LIMITS OF DETECTION AND QUANTITATION IN ... - Science Direct

57

Nuclear Instruments and Methods in Physics Research B35 (1988) 57-66 North-Holland, Amsterdam

LIMITS OF DETECTION W.J. TEESDALE,

AND QUANTITATION

J.A. MAXWELL,

A. PERUJO

IN PIXE ANALYSIS

OF THICK TARGETS

* and J.L. CAMPBELL

Guelph- Waterloo Program for Graduate Work in Physics, University of Guelph, Guelph, Ontario, Canada NIG 2 WI

L. VAN DER ZWAN

and T.E. JACKMAN

Division of Physics, National Research Council of Canadq

Ottawa, Canada KIA OR6

Received 16 May 1988 and in revised form 20 July 1988

X-ray spectra induced by the impact of l-5 MeV protons on pure single-element matrices of carbon, aluminum, silicon, titanium, iron, germanium, molybdenum, silver, tin, ytterbium and lead have been used to investigate analytical detection limits in thick-target PIXE. Particular attention is paid to the choice of appropriate aluminum X-ray filters for suppression of the matrix characteristic X-ray lines and their pile-up peaks, and to the choice of optimum proton energy.

1. Introduction The bulk of published PIXE work deals with thin specimens whose effective matrix atomic number is low, and through which the proton beam passes with a relatively small energy loss; examples are biological materials and aerosol deposits. Recently PIXE and micro-PIXE have found increasing use in analysis of thick specimens in which the beam is completely stopped. An additional complicating factor is that these specimens often have matrices of sufficiently high atomic number (e.g. mineralogical samples) that the dominant feature of the PIXE spectrum is the characteristic K or L X-ray multiplet of the major matrix element. This is akin to the situation commonly encountered in electron probe microanalysis (EPMA), and indeed the two techniques are increasingly being deployed in complementary fashion upon the same specimens [l]. While PIXE’s limits of detection are quite well known in the case of thin specimens whose matrix has low atomic number [2], there is very little systematic information for thick specimens, whatever the matrix atomic number. Among major contributions by Folkmann and various collaborators to the early development of PIXE was a theoretical-cum-experimental study [3] of the processes that in the proton case generate the background that is responsible for the limits of detection (LODs). This focussed upon thin targets with matrices of low atomic number, concluding that LODs as low as 1 part per million by weight (ppm) could be reached for these

* Now at EURATOM, Geel, Belgium. 0168-583X/88/$03.50 0 Elsevier Science Publishers (North-Holland Physics Publishing Division)

B.V.

under favourable conditions. Semi-quantitative arguments were given which suggested that peak-to-background ratios could be an order of magnitude smaller for thick specimens, with consequently poorer LODs. The only comprehensive experimental study for thick specimens is that of Mommsen et al. [4] using 30 MeV $He ions; this work presents plots of the LODs versus atomic number for essentially all trace elements in eight chosen matrices, namely titanium, iron, copper, germanium, silver, tantalum, gold and lead. The LODs, quoted for 1 PC of integrated proton charge, depend strongly upon the matrix but can reach 20-30 ppm for favourable cases. Various authors, reporting analyses of specific specimen types, have included LODs (with varying definitions) based upon their observed backgrounds. For example: Khaliquzzaman et al. [5] using 2.61 and 4.22 MeV protons present LODs as a function of trace element atomic number Z for the NBS bovine liver standard (SRM 1577a); these curves have minima at - 1 ppm concentration around Z = 30, the charge collected being about 5 l.tC. This accords with other estimates for organic matrices scattered through the literature. Cabri et al. [6] quote LODs achieved in their micro-PIXE analysis of sulfide minerals using 4 MeV protons; with 0.225 pC of accumulated charge they reported LODs of - 10 ppm for elements As-Sn in pyrite (FeS) and 12-16 ppm for elements In-Ag in sphalerite (ZnS). Ahlberg et al. [7] have examined LODs for steel in some detail using 2.5 MeV protons and 840 PC of charge; in the 35 < Z < 40 region their limits were a little below 10 ppm, while at lower and higher Z the results rose rapidly towards 100 ppm.

58

W.J. Teesdale et al. / Limits of detection in thick target PIXE

Further examples are quoted in the review by Campbell and Cookson [8] who concluded that limits no worse than 100 ppm are possible for elements of Z > 20 in many matrices. The best values could reach - 1 ppm for the most favourable elements, somewhere in the range 25 < Z < 40 (depending on proton energy) for matrices of very low atomic number (Z,). They felt however that the sparseness of experimental data indicated the need for a systematic study of LODs in thick-target PIXE (TTPIXE), along the general lines of the 30 MeV +He study mentioned above [4]. This paper, after attempting to clarify the definition of LOD and to review the processes that determine its value, reports upon such a study and its results. Brief conference reports [9,10] have already dealt with restricted aspects during the progress of the work.

2. Definition of the “limit of detection” A variety of definitions of limit of detection are to be found in the PIXE literature, especially in the early phase of the technique’s development. Here we take as starting point the IUPAC definition [ll] of instrumental detection limit (IDL), which is IDL = &, + ko,,

(1)

r,, is the mean value of blank measurements, et,, their standard deviation and k a numerical factor determining confidence level. For a TTPIXE spectrum we take j,, as the area of the predominant peak of the element of interest that arises from sources other than the presence of the element in a specimen; since this arises from protons interacting elsewhere than in the specimen, good design should render j,, negligible in comparison to the background intensity due to bremsstrahlung, matrix characteristic X-rays and nuclear reaction gamma rays. ub, may then be set as the standard deviation of the background intensity Na and so ut,, = fi; k is taken as 3 to give a 99.86% level of confidence. Nn has been variously defined in the PIXE literature as the background intensity contained within one, two or three full-widths at half maximum of the predominant X-ray peak of the element of interest. This range causes a variation of 1.7 in the instrumental detection limit deduced from a given spectrum. Our preference is for one FWHM, since we have noted in practice that with the wider ranges, the deduced limits on occasion exclude peaks whose reality seems assured by subjective judgment. For a homogeneous specimen analysed with protons of energy E, the characteristic X-ray yield in any particular line ‘ p’ of the K or L series is proportional to the

concentration C, of the element concerned, well-known equation Y’(Z)

=

N o bPrA

av A” = = NC,/ Z

0 oz(E$$)

via the

dE ,

t2j

-%

where N,, is Avogadro’s number, a,(E) the ionization cross-section of proton energy E, wz the fluorescence yield, bs the fraction of the X-ray intensity in the line of interest, e$ the corresponding absolute X-ray detection efficiency, N the number of protons, S(E) the stopping power and Z’,(E) the X-ray transmission factor [8]. In practice the proportionality constant between YP(Z) and C, is often determined through use of standards. This constant, however determined, converts the IDL (peak intensity or X-ray yield) to limit of detection (LOD) which is usually expressed in concentration units such as parts per million (ppm). Finally we note another useful criterion, which is the limit of quantitation or LOQ. It defines the lower limit of the useful range of measurement methodology and is a level above which quantitative results may be obtained with a defined degree of confidence. Keith et al. [13] recommend defining LOQ as 10 standard deviations, corresponding to a +30% uncertainty in the measured concentration (100 + 30) at 99% confidence level. The concentration region between 30 and lOa is a region of “less-certain quantitation”, and that above 100 is the actual region where quantitation is feasible. Our present LOD results can be converted to LOQ’s by multiplying by 3.3. It should be noted that our present results differ slightly from those we have previously published [9,10] due to the changes in our definition of the limit of detection.

3. Sources of background Part of the observed background is not proton-induced but arises from cosmic rays and environmental radioactivity, the resulting spectrum in a Si(Li) detector being essentially flat in the l-40 keV energy region. In long measurements this could contribute significantly in the higher-energy region where the proton-induced background is least intense; in our experience efficient shielding of the Si(Li) detector with at least 1 cm of lead precludes this possibility. The physical origin of the proton-induced background continuum is now rather well understood due in the main to the early work of Folkmann et al. [3] and a series of papers by Ishii, Morita and coworkers. One of the most recent of these [14] demonstrates via measurements and theory that secondary electron bremsstrahlung (SEB) is the dominant contribution at photon energies hw below T, (the maximum energy transferred from a proton to a stationary free electron),

W.J. Teesdale et al. / Limits 106

of detectionin thick target PIXE

59

a low-Z absorber, but this must not generate nuclear reaction y-rays. Low-energy peak tailing, seen mainly as a roughly flat shelf of height up to 1% of the peak height is largely beyond the control of the experimenter once a Si(Li) detector has been purchased. Charging of an insulating specimen, with consequent background due to discharge, can be mitigated by the electron flood method.

4. Experimental arrangement 100 5

10

15 ENERGY

2!ke”l 25

II

I

: 30

35

Fig. 1. PIXE spectrum due to 2 MeV proton bombardment of an iron specimen. The counting rate was 6000 s-’ and no pileup rejection devices were used. The pileup peaks increase the background locally in the region where the K X-rays of elements Kr-Sr would lie.

whereas atomic bremsstrahlung (AB) and radiative ionization exceed SEB when trw > T,. Thus for 1 MeV protons incident on aluminum, the observed strong background below - 6 keV X-ray energy is mainly AB, while for 4 MeV protons it is mainly SEB. In a thick target wherein the proton energy is reduced from its entrant value to zero, the lower-energy portion of the observed background is thus a very complex mix, further modulated by photon attenuation within the target. At higher X-ray energies primary bremsstrahlung from the protons becomes comparable in intensity to SEB and AB. These bremsstrahlung contributions vary smoothly in intensity as a function of target atomic number and of proton energy. In contrast background arising from detection of y-rays from nuclear reactions varies greatly from one target to another. Target constituents such as Na and F result in strong nuclear reaction contributions, usually in the form of an almost flat spectrum resulting from Compton interaction of y-rays in the Si(Li) detector. Contributions also arise from reactions induced by scattered protons in target chamber materials, absorbers etc, necessitating again shielding of the Si(Li) crystal and also careful choice of materials. For matrices other than those of very low atomic number, the characteristic X-rays of the matrix constitute a major component of the background and their pile-up peaks are also a major contribution. This is illustrated by spectra taken for an iron matrix in fig. 1. The pileup can be minimized by electronic rejection or by on-demand beam deflection and also by inserting carefully chosen absorbers between target and detector to reduce the matrix X-ray intensity. Finally there are minor contributions of varying tractability. Elastically-scattered protons can be prevented from entering the Si(Li) detector by interposing

The TTPIXE beamline and target chamber at the University of Guelph were used; all aspects of the arrangement are fairly standard in design. A proton beam of l-2 mm diameter reaches the target via an on-demand beam deflector and a system of tantalum and graphite collimators. Targets are held on an XYZ manipulator and their front surfaces brought to a reproducible position in the focal plane of a x60 optical microscope. A 26 mm* Si(Li) detector views the target from a distance of about 45 mm through a 0.0125 cm thick beryllium window in a recessed port in the chamber wall. The solid angle is 0.013 sr. Energy resolution is 170 eV at 5.9 keV. Protons are incident normally on the specimen and the X-ray take-off angle is 45 O. The target holder is insulated and surrounded by a Faraday cage held at -90 V potential to return secondary electrons to the target. The entire target-cage arrangement is within a well-grounded chamber and the target charge is measured by a Red Nun 8111 current integrator. The absolute efficiency of the Si(Li) detector was measured with calibrated radionuclide X-ray emitters [15]. Spectra spanning the l-35 keV X-ray energy region were recorded from thick pure targets of carbon, aluminum, silicon, titanium, iron, germanium, molybdenum, silver, tin, ytterbium and lead. Aluminum absorbers ranging in thickness from 0.025-0.75 mm were placed between the 0.125 mm beryllium chamber window and the 0.025 mm beryllium window of the Si(Li) detector. Data were taken at proton energies 1, 2 and 3 MeV using the Guelph Van de Graaff and at 4 and 5 MeV using the NRC Van de Graaff; for the latter runs the chamber and beamline were transported in their entirety to Ottawa. Iron and molybdenum data were taken at 3 MeV using both facilities and the two sets agreed closely, thus providing assurance that the entire set of results was internally consistent.

5. Design of study 5. I. Numerical procedures We define Y,(Z) as the characteristic X-ray yield lying within a region of width one FWHM centred

W.J. Teesdale et al. / Limits of detection in thick target PIXE

60

upon the principal line in the K or L X-ray spectrum of trace element Z per microCoulomb (PC) of proton charge and per unit concentration, Then using eqs. (1) and (2) the minimum detectable concentration for 1 IJC of charge can be derived from a spectrum generated using Q PC via

c,=

3@E

IRON

S2Y,(Z)ek(e-PX)z’

--

where D is the detector solid angle and E: its intrinsic efficiency for the line energy; the exponential factor is the X-ray transmission through any absorber; B is the background intensity in a spectral interval of width one FWHM centred at the line energy. In our case, where the absolute detection efficiency e$ (= e: G/417) is directly measured, we use the form

In evaluating the theoretical X-ray yield we use the stopping powers of Biersack et al. [16] and the attenuation coefficients of Leroux and Thinh [17]. The X-ray production cross sections are obtained from semi-empirical fits to a self-consistent theoretical data base [18]. 5.2. Alternative

analysis scheme

The need for absolute efficiency (or solid angle) can be bypassed by using the observed intensity of the matrix characteristic X-ray peak (where one exists) per PC. This is M/Q

= Y,tieF(e-Px),

,

(5)

where the suffix m denotes matrix and Y,,, is the matrix Ka yield per steradian per PC. Then

This scheme is in some cases more susceptible to error due to its explicit use of matrix X-ray attenuation in the aluminum absorber. In practice we determined our Al absorber thickness by demanding consistency between LODs obtained via the two schemes. The values obtained agreed acceptably with micrometer measurements: e.g. for a nominally 0.35 mm foil, consistency gave 0.375 mm and a micrometer 0.37 mm, both within the &lo’% tolerance of the manufacturer. 5.3. Experimental

variables

With the detector placed as close to the target as possible and its resolution optimised, we are left with proton energy, absorber choice and counting rate as experimental parameters at our disposal. These are in-

100

1""20

500

MOLVBDENW s-1

1

-15oos-’

---6oooo-’

I

---8000s~’

I 30

40

50”

20

30

40

50

z Fig. 2. Effect of counting rate upon LODs of trace elements 20 5 Z I 50 in iron and molybdenum matrices using 2 MeV protons and aluminum absorbers of respective thicknesses 0.12 and 0.05 mm. Counting rates of 500 s-l and 6000 s-’ were used for iron, the collected charge being the same in each case; double and triple pileup peaks cause local worsening of LODs. For molybdenum the rates were 1500 ss’ and 8000 s-t.

terdependent

in their

effects

on LOD’s,

making

it dif-

to design an experiment that provides absolute conclusions as opposed to general guidelines. There is also some subjectivity in the decision as to whether the LODs should be presented relative to unit accumulated proton charge, unit measurement time or some other variable. These choices will be explored later, but for the moment our LODs will be quoted relative to 1 PC charge i.e. in the conventional manner. Correspondingly the symbol used to represent the result of eq. (4) will be LODo. Fig. 2 illustrates for two different matrices the effect on LODs of increasing the counting rate with a fixed absorber thickness. The pileup continuum is effectively suppressed by the on-demand beam deflector and so increased rate worsens the LODs only for those elements whose characteristic X-rays coincide with the matrix double or triple pileup peaks. For those matrices where X-ray peaks are present in the spectrum we chose to adopt a counting rate range of 1000-2000 s-i and then to determine appropriate aluminum absorber thicknesses. Aluminum and Mylar are the most widely used absorbers and the choice of aluminum is made because smaller thicknesses suffice. The aluminum was placed outside the 0.125 mm beryllium window of the chamber, hence eliminating any background due to scattered protons inducing (p, v) reactions in aluminum. Background from the ‘Be(p, n)9B reaction due to protons scattered with energies above 2.06 MeV is a potential problem, but various tests indicated this was not a significant effect. The use of critical absorbers is not explored here since the intent is to examine general trends in simple situations. ficult

W.J. Teesdale et al. / Limits of detection in thick target PIXE

61

The final step in examining experimental variables is to vary the proton energy, with the absorber thickness set at the chosen value for each matrix.

6. Results and discussion 6.1. Choice of absorber thickness Figs. 3-5 present limits of detection LODo obtained for matrices ranging from carbon to tin using 2 MeV protons and a variety of aluminum absorber thicknesses. As previously indicated the results are normalized to 1 PC of collected charge and so are directly comparable with those of Mommsen et al. [4] and indeed with most other literature results. The left-hand portion of each figure deals with those trace elements having 20 I Z I 50, via their Ka X-ray lines; the righthand portion is for 70 I Z I 92, using the La lines. In the carbon case (fig. 3) the matrix K X-rays do not appear in the spectrum and so the counting rates are very much lower than those encountered with the heavier matrices. A second consequence is that there is no benefit in using an absorber any thicker than that needed to keep bremsstrahlung to a tolerable level. Replacement of the 0.025 mm absorber by one twice the thickness has little effect except for the lighter trace elements (Z < 30) which are more strongly attenuated and therefore have slightly poorer detection limits. The overall behaviour of the LOD-Z curve is the U-shape familiar from early work on thin targets of low atomic number matrix. The aluminum case is an intermediate one in that with the thinnest filter used (0.025 mm) the matrix K X-rays appear in the spectrum, but for the thicker

I

'O",O

30

40

50

60

I 70

80

90

2

Fig. 3. Limits of detection for trace elements in carbon and aluminum matrices using 1 PC of 2 MeV protons. The beam current i (nA) and the time T (min) to accumulate 1 pC of charge are indicated for each aluminum absorber thickness x (mm).

Fig. 4. Limits of detection for trace elements in titanium, iron and germanium matrices using 1 PC of 2 MeV protons. The beam current i (nA) and the time T (mm) to accumulate 1 pC of charge are indicated for each absorber thickness x (mm).

absorbers they do not. Thus for the typically 30 nA currents used here, the counting rate was 1500 s-i with the 0.05 mm absorber, but only a few tens of counts per second with the thicker ones. Again the thicker absorbers confer no benefit but merely worsen the light element detection limits by causing heavier attenuation of their characteristic x-rays. These observations were confirmed by measurements on a silicon matrix. All of these carbon and aluminum runs were done with currents of 15-30 nA and it took 30-60 s to collect 1 /.LC of charge. In a typical microbeam situation with 1 nA current for about 15 min (resulting in 1 PC) similar detection limits would result. For titanium, iron and germanium (fig. 4) the LOD-Z curve has structure superimposed on the familiar U-shape, due not only to the intense matrix X-rays but also (with thinner absorbers) due to their pileup peaks. Naturally in these plots there is no data point at Z = Z,. The effect of the matrix K absorption edge is very clear in each case. There is also a local maximum for that trace element whose K, X-ray energy coincides with the matrix Kg X-ray energy; that is seen best in the germanium case. At the typically 1500 s-i counting rates used to accumulate these spectra the titanium and iron pileup peaks were effectively suppressed by absorber thicknesses of 0.12 and 0.37 mm respectively; however an aluminum absorber thick

u/X Teesdale et al. / Limits of&e&on

62

z

Fig. 5. Limits of detection for trace elements in molybdenum and tin matrices using 1 pC of 2 MeV protons. The beam current i (IA) and the time T (min) to accumulate 1 PC of charge are indicated for each absorber thickness x (mm).

enough to suppress the germanium pileup would have had too great an attenuating effect on the rest of the

spectrum to be acceptable; the merit of a critical absorber in such a case is obvious. It should be noted that for matrices of m~Iybdenum and tin (fig. 5) the pileup peaks fall outside the region of interest. The basic U-shape prevails, interrupted only by the matrix K X-rays at the extreme right. Data for a silver matrix were similar. In these cases the K X-ray production cross-sections have fallen by a factor of about 250 relative to that for iron. IS X-ray suppression is therefore much less critical and an absorber just thick enough to keep the bremsstrahlung rate tolerable should be used. Any increase in thickness causes greater attenuation of K X-rays of elements having Z < 2, and so worsens their LODs. Finally the reader’s attention is drawn to numerical errars in the figures of ref. [lo] for Ti, Ge and MO; these have been corrected here. 6.2. Presentation

of LOBrelative

to accumulated counts

For those cases where the matrix X-rays are a dominant feature of the spectrum the conventional presentation of detection limits relative to 1 PC of collected charge, which we have followed to this point, does not convey in the most practical terms what can be achieved in convenient measurement times with practical beam currents. This disadvantage offsets the advantage that LODo is (except where peak pileup occurs) rate-independent, an observation justified by the experimental data of fig. 2. However a presentation in terms of time begs the fact that depending on the beam current the counting statistics accumulated in that time (T) may vary greatly, so that the detection limit for given measurement time

in thick target PIXE

is not a *unique quantity. This problem is solved by normalization to a given measurement time at a given counting rate R, which is equivalent to a given total spectral intensity I = RT. The quantity LOD, has no great intrinsic merit; its usefulness lies in the opportunity it provides for the reader to normalize to punting times and counting rates pertinent to his own arrangement. We define LQD, in terms of a half-hour measurement at 1100 counts/s, thus providing a summed spectral intensity X of about two million. In presenting the data in this format we indicate also the co~~p~~di~g beam current i in our arrangement. This should enable the reader to normalize immediately to other beam currents, whmh conld in the case of micro-PIXE be significantly smaller than those quoted here. This definition of LOD, suffices well for those matrices (Z r 20) whose own characteristic X-rays are major spectral features; in these cases the matrix X-rays are the principal contributors to the counting rate, and as we saw above absorbers are necessary to diminish this contribution in favour of the X-rays of trace elements in the matrix. It does not however add anything to our perspective on the low atomic number matrices such as carbon and alu~num (with thicker absorbers in the latter case) where the matrix K X-rays do not contribute, Fig. 6 presents our LODr values for the titanium, iron and germanium matrices. For the titanium matrix the thicker absorber (0.12 mm) preferred above is now seen to have a major advantage for trace elements having Z > 22. This arises very simply. The matrix X-ray contribution is suppressed relative to that from trace element X-rays of higher atomic number than the matrix; the beam current may then be increased considerably to maintain the same counting rate overall. The statistical accuracy of the trace elements ~format~on is now improved as are the detection limits. However the monotonic improvement conferred by increasing the absorber thickness eventually becomes somewhat academic, because the beam current necessary to achieve 2 x lo6 counts in half an hour rises very rapidly. In the titanium case 1.93 PA would be needed if one were to take advantage of the further ~provement conferred by a 0.26 mm absorber; this is impractical. For trace elements of 2 < 22 of course, increased absorber thickness has the converse effect of worsening LODs. The same effects are seen for the iron matrix. For trace elements of Z > 26 the increasing absorber thickness is most beneficial, but when it reaches 0.37 mm, the current needed has risen to 0.24 PA. Thus the detection limits of a few ppm obtained with the 0.37 mm absorber are not attainable in micro-PIXE. In that context the limits of about 20 ppm achieved with the 0.12 mm absorber do correspond to the currents of the nA level attainable in micro-PIXE.

63

W.J. Teesdale et al. / Limits of detection in thick target PIXE

1

MOLYBDENUM z

I

109-

::;:

2.64

,.o,

I \ I’

\

/’

\ \

\

v

\ \

\ ‘_

P D 104110’ CL

w

!

109

\ \

\ \

\ \

\

10’

\

\

‘.

\ 10’

t

‘. I

104HOO

--_-

\

‘03$1

y

100 TIN =

109 ii lW;o

+-d/’ II

'O"20

\ .----_

I

40

40

50

60

70

90

121 1). 90

z

A-/

30

30

::;:

50

60

70

60

90

I

Fig. 7. Detection limits for trace elements in molybdenum and tin using 2 MeV protons to induce spectra containing 2 x lo6 counts in all. The currents required to obtain these in 30 min measurement times in our arrangement are indicated.

2

Fig. 6. Detection limits for trace elements in titanium, iron and germanium matrices using 2 MeV protons to induce spectra containing 2 x lo6 counts in all. The currents i (nA) required to obtain these in 30 min measurement times in our arrangement are indicated.

Similar remarks pertain to the germanium matrix. The improvement that results in increasing the absorber thickness from 0.77 to 1.015 mm demands an increase in current from 30 to 150 nA. The practical curve for micro-PIXE is that for the 0.37 mm absorber, which has its minimum around 30 ppm. As before the situation is inverted for the molybdenum and tin cases, results for which are summarized in fig. 7. There the matrix K X-rays are at high energy but their contribution is now significantly lower. The best detection limits are a few ppm in each case, and a thicker absorber is of no benefit. 6.3.Dependence

ment up to a proton energy of 4 MeV; at higher proton energies the detection limit deteriorates, presumably due to increased reaction gamma-ray or neutron background. For the remaining matrices the figures show LODo and LOD, for trace elements of Z I 50, detected via their Ka X-rays. The aluminum matrix data are in fig. 9. LODo improves monotonically with proton energy, although

CARBON --.-----

Eo : 3 4 5

I 203 118 38 5.8 14

T 0.082~ 011 0.44 2.8, 12

of detection limits on proton energy

Fig. 8 shows the dependence of LODo upon proton energy for the lightest matrix i.e. carbon with the thinnest possible aluminum absorber in place. For the lighter trace elements having X-ray energies below about 5 keV, the rapid increase in energy and intensity of electron bremsstrahlung causes LODo to worsen steadily as the proton energy rises. For trace elements having Z > 30, whose X-rays he beyond the bremsstrahlung cut-off, the opposite is the case, i.e. there is a steady improve-

Fig. 8. Dependence of LODQ upon proton energy for a carbon matrix with a 0.025 mm absorber.

W.J. Teesdale et al. / Limits of detection in thick target PIXE

64

--.----

10-l 20

.

30

Eo

1

t 2

10.2 J.0

4 5

0.8 1.38

40

ALUMINUM --.-

T

1.63 15 20.8 121

----

r\ 50 “20 2

EC, , * -.~

t 30

i a.2 2.8 2.1 2.3 2.1

4 5

! 40

Fig. 9. Proton-energy dependence of LODq and LOD, for an aluminum matrix using an 0.025 mm aluminum absorber.

the most dramatic gain is made in moving from 1 to 2 MeV. Since the 0.025 mm absorber was used the spectra were dominated in intensity by the aluminum K X-rays, the rates being typically about 1000 s-l. The same behaviour is shown by LOD, in the right-hand portion of the figure. It may be noted that in our ~rangement

currents of about 2 nA provide the defined 2 million counts in half an hour, and so the data are directly relevant to the typical micro-PIXE arrangement. Figs. 10 and 11 present the titanium and iron data using respectively the 0.12 and 0.37 mm aluminum TITANIUM --.-

E.

I

:

293 28.3 10I 5.7 5..

3

---_

~- :

-

I 50

30

40

50

Fig. 11. Proton energy-dependence of detection limits (two definitions) for an iron matrix using a 0.375 nun absorber. Note that in the right-hand plot the 4 and 5 MeV data are omitted since they duplicate those at 3 MeV.

filters selected earlier. Both presentations indicate that little gain is made at proton energies above 3 MeV. Very similar conclusions may be drawn for iron. In these two cases optimum LOD, values close to 1 ppm are obtained. However at 3 MeV, currents of 10 and 70 nA respectively would be needed to achieve 2 X lo6 counts in half an hour. A half-hour run with the 1 nA current typical of microbeams would yield detection limits worse by factors of 3 and 8.5, respectively.

103 /

L

/’

/‘/

/‘,.

__’

P

/!

102

,,’

4 a 5

,/,I _./

10’ :u

/...~:’ ....... ...tt’

,’

.A

100

t

m Fig. 10. Proton energy-dependence of detection limits (two definitions) for a titanium matrix using a 0.12 mm aluminum absorber. Note that in the right-hand plot the data at 4 and 5 MeV duplicate those at 3 MeV and hence are omitted.

lo-'1 20

30

40

I

nl 50 v20

30

40

1,

50

I

Fig. 12. Proton energy-de~ndence of detection limits (two definitions) for a silver matrix using a 0.05 mm absorber. Note that the 5 MeV data are omitted due to their partial overlap with those at 4 MeV.

W.J. Teesdale et al. / Limits of detection in thick target PIXE

65

7. Summary

1001 20

30

40

50

60

70

80

90

2

Fig. 13. Detection limits for trace elements of 20 < 2 I 50 in a lead matrix using 1 PC of 2 MeV protons.

Unfortunately data were not taken for the germanium matrix with the 0.77 mm absorber that appeared preferable. However data taken using the 0.37 mm absorber showed a significant worsening when the proton energy was raised from 4 to 5 MeV. The optimum LOD, values obtained with sub-nanoampere currents were comparable with the titanium and iron data when the different currents needed were taken into account. The cases of molybdenum and tin are rather similar to one another, and so silver is taken as a single representative of the regin 40 I Z, I 50 in fig. 12. The worsening of LOD, as proton energy increases is at first sight surprising, but is to be expected. As E, increases the K X-ray yield from trace elements having Z < 47 increases less rapidly than the yield of silver (matrix) K X-rays. Expressing this another way, increase of E,, shifts an increasing fraction of the total spectral intensity into the matrix peak, with consequently poorer statistical definition of the trace element intensities. A thicker filter would accentuate this effect through preferential absorption of the latter.

6.4. Matrices of high atomic number

For a matrix that emits L X-rays in the spectral range of interest, matters become quite complicated as shown by the data for lead (fig. 13). The underlying behaviour is the familiar U-shaped curve and the peaks superimposed upon it are due to overlap of the trace element Ka or (La) X-rays with the L X-rays of lead. The result is a curve which somewhat resembles the L X-ray spectrum of lead, with maxima corresponding to the L,, La, L/3 and Ly groups. Since these extend over the region 9-15 keV, the detection limits for a wide range of elements (Z = 31 to 40 in the K X-ray case) are rendered disappointingly large; an increased absorber thickness obviously is not a remedy.

Several general principles have been illustrated here, as regards both the choice of proton energy and of aluminum filter thickness. Increase of energy up to 3 MeV is profitable but further increase confers only small benefits. For matrices having Z, < 15 or 40 < Z, < 50, the matrix K X-rays are not a serious perturbing influence and a filter thick enough to absorb most of the bremsstrahlung suffices. In the intermediate range 15 < Z, < 40, absorbers of increasing thickness in the 0.1-l mm range are needed to suppress the matrix K X-rays. Our presentation in terms of LOD, illustrated the absorber’s role in increasing the relative contribution (to overall intensity) of K X-rays of trace elements having Z > Z,. However the practical limit on absorber thickness is set by the available beam current. For Z < Z, a thick absorber is undesirable since it differentially suppresses the trace element K X-rays. Mommsen et al. [4] presented a single plot of LODo versus Z for several Z, values using a single absorber thickness. We do not emulate this since we have been at pains to show that different parts of the X-ray spectrum demand different absorber thicknesses, which depend on the matrix. Rather, we conclude by re-examining the optimum LODs at the U-curve minima, in terms of typical micro-PIXE conditions of a 1 nA beam incident for 15 min, corresponding to - 1 /.LC charge collected. For light matrices (C, Al) this provides detection limits of a few ppm. For the intermediate matrices Ti-Ge, using successively thicker absorbers, this micro-PIXE LOD lies in the lo-50 ppm region. When Z, exceeds 40, at which point the importance of the matrix X-rays is again decreasing, a 0.05 mm absorber provides limits of just over 10 ppm. In conventional ITPIXE with 100 nA current for 15 min, the limits would be ten times better than these values. These examples illustrate how the data presented here may be used to estimate detection limits corresponding to other situations such as TTPIXE with more intense beams or micro-PIXE with nA and sub-nA beams. Finally the present work is based on aluminum absorbers; the introduction of critical absorbers will provide further improvement in limits as demonstrated by, for example, the work of Swarm and Fleming [19].

This work was supported in the main by the Natural Sciences and Engineering Research Council of Canada. The generous assistance of the Radiation Standards Section and particularly of Dr. Bob Storey in conducting the measurements at NRC is much appreciated. Throughout the work, the advice of Dr. J.A. Cookson has been a valued stimulus.

66

W.J. Teesdale et al. / Limits of detection in thick target PIXE

PI G. Remond, F. Cesbron, K. Traxel, J.L. Campbell and L.J. Cabri, Scanning Microscopy 1 (1987) 1017. PI S.A.E. Johansson and T.B. Johansson, Nucl. Instr. and Meth. 137 (1976) 473. C. Gaarde, T. Hum and K. Kemp, Nucl. [31 F. Folkmamt, Instr. and Meth. 116 (1974) 487. [41 H. Mommsen, K.G. Bauer and Q. FazJy, Nucl. Instr. and Meth. 157 (1978) 305. S.T. Lam, D.M. Sheppard and L.G. [51 M. Khaliquzzaman, Stephens-Newsham, Nucl. Instr. and Meth. 216 (1983) 481. PI L.J. Cabri, J.L. Campbell, J.H.G. Laflamme, R.G. Leigh, J.A. Maxwell and J.D. Scott, Canad. Mineralogist 23 (1985) 133. 171 M. Ablberg, R.L. Akselsson, D. Bnme and J. Lorenzen, Nucl. Instr. and Meth. 123 (1975) 385. PI J.L. Campbell and J.A. Cookson, Nucl. Instr. and Meth. B3 (1984) 185. [91 A. Perujo, J.L. Campbell and J.A. Maxwell, Proc. 11th

[lOI

P11 WI 1131 1141 1151 Ml P71 WI 1191

Int. Cong. on X-Ray Optics and Microanalysis, ed. J.D. Brown and R.H. Packwood, (Univ. of Western Ontario, London, Canada, 1987). J.L. Campbell, A. Perujo, W.J. Teesdale and J.A. Cookson, Proc. 1st. Conf. on Nuclear Micorprobes, Oxford (1987), Nucl. Instr. and Meth. B30 (1988) 317. International Union of Pure and Applied Chemistry, Spectrochim. Acta 33B (1978) 241. P. Van Espen, H. Nullens and F. Adams, X-Ray Spectrom. 9 (1980) 126. L.H. Keith, W. Crummett, J. Deegan Jr, R.A. Libby, J.K. Taylor and G. Wenther, Anal. Chem. 55 (1983) 2210. K. Ishii and S. Morita, Phys. Rev. A5 (1984) 2278. J.L. Campbell and P.L. McGhee, Nucl. Instr. and Meth. A248 (1986) 393. J.F. Ziegler, J.P. Biersack and U. Littmark, The Stopping and Range of Ions in Solids (Pergamon, New York, 1985). T.P. Thinh and J. Leroux, X-ray Spectrom. 8 (1979) 85. J.L. Campbell, Nucl. Instr. and Meth. B31 (1988) 518. C.P. Swann and S.J. Fleming, Nucl. Instr. and Meth. 197 (1982) 237.