An intercomparison of spectral data processing techniques in PIXE

Nuclear

204

AN INTERCOMPARISON

OF SPECTRAL

Instruments

and Methods

DATA PROCESSING

J.L. CAMPBELL”, W. MAENHAUT 21, E. BOMBELKA”‘, J.A. MAXWELL It. J. PALLON ‘) and J. VANDENHAUT~

in Physics Research B14 (1986) 204-220 North-Holland. Amsterdam

TECHNIQUES

E. CLAYTON

IN PIXE

4), K. MALMQVIST

5),

‘)

” Cuelph Ware&m Program for Graduate Work in Physics, Untuersity of Guelph, Guelph. Canudu .h’l G 2 WI ‘I Instituut vow Nuclecrire Wetensrhappen, Rijksunioersrteit Gent, Proeftuimtraat 86, B 9000 Gent, Belgium ‘) Fachbereich Physik, Universitiit Marburg 0355 Marburg/Lahn, FRG 41AAEC Research Establishment. Privute Mail Bag. ‘ Sutherland. NS W 2232, Austruliu ‘) Department of Nuclear Ph_wics, Lund Institute of Technolom, Siilvegutan 14. S- 223 62 Lund, Sweden Received

3 September

1985

Least-squares fitting codes developed independently at five different laboratories are used to analyse PIXE spectra of a set of biological, environmental and geological specimens. A detailed comparison of the resulting five sets of X-ray intensity data reveals a remarkahly good agreement among the five techniques, despite major differences in their methodologies. This conclusion strengthens PIXE’s claim to have reached maturity as a trace element analysis technique.

1. Introduction In terms

of experimental

technique,

elemental

analy-

(PIXE) has reached a high degree of maturity [l]. The trace element masses present in a very thin specimen, i.e. one that only negligibly degrades the proton energy, can be determined by direct comparison of X-ray yields with the yields from commercially available thin standards. If the thickness is finite (a few mg/cm’) corrections can be computed to adjust observed X-ray yields for the effects of proton energy loss and X-ray attenuation [2]; this is straightforward when target thickness is known (e.g. powder layers), and in other cases (e.g. dried liquid droplets) the thickness can be measured via a Rutherford backscatter measurexllent of the transmitted proton energy [3]. Internal standards can be added to specimens before the preparation of thin targets to further refine analytical accuracy [2]. In the other extreme case, viz. that of specimens that are thick enough to stop the beam, calibration against thick single-element standards provides an effective cancellation of various sources of error (e.g. ionization cross sections and charge integration), thus providing a high degree of accuracy [4]. Many studies of the accuracy of PIXE have been reported, usually based on standard reference materials. The quality of results achieved reflects all stages of the analysis, including specimen preparation, specimen homogeneity, target backing, target uniformity, chamber design, beam-handling, standardization, and spectral data processing. We believe that the last of these is now a (if not the) sis by

proton-induced

X-ray

emission

0168-583X/86/$03.50 0 Elsevier Science Publishers (North-Holland Physics Publishing Division)

B.V.

principal determinant of PIXE’s accuracy, especially in the case of elements of low concentration in a multielement specimen. While a broad consensus has emerged on most of the topics mentioned, there does not exist a full appreciation of how different approaches to spectral analysis affect the extracted X-ray peak intensities. We therefore judged it worthwhile to carry out an intercomparison exercise limited specifically to spectral data processing, and explicitly excluding any experimental aspects such as standardization. In principle. if sufficient different approaches to spectrum analysis were available, this would allow us to isolate the uncertainties of data analysis from all the other aspects of PIXE.

2. Outtine of the inte~omparison

exercise

A set of PIXE spectra was recorded using the PIXE system at the University of Gent. The spectra covered a representative group of specimen types together with a large number of thin single-element standards; details are given in sect. 3 below. The Gent system has been described in detail in this journal [S] and so only a few salient points are needed here. A 2.4 MeV proton beam from an isochronous cyclotron enters a chamber with a Si(Li) X-ray detector at 135” to the beam direction. The normal to the target plane is inclined equally (22.5’) to the beam axis and the target-detector axis. The spectra were distributed on magnetic tape to the various authors of this paper. The participants were asked to extract the areas of the principal X-ray peaks for all elements observed by them in each spectrum.

J. L. Camphell ef al. / Intercomparison

They were also asked to provide the ratios of these areas to those of the corresponding lines in the appropriate standard spectra. For elements up to and including Sb, the principal peak is defined as K, (sum of K,, + K,,); for heavy elements it is L, (= L,, + Ln2). For the light elements Na, Mg, Al, Si the sum K, + K, was acceptable. The peak areas requested are those observed in the actual spectrum, i.e. not corrected for filter attenuation, detector efficiency or self-absorption (although these factors may be employed during the data processing). As ancillary information participants were supplied with ref. [S] which gave full details of the efficiency of the Gent Si(Li) detector; details of the attenuating filters used in recording the spectra were also supplied. This ensured a common approach on these matters. The results were collated by the two first-named authors, who are responsible for the conclusions expressed below.

3. The spectra

All the spectra were obtained with either a 660 ym thick Mylar absorber or a composite “funny filter” placed in front of the detector. The latter comprised a 52 pm beryllium foil and a 324 urn Mylar foil with a 6.22% circular aperture; the hole fraction was obtained by experimental measurements of various X-ray intensities with and without the filter present. The main standard targets were a set of thirty Micromatter standards; these are mono-elemental films of thickness 20-60 us/cm2 on a 2.5 pm Mylar substrate. For a few elements standards were prepared at Gent by spotting simple compounds or evaporating elements

sum

of PIXE

peaks

Channel (high statistics).

205

onto Mylar foils; these were used where no Micromatter standard of a specific element was available and where high counting statistics were desired. Various biological samples were prepared by gluing finely powdered material to aluminized Mylar backings. Materials used were NBS bovine liver, NBS orchard leaves, human liver and human kidney; each target contained added yttrium or silver as a dopant. The area of each deposit was about 1 cm2 and it was bombarded with an 8 mm diameter beam. Target thickness was about 4-5 mg/cm2. An additional run to very high counting statistics was done for the bovine liver and orchard leaves targets; these runs are identified by the letter B. Four Nuclepore aerosol filters were used, three of which had been exposed in Katowice, Poland and contained less than 1 mg/cm2 deposit on the surface of the 10 pm thick filter. The deposit area exceeded the beam area. Three geological targets were prepared, again by powder deposition. The first was made from about 2 mg of fine fired clay powder sandwiched between two thin Formvar films, with the sample entirely enveloped by the beam. The second was a 5 mg/cm2 sample of soil powder placed on aluminized Mylar and covered with thin Formvar; the sample area here was larger than the beam. The third one consisted of about 5 mg/cm2 of USGS SGR-1 powder on aluminized Mylar and covered with thin Formvar; the deposit area was again larger than the beam. Figs. l-6 show a selection of the recorded PIXE spectra. Spectra were also recorded from all substrates used and from the case where no target was present. To provide some further indication of the detector’s intrin-

600

Fig. 1. Bovine liver spectrum

data processing

1000

Number

Fig. 2. Orchard (high statistics).

leaves spectrum

Number

Number

Fig. 3. Human

kidney spectrum.

1000

800

Channel

Channel

100

100

200

300

LOO

500

600 Channel

Number

Fig. 4. Nuclepore

(A) spectrum.

J. L. Cumphell et al. / Intercomparison

of PIXE data processing

1000

800

Channel

207

Number

Fig. 5. USGS rock spectrum

sic lineshape, spectra from two radioactive sources, 55Fe and ‘09Cd, were recorded. Almost all of the spectra were recorded with the 30 mm’ x 3 mm Si(Li) detector whose properties were thoroughly investigated by Maenhaut and Raemdonk in ref. [5]. The main property needed here is the relative efficiency, which may be calculated from the known detector thickness, the known thicknesses of absorbing layers of beryllium, gold and silicon, and a model for the Si X-ray escape process. Due to the untimely demise of this detector the blank spectra and the USGS powder spectrum had to be accumulated with a new detector. Its spectral response above 3-4 keV was similar to that of its predecessor. Ref. [5] showed that the lineshape of the main detec-

tor had minimum low-energy tailing at around 5-10 keV. With decreasing energy the tailing increased steadily due to degradation in the dead layer. With increasing energy above 10 keV, the tailing also increased; presumably this is due to Compton-scattering of photons en route to the detector. These two effects in Si(Li) detectors are discussed in detail by Campbell et al. [6]. Participants using non-Gaussian “additives” in their lineshape representation were requested to submit the areas of the Gaussian components.

4. Data processing techniques Rather than describe sequentially the particular methodology of each participant, we shall describe first the general approach common to most PIXE analysts; then we shall indicate the special variations on this main theme taken by each participant. The basic philosophy is to construct a numerical model of a spectrum and then vary its parameters to achieve a best fit to the measured spectrum. The matching is usually done by either linear least-squares or nonlinear least-squares fitting. 4. I. X-ray data

LOO

600

Channel Fig. 6. Spectrum

from copper

standard

with mylar

Number

filter.

To model the K X-ray spectrum of an element one needs first of all a data-base containing the energies and relative intensities of the K X-ray components for all possible elements of interest in the region 10 < Z < 60; this must be supplemented with a similar L X-ray data-base for heavier elements. X-ray energies are well known, but relative intensities less so. There are several

208

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x

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Cr

L

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G

GU

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--

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3720

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1.02 .&

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1.02 .96

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S/S Fig. 7. S/g

for the K X-ray standards with Mylar filter.

tabulations of theoretical relative K X-ray intensities, the Dirac-Hartree-Fock calculations of Scofield [7] being the most sophisticated. The most recent compilation founded on experimental data is that of Salem et al. 181. Some PIXE workers however prefer to determine the relative K X-ray intensities from their own protoninduced spectra. Modelling of the L X-ray spectrum is more complicated because there are three L subshells as opposed to the single K shell. Theoretical transition probabilities are again availabie from the work of Scofield [9] for each of the L,, L,, L, subshells. Various intensity ratios are also given in the Salem et al. review IS]. But the initial distribution of subshell vacancies depends upon the relative ionization cross sections ( uL,) and the probabilities of Coster-Kronig vacancy transfer processes (f,,). Thus the relative numbers of Lt. L, and L, X-rays are N, = e,w,,

4 = (02 + ~,z)ws,

(1)

with W, the fluorescence yields. Each of the groups is then subdivided into the various L,, L,, L, X-ray lines by multiplying N, by the radiative branching probabilities [9]. There are various theoretical treatments of cross sections, but presently no extensive and accurate tabulations which would lend themselves to easy interpolation. Some PIXE groups use L subshell cross sections derived from the ECPSSR treatment of Brandt and Lapicki [lo], but various experimental studies e.g. ref. (111 indicate discrepancies between these predictions and experiment. For this reason, and due to the complexity of the calculations, severat PIXE groups simply determine the relative L X-ray intensities experimentally using thin targets of the elements of interest to them. Krause [12] has prepared empirical tables of the fluorescence and Caster--Kronig probabilities based on experimental data: the most sophisticated theoretical

209

J.L. Campbell er al. / Intercomparison of PIXE data procmq

treatment is that of Chen et al. [13], which employs Dirac-Fock atomic wave functions. From whatever X-ray data base is chosen, one obtains for each element n the relative intensities R,, of its various K or L X-ray lines; in the absence of attenuators and assuming 100% detector efficiency these would be the relative areas of the corresponding peaks in the Si(Li) spectrum. For the dominant line the corresponding component of the vector R,, is set equal to 1.0. 4.2. Spectrum

of an element

The action of the detector/analyser system is to convert an X-ray spectrum (X-ray intensity versus energy) into a pulse height spectrum (counts versus channel number); x denotes channel number. In constructing the model pulse height spectrum for a given element (designated n), the mth characteristic line is represented by a Gaussian or quasi-Gaussian peak whose centroid C,, (in channels) and width CT~,,~ are determined from the energy E,?,,, by C,,,, = P, + P&,m

(2)

‘Jnm= (PC + PdEnm)1’2.

(3)

These relations reflect the linearity of spectrometer response and the peak broadening due to both noise and charge formation statistics. Tailing on the low-energy side of peaks, due to incomplete charge collection may be catered for by adding a flat step, exponential tails, or other artefacts to the left-hand side of the Gaussian [6]. The parameters of these components may, like C-J,be functions of energy. We use F(x-, n. m) to denote the overall peak function and G(x. n. m) its Gaussian component. The relative areas of the m peaks from element n are required to be in the ratio of the corresponding X-ray line intensities. The latter are denoted R’,, and are obtained by correcting the basic “library” in filters and values R ,i,n for the effects of attenuation detector efficiency. A further correction is required if the specimens have finite thickness, since each photon energy has a different attenuation factor within the target. This is a straightforward correction provided the thickness and the major element composition of the target are known [2,3]. Thus the spectrum of full-energy peaks from an element n is xF(x, V1

n. m)R:,,.

(4)

In addition each of these peaks is accompanied by a silicon K X-ray escape peak whose energy is nominally 1.742 keV less than its parent. A consideration of the escape process leads to a simple expression for the intensity ratio fEsc of an escape peak to its parent; this can be parameterised as a simple function of photon

energy. as has been Reed and Ware [14] expression has been with experiment in ergetic photons. We now have for S,,(x)=xF(x, +xfEsc(n, m

done by various authors including and Johansson [lS]. The Johansson shown to give excellent agreement a recent study [6] using monoenthe overall spectrum

of an element

n. m)R’,,

m)G(x, n, m)R’,,,

(5)

where the Gaussians representing the escape peaks are constructed at centroid channels 1.742 keV below the centroids of the main peaks. Since the escape peaks are of low intensity it is not necessary to accord them the full lineshape representation F,,,,. 4.3. Characteristic portion of a PI/YE spectrum The characteristic X-ray component of a multielement spectrum is now obtained by summing the model spectra of these elements believed to be present. The height of the dominant line for each element n is taken as an unknown variable P,,. The overall spectrum is then s(x)=~P,s”(x). ,l

(6)

At sufficiently high counting rates. pileup of peaks will be created in the spectrum by the random summing of the most intense X-ray lines. An elegant means of incorporating these peaks in the model spectrum [15] is widely used in PIXE. This is based on the concept of a single extra “element” due to pileup. 4.4. Background in PIXE spectrum Various approaches have been tried to deal with the continuum background that arises from secondary electron bremsstrahlung and other processes. The first is to use a suitable analytical function B(x) with the smallest possible number of free parameters to model the background; various such models have been proposed. The full PIXE spectrum is then obtained by adding the background model B(x) to the peak model S(x) of sect. 4.3. A different approach is to have the free parameters of B(x) determined at the outset by fitting the function to a set of minima in the experimental spectrum; these should be chosen as remote as possible from peaks, but in “crowded” spectra this can be difficult. The difficulty can be obviated by using an iterative mathematical technique to remove peaks and progressively reduce the spectrum to the background continuum. This continuum may then be used along with the peak model in conducting the least-squares fit, or it can be subtracted from the spectrum prior to fitting.

The background

This avoidance of mathematical assumptions about the background’s form is characteristic also of the top-hat filter technique. The latter applies a single mathematical filtering operation which effectively removes lowfrequency components, i.e. the continuum background, from raw spectral data. The final alternative is to record a spectrum from a matrix similar to that of the specimen; this could then be normalised at some energy to the experimental data and stripped off or it could be built into the spectrum model with its height as a single parameter of the fit.

B(E)=R,,+B,explB,,(E-E,)l b[max]

+B,,ABS(E).exp

B,,(E-E,)k

1

(8)

with E, a constant. Here the first two terms represent background not affected by absorption, and the third is the bremsstrahlung background, which is affected by an energy-dependent efficiency-cum-abso~tion factor. In the least-squares fit the calibration parameters P, . ‘ . Pr, the heights of the main line of each element, and ail background intensity parameters are varied. Initial values for the background parameters are predetermined from fits to spectra of high intensity from similar specimens. The escape peak parameterization is the authors’ own version, viz

The approaches of the five participating laboratories to spectrum analysis are summarized in table 1. In this section we detail specific important differences. (Maenhaut.

c

[ h=l

5. Individual meth~olo~~

5.1. The GENT progrum

model is

*n fnsc = - 3.1312 - 0.45109E + 0.007945E2

Vundenhaute)

(9)

with E in keV. This code derives from one of Van Espen et al. [16] and is described by Van Espen et al. [17]. Eq. (2) is replaced by C,,, = P, + p&,,,

+ p, exp( -P&,,)

(7)

to allow for slight deviations from linearity in the spectrometer response. The lineshape is non-Gaussian, with the low-energy tailing portion represented by a numerical correction, different for each element, stored in a library file. These correction spectra were generated by performing Gaussian fits to the spectra of single-element standards, then subtracting the resulting Gaussians and the blank substrate spectrum From the data and smoothing the remainder. When used, these “correction” spectra are normalised to the Gaussian intensity of a K, peak.

The program HEXLUND [15] is a derivative of the early Lund/Tallahassee HEX code [lS]. It is our second example of use of an analytic background, the continuum being given by B ( x ) = CONTI

+ CONTZ,

(LO)

where CONTl

= Texp( -PsC,x)

X(F,Xi- P,x’ -FF,x3+ Pqx”),

(11)

cONT2+Pii + T( P,, -+ F,,x +

F,,x’ + P,,s”).

Table 1 Details of the fitting codes Gent

K X-ray intensities L X-ray intensities Thickness correction to relative intensities

theory (71 theory [9] and measurement

Lund 171 measured

Marburg measured measured

Guelph

Lucas Heights

I71 measured

Salem et al. [g] theory [lo]. review (81. measured [ 121

JJC?S

n*

no

no

yes

Gaussian plus numerical tail correction own parameterization

Gaussian plus step on left

Gaussian plus exponential tail

Gaussian

Gaussian plus exponential tail plus step between K, and Kli

parameterized via 1151

parameteri~ed via [lS]

prestripped

Pileup peaks

WI

[IsI

[ 151

USI

Background

analytic expression

analytic expression

own parameterization [14] energy-dependent version of [15] analytic expression

removed by top-hat filter

removed by iterative channel comparison

Fit procedure

NL/LSF

(L+NL)/LSF

L/LSF

NL/LSF

NL/LSF

Peak shape

Escape peaks

1231

J. L. Campbell

et al. / Intercomparison of PIXE duta processq

in which C, is a constant, T the transmission through absorbers. The parameter Ps is the area of the analysed target and is fitted when analysing spot samples of unknown area to facilitate making self-absorption corrections. The calibration is given as E=P,+P,x, fwhm = ( P; +

(12)

P,"E )'j2

(13)

First the code fits the linear parameters (which include the principal peak height for every element) using fixed starting values of the nonlinear parameters P, - I’,. There follows a number of fits to all parameters, and the final step again fits the linear ones only. 5.3. The ~ffrburg program (~~~~be~~a) As yet there is no easily accessible publication in English on this code entiled SESAM-X which is our only example of a linear least-squares fit. It is based on a development of W. Koenig; a short description is published [19]. The peak shape includes a low-energy exponential tail, whose height, slope and high-energy cutoff are parameterized as functions of energy following measurements of X-ray spectra on the detector of interest. In the current work, due to pressure of time, the parameterization appropriate to the Marburg group’s own Si(Li) detector was used. This caused slight misfits in the tail regions of the standard spectra for X-ray energies < 3 keV and P 9 keV, but no such effects were obvious in the specimen spectra due to lower counting statistics. The background has two components. At high energies it is given by a constant. At low energies is is given by

where xa is the channel corresponding to photon energy E, (keV)= 2Er, (MeV). The coefficients a, are found by fitting blank spectra (e.g. Mylar and Nuclepore) or pure elemental standards. The operator makes a manual decision about the boundary between the two parts of the background and the relative heights of the two components. For further slight corrections a second order polynomial background with variable coefficients may be added. 5.4. The Guelph program (Maxwell,

Campbell)

There is no full published article on this code. but some brief comments are given in ref. [20]. The principal point to be made here is that the background continuum is removed by a single mathe-

211

matical filtering operation from the data, and the resulting spectrum then fitted with a similarly-filtered model spectrum that contains only peaks. Background suppression by convolution with a “top-hat” filter is described in detail by both Schamber [21] and Statham [22] and is widely used in X-ray emission analysis with electron microprobes. The K X-ray relative intensities normally used are those of Scofield (71, but the library was altered for the present exercise. At the outset the standard spectra were fitted with a general-purpose Gaussian code free of any constraints on relative line intensities. This served two purposes. First it indicated a small but systematic deviation of a few percent in the KB/K, intensity ratios relative to Scofield’s values between 2 = 20 and Z = 40; this is more likely due to neglect of both tailing and radiative Auger lines than to any deficiency of the theory. Therefore all K, intensities in the disk file were normalised accordingly. Second, it provided the L X-ray data file. The modified K X-ray intensity library was augmented in the specimen analyses by inclusion of the KMM radiative Auger lines [7] for the dominant elements Fe, Cu and Zn. This was done because it was observed that omission of the Fe KMM line resulted in a spuriously high cobalt K, intensity. The omission of low-energy tailing is deliberate, reflecting the fact that the Guelph group’s work on reaching an integrated peak description including deadlayer tails, Compton-scatter tails and radiative Auger satellites [6] is not yet complete. The neglect of tailing will be to some extent compensated by the top-hat filtering, which will tend to suppress long-term tails along with the background continuum. In a first fit to each specimen spectrum essentially all elements from K to Sb were included; the code indicated many to be absent and a second fit was then done with the absentees excluded. The Guelph code did not correct relative X-ray intensities for specimen self-absorption. This option was added to the code after the present exercise. 5.5. The Lucas Heights program (Cluytnn) This derives from Clayton’s fully documented earlier method (231, but a quite different background treatment, as yet unpublished, is now used. In the peak shape, the K, and K, peaks are given exponential tails in proportion to their heights. while a step function is added between the 2 peaks. However this full description is only used for very strong peaks. viz. Ag in the biological spectra and Fe in the geological cases. All other elements use simple Gaussians. A different approach to escape peaks is taken here: these are stripped, channel-by-channel, from the spectrum, before the fitting is initiated [24]. Another dif-

.I.L. Campbell et al. / Intercomparison of PIXE data processing

212 ference by

below 10 keV and every fifth point above that energy. An iterative procedure is then used to remove peaks from this spectrum by testing whether

from the other codes is that eq. (3) is replaced

u= Pj+ P,E.

(15)

I; b ;(%-I

The major difference of the Lucas Heights code with respect to the others is its treatment of background. It uses a background algorithm which examines each channel’s intensity compared to the average of points either side. It is not necessary to use all the points in the spectrum for this determination, and the spacing chosen will depend on the magnitude of the background. Above 10 keV where the background is simple every fifth point is used. Below 10 keV where the background may be large and complex in shape. more points are needed (say every second point). A first approximation to the background (.,;) is given by selecting every second point

LH

x

Al -

.

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If ,y, is greater than the mean (m,) it is replaced by the mean. After 500 passes through the spectrum, a relatively smooth background is left. For a background which is not linear, the mean can be replaced by CM, where c is a parameter modelling the curvature of the background. Normally, a linear variation between channels is sufficient and c would never be greater than 1.001. There are thus three parameters in the background; the spacing of the points chosen for its estimation, a parameter relating to the curvature and the number of passes through the spectrum.

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J. L. Campbell et al. / Intercomparison of PIXE data processing

6. Discussion of results for standards

laboratory’s result P to the mean p taken over the five laboratories. An individual result was deemed to be zero when the fitting code dropped the element or when the reported intensity was less than three standard deviations; such results are excluded from the calculation of the mean. This approach is not meant to imply that the mean value is the correct value and that P/P = 1 is thus the most desirable result; it is simply a vehicle for comparing numerically the results of the five codes. It should be noted that the overall mean of all the P/P results in the array of fig. 9 (and those following) is by definition precisely 1.0. while the average over elements for any given laboratory will not necessarily be 1 .O. We shall discuss some details of the figures below, but first we examine a further condensation of the data in table 3. This table averages a given laboratory’s P/P values over all n detected elements in each specimen giving the quantity denoted x; it also gives the rms deviations of the n values of P/P taken relative to the overall mean of 1.0. Hence table 3 in some sense tests a given analysis method across an entire X-ray spectrum from a particular specimen type. The data are grouped according to three distinct specimen types. First are the six biological targets where peak areas in one spectrum can vary from under lo* to over 10h counts. Then there are the three Nuclepore filters, which do not show the very intense peaks of the first subgroup but have a narrower distribution of peak areas. Finally the group of soil, clay and rock targets have a matrix of higher effective atomic number and correspondingly more important matrix corrections. Interlaboratory agreement is good for all three specimen types, but interesting trends are visible. In the biological case the Marburg data are closest to the mean, with Lund and Guelph running a few percent high, and Lucas Heights and Gent a few percent low. This behaviour is not continued with the filter specimens; here, although the Guelph data still tend to be high and the Lucas Heights data low, the Lund and Gent data are closest to the mean. The spectra of the geological group tend to resemble those of the biological group in that some peaks are extremely intense. It is interesting that the mean Marburg result closely resembles its biological counterpart while again the Lucas

The derived K, intensities for the micromatter standards are collected in figs. 7 and 8 in terms of the quantity S/s. For a given element this is the ratio of an individual laboratory’s result S to the mean s taken over the five laboratories. This quantity shows some well-defined trends. Fig. 7 shows the K, X-ray intensities from K to Sb taken with the Mylar filter. For the Lucas Heights results S/.? tends to be constant a little above 1.0 and the Gent data are generally below 1.0. Both the Lund and Marburg data shift uniformly from low to high S/.? with increasing Z, while the Guelph data do precisely the opposite. However the differences are not large, almost all data points falling within +2% of the relevant mean. Fig. 8 shows the funny filter data and extends the elemental range downwards to Mg. Above Ca the trends are fairly similar to those of fig. 7, but below Ca agreement is very poor indeed. All the lineshapes used perform acceptably well for K, X-rays of elements in the range V-Rb. At low Z, where deadlayer effects influence the lineshape, the situation is not satisfactory. There are also problems of varying degree for Sr-Sb; here the photon energy is above 14 keV and Compton scattering effects are playing an increasing role in the lineshape [6]. The scatter is somewhat worse for the small number of L, results and is attributed not just to lineshape variation but also to the variation in the L X-ray relative intensities used by the five codes. The mean values of S/s are collected in table 2. Taken alone they would indicate excellent agreement on average for K, X-rays. It is only via figs. 7 and 8 that the Z-dependent trends of each code’s response become apparent.

7. Discussion of results for specimens The basic analytical results are summarised in figs. 9-13 in terms of the quantity P/p. For a given element in a given specimen this is the ratio of an individual

Table 2 Mean value and rms deviation

IJ of S/s

X-ray line

Standard

set

K

Micromatter

K K L

spot Micromatter Micromatter

(Mylar filter) (Mylar filter) (funny filter) (Mylar filter)

L

Micromatter

(funny

filter)

for different

standard

213

sets analysed

by the five laboratories

Number of targets

Laboratory Lucas Heights

Guelph

Gent

Marburg

Lund

21 5 26 4 4

1.002 * 0.007 0.993 k 0.010 1.001 fO.O1l 1.016+0.016 1.010*0.013

1.002 + 0.014 0.999 + 0.016 0.994 + 0.019 1.002 k 0.016 0.993kO.013

0.995 + 0.010 0.998 k 0.009 0.990 * 0.014 0.998 + 0.015 0.994&0.016

0.997 i 0.011 1.012*0.013 1.004+ 0.011 0.976 k 0.025 0.996+0.012

I .003 i 0.013 0.999f0.017 1 ,011 k 0.023 1.019+0.021 1.014kO.019

J. L. Campbell et 01. / Inrercomparivon of PIXE data processmg

214

K

-

Ca

-

LH . .

Mn -

Ga -

7’ .

Se Br Rb -

7 .

,: >: I: I

cu -

.

M

. .

. 7’

Zn -

G .

x.

Ti -

Fe -

GU x x

,

x x 1: ,

AB Sb -

PbL-

Fig. 9. P/P

.

2490

-

21260

0

I

-

24830

-

286

.

,

.

x

5291

-

I:

BaL-

81920

.

.

0

x

-

4

.

I!

4126

-

.

.

x

49710

-

- 881600

.

,I

. 7’ .

-

-1.419E6

I

.

256700

-2.335E6 I

.

Sr MO-

I

I,

4’

-

.

.

-

1503

-

158900

-

1771

-

1060

-

753

for bovine liver (high statistics).

Heights result tends to be lower and the Guelph result (where no thickness correction was made to the K,/K, ratios) remains on the high side. Only the Lund result changes dramatically, moving from the high side in the biological case to the low side in the geological case. Overall then table 3 seems to suggest that the Lucas Heights approach slightly underestimates peak areas and the Guelph method overestimates them relative to the mean. However this comparison is distorted by the inclusion of weak elements that are usually reported by less than five laboratories, and there are often large disagreements, i.e. all reported P/P values differ greatly from 1.0. Laboratories reporting such values are “penalised”; their “detecting power” as measured by n appears superior, but their ?? values are adversely affected and their e values are increased. The exercise of table 3 was therefore repeated retaining only the elements with mean peak area p above the determination limit, L,, defined by Currie [25] as: (17) with B the background in the PIXE spectrum at the K,, or L, line of the element. The background calculated by the Gent code was used and it was integrated over a

region of 3 times the fwhm of the K, (or L,) line. The new R values are reported in table 4. Now for the biological specimens the Marburg data are no longer closest to the mean, but are replaced there by the Guelph data. The Lund, Gent and Lucas Heights data all move closer to the mean. The Lucas Heights data are furthest from the mean in the filter spectra but the spread among the other four sets is small, the four being within a range of 1.7%. For the geological targets, the Lund data still give the lowest R, and Guelph is at the high end. However examination of the data for individual elements show that V and Cr have very large spreads with P/P ranging typically from 0.5 to 1.5. Hence, these two elements were removed, leading to the results of table 5. Now we observe the previous pattern of good agreement, with the Lucas Heights data still running lowest. We now discuss individual elements. Space limitations restrict us to presenting only five of the twelve figures containing P/P data. However the following remarks are based upon the complete set of results. 7.1, Biological specimens In these targets there is excellent the five data sets for the dominant

agreement across elements in each

J. L. Campbell er al. / Inrercomparison of PIXE &la processing

G

LH . r

K Ca

129600 S33E6

I

*

I

19680

.

Cr

3898

1’ ,

Mn Fe Ni

.

.

Ti

237200 311500

.

.

.

3455

. 1

cu Zn

29370 58690

.

Ga

1934

1

I

. 1 ,r 0

AS Br Rb Sr

13080 8954 5365 13010 278

Y

.

A9

54390

.

Sb

808

x

. .

Bal Pbl

t

Fig. 10. P/P

215

6878 19070

1

--

1.3

.7

1:3

for orchard leaves (high statistics)

spectrum, e.g. Fe and Ca in orchard leaves; Fe and Zn in kidney; Fe, Cu. Zn in liver; etc. The Mn and Cr K, lines fall on the low-energy tail of the dominant Fe K, peak. When the Mn K, intensity is strong compared to the Fe K,, as in the orchard leaves spectra, the five values for it agree with a +l% spread. As the Mn K, decreases relative to the Fe K,, the spread in values becomes worse; this is shown in table 6. In the two worst cases, liver and kidney, one might expect that inclusion of peak tailing (Gent, Marburg) would lead to lower Mn K, intensity, while its exclusion (LH, Guelph, Lund) might cause a larger value. The Lund data are indeed the largest and the Marburg data the smallest; however the Guelph and Gent data are both very close to the mean, while the LH data do not behave systematically. Presumably this means that the Marburg tailing function is an overestimate, the Gent tail is (as expected) quite accurate

and the Guelph approach absorbs the tail partly into the background. The Cr K, is an even more difficult case. Not only does it ride on the Fe K, tail but it coincides in energy with the Fe KB escape peak. The spread is very large in the orchard leaves spectra despite the intensity ratio of Cr K, to the Fe KB escape being about 15/l. The Ti K, coincides with the Fe K, escape peak. However the two codes that use the same escape model (Guelph and Lund) give significantly different results for Ti K,. The K and Ca K, lines are in the bremsstrahlung region of the spectrum. If one or other is strong, e.g. K in liver or bovine liver, the 5 codes agree well on its intensity. But if the other line is weak, e.g. Ca in bovine liver. agreement is poor. The roles are reversed in orchard leaves where the strong Ca gives agreement and the weaker K shows a spread. This energy region provides a

J.L. CumpheN et al. / Intercomparison of PIXE dutu processing

216

LH . .

-

K

Ca Ti

L 56100 *

-

i

Mn -

52590 I

955

b

.

-

4799

Fe

-

- 936400

cu

-

-

Zn

-

Ga

-

As

-

Br

-

- 16130

Rb

-

*

Sr

-

114

Y

-

18380

MO -

132

Cd

-

Sb

-

16490

-271400 )I

-

1105

-

170.5

4543

954

i

326

PbL -

955

i-l---I .7 1

1.3

.7

1

1.3 .7

1

PIP P/Pfor

Fig. 11

human kidney.

Table 3 Mean

value 2

definition

and rms deviation

e of

P/P

taken over all nonzero

elemental

intensities

from

each laboratory

(see text for full

of e)

Snecimen

Laboratorv Lucas Heights

Guelph

Gent

Marburg

Lund

1.029 + 0.096 (10)

1.071 kO.129

1.01

1.034 t 0.084 (13)

Bovine liver A

0.948 + 0.078 (13) ‘)

1.025+0.136

(16)

0.939 It 0.127 (14)

Bovine liver B

1.007~0.130(15)

0.982kO.142

(16)

0.976 rt 0.082 (16)

1.061 kO.128

(17)

1.00

Orchard

leaves A

0.935*0.134

Orchard

leaves B

0.947~~.104(18)

(18)

(12)

(19)

1.02310.122

0.984+_0.096

(16)

1.047+0.117(1x)

1.007rto.099

(19)

0.998 I 0.099 (16)

1.00

(16)

0.981 kO.091

(16)

0.940~0.171

(17)

1.~7~0.~0~

(14)

1.114i:O.243

(15)

0.945JFTO.148 (17)

0.984rtO.119

(15)

1.061 LO.113 (IS)

0.969

1.009

Human liver

0.957+0.117

Human kidney

0.945~0.126(16)

1.056&0.168

Bwk@ul

0.960

1.025

mean:

(16)

&0.168(13)

10.144

(17)

kO.069

(17)

1.044

Nuclepore

A

0.989 i 0.080 (20)

0.996?0.155

(21)

1.006~tO.107

0.998 IO+037 (18)

I.011 kO.105 (1X)

Nuclepore

E

0.977+0.109(19)

1.024+0.127

(17)

1.018 i_ 0.087 (22)

0.981 f0.153

(19)

1.00

Nuclepore

C

0.977 kO.148 (21)

1.07

1.008$0.127

0.963iO.167

(20)

0.983f0.068

0.981

1.030

1.011

0.981

1.051i0.170(15) 1.041 ~0.160 (16)

1.016+0.094(17)

1.026+0.141

(16)

0.991 kO.055 (18)

1.025~0.083

(17)

0.991 kO.113

(16)

0.981 kO.187

(20)

0.981 iO.203

(16)

Nuclepore mean.

kO.225 (19)

Soil

0.987 of 0.187

(17)

Clay

0.958+0.167

(18)

USGS rock

0.978 + 0.249 (20)

1.077~O.l50(21)

0.978i

Ge&gicuI

0.974

1.056

0.995

~reiwr:

‘) Numbers

in parentheses

indicate number of values used in calculating

(22) (22)

0.123 (22)

1.011 the mean.

10.104(19) (16)

0.998 0.923~tO.214(16)

0.965

J.L.

Campbell

et al. /

Intercomparison

G

1 Mg

of PIXE

L

M

0

Al ,

I

P

-

.

.

,

Si

7

- 34340

-.

Cl

I

1

.

.

K

, .

Ti

.

CI

. I

. .

.

b

Fe

, .

cu . 7

.

1

L

1 .

.

.

Ge

.

.

.

Zn

0

Se Br

.

Sr

I

EaL

.

.

.

-

.7

.

.

x

Pbl

I

4

----73.7+3.+

r

.

.

.7‘3

6005

-

413

-

1221

-

2127

1

7

-

145

-

390

-

3693

-

115

-

37

-

94

-

212

-

35

-

444

-

502

1

I

1.3

-

- 36100

I

Ni

Ga

.

.

4

Mn

- 26150

.

.

x

.

- 23910

.

.

,I

V

- 12670

.

I

Ca

1175

- 50070

.

.

969

-110000

L

.

s

217

data processing

I

1.3

PIP Fig. 12. P/P

for Nuclepore

A

test not only of the background continuum treatment but also of absorption effects. In the bovine liver matrix (- 5 mg/cm2) the potassium Ka/Ka intensity ratio is increased 5% by absorption effects, causing in turn a 20% change when the calcium K, intensity is extracted from the overlapping K K,/Ca K, complex. The two groups who included this effect (Lucas Heights and Gent) report the lowest values, which in this case must be closest to the correct value; the Guelph result, omitting absorption, is about 15% higher than the Lucas Heights and Gent values, which is close to what one should expect. The fact that the Lund and Marburg results are about 50% higher may indicate a further problem connected with background treatment in this energy region. We now discuss the peaks to the right of Fe K, in the spectra. stringent

The spread in the weak Ni K, intensity is attributed mainly to its position between two strong neighbouring elements. The spread in Ga K, is very large. The presence of Ga is at first sight surprising. However the “blank” spectra from Mylar and aluminized Mylar indicate that it is an impurity in the aluminium. For Kn lines of Se, Br, Rb, Sr. MO, Ag, Cd, Sb, the agreement correlates with peak intensity. For the weaker peaks. the spread in the results is greatest. Not all codes succeed in revealing all the peaks in this region; the Marburg code tends to “see” the least elements. But this may reflect a subjective choice of elements to be included in the fit. Two elements, Pb and Ba, are treated via their L,, lines. For Pb. the spreads among the five results vary and do not correlate with the statistical quality of the data. Ba shows rather large spreads despite having L,,

218

J. L. Campbell et al. / Intercomparison of PIXE data processq

K

.

x

Ca

I

I

GU

.

- 5645 -232800

x

Ti

- 61540

a:

.

.

-

10760

-

2960

Mr I-

-

39050

Fe

- 3.56E6

V

x

.

Cr

.

1

. .

.

Ni cu

.

I

,-

7-n

.

Ga I-

.

.

.

,

AS

.

Se

1

.

.

Br

.

Rb ISr

.

Y

.

.

Zr

.

.

.

Mc3-

.

.

a

1

Pb 1

5253

-

10290

-

11400

-

953

-

5032

-

205

-

150

-

2514

-

9560

-

213

-

488

-

Nt ,-

Ba

-

.

.

*

.

Th I

.?

Fig. 13. P/P

--

-

I-

1.3

.7

-

99

-

306

-

2219

-

958

-

147

1.3

for USGS rock.

peak intensities between 1060 and 6878. The Ba energy the Ba L, line overlapping with region is “crowded”, both the Ti K, line and the Fe K, escape peak. 7.2. Nuclepore filters In these specimens the range of elemental intensities is much less than for the biological specimens and the problem of weak peaks beside strong neighbours is correspondingly reduced. For example the agreement among the Mn data is now excellent. However this problem does persist in the case of phosphorus, whose weak K, line is sandwiched between the very strong S and Si K, lines, and in some cases chlorine which overlaps with sulfur K,. Apart from those cases of neighbouring peaks, the only significant disagreements occur for lines that are very weak indeed, i.e. with only

a few tens of counts and for the barium L, line. The good agreement in the low-Z region Mg-Ca is remarkable in view of the inadequacies encountered there in fitting the corresponding standard peaks. Apparently significant imperfections in the lineshape description may be tolerated, but this should not prevent efforts to improve the lineshape description. 7.3. Geological turgets Many of the comments made above apply here also. In addition we have already noted serious problems with chromium and vanadium, despite respectable intensities. Several factors are at work here. The Cr and V lines suffer from severe overlap with the much more intense Ti and Mn lines. The multiplicity of lines in this energy region poses the maximum challenge to the

.I. L. Campbell et ul. / Intercompurison UJ”PIXE data proce.wssrng Table 4 Mean &ue

R and rms deviation

determination

CJ of P/P

taken

over those

elements

where

the mean

reported

Laboratory Lucas Heights

Guelph

Gent

Marburg

Bovine Bovine Orchard Orchard Human Human

0.973 * 0.053 (9) d’ 1.011~0.134 (14) 0.988 f 0.026 (14) 0.947~0.104(18) 0.955+0.121 (15) 0.938 + 0.104 (14)

0.992 i 0.023 (9) 0.960+0.134(14) 1.029rtO.169 (14) 1.047~0.1~7(18) 0.994 * 0.074 (15) 1.033kO.144 (14)

0.974t0.068 (9) 0.961 iO.077 (14) 0.982 & 0.046 (14) 1.008+0.102 (18) 0.948~0.170(15) 0.982 $0.083 (14)

1.043 h 0.096 1.0421tO.136 0.989 rt 0.068 0.998 rfr0.099 1.007*0.108 0.995f0.114

Blolngicul mean:

0.969

1.009

0.976

1.012

Nuclepore Nuelepore

A B

0.988 & 0.064 (14) 0.970~0.112(13)

Nuclepore

C

0.948&0.138

0.978 * o.os4 (14) 0.985 i. 0.031 (13) 1.027&0.124 (18)

1.005 t 0.017 (15) 0.998 ?- 0.028 (14) 1.024iO.077 (19)

1.004io.035 l.Of31t0.092 1.013+0.106

1.009

1.010

1.018&0.093 (13) 0.991 it 0.056 (17) 0.989rtO.129 (18)

1.056rtO.142 1.015i:O.O72 0.9541tO.182

0.989

1.008

liver A liver B leaves A leaves B liver kidney

(18)

Nuclepore meon.

0.969

0.997

Soil Clay USGS rock

0.983~0.210(13) 0.963kO.169 (17) 0.987 i 0.260 f 18)

1.056_~0.189 1.041 iO.160 1.087iO.161

Geol0gical WzeWI:

0.977

7.061

in parentheses

indicate

number

Specimen

(12) (16) (18)

of values used in calculating

Table 5 Mean value R and rms deviation n of P/F for geological intensities are below the determination level Lg.

the

targets,

Lund 1.018+0.043 (9) 1.034~0,084(13) 1 ,012 + 0.068 (I 3) ~.0~~0.068 (16) 1.09610.228 (15) 1.052~0.107 (14)

(9) (12)

(14) (16) (14) (14)

1.035 (14) (13) (17)

1.024+0.047 (14) 1.035 + 0.077 f 13) 0.983 f0.063 (14) 1.014 0.882+0.227 0.990+0.121 0.981 +0.203

(13) (16) (18)

(12) (14) (16)

0.951

the mean.

excluding

vanadium,

chromium

and elements

whose mean reported

Laboratory Lucas Heights

Soil Clay

USGS rock

0.961 iO.049 0.972&0.053 0.947kO.196

Geolo~lcal mean:

0.960

” Numbers

intensity exe&

peak

level L,.

Specimen

d, Numbers

219

in parentheses

(11) a’ (15) (16)

indicate

number

Guelph

Gent

Marburg

Lund

1.022 + 0.041 (IO) 1.013~~.06~(14) 1.07910.159(16)

1.044 * 0.081 (11) 0.998 sro.037 (15) 1.00310.128 (16)

1.025~0.112(11) 1.002 & 0.054 ( 14) 0.946-(_0.391 (16)

0.945*0.154 (10) 1.02O-r_O.O91 (12) 1.030+0.150(14)

1.038

1.015

0.991

0.998

of values used in calculating

background modelling approach. This can easily be seen by a visual comparison of fig. 5 with figs. 1-3. Ni and Cu are also interesting. When the Ni/Cu ratio is about 5/l (clay) agreement is good. When it is - l/l and both are weak, there is a significant spread. In the rock

Range of P/P for Mn K,

MnK,

Bovine liver B Kidney

0.29 0.035 0.005

0.987-1.013 0.947-1.043 0.856-1.22

237200 81920 4799

Liver

0.004

0.894-1.156

Orchard leaves B

case, when Ni/Cu - l/2, the spread in Ni is much greater than in the copper, indicating again the effect of tailing of the right-hand partner upon the intensity of the left.

8. Specimen /standard

Table 6 Specimen

the mean.

Mn K, FeK,

18880

ratios

The ratios of K, and L, peak intensities in specimen spectra to those for the same element in the standard spectra specimen

were peak

compiled

in precisely

intensities.

Figures

the same

way

corresponding

as the to figs.

9-13 and tables corresponding to tables 3 and 4 were prepared. The intensity ratios behaved numerically in a manner

very

similar

to the intensities,

so much

so that

220

J. L. Campbell et al. / Intercomparison of PIXE data processing

there is no value in reproducing the graphic and tabular data. We conclude from this that taking the ratio of a specimen peak to its standard analogue does not significantly decrease the error incurred in obtaining the specimen peak’s intensity. The errors, as seen here in spreads relative to means, arise in the fitting of the multielement spectra.

versitair Instituut voor Kernwetenschappen” (W.M., J.V.), the Natural Sciences and Engineering Research Council of Canada (J.A.M., J.L.C.). Discussions with Dr. Uwe W%tjen (Euratom, Geel) were much appreciated.

9. Conclusions

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The results of this intercomparison are extremely encouraging. The principal objection levelled at PIXE has concerned the accuracy of extraction of areas of overlapping peaks superposed on a rapidly varying background. The five background approaches described here include four radically different techniques, yet all give results that are in excellent internal agreement. The differences among the five codes are not alleviated by comparing peak areas with the corresponding standard peak areas. They arise from the background treatment and its interplay with the peak model. Where the most serious disagreement occurs is for weak peaks riding on the low-energy tails of intense neighbours e.g. Mn K, on Fe K,. The study demonstrates a need for better analytic description of peak tailing and better understanding of its causes. Work to that end has already been reported by one of the participating groups [6]. Once this tailing is better understood, it may be possible to include in model spectra the weak KLM and KMM radiative Auger lines that further complicate the low-energy sides of peaks. The disagreement among results for standard spectra at Z < 20 points to the need for a much improved understanding of how the frontal dead layer affects the detector lineshape. It also indicates to detector manufacturers the desirability of minimal dead-layer thicknesses in this application. However the effects of inadequate lineshape description upon analytical results are less serious than we would have expected. A final comment concerns the much-repeated claim that nonlinear least-squares fitting is preferable to linear least-squares on the grounds that it is more forgiving of electronic instabilities. The excellent performance of the Marburg code, which employs the linear approach, shows that this need not be the case. We wish to acknowledge our various sources of financial support, namely the Belgian “Nationaal Fonds for Wetenschappelijk Onderzoek” and the “Interuni-

References