118 Nuclear Instruments and Methods in Physics Research B34 (1988) 118-121 North-Holland, Amsterdam

PIXASE: A COMPUTER PACKAGE FOR EVALUATION OF PIXF, SPECTRUM SERIES Part I: Spedrum evaluation

L. ZOLNAI and Gy. SZABd

Institute of Nuclear Researek of fhe ~unguri~ Academy of Scieptces, H-4001 Debreeen, Pf: 2, Hungary

Received 5 November 1987 and in revised form 1988

The spectrum evaluation part of a programme package for PIXE spectrum analysis is discussed. Attention is focussed on the method used for the evaluation of the pileup contribution in the PIXE spectra. Different methods for the evaluation of series of the PIXE spectra measured on samples having identical matrix composition are described.

Proton induced X-ray emission (PIXE) has been widely used in recent years for trace element analysis. To complement the existing possibilities for element analysis in our institute a PIXE setup was built for the analysis of thin and thick samples. During that stage of the work a programme package for PIXE spectrum analysis was developed [1,2J.

With the increasing experience it was decided to write a new computer package (PIXASE) which is im- proved in the following points: a} the handling of the pile-up contribution is more

exact; b) the L lines also can be used for the analysis; c) the secondary fluorescence effect is treated exactly.

The PIXASE programme package consists of four programmes. The code ASELES to be discussed in details here is used to analyse PIXE spectra. The code PIXEKL, which is used to calculate the X-ray yield and the relative intensities of lines of the elements in a given matrix will be pubIished later 131. Two smaller programs were developed to make the use of ASELES easier: PREASE to estimate the starting values of the parame- ters to be fitted and ASEDIT which is a menu-driven input file editor for ASELES.

2. Speetruin analysis

Several approaches listed in ref. [4] have been made to the problem of the analysis of PIXE spectra. Roughly speaking they can be divided into spectrum stripping and spectrum synthesis techniques. Our approach be- longs to the latter set. In this technique a model spec- trum for the pulse height spectrum is used in a least- squares fitting (LSF) procedure to determine the param-

0168-583X/88/$~3.50 0 Elsevier Science Publishers B.V. (North-Holland Physics Publishing Division)

eters of the model and thus the peak areas. The princi- ple of the LSF is based on the ~~~ation of the x$(p) reduced x2 function in the space of the p = (pI . . . pr) parameter vectors. The xi fuction is given by:

where nr and n, are the first and the last channel numbers of the region to be fitted; f is the number of the fitted parameters; S(i) is the measured, Tr( i) is the model function value and w(i) is the weight for the channel i, usually

i

S(i) w(i)= ,,

if S(i) f0,

if S(i) =O. (2)

The T(i) model function can be split into three parts, one being the sum of the X-ray peaks for all elements included in the analysis, the other describing the smoothly varyng background and the third one describ- ing the pileup con~bution.

According for the PIXE spectrum at channel i the yield is given by

T(i) = 5 pj STRUCTU~~~ d) j=l

~p~~BACKGR~UND( i)

+p5sPILEUP( i), (3)

where STRUCTUREj(i) is the yield of the jth group of Iines (this notation makes it possible later to use the program for the determination of the intensity ratio of the different lines belonging to the same element), n, is the number of groups in use (in the present version 12, LS 32). It should be mentioned that the indexing of

L. Zolnai, Gy. Szab6 / Computer package for evaluation of PIXE spectra 119

the components of the p parameter vector is not con-

tinuous for technical reason. BACKGROUND(i) and PILEUP(i) are the background and pileup contribu- tions for channel i respectively.

2.1. ~t~ctures

In our technique if the intensity ratio of the different lines is known for every element in a given matrix, one STRUCTURE,(I) in (1) represents the group of the different lines belonging to the jth element.

STRUCTUREj( i) = xRjkPjk( i)$ (4) k

where Rjk is the relative intensity ratio of the line k of element j to the main line of the structure j is and Pjk( i) is the characteristic peak shape function. Usually the most intense lines belonging to the elements are chosen to be the main lines.

In our model R,, is chosen to be 1. The licjk with the effective cross-sections for the Rj, main lines can be measured for the given setup and matrix, using stan- dards but they can be calculated including all other effects (absorbtion in the matrix and in the different filters; secondary fluorescence effect, detector efficiency etc. [2,3]) The escape peaks are treated as normal peaks, their intensity ratios to the main line are also calculated.

All these data are stored in a reference library with the energy of the different lines and with the atomic mass of the elements. This library is the output file of the code PIXEKL [37_

2.i.2. Peak shape f~nc~~#n The peak shape function was chosen to be almost the

same as in [5]. Because of the normalization for Rj, its form is given by

pjk(i) = (GAUSS,~(~) + TAILjk(i)

+STEp,,(i))COR&)/CORjk(i),

where (5)

GAUS& ( i) = exp -(i--l*jk)2

i i 25;

TAIL,,(i) = i

pso exp~~~~(~-~~~)) if i<pjk. o.

if i> Cqik.

STEPjk( i) = ps2 erfc

Sk = P53 $- Ps4Ejk 9

pjk = PSS + p%Ejk + PSI$)

(6)

where Ejk are the energies of the lines for the ith element.

2.2. Background

The background is given by the following formula:

BACKGROUND{ i)

= ~~BG~O~( i ) 3 p~~BGRBREM( i >

~~~~BGR~IGH( i ) . (7)

The three terms on the right-hand side of (7) have approximately the same form as in [5] (if the channel-energy function is almost linear):

BGRLOW( i) =p41 ew( p42i),

BGRBREM(i)=: ~XP 5 p42+j(i-io)j-1 ,

i I

09 j=l

BGRHIGH(i) =p4s exp(p,si).

In (8) i, is a fixed channel number used for techni- cal reason. It is usually chosen at the middle of the fitted region.

2.3. Pileup contribution

For calculation of the pileup contribution the first order approximation of [6] has been applied. If the sum of the first two terms in (3) is denoted by P(i), the pileup contribution is given by:

PILEUP(i)= j,$n F(i’)P(i-i’), /

(9)

The sum in (9) is made on the subset of the channels in the fitted region where a) the counting rate is greater than a level given to the

program, b) E(i) s E(i’) + E(i - i’) < E(i + 1).

The E(i) is the channel-energy function (the inverse of the’function p(E) in (6)).

To show this effect of pileup contribution the PIXE spectrum of a red cell sample was measured with the setup described in [2]. During the measurement an electronic pileup rejection system [7] was applied. The total count rate for the spectrum was about 1000 cps. Under these conditions the pileups in the spectrum are the result of the finite resolving time of the pileup rejection system. The measured spectrum was evaluated with different limits for the counting rate. The evaluated spectra are shown in fig. 1 and the data belonging to the different cases in table 1. Through the change of the background belonging to the different cases all con- centrations belonging to the elements involved in the analysis were more or less changed. Especially the ele- ments (in this case the manganese) situated to the place (in the region between channels 12%180), where the pileups are concentrating, change their concentrations strongly. As one can see the apparent Mn concentration

120 L. Zalnai, Gy. Szab6 / Computer package for eualuation of PIXE spectra

channel number

Fig. 1. The effect of the number of channels taking part in pileup calculation for the fitted spectra. Dots: measured points, squares: measured points, channels taking part in pileup calcu- lation, solid line: fit, dashed line: calculated real background,

hatched ares: calculated pileup contribution.

as evaluated the computer program is drastically de- creasing with increasing number of channels taken into account for the pileup calculation. This corresponds to the data known from the literature [8] i.e. in red cell samples the Mn concentration is below the detection limit of the PIXE method (< 0.07 ppm). It should be mentioned that the errors given in table 1 contain the statistical errors only. For other samples similar effects can be observed. It is surprizing that the counting rate in the channels used for the pileup calculation is not so large.

Table 1 The effect of the increasing number of spectrum channels taking part in pileup calculation for calculated Mn concentra- tion values

SptX- Counting rate Number of xi Mn-cont. ttum limit for “pileup” -__ [ppm]

“pileup” channels channeis

kP4

loo 0 4.7 25.9 k2.2 b) 70 6 6.2 41.6 f 3.5 c) 40 11 5.3 0.0003 * 3.8 d) 20 22 3-5 0.0003 I? 2.9 e) 5 43 2.8 0.0003 +_ 2.6

The above mentioned technique of the pileup calcu- lation is a litle bit time-consuming that is why we have limited the calculation for channels where the counting rate is relatively high (the m~mum number of such channels is 64).

2.4. Iteration process

In minimalization of the xi a simple grid search technique [9] has been applied. To avoid getting non- physical parameter values the change of the parameters is limited through their minimum and maximum values given as input data for the program.

2.5. Concentrations

The concentrations for the elements included into the analysis are calculated from the peak areas of the main lines in the usual way. In case of absolute mea- surements the Cj concentration of the j th element is given by:

where A, is the area belonging to the main line of element j, iUj is the atomic mass of the jth element, in atomic mass units, n is the number of protons collected during the measurement, f2 is the solid angle of the detector in steradians, W’J is the effective cross-section corrected for the absorption, selfabsorbtion, target thickness, the angle of the beam with respect to the sample normal, the angle of the detection with respect to the sample normal and the X-ray energy dependent detector efficiency for the main line of the jth element, N is Avogadro’s number. The number of protons is calculated from the integrator counts stored in the spectrum and from the coefficients of the integrator which are among the input data. The solid angle of the detection is also given as input.

L. Zolnai, Gy. Szabb / Computer package for evaluation of PIXE spectra 121

3. Evaluation of the series of spectra

In the practice of the PIXE work the samples are quite frequently very similar to each other. It means that the experimental arrangement and the macromatrix containing the trace elements are not changed. For these cases the program discussed above has special modes of its working regime.

For one spectrum the program can work in nonlin- ear or linear mode. In the linear case all nonlinear parameters are fixed and in the calculation of pileup contribution the function S(i) is used instead of F(i). In this case the shape of the background, the peaks and the pileup contribution are not changed, only their amplitudes are fitted through the linear decomposition of the main constituents of the spectrum.

For series of spectra there are three combinations of the evaluation modes: a) All spectra in the series are evaluated in nonlinear

mode. In this case the fitted parameter values are serving as starting values for the next spectrum.

b) The first spectrum is fitted in nonlinear way, the remaining part of the spectrum series is fitted in linear mode, fixing the values of the nonlinear parameters at the values received in the nonlinear fitting procedure.

c) All spectra are fitted in linear mode. In the cases of b) and c) the first linear fitting the

program sets up a library file of the calculated spectrum components - if no such library file exists with the same values of the nonlinear parameters. In these cases the spectrum of the pileup contribution is calculated for every spectrum.

In case of the evaluation of a whole spectrum series a list of all the elements which could appear in the spectra is read in only once except in the case of a) where it is possible to change this list for every spec- trum.

4. Application

In its present form the program ASELES has the following limitations. The maximum number of chan- nels to be evaluated is 512, the maximum number of

lines is 128, the maximum number of fitted parameters is 32.

We have executable versions of the program on PDP-11/40, DEC-350 and IBM PC/XT/AT. A more detailed user’s guide of the programme is available from the authors on request.

The program is routinely used to evaluate thin and thick biological samples and mainly thin aerosol sam- ples.

5. Conclusion

After several stages of the development the computer package PLXASE is in routine operation at our labora- tory. The special way of calculating the pileup contribu- tion has made it possible to improve the description of the PIXE spectrum shape compared to the earlier ap- proaches listed in ref. [4], and consequently improve the accuracy of the analysis of the PIXE spectra.

The authors are very grateful to Dr. Ildiko Borbely- Kiss for valuable discussions on the subject of the problems of the spectrum evaluation in different stages of the program development.

References

[l] L. Zolnai, ATOMKI KBzl. 24 (1982) 229.

[2] I. Borbely-Kiss, E. Koltay, S. Laszlb, Gy. Szabo and L.

Zolnai, Nucl. Instr. and Meth. B12 (1985) 496.

[3] Gy. Szabo, and L. Zohmi, submitted to Nucl. Instr. and

Meth. B.

[4] U. Watjen, Nucl. Instr. and Meth. B22 (1987) 29.

[5] E. Clayton, D.D. Cohen and P. Duerden, Nucl. Instr. and

Meth. 180 (1981) 541.

[6] F.H. Temey, Nucl. Instr. and Meth. 219 (1984) 165.

[7] T. Lakatos, Proc. of 10th Int. Symp. on Nucl. Electronics,

Dresden (10-16. April, 1980) p. 204.

[S] G.V. Iyengar, W.E. Kollmer, H.I.M. Bowen, The Elemental

Composition of Human Tissues and Body Fluids (Verlag

Chemie, Weinheim, New York, 1978).

[9] I.A. Slavic and S.P. Bingulac, Nucl. Instr. and Meth. 84

(1970) 261.