h i s by t h e volume, V , of t h e r i n g .
F i g . 1 shows t h e X-ray g e n e r a t i o n d e n s i t y f o r a 100 kV e l e c t r o n beam a s a f u n c t i o n of R f o r i n d i v i d u a l s l i c e s taken a t s u c c e s s i v e l y lower depths i n t o t h e f o i l . The g e n e r a t i o n d e n s i t y ( a r e a under curve) i s l a r g e r f o r t h e l a y e r s n e a r t o t h e s u r f a c e because a h i g h e r d e n s i t y of b a c k s c a t t e r e d e l e c t r o n s e x i s t s i n t h e s e r e g i o n s . This i s shown i n F i g . 2 where G is very high i n t h e s u r f a c e l a y e r s . Although t h e gener- a t i o n d e n s i t y appears t o f a l l o f f w i t h depth i n t h i s f i g u r e , i t i s misleading because t h e volumes c o n t a i n i n g X-ray g e n e r a t i o n s i t e s a r e much l a r g e r a t g r e a t e r depths and s o t h e
total
X-ray g e n e r a t i o n i s i n c r e a s i n g s t i l l f o r 100 kV e l e c t r o n s a t depths g r e a t e r than ll-lm.X-ray Generation I n t e n s i t y a s a Function of Depth and R The p r e d i c t e d X-ray d e n s i t y i s given by 2
X-ray d e n s i t y =
-
G (1)Jgr S
where S i s t h e s t a n d a r d d e v i a t i o n d e s c r i b i n g t h e normal d i s t r i b u t i o n of X-ray d e n s i t y , G , with R. S i s d i f f e r e n t f o r each d e p t h l a y e r c o n s i d e r e d (Fig. 3.). A s e t o f t h r e e dimensional c o o r d i n a t e s i s now s e t up where X and y a r e i n d i r e c t i o n s normal t o t h e beam, p a r a l l e l t o R and where z i s t h e depth. Equation (1) shows t h e d i s t r i b u t i o n of X-rays i n X and y f o r a s e r i e s of d e p t h s , z, which have t h e d i f f e r - e n t G ' s d e s c r i b e d i n F i g . 1.
Determination of X-ray I n t e n s i t y Reaching D e t e c t o r
Once t h e X-ray g e n e r a t i o n d e n s i t y a t any p o i n t r e l a t i v e t o t h e beam d i r e c t i o n and depth i n t h e f o i l has been d e f i n e d (Fig. 4) i t remains t o c a l c u l a t e t h e e f f e c t of a b s o r p t i o n on t h e X-rays produced. The p a r t i c u l a r X-ray g e n e r a t i o n d e n s i t y , C nw/V a t any p o i n t ( x , y , z ) w i l l b e converted t o X-ray i n t e n s i t y , I A by
where i s t h e mass a b s o r p t i o n c o e f f i c i e n t f o r A i n t h e a l l o y (13) and d is z / s i n @ cos 45 O
where z i s t h e d e p t h , @ i s t h e specimen t i l t angle and 45' i s t h e azimuth angle a t which t h e d e t e c t o r i s p l a c e d t o t h e t i l t a x i s i n t h e microscope. This can be
a l t e r e d f o r d i f f e r e n t specimen-microscope geometries. No f l u o r e s c e n c e e f f e c t s a r e considered s i n c e they were n o t a p p l i c a b l e t o t h e n i c k e l a l l o y s s t u d i e d i n t h e e a r l y p a r t of t h i s work.
C o r r e c t i o n F a c t o r Determination, k k i s determined from
CA = k I A
I A i s t h e normalised t o t a l X-ray i n t e n s i t y g e n e r a t i o n p r e d i c t e d f o r element A when t h e X-ray i n t e n s i t y c o n t r i b u t i o n s from 100k s i d e l e n g t h cubes covering t h e whole X-ray g e n e r a t i o n volume a r e summed. Each i n d i v i d u a l cube i s a s c r i b e d X , y and z c o o r d i n a t e s and t h e X-ray i n t e n s i t y c a l c u l a t e d from e q u a t i o n (1) f o r t h e G and S v a l u e s a p p r o p r i a t e t o t h e cube concerned f o r each d e p t h l a y e r . Each of t h e s e small c o n t r i b u t i o n s i s summed t o g i v e t h e t o t a l X-ray i n t e n s i t y . The same procedure y i e l d s r e l a t i v e i n t e h s i t i e s f o r t h e o t h e r elements p r e s e n t . The t o t a l of t h e s e i n t e n s i t i e s , CI, i s c a l c u l a t e d and t h e p e r c e n t a g e of t h e t o t a l i n t e n s i t y p r e d i c t e d f o r element A i s I
A '
I t e r a t i o n
The newly c a l c u l a t e d X-ray i n t e n s i t y , I A i s now made CA and t h e c o r r e c t i o n procedure i s r e p e a t e d t o g i v e a new I A and k . E v e n t u a l l y , a f t e r s e v e r a l i t e r a t i o n s t h e v a l u e s of k used converge t o a f i n a l c o r r e c t i o n f a c t o r which i s used i n subsequent c o r r e c t - i o n s of raw i n t e n s i t y d a t a f o r s i m i l a r g e o m e t r i c a l , compositional and i n s t r u m e n t a l s i t u a t i o n s .
JOURNAL DE PHYSIQUE
A p p l i c a t i o n s
Examples of c o r r e c t i o n f a c t o r s n e c e s s a r y f o r elements i n a t h i n f i l m MC phase i n a s u p e r a l l o y a r e shown i n Fig. 5. I t should be remembered t h a t t h e s e f a c t o r s c a t e r f o r i o n i s a t i o n e f f i c i e n c y as w e l l a s a t t e n u a t i o n e f f e c t s . Therefore t h e y a r e n o t t h e same a s conventional e l e c t r o n probe microanalyser c o r r e c t i o n f a c t o r s , which only c o n s i d e r a t t e n u a t i o n . The i o n i s a t i o n e f f i c i e n c y e f f e c t i s removed normally because d a t a i s f e d i n i n t h e form of i n t e n s i t y r a t i o s from t h e unknown and s t a n d a r d and h e r e t h e i o n i s a t i o n e f f i c i e n c y component c a n c e l s o u t .
Hence t h e k f a c t o r s a r e lower f o r K , L o r M l i n e s with h i g h e r atomic number because g e n e r a l l y t h e s e l i n e s w i l l have a h i g h e r X-ray g e n e r a t i o n e f f i c i e n c y p e r u n i t volume compared w i t h t h e lower atomic number elements. The e x c e p t i o n i s Hafnium (atomic number 72) because t h i s has an unusually high c r i t i c a l e x c i t a t i o n p o t e n t i a l . Fig. 5 shows t h a t Titanium (atomic number 22) i s t h e only element g r e a t l y a f f e c t e d by a b s o r p t i o n . The c o r r e c t i o n f a c t o r i s i n c r e a s e d by almost 1 . 5 times on going from very t h i n t o l U m t h i c k f o i l s . This i s convincing evidence f o r t h e need of c o r r e c t - ion procedures f o r t h i n f i l m samples i n STEM which commonly a r e 2-30008 t h i c k . Examples of f u r t h e r a p p l i c a t i o n s of t h e procedure a r e found elsewhere i n t h e s e
conference proceedings (14).
Summary
A c o r r e c t i o n procedure f o r X-ray m i c r o a n a l y s i s of t h i n f o i l s i n STEM i s d e s c r i b e d . I t i s based on a s s e s s i n g t h e t o t a l i n t e n s i t y i n t e g r a t e d from t h e c o n t r i b u t i o n s of small 1001 s i d e l e n g t h cubes of m a t e r i a l under t h e e l e c t r o n beam. The i o n i s a t i o n e f f i c i e n c y and a t t e n u a t i o n c h a r a c t e r i s . t i c s f o r each cube a r e a s s e s s e d s e p a r a t e l y f o r t h e s p e c i f i c i n s t r u m e n t a l and specimen geometry c o n d i t i o n s a p p l i c a b l e t o t h e a n a l y s i s . C o r r e c t i o n f a c t o r s a r e e v a l u a t e d which show t h a t a b s o r p t i o n e f f e c t s become important i n t h i n f o i l s of t h i c k n e s s e s g r e a t e r than 10001.
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CwrRano" F I I C T ~ Flg 1 GENERATION FACTOR VS BEAM DEPTH IN FOIL. BE NERA,10 X,.,-'
'7
20' 1 Fig 2 X-RAY GENERATION IN DEPTH INCREMENTS.SrnNnalo orvlello* F I ~ 3 STANDARD DEVIATION vs B U N DEPTH I N FOlL 7703
Fig.4 GEOMETRY OF THlN FOlL X-RAY ANALYSIS
Cube Coordmtes
-
Ix,y.ilT ~ l t Angle = 0 Fool Thickness
-
TBg. S CORRECTION FACTORS, h . FOR T H l N FOILS CmI1ECTIOI1 MTQ?,K-ELEWUT
x10-I
121
H C C * I B I K . R
- T L C I Y N I W " 7 . Z
Equatlom are far por~tiie X. Uuqe a w e d signs fw negative X
