A PARAMETERLESS METHOD TO CORRECT FOR X-RAY ABSORPTION AND FLUORESCENCE I N THIN FILM MICROANALYSIS

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A PARAMETERLESS METHOD TO CORRECT FOR X-RAY ABSORPTION AND FLUORESCENCE I N

THIN FILM MICROANALYSIS

E. van Cappellen, D. van Dyck, J. van Landuyt, F. Adams

To cite this version:

E. van Cappellen, D. van Dyck, J. van Landuyt, F. Adams. A PARAMETERLESS METHOD TO CORRECT FOR X-RAY ABSORPTION AND FLUORESCENCE I N THIN FILM MICROANAL- YSIS. Journal de Physique Colloques, 1984, 45 (C2), pp.C2-411-C2-414. �10.1051/jphyscol:1984293�.

�jpa-00224008�

Colloque C2, suppl6ment au n02, Tome 45, f6vrier 1984 page C2-4 1 1

A PARAMETERLESS METHOD TO CORRECT FOR X-RAY ABSORPTION AND FLUORESCENCE I N T H I N F I L M M I C R O A N A L Y S I S

E . Van Cappellen

+*

dams*

+ ~ n i v e r s i t e i t Antwerpen, RUCA, GroenenborgerZaan 272, B-2020 Antwerp, PZgiurn

U n i v e r s i t e i t Antwerpen, UIA, U n i v e r s i t e i t s p l e i n 2, B-2620 FjiZr,rijk, Belgium

Resume - Dans l a p r e s e n t e c o n t r i b u t i o n une methode de c o r r e c t i o n pour l ' a b - s o r p t i o n e t l a f l u o r e s c e n c e en s p e c t r o s c o p i e p a r rayons X d ' e c h a n t i l l o n s t r a n s p a r e n t s aux e l e c t r o n s e s t p r e s e n t e e . La methode, q u i ne n e c e s s i t e aucun paramGtre n i c o e f f i c i e n t , s e b a s e s u r p l u s i e u r s a n a l y s e s 2 d i f f e r e n t s p o i n t s d'un mdme & c h a n t i l l o n . De meme l a p o s s i b i l i t e de d e d u i r e 1 1 8 p a i s s e u r massique aux p o i n t s a n a l y s e s S p a r t i r des donnees expdrimentales e s t examinee.

A b s t r a c t - I n t h e p r e s e n t c o n t r i b u t i o n a method i s p r e s e n t e d which e n a b l e s t o perform a b s o r p t i o n and f l u o r e s c e n c e c o r r e c t i o n s i n X-ray spectroscopy of t r a n s p a r e n t specimens. The method i s based on s e v e r a l measurements a t d i f f e - r e n t s i t e s of t h e same specimen, b u t does n o t r e q u i r e i n p u t parameters o r c o e f f i c i e n t s . Moreover t h e p o s s i b i l i t y t o deduce t h e mass t h i c k n e s s i n every analysed a r e a from t h e a c q u i r e d experimental d a t a w i l l be d i s c u s s e d .

I - INTRODUCTION

I n p r a c t i c e when a q u a n t i t a t i v e X-ray m i c r o a n a l y s i s o f a t h i n f o i l i s performed, ab- s o r p t i o n and f l u o r e s c e n c e c o r r e c t i o n s a r e o f t e n o m i t t e d s i n c e t h e y r e q u i r e a number of i n p u t parameters such a s t h i c k n e s s and d e n s i t y of t h e specimen, t h e take-off a n g l e , mass a b s o r p t i o n c o e f f i c i e n t s , f l u o r e s c e n c e y i e l d v a l u e s , a b s o r p t i o n jump r a t i o s and t h e corresponding c h a r a c t e r i s t i c f r e q u e n c i e s . I n t h e p r e s e n t paper a new method i s p r e s e n t e d which e n a b l e s t o perform a b s o r p t i o n and f l u o r e s c e n c e c o r r e c t i o n s w i t h o u t knowing t h e above mentioned parameters. The method i s t h e r e f o r e s u i t a b l e f o r r o u t i n e t h i n f i l m m i c r o a n a l y s i s and t h e r e s u l t s a r e more a c c u r a t e i n c a s e s where t h e i n p u t parameters a r e not o r o n l y approximately known.

I1 - GENERAL CORRECTION FACTOR FOR THE CLIFF-MRIflER EQUATIONS

In o r d e r t o d e v e l 0 ~ t h i s c o r r e c t i o n method we s h a l l s t a r t from t h e w e l l known CLIFF- LORIMER e q u a t i o n s / l / . For every element "X" o f an unknown specimen t h e mass concen- t r a t i o n r a t i o (C /C ) o f t h a t element w i t h r e s p e c t t o a r e f e r e n c e element "R" i s

given by : X R

,-.

where " I X " and "IR" s t a n d f o r t h e n e t peak i n t e g r a l o f "X" and "R". The r e l a t i o n - s h i p between t h e mass c o n c e n t r a t i o n r a t i o and t h e n e t peak i n t e g r a l r a t i o i s given by t h e CLIFF-LORIMER km f a c t o r . The c o n c e n t r a t i o n r a t i o c a l c u l a t e d i n t h i s way i s n o t c o r r e c t e d f o r a b s o r p t i o n and f l u o r e s c e n c e e f f e c t s o c c u r r i n g i n r e a l specimens, and w i l l t h e r e f o r e be c a l l e d t h e " u n c o r r e c t e d mass c o n c e n t r a t i o n r a t i o " , and i t w i l l be denoted : " ( C X / c R ) ,,'l.

This u n c o r r e c t e d r a t i o i s a f u n c t i o n of t h e mass t h i c k n e s s (Apz)and can be w r i t t e n a s t h e e x a c t r a t i o (cX/CR) m u l t i p l i e d by a mass t h i c k n e s s dependent a b s o r p t i o n and f l u o r e s c e n c e c o r r e c t i o n f a c t o r (PRX) :

Article published online by EDP Sciences and available at http://dx.doi.org/10.1051/jphyscol:1984293

C2-412

whereby :

JOURNAL DE PHYSIQUE

"A" s t a n d s f o r a b s o r p t i o n c o r r e c t i o n and "F" f o r f l u o r e s c e n c e c o r r e c t i o n , t h e sub- s c r i p t denotes t h e chemical element. Being a f u n c t i o n o f t h e mass t h i c k n e s s Apz, P% can always b e expanded i n terms o f Apz :

The c o n s t a n t s "aRX", ^" 8, ^" e t c .

. . .

With t h e formulae f o r " I $ ~ / I ~ " and " I ~ / I Y Y " of PHILIBERT and TIXIER /3/ ( g e n e r a l i z e d f o r specimens o f n elements (n ^E d) one can c a l c u l a t e t h e f l u o r e s c e n c e c o r r e c t i o n s

"FX,R". I t i s c l e a r t h a t t h e t o t a l f l u o r e s c e n c e c o r r e c t i o n "FX/FR" i s o f t h e o r d e r of (Apz) 2. I n o r d e r t o account f o r f l u o r e s c e n c e (mainly c h a r a c t e r i s t i c f l u o r e s c e n c e ) Pm i s needed a t l e a s t up t o second o r d e r i n Apz. To do s o c o n s i s t e n t l y one needs an a b s o r p t i o n c o r r e c t i o n formula up t o second o r d e r i n Apz. PHILIBERT and TIXIER t r u n c a t e d t h e i r formula a f t e r t h e f i r s t o r d e r b u t a simple s t r a i g h t f o r w a r d c a l c u l a - t i o n s t a r t i n g from t h e same model e n a b l e s t o f i n d t h e r e q u i r e d formula. The expres- s i o n s f o r A and F t h e n p e r m i t t o c a l c u l a t e ^" " and "BRX". Apart from n e g l i g i b l e continuous f l u o r e s c e n c e c o n t r i b u t i o n s , "a 'ra%ly c o n t a l n s a b s o r p t i o n e f f e c t s while

"BRX" i s a very complex c o e f f i c i e n t c o n t a m i n g a b s o r p t i o n and f l u o r e s c e n c e e f f e c t s . Rx

111- PRINCIPLE OF THE PARAMETERLESS CORRECTION METHOD

(C / c ~ ) ~ ~ , t h e measured mass c o n c e n t r a t i o n r a t i o i f t h e c o r r e c t i o n s a r e o m i t t e d , i s onry I n good agreement w i t h t h e e x a c t v a l u e ( C /C ) i f "Pmn n e a r l y e q u a l s one

(PRX

2

(Apz + O ) s i n c e : X R

Cx Cx

pm(Apz) l=+(-) A - ( 5 )

APZ -+ o 'R un ~ p z ⁺ 0 'R

Since measuring t h e mass t h i c k n e s s i s i n p r a c t i c e a time consuming o p e r a t i o n and s i n c e we t r y t o avoid parameters such a s specimen t h i c k n e s s and d e n s i t y , a r e l a t e d q u a n t i t y must be used f o r a r o u t i n e curve f i t . his s u b s t i t u t e should monotonically t e n d t o z e r o f o r v a n i s h i n g specimen t h i c k n e s s . JACOBS and BABOROVSKA (1972) /4/ used a w h i t e r a d i a t i o n window i n t h e s p e c t r a a s an i n d i r e c t measure f o r t h e mass t h i c k n e s s

( i n s p i r e d by t h e HALL method f o r b i o l o g i c a l specimens).

Another p o s s i b i l i t y i s t o use a n e t peak i n t e g r a l i n s t e a d o f white r a d i a t i o n . However s e v e r a l experiments r e v e a l e d a s y s t e m a t i c d i f f e r e n c e between t h e r e s u l t s o b t a i n e d w i t h t h e n e t peak i n t e g r a l s and t h o s e o b t a i n e d w i t h white r a d i a t i o n windows.

T h i s can b e explained by t h e f a c t t h a t n o t a l l t h e white r a d i a t i o n o r i g i n a t e s from t h e specimen. A s m a l l f r a c t i o n i s due t o e x t e r n a l f a c t o r s such a s microscope p a r t s , t h e specimen h o l d e r (even i f it i s a low background h o l d e r ) p o s s i b l y t h e specimen

completely when t h e specimen t h i c k n e s s e q u a l s z e r o ; w h i t e r a d i a t i o n does n o t f u l f i l 1 t h e p r e v i o u s l y mentioned c o n d i t i o n . A s a r e s u l t o f t h i s one always e x t r a p o l a t e s t o o

" f a r " when u s i n g white r a d i a t i o n a s a s u b s t i t u t e f o r t h e mass t h i c k n e s s .

F i g u r e 1 shows t h e r e s u l t s of an experiment i n a t h i n r e g i o n o f an Cr-A1 a l l o y where we could r e s t r i c t o u r s e l v e s t o l i n e a r f i t s . Ten a n a l y s i s p o i n t s were taken and t h e r e s u l t s were p l o t t e d a g a i n s t a 19.5 t o 20.0 keV window i n t e g r a l and a g a i n s t t h e C r K n e t peak i n t e g r a l . From both graphs one can deduce t h a t about 5 40 c o u n t s i n t h e C1 white r a d i a t i o n window do n o t come from t h e specimen i t s e l f . Not o n l y we checked t h a t t h i s d i f f e r e n c e i s s y s t e m a t i c b,ut a l s o t h a t it i s n o t i n f l u e n c e d by b o t h p l a c e and width o f t h e window. For t h i s r e a s o n and t h e f a c t t h a t t h e l a r g e r n e t peak i n t e - g r a l s y i e l d b e t t e r s t a t i s t i c s one should p r e f e r t h e l a t t e r a s a s u i t a b l e s u b s t i t u t e f o r t h e m a s s t h i c k n e s s .

Experiments w i t h Cr-A1 a l l o y s have shown t h a t a l i n e a r f i t a s i s shown i n f i g . 1 i s not always s u f f i c i e n t i f one wants t o measure through t h e whole t r a n s p a r e n c y range a t 100 kV. On t h e o t h e r hand a p a r a b o l i c f i t t u r n e d o u t t o be v a l i d f a r beyond t h i s l i m i t ( s e e f i g . 2 ) . T h i s means t h a t i n t h e t h i c k e r p a r t s a l t h o u g h s t i l l t r a n s - p a r e n t a t 100 kV, f l u o r e s c e n c e and second o r d e r a b s o r p t i o n e f f e c t s s t a r t t o become important. However i f one measures only i n t h i n r e g i o n s o f t h e specimen, t h e curve i s approximately l i n e a r . S i n c e t h e experimental p o i n t s a r e always s u b j e c t t o s t a t i s t i c a l e r r o r s , it can be q u i t e erroneous t o f o r c e a p a r a b o l a through t h e s e p o i n t s . I n t h a t c a s e a simple l i n e a r curve f i t w i l l y i e l d t h e most a c c u r a t e r e s u l t s . I n p r a c t i c e it can be u s e f u l t o p l o t t h e experimental p o i n t s b e f o r e choosing t h e kind of curve f i t .

F i g . 1 - I n s p i t e of t h e use of a low back- F i g . 2

-

+ 40 counts i n t h e white r a d i a t i o n window C a l c u l a t e d w i t h formula ( 7 ) 1 2 . 1 0 ~ -

do n o t o r i g i n a t e from t h e specimen. c o u n t s correspond w i t h 385 nm.

C2-414 JOURNAL DE PHYSIQUE

I V

-

The mass t h i c k n e s s can a l s o be c a l c u l a t e d a s a f u n c t i o n of t h e n e t peak i n t e g r a l . The r e q u i r e d parameters a r e : t h e take-off a n g l e and t h e mass a b s o r p t i o n c o e f f i c i e n S , which a r e c u r r e n t l y a v a i l a b l e i n t h e software o f a l l modern m i c r o a n a l y s i s systems.

The n e t peak i n t e g r a l ( I ) used f o r t h e a n a l y s i s i s e q u a l t o :

"€" i s given by CASTAING's formula /2/, and c o n t a i n s a l s o an a p p a r a t u s c o n s t a n t . The f a c t o r between b r a c k e t s i s t h e a b s o r p t i o n c o r r e c t i o n of PHILIBERT & TIXIER /3/ and

"X" i s t h e i r n o t a t i o n f o r 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 m u l t i p l i e d by t h e cosecant of t h e take-off a n g l e 8. The mass t h i c k n e s s Apz can be s o l v e d from e q u a t i o n ( 6 ) :

9 , E 1,

being t h e i n v e r s e o f t h e c o n s t a n t "€". T h i s e x p r e s s i o n can now be s u b s t i t u t e d i n t h e formula ( 3 ) f o r P=(APz) :

The experimental curve i s given by e x p r e s s i o n ( 8 ) m u l t i p l i e d by t h e e x a c t mass con- c e n t r a t i o n r a t i o (C /C ) . One can now c a l c u l a t e E from t h e s l o p e s o f t h e l i n e a r

X R p a r t o f t h e experimental curve.

s . C

E = R

a _{RX '} Cx ⁽⁹⁾

I f continuous f l u o r e s c e n c e i s n e g l e c t e d t h e c o e f f i c i e n t am e q u a l s :

a RX = - $(ux - uR) cosec 8 (10)

where "pX'' and "pR" a r e 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 s of "X" and "R". The mass t h i c k n e s s can now be c a l c u l a t e d a s a f u n c t i o n o f "I" with formula ( 7 ) , ^E being c a l - c u l a t e d w i t h e q u a t i o n s (10) and ( 9 )

.

V - CONCLUSION

The d e s c r i b e d method c o r r e c t s f o r a l l mass t h i c k n e s s dependent phenomena which vanish when t h e specimen t h i c k n e s s t e n d s t o z e r o . I t a v o i d s t h e use of e x t e r n a l parameters and i s r o u t i n e l y a p p l i c a b l e . The accuracy of t h e r e s u l t s which can be computed from t h e curve f i t ( t y p i c a l l y l e s s t h a n 1 a t %) a r e a rough e s t i m a t e f o r t h e r e p r o d u c i b i l i t y of t h e experiment. However e f f e c t s which do n o t vanish w i t h d e c r e a s i n g specimen t h i c k n e s s such a s t h e B0RRM.W e f f e c t /5/ and t h e i n f l u e n c e of s u r f a c e l a y e r s due t o t h e p r e p a r a t i o n /6/ a r e n o t c o r r e c t e d f o r .

Another s y s t e m a t i c e r r o r can occur i f a wrong CLIFF-LORIMER f a c t o r i s used. I n t h a t case t h e e x t r a p o l a t e d c o n c e n t r a t i o n r a t i o r e v e a l s t h e same s y s t e m a t i c e r r o r .

/ l / CLIFF G . , LORIMER G.W., J . of Microscopy, v o l . 103 (1974) 203-207.

/2/ VAN CAPPELLEN E., VAN DYCK D . , . V A N LANDUYT J . , ADAMS F., t o be p u b l i s h e d . /3/ PHILIBERT J . , TIXIER R., P h y s i c a l Aspects of E l e c t r o n Microscopy and Microbeam

Analysis (1975) 333.

/4/ JACOBS M.H., BABOROVSKA J . , Proc. F i f t h Europ. Cong. on E l e c t r o n Microscopy (1972) 136.

/5/ CHERNS D . , HOWIE A., JACOBS M.H., Z. Naturforsch. 28a (1973) 565.

/6/ DOIG P . , FLEWITT P.E.J., J. of Microscopy, vol. 110 (1977) 107.