HISTORY OF QUANTITATIVE ELECTRON PROBE MICROANALYSIS

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HISTORY OF QUANTITATIVE ELECTRON PROBE MICROANALYSIS

K. Heinrich

To cite this version:

K. Heinrich. HISTORY OF QUANTITATIVE ELECTRON PROBE MICROANALYSIS. Journal de

Physique Colloques, 1984, 45 (C2), pp.C2-3-C2-8. �10.1051/jphyscol:1984201�. �jpa-00223756�

HISTORY OF QUANTITATIVE ELECTRON PROBE MICROANALYSIS

K.F.J. Heinrich

NationaZ Bureau of Standards, Washington, DC 20234, U.S.A.

RdsumQ - La microanalyse quantitative estbasde s u r u n a j u s t e m e n t e m p i r i q u e P d e s modbles simples de l'interaction Qlectron-cible. L'exactitude de l'analyse ddpend de la mesure de l'dmission de tdmoins homogPnes et bien caractdrisds.

L'utilisation de meilleurs tQmoins et d'ordinateurs plus performants permet d'abandonner des modbles simplistes et d'amdliorer la qualitd de l'ajustement.

On peut aussi inclure des processus de second ordre tels que l'excitation des Rayons X par des Blectrons secondaires de haute Qnergie prdcQdemment nggligde.

Abstract - Quantitative microanalysis is based on empirical adjustment of simple models of electron-target interaction. The accuracy of analysis depends on measurements of X-ray emission from homogeneous well-characterized standard materials. As better standards and larger and faster computers become

available, simplistic models can be replaced and the quality of adjustment improved. It is also possible to include some secondary processes such as excitation of X-rays by high-energy secondary electrons which were overlooked in the past.

Introduction

The term "microanalysis" was first used by the Austrian chemists Emich [l] and Pregl [ 2 ] , who adapted the procedures for elemental organic analysis to reduce specimen size to the order of milligrams. Techniques for inorganic microanalysis were developed by Chamot and Mason [3] who used crystalline precipitations under the microscope, and by Feigl [ h ] , who avoided the tedious separative manipulations of

small volumes of liquid by performing specific reactions in droplets. The use of these techniques was often limited by the difficulty in separating the specimen regions of interest from the surrounding material. Metallurgists developed decora- tion techniques based on chemical reactions in situ [ 5 ] , but in general local micro- analysis requires the replacement of chemical reagents by physical agents such as focused particle or photon beams. The observed reaction is then also a physical process, such as the emission of photons or particles. Excitation in situ requires, for the selection of the site of analysis, that a microscopic specimen area around it be observable, by scanning or projective techniques. Therefore, instrumental microanalysis combines features of both analysis and microscopy [61.

For an evaluation and classification of such a technique the following aspects are important :

O the nature of the specimen (alloy, mineral, biological), and its preparation,

the nature of the measurement (isotopic, elementary, molecular, or structural),

O its specificity, sensitivity, and accuracy in quantitation,

O its spatial resolution in depth and across the surface, (which may be defined by the technique, the specimen dimensions, or both).

Other aspects, such as the cost and speed of analysis and the cost of the equipment, may also affect the choice of technique.

Article published online by EDP Sciences and available at http://dx.doi.org/10.1051/jphyscol:1984201

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ZAF Corrections

Electron beam microanalysis is based on the spectra of X-rays excited by an electron beam. The spectral lines are characteristic of the emitting elements, as first described by Moseley

[TI.

Hence, qualitative analysis can be based on their dis- tribution. Experiments on alloys also indicate that the observed intensity of X-ray emission is approximately proportional to the mass fraction ("concentration") of the constituent elements

181.

Strong deviations from this simple relation may be due to absorption of the emerging primary (i.e., electron-excited) X-rays, or to the production of fluorescent (i .e.

,

X-ray excited) X-rays. Castaing and Descamps

[ g ] therefore proposed that a linear approximation is valid for the primaq

generated X-radiation; to obtain an estimate of generated line intensities,

"corrections" for X-ray absorption and fluorescence were applied to the observed line intensities. However, the calculation of absolute X-ray intensities entails the accurate knowledge of instrumental factors difficult to determine. Therefore composition estimates are usually derived from intensities relative to those obtained from standards of known composition.

Accurate measurements indicate that even after correction for absorption, primary radiation is not strictly linear to concentration, but that matrix effects are present which depend on the atomic masses of the specimen components (atomic number effect). Castaing therefore developed a system of quantitation in which the con- centration of the element to be determined, C, is approximately by multiplying the observed ratio, k, of X-ray emission between the sample and the pure element by three "correction factors", related, respectively, to atomic numbers, to absorption of primary X-rays, and to production of secondary X-rays excited by primary X-ray emission [lo]:

This method is usually called the "ZAF" method. The name "correction factor"

suggests that the real intensities are still considered to deviate from an ideal law of linearity. Such a law is difficult to conceive, however, when the complexity of the event in the excited target is considered. The correction factors are obtained by analysis of the generation process, and by the use of parameters which are either observable or derived from observable quantities related to the macro- scopic process of X-ray excitation. Among such parameters are:

O for primary X-ray generation: the generated X-ray intensity, I

,

and the loss of X-ray generation due to electron backsoatterinz R,

O for X-ray absorption: the depth distribution of primary X-rays in the target,

b ,

the X-ray mass absorption coefficients, u , and the mean X-ray emergence' Qgle, q ,

O for secondary X-ray production (fluorescence): the generated primary intensity, I

,

the X-ray yield, w , X-ray mass absorption coefficients, and emergence angle.

These observable parameters, depend in turn on more basic properties of the specimen atoms, electrons and photons. The relations are indicated in Table I, which shows that the interaction between the parameters at the atomic level and the correction factors is quite complex.

...

electron penetration

...

electron scattering

electron deceleration ionization

... ...

...

X-ray yield

relative line intensity

...

X-ray absorption coefficients

.

I

parameters at the atomic level:

Table I. Effect of parameters at the atomic level on correction terms.

IP R F~

The original scheme of Castaing and Descamps only accounts for the X-ray production caused by primary electrons, by fluorescence excited by primary X-ray photons, and for the absorption of these X-ray emissions. In 1960, Castaing included in the ZAF scheme the loss of primary excitation due to electron backscattering [ll]. The model for ZAF corrections was later modified by several authors. A particularly useful step was the proposal of a generalized model for the absorption of primary X-ray photons by the target, made by Philibert [12], and subsequently modified by Duncumb and Shields [13] and by Heinrich [lh], among other investigators. The resulting scheme, with multiplicative correction factors, is widely used in computer programs for data reduction (e.g. [15].)

In 1967, Henoc presented a detailed analysis of the emission of X-rays excited by continuous X-radiation (continuum fluorescence) [16], and while visiting the National Bureau of Standards, he wrote a computer program which included terms for this emission 1171. Reimer et al. [I81 pointed out in

1976

that X-ray excitation by high-energy electrons amounts to 15% of the aluminum K ~ L emission in aluminum metal. These additional X-ray sources should be incorporated in all data evalution schemes, since powerful computers are now available for such a task. At this point, the concept of multiplicative correction coefficients becomes impractical: the process requires the addition of components for both specimen and standard, of the form [19]:

The variables in this equation follow the nomenclature of reference [lg]: I and I' are generated and emergent intensities; the subscripts p, c and f refer, respec- tively, to primary radiation, to fluorescence due to continuum, and to fluorescence due to a characteristic line. The superscript s denotes the standard, and the asterisk ( * ) indicates variables depending on the composition of the specimen. The summation marks indicate that characteristic fluorescence may be due to more than one line.

The calculation of the fluorescence by the continuum requires an integration over the relevant range of energy of the continuum, which is best done by a numerical method. Furthermore, since the quantities marked in the above equation depend on the unknown specimen composition, an iteration method must be used to arrive at the results by successive approximations. These operations present no major problem with the computers now available, even if the calculations are performed in an interactive mode which is preferable to a batch calculation.

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Alternative methods

I n t h e p a s t t h e r e was great i n t e r e s t i n avoiding t h e l a r g e amount of calculations i m p l i c i t i n t h e ZAF method, by using empirical techniques based on t h e assumption of l i n e a r o r of simple hyperbolic c a l i b r a t i o n functions [20, 211. Such techniques were p a r t i c u l a r l y advocated f o r mineralogical specimens, f o r which standards closely matching t h e specimen i n composition are frequently available. It can be argued t h a t t h e empirical method with matching standards minimizes e r r o r s caused by f a c u l t y parameters o r e r r o r s i n t h e theory. But i s was shown by Bence and Holtzwarth [22]

t h a t deviations from t h e parabolic model i n mineral systems can be s i g n i f i c a n t . Now t h a t f a s t computers a r e available, t h e r e i s , of course, no reason why c l o s e l y matching standards should not be used i n combination with t h e b e s t available theory.

The ZAF method i s therefore used even f o r s o l i d - s t a t e detector systems, i n which a d d i t i o n a l complications a r i s e due t o t h e need f o r c a r e f u l background correction and separations of overlapping l i n e s .

A very d i f f e r e n t , and very f r u i t f u l approach, i s the simulation of t a r g e t events by summation of individual electron paths i n a Monte-Carlo calculation [ 2 3 ] . This method i s even now t o o slow f o r routine a n a l y t i c a l procedures, although a simplified approach was advocated by Pascal [24]. The success of t h i s method depends on t h e accurate knowledge of t h e e f f e c t s of deceleration and s c a t t e r i n g of electrons i n a t a r g e t , and on t h e need of c o l l e c t i n g a l a r g e number of t r a j e c t o r i e s so t h a t s t a t i s t i c a l s c a t t e r becomes i n s i g n i f i c a n t . The g r e a t e s t advantage of t h e method i s t h e f l e x i b i l i t y concerning t h e shape of t h e specimen. The method can therefore be t e s t e d , not only by means of t h e usual s e t of analyses of known standards of i n f i n i t e thickness, but a l s o by t h e calculation of e l e c t r o n backscatter c o e f f i c i e n t s , by means of r e s u l t s obtained from t h i n specimens, inclined t a r g e t s , e t c . Conversely, once t h e method i s proven, it can be adapted t o any v a r i a t i o n i n geometrical

r e l a t i o n s among t h e relevant p a r t s of instrument and specimen, a s well a s t o specimen s i z e and shape.

Testinn o f Data Evaluation

The sources of e r r o r i n microanalysis include deficiencies i n specimen preparation and measurement procedures, instrumental e r r o r s , e r r o r s i n constants and parameters, deficiencies and omissions i n models, and, l a s t but not l e a s t , e r r o r s i n t h e assumed standards used f o r t e s t i n g and analysis. The f i r s t large-scale evaluations of diverse techniques by Poole [25] put i n evidence disappointingly l a r g e e r r o r d i s t r i - butions, and t h e q u a l i t y of standard materials f o r t e s t s , a s well as t h e d i f f i c u l t y i n unraveling t h e diverse causes of e r r o r , s e t a l i m i t t o what can be achieved i n improving accuracy. The l a t t e r problem i s i l l u s t r a t e d i n Table I which shows t h a t t h e same primary parameters (e.g., electron deceleration and X-ray absorption) in- fluence several o r a l l of t h e ZAF f a c t o r s which we pretend t o separate.

A t present t h e search f o r higher accuracy seems t o have abated, and t h e emphasis i s on mapping and f a s t data output. It seems, however, t h a t the current s t a t e of a r t of standard material preparation

-

with synthesis of oxide and m e t a l l i c g l a s s e s , t h e l a t t e r with f a s t cooling techniques

-

would be able t o y i e l d a highly improved s e t of standard materials. A t t h e same time, t h e s i m p l i s t i c geometric o r algebraic models which were required i n a period of l i m i t e d computational resources, could be abandoned, together with t h e s t r i c t separation of t h e Z , A , and F factors.

A multiparameter matching based on a model i n function of b a s i c e l e c t r o n properties and X-ray absorption c o e f f i c i e n t s could y i e l d a new s y n t h e t i c model, t h e co- e f f i c i e n t s of which could be optimized a s new standard materials become available.

Utimately t h e achievable accuracy seems l i m i t e d only by t h e e f f o r t we can exert i n t h i s direction.

[2] PREGL F., Die Quantitative Organische Mikroanalyse, Berlin;

Springer-Verlag

,

^{193 1.}

[3] CHAMOT E.M. and MASON C. W., Handbook of Chemical Microscopy, New York; Wiley, 1940, 2d. ed.

[4] FEIGL F., Qualitative Analyse mit Hilfe von TOpfelreaktionen, Leipzig: Akademische Verlagsgesellschaft, 1931.

[S] KEHL J.L., The Principles of Metallographic Laboratory Practice, New York: McGraw-Hill, 1949.

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Analytical Electron Microscopy 1981, San Francisco; San Francisco Press, 1981, p. 467.

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27

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BROWN B.D., Adv. X-ray Analysis

L

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CASTAING R. and DESCAMPS J., J. Phys. Radium

16

(1955) 304.

PHILIBERT J., and TIXIER R., in "Quantitative Electron Probe Microanalysis", NBS Spec. Publ.

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National Bureau of Standards, US Dept. of Commerce, Washington DC, 1968, p.13.

CASTAING R., Adv. Electron. El. Phys.

12

(1960) 317.

PHILIBERT J., Proc. 3d Internat. Conference on X-Ray Optics and Microanalysis, Pattee H.H., Cosslett V.E., and Engstr8m A., eds.

Acad. Press, New York 1963, p. 379.

DUNCUMB P. and SHIELDS P.K., The Electron Microprobe, McKinley T.D., Heinrich K.F.J., and Wittry D.B., eds., J. Wiley & Sons, New York, 1966, p. 284.

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521,

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Washington DC, 1973.

HENOC J., "Quantitative Electron Probe Microanalysis, NBS Spec. Publ.

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-

DC, 1968, p. 197.

HENOC J., HEINRICH K.F.J., and MYKLEBUST R.L., NBS Tech. Note

769,

National Bureau of Standards, US Dept. of Commerce, Washington DC, 1973.

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National Bureau of Standards, US Dept. of Commerce, Washington DC, 1976, p. 45.

HEINRICH K.F.J., Electron Beam X-Ray Microanalysis, New York;

Van Nostrand Reinhold, 1981.

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[ 2 0 ] ZIEBOLD T.O., OGILVIE R.E., Anal. Chem.

2,

322 (1964).

[ 2 1 ] BENCE A.E., ALBEE A.L., J. Geology

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382 (1968).

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[ 2 4 ] PASCAL B., J. Microscopic

5,

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1251 POOLE, D. M., Ref. [ 1 6 1 , p. 93.