mta,83-stem-eds xray microan of small prec in fe bas th foils

8/12/2019 MTA,83-STEM-EDS Xray Microan of Small Prec in Fe Bas Th Foils

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S T E M E D S X R a y M ic ro a na ly sis o fSm al l Prec ip ita tes in I ron B ase T h in Fo i lsP . D O I G a n d P . E . J . F L E W l T TThe expe r im enta l condi t ions fo r de tec t ion o f s egrega ted e lem ents in the X-ray spec t rum recorded f romsm al l p rec ip i t a te s _< 100 n m d iam ete r con ta ined wi th in a th in fo i l o f an i ron base a l loy us ing S TEM -EDS X-ray m ic roana lys i s a re desc r ibed . Th e in f luence o f p rec ip it a te s i ze, pos i t ion and com pos i t ion ,foi l thickness , e lectron accelerat ing vol tage, and X-ray emiss ion intens i ty on i ts detectabi l i ty areeva lua ted . O pt im um exper im enta l condi t ions fo r m ic roana lys i s o f these p rec ip it a te s a re e s tab l i shedand the l im i ta tions o f cur ren t t echn iques d i s cus sed .

I . I N T R O D U C T I O NS M A L L prec ip i t a te s , -


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(a)

u . - d . ~

t

(b)

Co

c)Fig. 1--(a) Transmission electron micrograph showing a typical smallsecond phase precipitate, P, contained in a thin foil sample. (b) Schematicdiagram showing the posit ion of the included precipitate within the thinfoil. (c) Schematic composition profile across a small precipitate.

precipitate volume gives the total electron flux withinthe precipitate and thereby from Eq. [1] its contributionto the total X-ray signal.The accuracy of this X-ray measurement is given by astatistical consideration of the finite number of detectedX-ray quanta. The significance of the measurement is re-lated to the counting statistics in the characteristic X-rayenergy peak, Np, compared with those in the background ofthe spectrum Nb (Figure 2). Confidence in any measuredpeak intensity (or integrated counts) is dependent on boththe peak and background such that for a large number ofcounts where Gaussian statistics may be assum ed (N - 20):

Peak intensity = Np + (Np ) I/2 [4]Background intensity = Nb + (Nb)~/2 [5]

Detection of a peak requires its magnitude to be greater thanthe error in its estimation such that:Up >-- (Up + Ub) 2 + (Ub)1/2 [6]

1944--V OLUM E 14A, OCTOBER 1983

I---ZI I

I[

\

i ~ Np

[N b IN RGY

Fig. 2- - Schematic diagram defining the number of X-ray counts recordedin the characteristic peak, Np, and in the background, No.

For any given electron source the total incident electronflux, le, is related to the incident probe size, B, by: 3 4 5le oc B 8/3 [7]

Thus, the total emitted X-ray intensity, I', increases withbeam size. The background X-ray intensity in a recordedspectrum is proportional to the electron probe current, Ie, thefoil thickness, tl, and the total recording time, T, such that: 6N b = K ' B S / 3 h T [ 8 ]

where K' is a constant for the particular X-ray energyand electron illumination system which characterizes theeffec tive electron intensity for X-ray generation anddetection. The X-ray intensity, Np, from the precipitateis given by the volume integral:Up = K RB8/3T JvI(V) dv [9]

where R is the characteristic X-ray peak-to-backgroundratio (Np/Nb) in the spectrum obtained from a thin foilsample of unit composition, and V is the volume distributionof the precipitate. Here, the integral term represents thatfraction of the foil volume which contributes to the charac-teristic X-ray peak.The inequality in Eq. [6] defines the condition for de-tecting a characteristic X-ray energy peak from the pre-cipitate in a recorded X-ray spectrum. Nb and Np may becalculated from Eqs. [8] and [9] for given values of foilthickness tl and material /3, spectrum recording time T,electron probe size B, effective electron intensity K', pre-cipitate composition Co, depth t', and diameter d. Thus,from Eqs. [6], [8], and [9], we may establish conditions fordetecting the segregated element in the X-ray spectrum froma precipitate of given composition contained within a thinfoil using STEM-EDS X-ray microanalysis.

III. RESULTS OF THET H E O R E T I C A L A N A L Y S I SFor a given precipitate geometry, the volume integralcomponent of Eq. [9] decreases with increasing incident

METALLURGICAL TRANSACTIONS A


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ow

o w f d v

N p / N b

Detected

low N b~

F i g . 3 - - S c h e m a t i c d i a g r am s h o w i n g th e r a n g e o f e l e c tr o n p ro b e s i z e , B ,r e q u i r e d f o r t h e X - r a y d e t e c t i o n o f a s m a l l p r e c i p i t a t e o f d i a m e t e r , d ,c o n t a i n e d w i t h in a t h i n f o i l . d * i s t h e m i n i m u m p r e c i p i t a te d i a m e t e r w h i c hm a y b e d e t e c t e d i n t h e r e c o r d e d X - r a y s p e c t r u m r e q u i r i n g a c r i t i c a l e l e c tr o np r o b e s i z e , B * .

O

a )0

30

10

log

e l ec t ron p robe s i ze , i.e. a sma l l e r p ropor t i on o f t he t o t a le l ec t ron f l ux i n t e r ac t s w i t h p r ec i p i t a t e . Conver se l y , t het o t al e l ec t ron cur r en t inc r eases r ap i d l y E q . [ 7 ] ) such tha tt he r e su l t i ng t o t a l e l ec t ron f l ux whi ch i n t e r ac t s w i t h t heprec i p i ta t e w i ll t end t o i nc r ease . T he re fore , f r om t hese t wocomp e t i ng e f f ec t s i t i s poss i b l e t o de f i ne a r ange o f e l ec t ronprobe d i ame t e r ove r whi ch t he i nequa l i t y i n E q . [ 6] may besa t is f ied such t ha t t he i n t ens i t y o f cha rac t e r i s t ic X - r ays em i t -t e d f r o m t h e e l e m e n t s e g r e g a t e d t o t h e p r e c i p it a te m a y b ede t ec t ed i n t he r ecorded spec t rum. C l ea r l y , f o r ve ry sma l lp r ec i p i ta t e s t he i nequ a l i t y w i l l neve r be sa t i s f i ed i n t ha t t hevo l um e in t egra l t e rm E q . [ 9 ] ) t ends t o ze ro and t he segre -ga t i on canno t be de t ec t ed . T h i s ove ra l l behav i or i s shownschema t i ca l ly i n F i gure 3 wh ere t he e l ec t ron p ro be s i zer ange fo r de t ec t i on i s g i ven a s a f unc t i on o f t he p r ec i p i t a t ed i amet e r . F or sma l l e l ec t ron p robes t he ove ra l l X- r ay coun tr a t e i s l ow such t ha t s t a t i s t i ca l no i se i n t he r ecorded spec -t rum prec l udes de t ec t i on whereas fo r l a rge p robes t he vo l -ume i n t egra l te rm dec rea ses such t ha t the m easured Np/Nb isr educed t o a l ev e l be l ow t ha t f o r whi ch t he i nc r eas i ng s t at is -t i ca l conf i d ence i n the da t a i s ab le t o compen sa t e . T he fo rmof t he curve de f i n i ng t he bou nd fo r de t ec t ab i l i t y d isp l ays ami n i mum a t a p r ec i p i t a t e d i ame t e r d* . T h i s d i ame t e r i s ameasure o f t he ove ra l l s ens i t i v i t y fo r mi c roana l ys i s .Ca l cu l a t ed curves de f i n i ng t he l i mi t s o f p robe s i ze B fo rde t ec t i on o f a s egrega t i on t o a p r ec i p i t a t e w i t h d i ame t e rd a r e show n i n F i gure 4 a s a f unc t i on o f a ) t he p roduc tMETALLURGICAL TRANSACTIONS A

2

t ~O

0 0 1 2b) log dF i g . 4 - - C a l c u l a t e d p l o t s s h o w i n g t h e r a n g e o f e l e c t r o n p r o b e s i z e , B , f o rd e t e c t i o n o f a p r e c i p i t a t e w i t h d i a m e t e r d i n t h e X - r a y s p e c t r u m a s afunc t ion o f : (a ) p roduc t Ro = RCo = 1 0 , 1 , 0 . 1 . ( b ) E f f e c t i v e e l e c t r o nf lux K T = 10 -I , 10 2, 10 3, 1 0 4 nm-l l / 3 .

VOLUME 14A, OCTOBER 1983 -- 1945


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o

c )

( e )

nmm

0I I I I i I i I I |

1l og

I I I I I I I I ]1

l o g

00

100

0 0

_ 2 0 0

I I I l I

I I I I I

I

o

3

t

0 1 2d ) l o g d

Fig. 4--Ca lculated plots showing the range of electron probe size, B, fordetection of a precipitate with diameter d in the X-r ay spectrum as afunction of: (c) foil thickness h = 1 0 0 2 0 0 300 nm . (d) Precipitate deptht' = top , center, and bottom of foil. (e) Electron accelerating voltageE0 = 100, 200, 300 kV for standard conditions given in the text.

Ro = RCo, ( b ) e f f e c t i v e e l e c t r o n f l u x , K T , (c ) fo i l th ick-n e s s , t l , ( d ) p r e c i p i t a t e d e p t h , t ' , a n d ( e ) e l e c t r o n a c c e l e r -a t i n g v o l t a g e , E 0 . T h e s e c u r v e s a r e e v a l u a t e d f o r t y p i c a ls t a n d a r d c o n d i t i o n s w h i c h r e l a t e t o t h e o p e r a t i o n o f a t y p i c a l1 0 0 k V S T E M i n s t r u m e n t f i t t e d w i t h a n e n e r g y d i s p e r s i v eX - r a y s p e c t r o m e t e r :

( i) i r o n b a s e f o i l s - - d e f i n i n g / 3 i n E q . [ 3 ]( i i) f o i l t h i c k n e s s = 2 0 0 n m

( ii i) e l e c t r o n a c c e l e r a t i n g v o l t a g e = 1 0 0 k V( i v ) e f f e c t i v e e l e c t r o n f l u x , K T = 0.0 1 nm -11/3( v ) a n a s s u m e d p r o d u c t R 0 = RCo = 1( v i ) w i t h t h e p r e c i p i t a t e d e p t h = t l / 2 , i . e . , a t t h e c e n t e r o f

the fo i l .A l l c u rv e s h a v e t h e f o r m s h o w n s c h e m a t i c a l l y i n F i g u r e 3w i t h a m i n i m u m i n t h e p r e c i p i t a t e d i a m e t e r , d * , a t a c r i t i c a l

v a l u e o f e l e c t ro n p r o b e s i z e, B * . F i g u r e 4 ( a ) s h o w s t h ei n f l u e n ce o f p re c i p i ta t e c o m p o s i t i o n . T h e v a l u e o f d * d e -c r e a s es b y a f a c t o r o f - 2 . 5 f o r a t e n f o l d i n c r ea s e i n p e a k -t o - b a c k g r o u n d r a t i o , R 0 , w i t h a n a s s o c i a t e d b u t s m a l l e rd e c r e a s e i n e l e c t r o n p r o b e s i z e , B * . B * t e n d s t o a l o w e rl i m i t w i t h i n c r e a s i n g R 0 w h i c h f o r t h e a b o v e s t a n d a r d c o n -d i t io n s i s - 2 0 n m .F i g u r e 4 ( b ) s h o w s t h e e ff e c t o f c h a n g e s i n t h e e f f e c t i v ee l e c t r o n f l u x , K T , w h i c h i n c l u d es b o t h t h e r e c o r d i n g t i m e ,

1 9 4 6 - - V O L U M E I 4 A O C T O B E R 1 9 8 3 M E T A L L U R G I C A L T R A N S A C T I O N S A


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T , and t he i n t ens i ty pa r amet e r K ' . T h i s l a t t e r te rm i s de -p e n d e n t o n t h e e l e c t ro n s o u r c e b r i g h t n e ss , t h e g e o m e t r y a n ddes i gn o f t he e l ec t ron op t i ca l i l l umi na t i on sys t em and t hee f f i c i ency o f X- r ay gen e ra t i on , emi s s i on a nd de t ec t i on fo rt he e l ement o f i n t e r e s t . T he pa r t i cu l a r va l ue o f K T fo r ami c roana l ys i s expe r i ment i s r e f l ec t ed i n t he backgroundi n t e n s i t y v a l u e Nb ( E q . [ 8 ] , F i g u r e 2 ) . T h e r e s u l t s i nF i gure 4 (b ) show t ha t i nc r eas i ng K T b y a f a c t o r o f t e ndec reases d* by abou t 30 pc t w i t h , a s be fore , a dec reasei n B * t o w a r d a l o w e r l im i t i n g v a l u e o f - 2 0 n m f o rK T = 1 0 - 3 nm -H/3.T he i n f l uence o f t he expe r i men t a l va r iab l e s o f f o i l t h i ck-ness , t l , p r ec i p i t a te dep t h , t ' , and e l ec t ron acce l e r a t i ng vo l t -age , E 0 , a re shown i n F i gures 4 ( c ) t o ( e ) . F i gure 4 ( c ) showst ha t i nc r eas ing t he fo i l t h ickness , t l , ove r t he r ange 100 t o300 nm i nc reases d* non l i nea r l y by a dec reas i ng am oun tf r o m 1 2 t o 1 7 n m o n l y w i t h a c o r r e s p o n d i n g c h a n g e i n B * .T h e m i n i m u m v a l u e o f B * f o r a 1 00 n m t h i c k n e ss f o i l i s15 nm. F i gu re 4 (d ) show s t he e f f ec t o f p r ec i p i t a t e dep t h , t ' ,f o r t h r ee pos it i ons w i t h i n t he fo i l : t he t op , cen t e r , and bo t -t om. Here , d* i nc r eases w i t h dep t h i n t o t he fo i l a s a r e su l to f t he i nc r eas i ng e f f e c t o f the e l ec t ron sca t t e r i ng wi t h i n t hefo i l reduc i ng t he p ropo r t i on o f t he t o t a l e l ec t ron f l ux i n t e r -ac t i ng wi t h t he p r ec i p i ta t e . F o r t hese cond i t i ons d* i nc r easesf rom 12 t o 18 nm wi t h an a s soc i a t ed change i n B* f rom 15t o 60 nm.Changes i n t he e l ec t ron acce l e r a t i ng vo l t age , E 0 , i n f l u -ence t he e l ec t ron sca t t e r i ng behav i or desc r i bed by / 3 i nE qs . [ 2] and [3 ] , and a l so the pa r ame t e r s K ' an d R0. Cons i d -e r i ng f i rs t l y t he i n f l uence on / 3 , i nc r eas i ng t he e l ec t ron ac -c e l e r a t in g v o l t a g e f r o m 1 00 t o 2 0 0 k V r e d u c e s d * b y- 1 0 p c t an d i s a g a i n a c c o m p a n i e d b y a c o r r e s p o n d i n gchange i n t he a s soc i a t ed e l ec t ron p robe d i am e t e r f rom 20 t o12 nm (F i gure 4 ( e ) ) . T h i s i mprov em ent in de t ec t ab i l i ty w i thi nc reas i ng e l ec t ron acce l e r a t i ng vo l t age i s eva l ua t ed fo r acons t an t e f f ec t i v e e l ec t ron f l ux , K T. F or a cons t an t t r uee l ec t ron p robe cur r en t , how ever , s i nce t he X- r ay i on i za t i onc ross s ec t i on , Q , and t he r e fo re K i s p ropor t i ona l t o t hef ac t o r ln(E~/Eo)/(E~Eo)whe re E c i s the cha rac t e r i st i c X- r ayene rgy , 6'7 i nc r eas i ng t he acce l e r a t i ng vo l t age f rom 100 t o2 0 0 k V d e c r e a s es t h e e f f e c t i v e e l e c t ro n f l u x b y - 4 0 p c t .Compl ement i ng t h i s dec rease , however , i s t he a s soc i a t edchange i n peak- t o -background r a t i o , R , f o r t h i s i nc r easei n e l ec t ron acce l e r a t i ng vo l t age . T heore t i ca l l y ,6,8 an im-p r o v e m e n t o f u p t o 4 0 p c t m a y b e a c h i e v e d , 8 b u t i n p r a c t ic et h is i s d i f f i cu l t t o r ea l i ze becaus e o f i nc r eas i ng con t r i bu t i onst o t he background f rom spur i ous X- r ays w i t h i n t he mi c ro-scope and de t ec t o r . T hus , f o r a cons t an t cu r r en t i n the e l ec -t ron p robe , i nc r eas i ng t he e l ec t ron acce l e r a t i ng vo l t age f rom100 t o 200 kV has a l mo s t no e f f ec t on t he va l ue o f d* . F ora cons t an t e l ec t ron source geom et ry , t he e l ec t ron p robe cur -rent increase s l ine ar ly wi th e lec t ron ac celerat in g vo l tage. 3,4,9However , f o r i ns t rument s w i t h va r i ab l e e l ec t ron acce l e r -a t i ng vo l t age , t he i l l umi na t i on sys t em geomet ry i s no t nec -es sa r i l y cons t an t and t h i s s i mpl e l i nea r r e l a t i onsh i p wi l lr a r e l y app ly . Ne ver t he l e s s , t he r e su l t s o f F i gure 4 (b ) showt ha t even a t wofo l d i nc r ease i n t he e f f ec t i v e e l ec t ron f l uxwi l l have l i t t le e f f e c t on d * .T h e i n f lu e n c e o f th e e f f e c t i v e e l e c t ro n fl u x te r m , K T,on t he mi n i mum d i amet e r , d* , i s mo re c l ea r l y i ll us t ra t ed i nF i gure 5 . Here , d* i s p l o t t ed a s a f unc t i on o f t he t e rm K Tove r the r ange 10 4 t o 1 0 - 1 nm 11/3 for R0 valu es of 0.1 , 1 ,a n d 1 0 , a n d t h e o t h e r c o n d i t i o n s a s d e f i n e d a b o v e f o r

F i gure 4 . I n add i t i on , r e su lt s a r e show n fo r R0 = 10 and fo i lt h ic k n e s s es o f 1 0 0 a n d 3 0 0 n m . T h e d a t a f o r 2 0 0 n m t h i c kfo i l s a r e desc r i bed by t he empi r i ca l equa t i on :l o g ( d * ) = 0 . 7 5 - 0 . 1 8 l o g ( K ' T ) - 0 . 3 7 l o g ( R o ) [ 1 0 ]T hu s , a t en fo l d i nc r ease i n t he e f f ec t i ve e l ec t ron f l uxd e c r e a s es d * b y a f a c t o r o f - 1 . 5 w h e r e a s a s i m i la r i n c re a s ei n R0 dec reases i t by a f ac t o r o f - 2 .3 . I n p r ac t i ce R0 i sl i m i t e d p r i m a r i l y b y t h e r e s o l u t i o n o f e n e r g y d i s p e r s i v es p e c t ro m e t e r s . T h e e f f e c t i v e e l e c t r o n f l u x t e r m , K ' T , h o w -eve r , may be i nc r eased mos t s i gn i f i can t l y by us i ng h i ghe rbr i gh t ness e l ec t ron sources such a s L aB6 or f i e l d emi s s i ont ip s w h e r e i m p r o v e m e n t s o f u p t o X 1 0 0 i n e l e c t ro n c u r r e n td e n s i t y m a y b e a c h i e v e d4 fo r sma l l e r p robe s i zes . A ny i n -c r ease i n K T by ex t end i ng t he spec t rum acqu i s i t i on t i me , T ,i s l i mi t ed by t he mechan i ca l and e l ec t r i ca l s t ab i l i t y o f t hem i c r o s c o p e . F o r t h e se s m a l l p re c i p it a te s i z es , - 1 0 n m , ar ea l i s t i c pe r i od fo r mi c roana l ys i s i s - 100 seconds .

I V . D I S C U S S I O NT h e a b o v e t h e o r e ti c a l c o n s i d e r a ti o n o f S T E M - E D S X - r a ymi c roana l ys i s o f sma l l p r ec i p i t a t e s i l l us t r a t e s t he compro-

mi se be t ween r educ i ng spa t i a l r e so l u t i on and i mprov i ngcount i ng s t a t i s t i c s a s soc i a t ed wi t h i nc r eas i ng t he e l ec -t ron p robe s i ze . F or g i ven expe r i ment a l cond i t i ons o f f o i lt h i ckness t l , p r ec i p i t a t e d i ame t e r ( d ) , pos i t i on ( t ' ) andsegrega t ed e l em ent co ncen t r a t i on (Co oc R0), e l ec t ron acce l -e r a t i ng vo l t age (E 0) , e f f ec t i ve f l ux i n t ens i t y i n t he p robe( K ' ) , a n d r e c o r d i n g t i m e ( T ) t h e r e e x i s t s a n o p t i m u mi nc i den t e l ec t ron p robe d i ame t e r (B*) fo r de t ec t i on o f t hepa r t i cu l a r e l ement o f i n t e r e s t w i t h i n t he X- r ay spec t rumrecorded f rom t ha t p r ec i p i t a t e . F o r i r on base fo i l s , e l ec t ronsca t t e r i ng wi t h i n t he fo i l , cha rac t e r i zed by t he t e rm / 3 i nE qs . [2 ] and [3 ] , r e su l ts i n op t i m um e l ec t ron p robe d i -ame t e r s i n t he r ange 10 t o 60 nm for the s t anda rd cond i t i onscons i de red i n t he p r esen t work . F or p r ec i p i t a t e s l oca t ed a tt he cen t e r o f a f o i l o f t h i ckness > - 100 nm t he op t i m um probes i ze i s > -20 nm r ega rd l e s s o f t he e f f ec t i v e e l ec t ron f l uxpa ramet e r K T. T hi s beam d i amet e r i s l a rge r t han usua l l yob t a i ned in cur r en t S T E M i ns t rument s wh en ope ra t i ng i n the

1.o

0 i i i I i I 1 [ i i i I I I i l l I i I i i i i 1 [ i4 3 2 I

1o9 K TF i g . 5 - - C a l c u l a t e d p l o t s o f m i n i m u m p r e c i p i t at e d ia m e t e r , d , w h i c h m a yb e d e t e c t e d i n t h e X - r a y s p e c t r u m a s a f u n c t i o n o f t h e e l e c t r o n f l u x , K Tnm i t /3) f o r R 0 = 0 , 1 a n d 1 , t~ = 2 0 0 n m a n d R o = 1 0 w i t h t ~ = 1 0 0 ,2 0 0 , a n d 3 0 0 n m .

C

M E T A L L U R G I C A L T R A N S A C T IO N S A V O L U M E 1 4A , O C T O B E R 1 9 8 3 - 1 9 4 7


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3 . F or EDS sys tem s where the s a tu ra tion X-ray count rateis -

mta,83-stem-eds xray microan of small prec in fe bas th foils

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