A CORRECTION PROCEDURE FOR CHARACTERISTIC FLUORESCENCE IN MICROPROBE ANALYSIS NEAR PHASE BOUNDARIES

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A CORRECTION PROCEDURE FOR CHARACTERISTIC FLUORESCENCE IN MICROPROBE ANALYSIS NEAR PHASE

BOUNDARIES

G. Bastin, F. van Loo, P. Vosters, J. Vrolijk

To cite this version:

G. Bastin, F. van Loo, P. Vosters, J. Vrolijk. A CORRECTION PROCEDURE FOR CHARACTER-

ISTIC FLUORESCENCE IN MICROPROBE ANALYSIS NEAR PHASE BOUNDARIES. Journal

de Physique Colloques, 1984, 45 (C2), pp.C2-43-C2-46. �10.1051/jphyscol:1984211�. �jpa-00223777�

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JOURNAL

DE PHYSIQUE

Colloque C2, suppl6ment au n02, Tome 45, f6vrier 1984 page C2-43

A CORRECTION PROCEDURE FOR CHARACTERISTIC FLUORESCENCE I N MICROPROBE ANALYSIS NEAR PHASE BOUNDARIES

G . F . Bastin, F.J.J. van Loo, P . J . C . Vosters and J.W.G.A. Vrolijk

Lab. for Physical Chemistry, Eindhoven University of TeehnoZogy, P. 0 . Box 523, 5600 MB Eindhoven, The Netherlands

RESUME

- On

propose une m6thode de correction des effets de fluorescence par raie caractdristique au voisinage des limites de phase. On donne les formules correspondant au cas d'une interface plane entre deux alliages homogdnes. Une m6thode

it6rative

en est d6duite pour le calcul des profils de concentration. La m6thode est illustrde par quelques exemples et on dis- cute brigvement de ses limites.

ABSTRACT

-

A correction procedure is proposed to correct for the effects z a c t e r i s t i c fluorescence in EPMA near phase boundaries. The necessary equations for the case of two homogeneous alloys sharing a common flat interface are given. Based on these equations an iterative correction pro- cedure is proposed for application to sloping concentration profiles. The procedure is illustrated on some practical examples and some of the factors connected with its performance are briefly discussed.

I

-

INTRODUCTION

The spatial resolution in quantitative EPMA can be badly affected by the occurrence of secondary characteristic fluorescence. In such cases the total volume of excitation (normally 2-4

pm

diameter) can be increased by one to two orders of magnitude! The effect is most pronounced in matrices containing elements with atomic numbers Z differing by two (for Z>21) like combinations of Fe-Ni, Co-Cu etc.

Though the established Reed (1) correction procedure is in general quite successful in correcting for these effects, it is bound to fail when the electron beam ap- proaches a phase boundary. This is due to the fact that the primary and secondary X-ray production as well as the subsequent absorption no longer necessarily take place in the same homogeneous matrix, which is a prerequisite for the Reed model.

An attempt to devise a correction scheme which is able to calculate a correction factor as a function of distance from the boundary, has previously been undertaken by Maurice et a1 (2) and H6noc et a1 (3) for the simple case of two pure metals sharing a flat interface. Their equations have been generalised by Bastin et a1

(4) for various geometries (flat and curved interfaces) by allowing variable con- centrations on both sides of the interface. These generalised equations for the case of a flat interface are used in the present paper as the basis for an iterative correction procedure.

I1 - THEORY

The necessary equations for the case of two homogeneous alloys sharing a flat interface have been derived using the schematic drawing in Fig. 1. Involved are the elements A and B and it is supposed that B-K radiation is capable of exciting A-Ka radiati The P c t r o n beam is located in oUin alloy LB (richest in B, concentra- tions ~F'and distance d from the interface separating it from LA (richest in A, concentr%iL?Ck and c~LA).

W o restrictions are made:

1. All primary radiation is assumed to be emitted from a point source in 0.

2.

Contributions from continuum fluorescence are not taken into account

For the alloy

LB

the total amount of emitted fluorescent A-radiation (1i) in rela- tion to the primary emitted A-radiation (IA) can be written as (4):

Article published online by EDP Sciences and available at http://dx.doi.org/10.1051/jphyscol:1984211

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JOURNAL DE PHYSIQUE

Fig. 1. Schematic drawing representing two alloys LB (B-rich) m d LA (A-rich), separa- ted by a straight interface. Primary B-K, radiation i s supposed t o e x c i t e secondary A-Ka radiation.

Electron beam

X-rays to Spectrometer

.rr

l a 1

: - (LB)

=

S .

^,

IA @=O q=o

LB

W~

r-1 with S

=

.

(T)

LA

in which

p

denotes the mass abs. coefficient (subscript indicates the type of characteristic radiation; superscript the type of alloy in which absorption takes place) and

p

represents the density.

w

is the fluorescence yield, (r-l/r) the absorption edge

jump

ratio, A the atomic weight and U the overvoltage ratio (acc. voltage/crit. excitation vo1tage)for the element in question.

Similarly we get for the contribution from alloy U:

n

a.

11 q . c y . I I ^sin$dqd@

- (LA)

=

S .

I A cf;"

@=o

$=o pFp,"cosqcosece .

with S having the same meaning as before.

The measured k-ratio (Int. from specimen Int from pure element standard) can 6 . .

now be corrected by multiplying it with 1/ (l+IA/IA)

m

which I ~ / I ~ now represents the added contributions from eqs. (1) and (2).

Integration over the spherical coordinates

$

and

@

for a given value of d is carried

out numerically with the aid of a computer.

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I11 - THE SUGGESTED CORRECTION PROCEDURE

After a number of successful t e s t s of eqs. (1) and (2) on undiffused couples (4) it was decided to use them as the basis for an i t e r a t i v e correction procedure.

This w i l l now be discussed with the Co-Cu system as an example. Essentially it comes down t o the following steps:

a. The i n i t i a l microprobe measurements are used t o make estimates of the average Co-concentrations

cLB

and C? over an area between 5 and 25 1~.m from the boundary.

The value of

cLA

wi$l be qulte reliable and w i l l henceforth be kept fixed. The value of

CY

,*on the other hand, w i l l be too high i n i t i a l l y .

b. The k-ratios f o r Co are corrected using equations (1) and (2).

c. The fluorescence correction i n the ZAF program i s disabled and new concentrations are calculated by the r e s t of the ZAF program.

d. The new concentration profile is used t o generate a new estimate for

CY

a f t e r which the procedure i s repeated.

The iterations are stopped as soon as the new estimate differs l e s s than, say, 0.05 wt % from the previous one,provided, of course, that convergence i s obtained. So f a r , however, t h i s has always been the case.

IV

-

RESULTS

AND

DISCUSSION

The f i r s t example of the performance of the procedure i s shown i n Fig. 2 in which the Co-concentration profi es crosses) are shown of two Co-Cu diffusion couples a f t e r annealing a t 1000 C; together with the results of the two necessary

b

⁽

Distance

(m)

Fig. 2. Performance of the correction proce- dure for two Cu/Co d i f f u s i o n couples, anneal- ed for 127 h (Top) and 720 h ( ~ o t t o m j a t 1000 O c .

x measured

o calculated a f t e r the f i r s t i t e r a t i o n .

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C2-46 JOURNAL DE PHYSIQUE

iterations. In both cases the i n i t i a l apparent boundary concentration of approx.

8.8 wt% Co i s reduced t o about 6.4 wt%, which i s i n close agreement with Co-measurements "by difference" (i.e. the Co concentration i s calculated as the balance).

A s e r i e s of calculations concerning the question of how c r i t i c a l the i n i t i a l values of C~ and choice of a%alue f&r

cLA EE

was hardly c r i t i c a l . as well as the area over which i s averaged,showed t h a t A too high i n i t i a l estimate f o r CA

dhe

was found t o merely inc4ease the number of i t e r a t i o n s , the f i n a l r e s u l t s being the same. An evidently too low i n i t i a l estimate led t o a higher estimate f o r the next iteration,thus showing the desired convergence from the reverse side.

Regarding the area over which C? should be averaged it can be stated t h a t t h i s should be adapted t o the type of problem. In diffusion couples with a very limited

(< 25 p) extent of the diffusion zone and i n which C soon approaches zero, more care should be exercised i n order t o avoid overcorrec4ion.

cup ^Cu^{c o o}C o

11 K w

^Co⁴

/

^C"⁴

=:'i

^1%.*. -*-

... ^..

^,

^?

^{- <} ^{c o o}

1 0

2 4 6

-

^number^of^iter

& x.x.P.%3.~P. Xxx.x*

ff -,

i6 $2 2)8 24 i0 Ik ¹^; 8 4 0 4 8 12 16

Distance (pm)

Fig. 3. Results of the correction procedure applied to a C"u O/Co diffusion couple anneal- ed for 70 h at ?000 OC.

x Co and Cu both measured

o Co concentration measured "by difference

".

In such cases it i s advisable t o reduce the area and/or t o take it closer t o the boundary. This leads t o slower convergence, as was observed i n a Cu20/Co couple

(Fig. 3) in which a f t e r diffusion a layer of Cu adjacent t o a COO layer was formed.

Here, averaging has been carried out over an area between 0 and only 10 lun from the boundary, with the r e s u l t t h a t 6 i t e r a t i o n s were necessary. The f i n a l boundary concentration of approx. 1.5 wt% Co was again i n close agreement with measurements "by difference" and contrasts sharply with the original value of more than 5 %!

Apparently a considerable improvement can be obtained with the proposed procedure.

I t is t o be expected t h a t similar procedures can successfully be applied t o small p a r t i c l e s (idealised as hemispheres), lamellae and epitaxial layers

.

REFERENCES

1. Reed, S.J.B., B r i t . J. Appl. Phys., 16 (1965) 913.

2. Maurice, F., Seguin, R. e t H6noc J.

,p

CongrSs International sur 1' Optique des Rayons X e t l a Microanalyse, Orsay 1965, 357.

3. Hgnoc, J., Maurice, F. e t Zemskoff, A., Proc.

vth

International Congress on X-ray Optics and Microanalysis, G. Mijllenstedt e t a l , Eds.

,

Springer Verlag, Berlin, 1969. 187.

4.

ast tin;

G.F.

;

van Loo, F.J.J., Vosters, P.J.C. and Vrolijk, J.W.G.A., t o be published i n Scanning, (1 983)