QUANTITATIVE ELECTRON PROBE MICROANALYSIS OF CARBON IN CARBIDES USING A GAUSSIAN ϕ( ρz) EQUATION

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QUANTITATIVE ELECTRON PROBE

MICROANALYSIS OF CARBON IN CARBIDES USING A GAUSSIAN Φ( ρz) EQUATION

J. Brown, P. Schwaab, A. von Rosenstiel

To cite this version:

J. Brown, P. Schwaab, A. von Rosenstiel. QUANTITATIVE ELECTRON PROBE MICROANALY- SIS OF CARBON IN CARBIDES USING A GAUSSIAN Φ( ρz) EQUATION. Journal de Physique Colloques, 1984, 45 (C2), pp.C2-609-C2-612. �10.1051/jphyscol:19842142�. �jpa-00223813�

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QUANTITATIVE ELECTRON PROBE MICROANALYSIS OF CARBON IN CARBIDES USING A GAUSSIAN < K P Z ) EQUATION

J.D. Brown, P. Schwaab* and A.P. von Rosenstiel

Faculty of Engineering Science and Centre for Interdisciplinary Studies in Chemical Physics, The University of Western Ontario, London, Canada NBA 5B9

*Mannesmann Forschungsinstitut GmbH, Postfach 25 11 67, D-4100 Duisburg, F.R.G.

**Metaalinstituut WO, Postbus 541, 7300 AM, Apeldoorn, The Netherlands Résumé - L'intensité des raies CKa caractéristiques émises par une série de carbures est mesurée pour plusieurs énergies des électrons et trois angles d'émergence. L'analyse quantitative est faite en utilisant une forme Gaussienne de 4>(pz). Les résultats indiquent que l'intégrale du pic doit être utilisée pour les analyses quantitatives. L'exactitude de l'analyse des carbures de Nb et Zr est limitée par la taille des particules ou les inexacti- tudes des coefficients d'absorption.

Abstract - CKa X-ray i n t e n s i t i e s from a number of carbides have been measured over a range of energies and a t 3 different take-off angles. Quantita- t i v e c a l c u l a t i o n s were performed using a Gaussian <(>(pz) equation. Analysis of the data shows t h a t peak area i n t e n s i t i e s should be used for q u a n t i t a t i v e a n a l y s i s . Problems s t i l l e x i s t in the analysis of Nb and Zr carbides e i t h e r because of the small s i z e of the p a r t i c l e s or due to inaccurate mass absorp- t i o n c o e f f i c i e n t s .

CKa X-ray l i n e i n t e n s i t i e s can be measured routinely with good s e n s i t i v i t y in modern electron probe microanalysers. The problems of q u a n t i t a t i v e analysis however are not completely resolved. The ZAF procedure using the simple P h i l i b e r t absorption correction is inadequate because the absorption correction is always large even for low electron energies / l / . Procedures using the full P h i l i b e r t absorption cor- rection such as those proposed by Ruste 111 or Love, Cox and Scott / 3 / y i e l d b e t t e r r e s u l t s , but cannot be the final answer since the depth d i s t r i b u t i o n of X-ray production is s t i l l not modelled c o r r e c t l y / 4 / . The thin film model proposed by Duncumb and Melford / 5 / can work well for high electron energies and highly absorbing matrices but i s not generally a p p l i c a b l e .

Packwood and Brown / 6 / have shown t h a t the depth d i s t r i b u t i o n of X-ray production i s Gaussian in character. The use of t h i s more accurate model for q u a n t i t a t i v e electron probe microanalysis of carbon in carbides i s examined in t h i s paper.

A complication in analysis using low energy X-ray l i n e s is the fact t h a t the " l i n e "

as measured by a crystal spectrometer using a s t e a r a t e crystal i s not a narrow Gaussian but a broader band whose detailed shape and width varies from compound to compound. Peak i n t e n s i t y , as usually measured, is not an adequate c r i t e r i o n for X-ray i n t e n s i t y and integrated peak area has to be used. Measurements of integrated peak areas have also been made.

SAMPLE PREPARATION AND k-RATIO MEASUREMENTS

A s e r i e s of carbides ranging from B4C through WC, with grain s i z e s from 10 to 50 ym were chosen for t h i s study. Fe3C was used as the reference standard. The composi- tion of the carbides was determined by wet chemical analysis and X-ray diffraction / ! / . To avoid the use of carbon containing mounting m a t e r i a l s , the carbide powders were mixed in a r a t i o of 1:50 with aluminum powder and cold pressed into specimen blocks of 8 mm thickness and 20 ram diameter a t ' 8 tons/cm^. The compacted specimen Article published online by EDP Sciences and available at http://dx.doi.org/10.1051/jphyscol:19842142

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b l o c k s had a d e n s i t y equal t o 96% o f aluminum metal. Specimen p r e p a r a t i o n proceed- ed b y s t a n d a r d techniques, w i t h diamond p a s t e used i n t h e p o l i s h i n g stages. A f t e r c a r e f u l c l e a n i n g , A1203 was used i n t h e f i n a l p o l i s h i n g s t e p .

The X-ray measurements were made on t h r e e d i f f e r e n t e l e c t r o n microprobes w i t h t a k e - o f f angles o f 30°, 40° and 52.5' r e s p e c t i v e l y . The e l e c t r o n beam i s normal t o t h e specimen s u r f a c e i n a l l t h r e e i n s t r u m e n t s . The e l e c t r o n beam e n e r g i e s used v a r i e d i n 2 keV s t e p s f r o m 4 t o 12 keV.. The a c t u a l energy was checked b y measurement o f t h e s h o r t wave l e n g t h c u t o f f o f t h e X-ray continuum. Both CKa and i f p o s s i b l e t h e metal c h a r a c t e r i s t i c 1 in e i n t e n s i t i e s were measured. F o r t h e CKa measurements , t h e p u l s e h e i g h t a n a l y s e r s e t t i n g s were c a r e f u l l y made t o e x c l u d e 2nd and h i g h e r o r d e r r a d i a t i o n . Repeat i n t e n s i t y measurements were made on a minimum o f 10 i n d i v i d u a l areas. An oxygen gas j e t was used t o remove carbon b u i l d u p . A f t e r a p p l y i n g c o r r e c - t i o n s f o r dead t i m e and background, k - r a t i o s were c a l c u l a t e d .

For some c a r b i d e s , i n a d d i t i o n t o t h e peak measurements, i n t e g r a t e d peak a r e a measurements on t h e CKa l i n e were made b y s t e p p i n g through t h e peak i n s m a l l a n g u l a r increments, e i t h e r manually o r a u t o m a t i c a l l y . The k - r a t i o s were c a l c u l a t e d as peak areas above background r e l a t i v e t o t h e Fe3C peak area measured u s i n g i d e n t i c a l con- d i t i o n s .

ABSORPTION COEFFICIENTS

Three s e t s o f a b s o r p t i o n c o e f f i c i e n t s f o r t h e Carbon Ka l i n e a r e a v a i l a b l e i n t h e l i t e r a t u r e /2,7,8/. Some s i g n i f i c a n t d i f f e r e n c e s e x i s t between s p e c i f i c values f o r t h e t h r e e s e t s . We have chosen t o use t h e values o f Henke e t a l . /7/. These appear t o be t h e most r e l i a b l e s i n c e t h e y a r e based on a n a l y s i s o f t h e most r e c e n t measurements.

RESULTS AND CALCULATIONS

The k - r a t i o s when u s i n g i n t e g r a t e d area measurements a r e d i f f e r e n t t h a n when u s i n g peak measurements. The r a t i o s o f a r e a t o peak i n t e n s i t y r a t i o s ( r e l a t i v e t o Fe3C) a r e shown i n Table 1. Note t h a t f o r t h e measurements made t h e area t o peak r a t ~ o s a r e d i f f e r e n t f o r t h e two i n s t r u m e n t s as y o u w o u l d expect i f t h e r e s o l u t i o n o f t h e two spectrometers i s d i f f e r e n t . W i t h i n t h e l i m i t s o f measurement, t h e r a t i o s a r e independent o f e l e c t r o n energy, s u g g e s t i n g t h a t a c o n s t a n t f a c t o r may b e s u f f i c i e n t f o r c o r r e c t i n g peak t o area measurements.

TABLE 1 : RATIO OF k-VALUES FOR CKa (RELATIVE TO Fe3C)

Carbide B4 C S i C

Cr23C6 Cr3C2 NbC Mo2C TaC

R a t i o o f k-val ues area/peak

30' T.O.A. 40" T.O.A.

1.045

The Cr c a r b i d e s p r o v i d e a good t e s t case f o r whether peak o r area measurements s h o u l d be used ( T a b l e 2 ) . Almost no atomic number c o r r e c t i o n i s r e q u i r e d s i n c e Fe3C and t h e C r c a r b i d e s have a l m o s t i d e n t i c a l average atomic number and when t h e resu7 t a n t c a l c u l a t e d compositions a r e independent o f energy, one has some c o n f i d e n c e t h a t t h e a b s o r p t i o n c o r r e c t i o n i s a c c u r a t e . Under t h e s e circumstances, t h e area measurements y i e l d r e s u l t s which a r e c l o s e r t o t h e known compositions a t a l l

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TABLE 2: COMPARISON OF RESULTS USING PEAK AND AREA k-RATIOS, CHROMIUM CARBIDES Electron Calculated Carbon Concentration, wt.%*

Energy T.O.A. = 30" T.O.A.=52.5"

keV Peak Area Peak Area

4 6.45 5.77 6.78 5.81

* Nominal Compositions 5.68 and 13.3 w t % Carbon.

In the a n a l y s i s of t h e o t h e r c a r b i d e s , Zr and Nb r e s u l t s a r e l e a s t a c c u r a t e . This may be due t o t h e small s i z e of t h e s e carbides o r t o u n c e r t a i n t i e s i n t h e mass ab- s o r p t i o n c o e f f i c i e n t s s i n c e t h e CKa l i n e f a l l s i n t h e s t r u c t u r e of t h e M edges f o r t h e s e elements

.

Except f o r t h e s e two c a r b i d e s , t h e r e s u l t s of q u a n t i t a t i v e a n a l y s i s using t h e Gaussian equation a r e accurate t o approximately 7.5% of t h e amount present.

CONCLUSIONS

Based on t h e measurements made, i n t e g r a t e d a r e a i n t e n s i t y r a t i o s must be used f o r q u a n t i t a t i v e a n a l y s i s . Since t h e f a c t o r r e l a t i n g peak i n t e n s i t y r a t i o s t o a r e a r a t i o s i s independent of e l e c t r o n energy, a simple f a c t o r could be determined t o c o r r e c t peak r a t i o s t o a r e a r a t i o s . This f a c t o r w i l l vary from instrument t o instrument ( s i n c e i t i s dependent on spectrometer r e s o l u t i o n ) and f o r d i f f e r e n t carbides ( s i n c e peak widths vary with carbide t y p e ) .

When a r e a k - r a t i o s a r e used, t h e expected accuracy f o r carbon concentration i s about + 7.5% r e l a t i v e . Some questions s t i l l remain about t h e accuracy of mass absorption - c o e f f i c i e n t s o f CKu f o r t h e elements Nb and Zr.

ACKNOWLEDGEMENTS

The authors wish t o thank t h e European Community f o r Coal and S t e e l f o r f i n a n c i a l support of t h i s i n v e s t i g a t i o n and t h e i r colleagues a t both TNO and Mannesmann f o r t h e i r h e l p and experimental s k i l l during t h e s e i n v e s t i g a t i o n s . Thanks a r e a l s o due t o Dr. G.F. Bastin of TH Eindhoven f o r a s s i s t i n g i n t h e measurements. One of us (JB) i s indebted t o t h e University of Vienna f o r f i n a n c i a l support during h i s s a b b a t i c a l 1 eave.

REFERENCES

1 . A . P . von Rosenstiel , P . Schwaab, J . D. Brown, accepted f o r pub1

.

i n Mikrochimica Acta (1983).

2. J . Ruste, J . Microsc. Spectrosc. E l e c t r o n . , 4, 123 (1979).

3. G. Love, M . G . C . Cox and J . S c o t t , J . Phys. D. 8, 1686, (1975).

4 . J.D. Brown, i n "Microbeam Analysis-1982," K.F. J . Heinrich e d . , San Francisco Press, 1982, pp. 151-158.

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5. P. Duncumb and D. Melford in "Proc. 4th I n t . Conf. X-ray Optics and Microanaly- s i s , " R. Castaing, P. Descamps, J . P h i l i b e r t e d s . , Hermann, P a r i s , 1966, p . 20.

6. R.H. Packwoodand J.D. Brown, X-Ray Spectrom.

10,

138, (1981).

7. B . L . Henke, P. Lee, T.J. Tanaka, R . L . Shimabukuro and B . K . Fujikawa, Atomic Data and Nucl. Data Tabl.

27,

1 , (1982).

8. W . Weiseiler, Mikrochimica Acta (1975), 11, p. 168.