application of reference materials for quality assessment in neutron activation analysis-use of...

Journal of Radioanalytical and Nuclear Chemisoy, Articles, Vol. 169, No. 2 (1993) 347-361

APPLICATION OF REFERENCE MATERIALS FOR QUALITY ASSESSMENT IN NEUTRON ACTIVATION

ANALYSIS - USE OF INFORMATION THEORY

1. OBRUSNIK,* K. ECKSCHLAGER**

*Nuclear Physics hlstitute, Czechoslovak A cademy of Sciences, 250 68 ~e~ (Czechoslovakia) **Faculty of Natural Sciences, Charles University, 128 40 Prague (Czechoslovakia)

(Received November 16, 1992)

It is generally accepted that an analytical procedure can be regarded as an information production system yielding information on the composition of the analyzed sample. Thus, information theory can be useful and the quantities characterizing the information properties of an analytical method may be applied not only as evaluation criteria but also as objective functions in the optimization. The usability of information theory is demonstrated on the example of neutron activation analysis. Both precision and biasof NAA results are taken into account together with the possible use of reference materials for quality assessment. The influence of the above-mentioned parameters on information properties such as informatiori gain and profitability of NAA results is discussed in detail. It has been proved that information theory is especially useful in choosing suitable reference materials for the quality assessment of routine analytical procedures not only with respect to matrix and analyte concentration in the sample but also to concentrations and uncertainties of certified values in the CRM used. In the extreme trace analysis, CRMs with relatively large uncertainties and very low certified concentrations can still yield rather high information gain of results.

Introduction

The use of information theo ry in analytical chemistry can yield rather

useful and interesting results. Both principles and applications of

information theory to analytical problems have been described in several

review articles and monographs. 1-4 As a rule, analytical information serves as

a basis for decision making in ecology, hygiene, medicine, economy, etc. As

the importance of such decisions has rapidly increased, the demands on the

quality of analytical results and their information content have also

increased.

The amount of information obtained from the analysis (Information Gain,

IG) is determined by metrological properties (precision, accuracy, detection

limit, etc.) of the analytical method used. Information Profitability (IP)

introduces the time or economic factoi" and the' relevamSe of results into

decision making. The information properties (gain, profitability) can be used

for comparison and optimization, o f various analytical metl{ods and procedures.

Elsevier Sequoia S. A., Lausanne, A kaddmiai Kiad& Budapest

I. OBRUSNIK, K. ECKSCHLAGER: APPLICATION OF REFERENCE

Up to now information theory has been applied to the evaluation and

optimization of various analytical methods including Neutron Activation

Analysis (NAA). s Instrumental (lNAA) procedures have been optimized by means

of information gain and profitability with respect to irradiation, decay and

counting times, precision, relevance and costs. In another work, e a possible

bias of ~t-ray spectrometric results has also been included in the optimization

procedure.

In this work, we have tried to investigate the use of information theory

for the optimization and evaluation of selected cases of INAA procedures

yielding biased results. Moreover, the use of Reference Materials (RMs) for

Quality Assessment (QA) has also been discussed. As the relations used for

optimization are derived for quantitative analysis we assume that the value of

a (method precision) usually does not exceed 10% relative.

We can suppose for simplicity that a can be estimated by the counting

(statistical) error. The value of this error can be controlled to some extent

by altering the decay, irradiation and especially the counting times, by

lowering of spectral background or by including a radiochemical separation

into the NAA procedure in extreme cases.

Theory

In general, the Information Gain IG is given by the extended divergence

measure as

x ~ - x I 1 , . ,, (3 z

E -~2~e "~ 2

We assume that the value of the elemental concentration x is known before

the measurement (a priori) to be only within the broad interval (xl, x ) with

the same probability at any x (rectangular distribution) and that after the

measurement (a posteriori), the value has been .determined with a standard

deviation a (normal distribution). The exponent k = (Or~a)" takes into account

by means of a the uncertainty of an elemental concentration in an RM used for r

QA, and 6 in the second term on the right hand side of Eq. (I) denotes a mean

error (bias). 4'6'7 For accurate results (6 ~ 0) this term vanishes.

In instrumental analytical technique, bias rather arises from improper

calibration or from the calibration procedure or standards available being

inadequate for a perfect elimination of errors appearing during the analysis.

Other sources of bias are inirerferences and contamination or losses in the

348

I, OBRUSNIK, K. ECKSCHLAGER: APPLICATION OF REFERENCE

elements determined. Eq. (1) can be applied in the cases where the bias 6 is

either known (or estimated) from the theory or can be established �9 6

experimentally.

Analytical information serves as a basis for making decisions on some

often non-chemical hypothesis. Information enabling a correct decision is

called relevant, s In analytical practice we should often take into account the

cost of an analysis. For this purpose another information property -

Information Profitability IP can be advantageously used and for multicomponent

analysis obtained as

~. I G t . k t I P = ( ,2)

"17

where IG i is the information gain and k i the relevance coefficient for the

i- th element, r denotes the cost of an analysis. In quantitative

multicomponent analysis the coefficients k i are often calculated as a function

of IG i (dynamic model). In some simple cases a static model can also be

untilized. 3'8

R e s u l t s a n d d i s c u s s i o n

Influence of bias 6

Though INAA can often produce rather accurate results (with low or

practically no bias), biased results cannot I~e quite avoided. Therefore, for

application of information theory, the general Eq. (!) for IG should be used.

It enables a comparison of analytical procedures yielding accurate and

inaccurate (biased) results directly from the value of the information gain.

Fig. 1 shows the dependence of IG on the value of a for three different values

of bias 6 (0%, 3% and 10% relative), calculated from Eq. (1).

It can be seen from the figure that 1G for unbiased results increases with

decreasing cr even for very low a values (see the curve for (S = 0%). However,

for biased results (3% or 10%), the IG curves decrease rather rapidly in the

region of highly precise (low a) results. The higher the level of bias the

lower value of IG is obtained. In general, the cases with IG < 0 can be 9

interpreted as a situation where incorrect results misinform us.

Fig. J can easily be applied to investigate the influence of the

ca l ib ra t ion procedure on IG of INAA results. The calibration by means of

synthetic standards prepared from pure elements and compounds can produce an

error (bias of the r e s u l t s ) u p to about 3% relative, Then, IG obtainable by

INAA with this kind of calibration is depicted by the area between IG curves

for 0% and 3% bias. This information gain is reasonably high. Only for highly

349

I. OBRUSNIIC K. ECKSCHLAGER: APPLICATION OF REFERENCE

6

0 5 10 15 20

sigma (~) Fig. i. Dependence os IG on 6" according to Eq. (1)

6 = constant (0%, 3% and 10%)

x e - x I = I 0 0 0 ppm, x = I 0 0 ppm, k = 1

precise results (below e = 3%) IG decreases as the 6 value becomes

s ta t is t ical ly s ignif icant . On the other hand, by using cer t i f ied reference

mater ia ls (CRMs) for cal ibrat ion with c, up to 20% relat ive (it corresponds to r

an uncer ta in ty of about 10% relat ive) for some elements , a rather wide range

(and mostly lower values) of IG can be obtained. Thus, informat ion theory

shows very clearly the disadvantages of using CRMs for cal ibrat ion in INAA, as

pointed out by B E C K E R 1~ and HEYDORN. n

hl/luence of the cost and relevance

It can be der ived from the Eqs (1) and (2) that the cost of an analysis

usually grows more rapidly than the informat ion gain of results. In the

analyses involving t h e measurement of act ivi ty , the value of ~r is inversely

proport ional to the square root of the count ing t ime te, and thus of the cost

of measurement . In this work, we assume for s impl ic i ty that the cost of

measurement is g iven only by the price of count ing t ime t . Fig. 2 shows e

di f fe ren t shapes of the dependence of IG and costs, respect ively, on the a

value.

3 5 0


Fig. 2.

O �9

~.4

.c �9

0 2 t4---

.c

0- 0 4 8 12

sigma (s~) D e p e n d e n c e os I G and t h e C O s t os a n a l y s t s on i f '

( i n a r b i t r a r y u n i t s ) f o r a n a l y s e s i n v o l v i n g t h e mea-

s u r e m e n t os act iv i ty , other p a r a ~ t e r s " l t k e t n F i g . 1

However, for calculation of information profitability (see Eq. (2)), not

only IG and the cost r but also the relevance of information 3,s should be

taken into account. This case is shown in Figs. 3a and 3b. The IP curve in

Fig. 3a exhibits a maximum while the IG curve does not (for unbiased results).

We applied the dynamic model for calculation of the relevance

coefficient, s with the assumption that we need the results having a between 1%

and 10% relative for our decision making. It can be seen from the figure that

highly precise results (low a) are rarely obtained as the cost of an analysis

grows too rapidly.

Fig. 3b shows the dependence of IP on a computed for several bias levels

and for the same way of relevance coefficient calculation. The higher 6 value

the lower level of IP is obtained. Moreover, the maximum : o n the IP curve

shifts in direction to higher cr for highly biased results. In our case, the

information profitabili ty will reach a maximum for a between 5 and 7% relative

as a further decrease of ~, by prolongation of t , is too expensive.

In the case of multielement INAA, where a group of several elements should

be determined with a good information gain (Mgb relevance), the counting time

35 t


6

(13

C 5

b4

_I~ 3 LP

0

2 m

(_3

0 i i i i i " i

2 4 6 8 10 12

sigma (%)

Fig. 3a. Dependence os IG and IP on ~ ( i n a r b i t r a r y u n i t s ) DYnamic

~ d e l aS r e l e v a n c e c ~ s 1 6 3 c a l c u l a t i o n s r e s u l t m With ~r

b e t ~ e n I% and IO~ - see 3,s d = 0%; o t h e r p a r a m t e r s l i k e in F i g . I

2.C j

1.8

, , ~ ,

1.5 - - / / ~ \ ,~ 1.3

_.Q

;4-~ 1.0

// �9

(3 ,-~ 0 .5

0.3

0 , 0 i J i J i w r ~ J I ~ i i i i F I I I I 1

0 4 8 2

sigma (~) Fig. 3b. D e p e n d e n c e 0 s I P on ~ ( i n a r b i t r a r y u n i t s ) r e l e v a n c e c o e s 1 6 3 c a l c u l a t i o n l i k e i n F i g . 3 a 3 l e v e l s os 6 (0%, 5%

and 10%) ; o ~ h e r p a r a m e t e r s 1 i k e i n F i g . 1 352


should be chosen with respect to achieving a satisfactory a level for elements

having the highest detection limits in the group. Otherwise, we will obtain

zero values for some IG i and, consequently, rather low values of IP (Eq. (2)).

In general, an optimization of irradiation , decay and counting times should

be carried out (seeS).

Moreover, in the cases, where we need highly accurate results (precise and

practically without bias) to make a decision, we have to use a different model

for relevance coefficient calculation to obtain maximum information

profitability IP for such highly precise (and expensive) results.

Figs 3a and 3b show quite clearly that it is often not effective to

measure with extremely high precision especially if a relatively high nonzero

bias of results can be present.

Eq. (1) should be discussed in more detail. Any value 6 > 0 should be

substituted regardless of its statistical significance. However, in analytical

practice, when testing by means of reference materials (quality assessment),

we can find out that: 7

a) 5 _< at (m,c0/~n, where t(m,c~) is the critical value of the Student

distribution with m = n-I degrees of freedom, i.e., the bias is not

statistically significant on the level c~; then we only know about the true

information gain of the results that

x ~ - - x I 1 x 2 - - x t I n t 2 ( m , ~ ) ~ I G , ~ I n ( 3 )

6" ,~2ne ~ 2 6" ~2n'e ~

b) 6 > at (m,~)/,] n, i.e., bias is statistically significant and the 6

value found by means of RM should be substituted in Eq. (1).

Fig. 4 shows an example where 5% bias has been found and a CRM with a = r

5% (uncertainty about 2.5%) has been applied for QA. One or two samples of CRM

have been analyzed with each batch of samples. When we apply three measure-

ments (n=3), the area between the curves for 0 and 3% bias depicting the

obtainable information gain (see Eq. (3) for o > 2)) is rather wide and IG can

reach low levels. Below cr = 2% Eq. (1) has to be applied. The information gain

can be improved by using more, e.g. n=5, measurements. Then Eq. (3) should

be applied for o > 4, and the area depicting a possible IG is much narrower

and closer to higher levels of IG. Fig. 4 clearly shows that a simple increase

of the number of measurements will significantly improve the information gain

of the results.

353


Fig. 4.

3-

.c

. c 1

o

0

L

5 10 15 20

sigma D e p e n d e n c e o s IG on ~" ,i"or b i a s e d r e s u l t s a n d

d i s 1 6 3 n u m b e r o s m e a s u r e m e n t s

CRH w i t h ~ r = 6 % u s e d s QA, 6 = 6 % ; o t h e r p a r a m e L e r s

l i k e i n F i g . l

~ / z ~ IG F o r P e s u l t s w i t h s t a t i s t i c a l l y i n s i g n i s

b i a s ( s ~ 2: 2%) s n = 3

I ~ . IG s r e s u l t s w i t h s t a t i s t i c a l l y i n s i g n i s

b i a s ( s ~ ~ 4%) s n = 5

Influence of the quality of the reference material

Eq. (1) includes many parameters , among them the parameter k =

(~ /~)2 charac ter iz ing the re l iab i l i ty of a qual i ty assessment procedure. The

general Eq. (1) for 6 = 0 models a- case where the exis tence of a nonzero bias

is admi t t ed but it is proved exper imenta l ly that 6 = 0. Therefore , for k < 1

the IG according to Eq. (1) for ~ = 0 is h igher than that according to Eq. ( I )

wi thou t the second term on the r ight hand side (presence of bias is not

assumed). The d i f fe rence is a cont r ibut ion to the informat ion gain fol lowing

f rom the fact that a qual i ty assessment is used. This d i f fe rence depends on

the qua l i ty ( re l iabi l i ty) of the reference mater ia l used (at). It can be as

high as 0.5 natural uni ts (see Fig. 5).

3 5 4

5 -

w ithou 2 RM for QA_

5 .

' - 1-

-1

Fig. 5.


i i i i t i r i i I I r i ~ I i i f I I i i J i J i i J " l '

5 I0 15

sTgrno RM (~) Influence of RM on IG

= 6%, 6 = 0% ; other parameters like in FJg. I

The values of a and a substituted (by means of k) in Eq. (1) should be r

expressed in absolute concentration units both in the unknown and the

reference samples. The c, value may be a problem - some producers of CRMs r

indicate this value in the certificate. If it is not the case we can estimate

c~ r from the uncertainty (usually expressed as 95% confidence interval) by

using an estimation of the number N of determinations employed for f inding the

certified value as N ~ <15,20> (see12). We assume for simplicity that the

matrix of the CRM is very similar to that of the sample.

Practical aspects of the use of information theory f o r choosing the

optimum RM for QA can be demonstrated by means of Figs. 6-9. Fig. 6 shows a

choice of 5 CRMs availabe for the determination of arsenic in a f ly-ash type

of matrix. These CRMs differ by the producer, the certified concentrations as

well as by the uncertainties (and err) of these concentrations. We assume that

the concentration range of As in analyzed samples of f ly ash is known apriori

to be less than 1000 ppm and real As concentrations in most of the samples are

close to 100 ppm (x2-x 1 = 1000, x = 100 ppm in Eq. (1)).

The calculated dependence of IG on the value of a for the above mentioned

CRMs exhibit maxima for k=l (or r = or). It can be seen that, for given

355


Fig. 6.

4 - 1 As in Fly Ash

0

- - 1 " F T ' T " T " T ~ L ~ i i i 1 ~ i i i i i i i i r ~ 1 I n 1 . r l i i ~ i i ~ i i ~ -

0 5 10 15 20

sigma (%) Use os CRIdS for QA - determination os As in fly esh

6 = 0 * 4 , x 2 - x t = i O 0 0 p p m , x = t 0 0 p p m

I - BCR CRM 03B Fly Ash 48 ppm • 4.8%

- IR~T ECH Fly Ash 56.gppm • 7.6%

3 - IRANT E O P F l y A s h 79.1ppm • 0 . 4 %

4 - N I S T SRbl 1 6 4 8 U r b a n P a r t i c u l a ' t . e 1 1 5 p p m • e . 7 %

6 - NIST S R H 1 6 3 3 a F l y Ash 1 4 5 ppm • l O %

E

~3 2 tgn

�9 " 4 - -

c- 1

conditions, the BCR 038 Fly Ash yields the highest information gain when used

for QA purposes - other CRMs have higher certified 'values and uncertainty

ranges and, consequently, higher cr values. The disadvantage of using SRM r

1633a in this case is its relatively high a value. The use of this CRM for r

sample containing more than I50-200 ppm of As in quite adequate. Moreover,

uncertainties of CRMs produced in NIST are rather too conservative (high) in

comparison with comparable CRMs from other vendors.

The determination of As in fly ash is a relatively simple case of

practical analysis. The situation can be much more complicated, as in the case

of the determination of Cd traces in biological materials (of living origin).

The range of possible Cd concentrations can cover almost 6 orders of magnitude

from 0.0002 to 200 ppml Here, only the use of CRMs with concentrations similar

356

L OBRUSNIK, K. ECKSCHLAGER: APPLICATION OF REFERENCE

Fig. 7,

7-

5.

C

0 C~

0 3.

- 1

s Cd in Biological Material 2 ~ t r a t i o n ) , ~ ~ i

1

i i i i l [ r i F [ I F I J r i i i i j l l l t l r l l l [ ' T l r l l r i ~

5 ~0 15 20

sigma (~) Use 0s CRHs s Ok - determina%ion of Cd in

cal matenial

6 = 0 % , x 2 - x t = 3 0 0 p p m , x = 5 p p m

I - N I S T S R M 1 5 6 6 O y s t e r 3 . 5 p p m • 1 1 %

2 - NIST SRM 1577a B. Llver 0.44 ppm • 14%

3 - N I E S C R M 6 Mussel O. B2 p p m • 3.7%

blologi-

to or lower than the concentrations of Cd in real samples yields a reasonably

high information gain.

Figs 7,8 and 9 show this situation for three levels of Cd concentrations

in real samples: 5, 0.05 amd 0.01 ppm (and apriori known concentration

intervals of 300, 1 and 0.1 ppm, respectively). For the highest concentration

region (Fig. 7) NIES CRM-6 Mussel and NIST SRM 1577a Bovine Liver give the

best information gain while NIST SRM 1566 Oyster Tissue has a relatively high

absolute a value (higher concentration level and higher uncertainty). The use r

of the IAEA H-8 Horse Kidney CRM with certified Cd concentration 189 ppm -+

2.4% contributes no positive IG, as the certified level (and %) is too high

in comparison with the Cd concentrations in the analyzed samples.

For medium concentrations (0.05 ppm of Cd), 4 CRMs with a milk matrix can

be used (Fig. 8). The highest information gain can be achieved by using

uncontaminated milk CRMs with rather low Cd concentrations, like SRM 1549

357

1. OBRUSNIK, K. ECKSCHLAGER: APPLICATION OF REFERENCE

Fig, 8.

5"

C

�9

0 3-

c

Cd in Biological Material 7- (lOW concentration)

1

/

0 5 10 15 20

sigma (~) U s e o s C R M s s Q A - d e t e r m i n a t i o n o s C d i n

c a l m a t e r i a l

6 = 0 % , x 2 - x I = 1 p p m , x = 0 . 0 5 p p m

- NIST SRM 1549 Milk

3 - BCR CRM OG3 M i l k

3 - BCR CRM 160 M l l k ( s p i k e d )

4 - BCR CRM 151 M i l k ( s p i k e d )

b i o l o g i -

0 . 0 0 0 5 p p m • 4 0 %

0 . 0 0 2 9 p p m • 4 1 %

0 . 0 2 1 8 p p m • 6 . 4 %

0 . 1 0 1 p p m • 7 . 9 %

(NIST) and CRM 063 (BCR) despite the uncertainties in these CRMs being at a

relative level of 40%. Quality assessment by means CRMs with higher Cd

concentrations like SRM 1566, CRM-6 or SRM I577a, cannot yield any information

gain as the certified concentrations are too high in comparison to the 0.05

ppm concentrations of Cd in the samples. It can easily be proved by using

Eq. 1). The CRMs with substantially higher certified concentrations and

low relative uncertainties can be used for the assessment of calibration

(standards, comparators).

Fig. 9 shows and extreme case of analysis of Cd in concentrations at the

0.01 ppm level. In this case, only 3 CRMs with the lowest certified

concentrations (SRM 1549, CRM 063 and CRM 150) can contribute a positive

information gain for quality assessment. The SRM 1549 Milk (NIST) is the best

CRM which could be found for this type of analysis even though the uncertainty

358

Fig. 9.

3

C

C3

O

1

I. OBRUSN1K, K. ECKSCHLAGER: APPLICATION OF REFERENCE

Cd in Biological Material (extra row concentration)

I 1 1 ; I I I T I ~ ] 1 1 1 1 1 I ~ ~ l f } 1 1 1 1 ] 1 1 ~ 1 f I I I I I I

0 5 10 15 2 0

s;gma (~;)

Use os CRMs s OA - d e t e r m i n a t i o n os Cd i n

c a l m a t e r i a l

5 = 0 % , x 2 - x i = O . t p p m , x = 0 . 0 1 ppm

1 - N I S T SRM 1 5 4 9 M i l k

2 - BCR CRM 063 M i l k

3 - BCI~ CRM 1S0 M i l k ( s p i k e d )

b i o l o g i -

0 . 0 0 0 5 ppm • 4 0 %

0 . 0 0 2 9 ppm • 4 1 %

0 . 0 2 1 8 ppm • 6 . 4 %

of the cer t i f ied concentra t ion is 40% relative! It can be expla ined by the

fact that more impor tan t than the relat ive value is a (or uncer ta in ty) r

expressed in concentra t ion units and its ratio to a of the analyt ical method

expressed in the same units. For instance for the last case (Fig. 9) these

values are: 0.00043, 0.0026 and 0.003 ppm for CRMs SRM 1549, C R M 063 and r

C R M 150, respect ively. Other pract ical examples can be explained in a s imi lar

way.

All three f igures show the dependence of IG on the ~ value over a wide

range. Usual ly , we do not expect to achieve bet ter precisions (a) for such

kinds of analysis than 5 - 10% relat ive, in the ext reme case even 10-20%

relat ive. A steep decrease of IG values for h ighly precise results,

p rac t ica l ly for all cases shown in Figs 7,8 and 9, is due to our inabi l i ty

assess the bias of so precise results by means of CRMs wi th much h igher

cr levels. r

359


All the above-mentioned examples of using information theory for the

evaluation of quality assessment by means of CRMs nicely show that the proper

choice of CRM is very important especially with respect to concentration

levels of the analyte. Moreover, an absolute value (in units of concentration)

of the CRM uncertainty has a crucial effect as it was pointed out by

RASBERRYJ a Information theory proves that for extreme trace analysis even the

use of reference materials with relatively wide uncertainty intervals, like

40% relative in the case of SRM 1549 Milk Powder, can increase the information

gain of the results. From this point of view, new CRMs with very low "natural

levels" of element concentrations - "second generation CRMs" like human

serum 14 will be very useful.

Influence of blank:

In analytical practice, especially in trace analysis, bias is frequently

determined by carrying out a blank experiment 6 o. By subtracting it, the bias

is eliminated or at least reduced; variance, s however, increases by the blank

experiment variance o 2, so that u

= ~(612 + ~02) (2 )

where (7 s is the measurement variance without blank subtraction. i

It has been proved that subtraction of the blank substantially increases

the information gain. z Therefore, blank estimation and subtraction should not

be omitted in NAA procedures used for the determination of extreme trace con-

centrations or in other cases influenced by the blank (INAA of aerosols on

filters, etc.).

Conclusions

This work has shown advantages of information theory for the evaluation

and optimization of some INAA procedures with respect to measurement

parameters like bias, profitability of the results, quality of reference

materials used for QA and blank. Many conclusions in this work could be

applied also to other modern analytical methods. Information theory

significantly helps to choose suitable reference materials for quality

assessment of routine analytical procedures not only with respect to matrix

and analyte concentrations in the sample but also to concentrations and

uncertainties of certified values in the CRM used. This work has proved that

in extreme trace analysis CRMs with relatively large uncertainties (but with

small absolute errors) can be very useful.

360


References

1. K. ECKSCHLAGER, V. ST~P,~NEK, Anal. Chem., 54 (1982) ll15A. 2. K. ECKSCHLAGER, V. ~TI~PANEK, Information Theory as Applied to Chemical Analysis, Wiley, New

York, 1979. 3. K. ECKSCHLAGER, V. ~TEPfiaNEK, Analytical Measurement and Information, Research Studies Press,

Letchworth, 1989. 4. K. ECKSCHLAGER, Collect. Czech. Chem. Commun., 56 (1991) 505. 5. I. OBRUSN~K, K. ECKSCHLAGER, J. Radioanal. Nucl, Chem., 112 (1987) 233. 6. I. OBRUSN~K, K. ECKSCHLAGER, Anal. Chem., 62 (1990) 565. 7. K. ECKSCHLAGER, J. FUSEK, Collect. Czech. Chem. Commun., 53 (1988) 3021. 8. K. ECKSCHLAGER, V. ~TI~PANEK, Chemometr. Intel. Lab. Sys., 1 (1987) 273. 9. K. DANZER, K. ECKSCHLAGER, D. W/ENKE, Frasen. Z. Anal. Chem., 327 (1987) 312.

10. D. BECKER, J. Radioanal. Nucl. Chem., 13 (1987) 5. 11. K. HEYDORN, J. Res. NBS, 93 (1988) 479. 12. J. MUSIL, Chem. listy, 80 (1986) 1233. 13. S. D. RASBERRY, J. Res. NBS, 93 (1988) 213. 14. J. VERSIECK et al., Anal. Chim. Acta, 204 (1988) 63.

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