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A discussion of the compared advantages and drawbacks of the use of the α parameters matrix effects correction method of PIXE measurements on infinite or intermediate thickness targets
RIOMI B
Nuclear Instruments and Methods in Physics Research B7.5(1993) 148-152 North-Holland
Beam Interactions with Materials&Atoms
A discussion of the compared advantages and drawbacks of the use of the cy parameters matrix effects correction method of PIXE measurements on infinite or intermediate thickness targets G. Weber a,*, J.M. Delbrouck-Habaru and G. Robaye a
a, P. Aloupogiannis
b, I. Roelandts
‘, M. Collet a
aInstitut de Physique Nu&aire Exp&mentale,
Uniuersite’ de LiZge, B15, Sart-Tilman, B-4000 Li.?ge, Belgium, b Institute of Materials Science, National Research Center “Democritos’: GR-153 10 Ag. Paraskeui, Athens, Greece ’ Institut de Gkologie, Uniuersite’ de LiGge, Belgium
The (I parameters intermediate
thickness
method samples.
for calculating matrix effects correction It consists
of the simultaneous
acquisition
factors in PIXE has been initially established for of the PIXE spectrum along with the energy distribution
of protons elastically scattered by a thin carbon foil located behind the PIXE target. These experimental data, associated with an experimental measurement of the X-rays transmission factor T, allow the calculation of the matrix correction factors CF. The main interest of the (Y parameters method is that contrary to other correction methods it does not require a priori knowledge of the major element composition of the matrix. We have demonstrated that the formalism of the (Y parameters method can be extrapolated to deal with infinitely thick samples. In this case, one obtains (Y’Sby two PIXE measurements performed either at different beam energies or in different geometric configurations. In this paper we summarize and compare the two methods for permitting one to choose between them when the type of sample to be studied allows it.
1. Introduction When samples studied are not infinitely thin, two main matrix effects must be considered. They are due to the slowing down of the incident protons and the absorption of the induced X-rays on their way in the sample toward the detector. The usual method for correcting these effects is based upon hypotheses concerning the composition of the sample. The corrections are computed using fundamental parameters [ 11. We have established [2-41 a new correction method, which contrary to the preceding ones, is completely experimental and avoids the use of hypotheses about the matrix composition. We shall see that the precision obtained is of the same order of magnitude than for the other methods in the case where the hypotheses are valid, and much better if they are not valid. Our method is based upon the definition of a socalled (Y parameter characterizing a given X-ray energy and a particular matrix at a given proton energy E,:
* Research Research
Associate (Belgium).
0168-583X/93/$06.00
of the
National
0 1993 - Elsevier
Fund
Science
for
Scientific
Publishers
where p is the X-ray absorption coefficient the stopping power for protons of energy matrix studied. The measured intensity Zi corresponding ment i (Fig. la) is given by:
z.=
AQci
and SE,) E, in the to an ele-
~ou(E~--u)T(u) du
’ S(Eo)/ Q [(E,-u)/E,]P
(2)
’
with
T(u)
= exp
--au
[
sin( p + 0) sin e
1+& i
0
iI
(3)
and u = E, - E. This relationship has been established using an approximation for the stopping power, proposed by Folkmann [5]:
with p = -0.65 [2]. The details of the experimental procedures for obtaining the (Y values have been described for different shapes and thicknesses of the samples [2,3,6,7,9,11]. As we shall see, the choice of a particular procedure is very frequently imposed by the type of sample. It may happen however that different solutions are B.V. All rights reserved
149
G. Weber et al. / (Y parameters matrix effects correction method
3. Infinite thickness
Ef
samples
For infinite thickness samples [2,7,10] the LYparameter can be obtained using a couple of measurements in different geometrical situations. The experimental setup is shown in fig. lb. It can be shown that the intensity measured in one geometrical situation j can be reduced to the following relationship:
la
‘=
AQc
-f(a> S(E,)
’
E”,
(11)
P* 0,)
The ratio Y is obtained by evaluating Ii at the same incident energy but by tilting the sample to change 0:
Fig. 1. (a) Definition of the parameters for intermediate thickness samples. (b) Definition of the parameters for infinite thickness samples.
possible and it is very interesting guiding the choice.
2. Intermediate
thickness
to have arguments
for
samples
The experimental setup for measuring intermediate thickness samples is described in ref. [4]. The proton beam with energy E,, crosses the target and induces X-ray emission. The X-rays are detected by a Si(Li) detector and the PIXE spectrum is recorded. The proton beam proceeds on its way with an energy E, A E and is partially diffused on a thin carbon secondary target. A charged particle Si detector positioned at 90” gives a spectrum of elastically diffused protons allowing the calculation of the energy loss AE. As T= e-pm,
(5)
where m is the superficial shown that (Y= -In
T/AE’
mass of the sample,
it can be
(6)
with
Transmission determination teristic X-rays LYvalues. The described and
measurements allow the experimental of the T coefficients for a set of characand the calculation of the corresponding target preparation procedure has been tested elsewhere [4,6,8].
As the experimental parameters E,, the incident energy, p, the angle between the proton beam and the detector, and 0,, the emergence angles, are well known, relation (121 gives r as a function of (Y. The best experimental conditions have been established [lo] by evaluating the influence of the errors affecting the different parameters on the (Y determination but also by taking into account practical aspects such as sample surface roughness and X-ray background (bremsstrahlung). These conditions are: /3 = 45”, 0, = 120”, 0, = 40”; and E, = 2.35 MeV.
4. Comparison
between the two procedures
Table 1 allows one to compare the (Y values experimentally determined using the two types of targets (thick and intermediate) with the corresponding “theoretical values” calculated with the databases and the known composition of the samples. A few remarks can be formulated. When the intermediate thickness targets are used, the weak absorption CT= 1) of the energetic X-rays emitted by the heavy elements may explain the larger error associated with the corresponding (Y parameters. The fact that for very large values of a the intermediate thickness target method gives values smaller than the theoretical ones could be explained by granulometric effects, which increase the transmission of a granulous target in comparison with a homogeneous one, particularly when the absorption coefficient is large 121.The associated errors allow one to estimate the ultimate precision of the two methods. For thick targets, ten couples of measurements in the same pellet were performed and averaged. For intermediate targets from three to five different samples were used. In these conditions, the quality of the II. X-RAY
DETECTORS
1
2.06 f 0.07
2.40 fO.07
Exp. int. target
1.95*o.of,
Exp. int. target
0.76f0.02
1.39f0.04
8.52 f a.25
Exp. int. target
11.95
11.75*0.72
10.21* 0.30
Tbeor.
Exp. th. target
Exp. int. target
(geol)
10.10*0.5
Exp. th. target
IRSID
10.46 f 0.6
Theor.
761
~tO.23
10.75 i 0.38
9.93 f 0.6
7.49
f0.2
5.41f0.16
6.6 4.74f0.14
4.92fO.l
4.75 f0.3
3.06*0.09
3.57*O.LO
6.09iO.36
3.09 +0.06
3.25fO.19
3.06~0.09
2.92 * 0.05
3.06*0.18
3.75 f 0.06
3.88 f 0.24
3.59*0.11
(geol)
Exp. int. target
GXR-4
3.58 * 0.04
Exp. th. target
Them.
GSN (g&I 3.66 * 0.22
2.23*0.065
2.92io.09
E&p. int. target
7.07
2.58 f 0.065
10.11
2.65kO.16
Theor. 3.37iO.l
0.66
0.77 * 0.02
0.66 * 0.015
0.7 * 0.004
3.43f0.2
6.6
0.81 f 0.05 0.78f0.015
1.37*0.03
1.03f0.03
1.77 *o.os
1.55 fO.10
0.72 *0.02
0.05
o.s1*
Ca
and from thick or intermediate
1.44 f 0.06
K
considerations
1..59*0.1
Cl
from theoretical
Exp. th. target
9.44
2.08 + 0.04
Exp. th. target
BR (seal)
2.07*0.12
Tbeor.
NBS 1577 (biol)
2.27 f 0.14
Exp. th. target
obtained
Theor.
S
of the (I parameters
NBS1571 (biol)
Comparison
Table
3.24
1.76f0.05
1.78f0.035
1.93 f0.12
1.86f0.06
1.82iO.02
1.86iO.11
1.89 f 0.06
1.39 * 0.04
1.78fO.OS
2.09f0.12
1.17
1.14
1.4
0.22
0.3
Cr
sample experiments
2.03 * 0.06
2.18f0.13
0.37
0.5
Ti
thickness
10.05
1.67f0.02
1.66fO.l
0.92
0.96 f 0.095
0.9
1.1 ltO.08
1.1 f0.065
0.17
0.23
Mll
fO.O1
0.7
f0.035
1.3 f0.015
1.33 * 0.08
0.65 * 0.03
0.72io.Gz
0.74 f 0.045
0.65 f0.03
0.7
0.72 f 0.04
0.69 f 0.035
0.84f0.03
0.88 f 0.055
0.13
0.18
Fe
fO.l 1.52iO.09
1.6
0.46f0.03
0.47 f 0.03
0.45
0.72
0.07
0.1
CU
1.12*0.11
1.35 * 0.02
1.32 f 0.08
0.38
0.36
0.6
0.06
0.08
zn
s
G. Weber et al. / (Y parameters matrix effects correction method
results is at first sight equivalent. However, the calculation of the (Y values is not the final aim of the method; indeed, the (Y values are useful for calculating correction factors. Table 2 shows the precision associated with the correction factors when, for evident reasons, one performs only one single measurement on each sample. The precision seems to be generally better for thick targets. This better precision has a direct repercussion on the calculation of relative elemental concentrations in the sample. If we want however to obtain absolute concentrations, we must take other factors, liable to influence strongly the accuracy of the method, into account. There is essentially the determination of the stopping power for the thick targets and of the superficial mass for intermediate targets. Let us recall the role of the CF correction factor calculated from (Y values in both thick and intermediate target methods. It allows one to convert experimental PIXE X-ray peak area on an X-ray peak area
Table 2 Comparison
of the precision
of the correction
s NBS1571 (biol) th. target
int. target NBS 1577 (biol) th. target int. target
BR (geol) th. target int. target
GSN (geol) th. target int. target
GXR-4 (geol) th. target int. target
IRSID (geol) th. target int. target
factor
corresponding to the irradiation of the same quantity m of sample material if no matrix effects are present (no change of proton energy and no X-ray absorption). Using a thin target calibration curve, one can then obtain the mass of each PIXE detectable element present in the sample and therefore the relative concentrations. To obtain absolute concentrations it is necessary to know the mass m of the material irradiated by the proton beam. For intermediate thickness samples, this information is obtained by weighing the sample and calculating the superficial mass. For thick targets, one must be able to calculate the range of the proton beam in the target. This can be done if one knows the stopping power S(E). This normalization problem is common to all PIXE matrix correction procedures including the (Y parameter’s method. Here we shall not discuss these correction methods, but let us recall that all of them, the (Y parameter
for thick and intermediate
Cl
K
Ca
5.75 0.8 1.38 2.2
CF dCF/CF(%) CF dCF/CF(%)
5.99 2.9 1.82 5.2
5.74 2.5 1.63 4.1
5.63 0.8 1.43 2.7
CF dCF/CF(%) CF dCF/CF(%)
6.1 1.5 1.81 5.2
5.68 1.45 1.6 3.9
5.65 0.8 1.4 2.6
151
thickness
samples
Cr
Mn
Fe
Ti
(one single measurement).
CF dCF/CF(%) CF dCF/CF(%)
7.8 3.6 1.75 4.7
7.32 2.3 1.61 4
7.24 2 1.44 2.7
6.93 2.7 1.31 1.9
6.86 1 1.28 2
CF dCF/CF(%) CF dCF/CF(%)
7.99 1.4 1.82 5.2
7.63 1.6 1.63 4.1
7.06 0.8 1.4 2.6
6.82 3.3 1.25 2
6.75 0.4 1.22 2
8.15 2.1 2.24 6.9
7.77 2.2 1.95 5.7
7.02 1.3 1.61 4
10.86 5.8 2.04 6.1
9.45 3.2 1.82 5.2
CF dCF/CF(%) CF dCF/CF(%)
13.7 12.5 4.19 10.2
CF dCF/CF(%) CF dCF/CF(%)
15.47 14.9 3.31 9.2
14.66 8.8 2.77 8.3
7.5 1.6 1.34 2
7.41 0.9 1.3 2
Cu
Zn
6.76 0.7 1.36 2.1
6.91 1 1.28 2
7.24 0.85 1.26 2
7.8 3.6 1.36 2
II. X-RAY
7.77 0.08 1.32 2
DETECTORS
152
G. Weber et al. / (Y parameters matrix effects correction method
correction method excepted, require the use of hypotheses about the sample composition. In the case of thick targets, it has been shown elsewhere [lo] that, due to the definition of (Y= p/S(E), it is possible to evaluate S(E) when a set of (Y parameters has been determined for different elements present in the sample. Generally S(E) can be estimated with a precision of about 8%. Evidently S(E) or m are not necessary in favorable cases where the concentration of one major element of the sample can be obtained by an independent reliable method. The calculation of the absolute concentrations from the relative ones becomes then much more precise. For intermediate thickness samples a study concerning a large range of reference materials has been performed. It has been shown [8] that the experimentally determined precision of the method is within the range of lo-14% for elements whose concentrations lie between 15 ppm and 25%. These precision values are experimental data which are influenced by all the parameters involved in the PIXE measurement and the correction method: homogeneity of the raw material, target preparation (specially the weighing), calculation databases, calibration curves, etc. Precision is of course very important, but there are many other points to consider. 1) The intermediate thickness option is of course compulsory in the case where the quantity of material to be studied is too small to make a pellet. The same choice holds also for samples presenting themselves immediately under the adequate form, such as filters. An important advantage is the fact that the use of a secondary target to measure transmission of X-rays makes the (Y directly available even for trace elements. There are however many drawbacks associated with the intermediate thickness option. The target preparation and the experimental protocol are rather slow and require meticulosity, namely during weighing. Some very small grains (below 0.4 urn> may cross the Nuclepore backing. Native sulfur contained in volcanic samples may be lost by this way. As the proton beam is not stopped in the sample, contamination of the backing may be a problem for trace analysis and bromine-free Nuclepore backings are preferable to standard ones. The total amount of studied material is smaller than for thick targets and the question of its representativity must be considered. Finally, as seen before, granulometric effects may play a large role here because of the small thickness of the sample. 2) The option of infinite thickness targets presents many advantages. The preparation technique is very simple and with few possibilities of contamination or element loss occurrence. The possibility of direct bombardment of the sample is a very important advantage
when the nondestructive feature is required (archeology, works of art, etc.). The measurements are easy and the correction calculation fast. When the experimental parameters are settled, general purpose tables can give the matrix correction factors immediately [lo]. The representativity of the samples is generally better than for intermediate targets. Among the drawbacks of this option, we point out the necessity to interpolate between (Y’S obtained for elements giving statistically good PIXE peaks to obtain the (Y’S corresponding to trace elements. Absorption discontinuities associated with the presence of some major elements in the sample may increase the difficulties. Due to the necessity of defining accurately the geometrical conditions, it is difficult to realize a setup allowing the measurement of several samples without breaking the PIXE chamber vacuum. Finally, as two successive measurements on the same sample are necessary, one must take care of having no variation of the sample residual humidity during the experiment.
Acknowledgement We are indebted to the Institut Interuniversitaire des Sciences Nucleaires (Belgium) for financial support.
References (11 S.A.E. Johansson and J.L. Campbell, PIXE: A Novel Technique for Elemental Analysis (Wiley, New York, 1988). [2] P. Aloupogiannis, Ph.D. Thesis, Paris (1988). [3] P. Aloupogiannis, G. Robaye, I. Roelandts, G. Weber, J.M. Delbrouck-Habaru and J.P. Quisefit, Nucl. Instr. and Meth. B14 (1986) 297. [4] P. Aloupogiannis, G. Robaye, I. Roelandts and G. Weber, Nucl. Instr. and Meth. B22 (1987) 72. [5] F. Folkmann, Ion Beam Surface Analysis, vol. 2 (Plenum, New York, London, 1976) p. 747. [6] P. Aloupogiannis, Analusis 15 (7) (1987) 347. [7] P. Aloupogiannis, G. Weber, J.P. Quisefit, J.M. Delbrouck-Habaru, I. Roelandts, M.C. Rouelle and G. Robaye, Nucl. Instr. and Meth. B42 (1989) 359. [8] P. Aloupogiannis, G. Robaye, G. Weber, J.M. Delbrouck-Habaru and I. Roelandts, X-Ray Spectrom. 19 (1990) 133. [9] M. Collet, Thesis, University of Liege (19901. [lo] J.M. Delbrouck-Habaru, G. Weber, P. Aloupogiannis, G. Robaye and I. Roelandts, Nucl. Instr. and Meth. B73 (1993) 71. [ll] P. Aloupogiannis, Int. J. PIXE, to be published.
Nuclear Instruments and Methods in Physics Research B7.5(1993) 148-152 North-Holland
Beam Interactions with Materials&Atoms
A discussion of the compared advantages and drawbacks of the use of the cy parameters matrix effects correction method of PIXE measurements on infinite or intermediate thickness targets G. Weber a,*, J.M. Delbrouck-Habaru and G. Robaye a
a, P. Aloupogiannis
b, I. Roelandts
‘, M. Collet a
aInstitut de Physique Nu&aire Exp&mentale,
Uniuersite’ de LiZge, B15, Sart-Tilman, B-4000 Li.?ge, Belgium, b Institute of Materials Science, National Research Center “Democritos’: GR-153 10 Ag. Paraskeui, Athens, Greece ’ Institut de Gkologie, Uniuersite’ de LiGge, Belgium
The (I parameters intermediate
thickness
method samples.
for calculating matrix effects correction It consists
of the simultaneous
acquisition
factors in PIXE has been initially established for of the PIXE spectrum along with the energy distribution
of protons elastically scattered by a thin carbon foil located behind the PIXE target. These experimental data, associated with an experimental measurement of the X-rays transmission factor T, allow the calculation of the matrix correction factors CF. The main interest of the (Y parameters method is that contrary to other correction methods it does not require a priori knowledge of the major element composition of the matrix. We have demonstrated that the formalism of the (Y parameters method can be extrapolated to deal with infinitely thick samples. In this case, one obtains (Y’Sby two PIXE measurements performed either at different beam energies or in different geometric configurations. In this paper we summarize and compare the two methods for permitting one to choose between them when the type of sample to be studied allows it.
1. Introduction When samples studied are not infinitely thin, two main matrix effects must be considered. They are due to the slowing down of the incident protons and the absorption of the induced X-rays on their way in the sample toward the detector. The usual method for correcting these effects is based upon hypotheses concerning the composition of the sample. The corrections are computed using fundamental parameters [ 11. We have established [2-41 a new correction method, which contrary to the preceding ones, is completely experimental and avoids the use of hypotheses about the matrix composition. We shall see that the precision obtained is of the same order of magnitude than for the other methods in the case where the hypotheses are valid, and much better if they are not valid. Our method is based upon the definition of a socalled (Y parameter characterizing a given X-ray energy and a particular matrix at a given proton energy E,:
* Research Research
Associate (Belgium).
0168-583X/93/$06.00
of the
National
0 1993 - Elsevier
Fund
Science
for
Scientific
Publishers
where p is the X-ray absorption coefficient the stopping power for protons of energy matrix studied. The measured intensity Zi corresponding ment i (Fig. la) is given by:
z.=
AQci
and SE,) E, in the to an ele-
~ou(E~--u)T(u) du
’ S(Eo)/ Q [(E,-u)/E,]P
(2)
’
with
T(u)
= exp
--au
[
sin( p + 0) sin e
1+& i
0
iI
(3)
and u = E, - E. This relationship has been established using an approximation for the stopping power, proposed by Folkmann [5]:
with p = -0.65 [2]. The details of the experimental procedures for obtaining the (Y values have been described for different shapes and thicknesses of the samples [2,3,6,7,9,11]. As we shall see, the choice of a particular procedure is very frequently imposed by the type of sample. It may happen however that different solutions are B.V. All rights reserved
149
G. Weber et al. / (Y parameters matrix effects correction method
3. Infinite thickness
Ef
samples
For infinite thickness samples [2,7,10] the LYparameter can be obtained using a couple of measurements in different geometrical situations. The experimental setup is shown in fig. lb. It can be shown that the intensity measured in one geometrical situation j can be reduced to the following relationship:
la
‘=
AQc
-f(a> S(E,)
’
E”,
(11)
P* 0,)
The ratio Y is obtained by evaluating Ii at the same incident energy but by tilting the sample to change 0:
Fig. 1. (a) Definition of the parameters for intermediate thickness samples. (b) Definition of the parameters for infinite thickness samples.
possible and it is very interesting guiding the choice.
2. Intermediate
thickness
to have arguments
for
samples
The experimental setup for measuring intermediate thickness samples is described in ref. [4]. The proton beam with energy E,, crosses the target and induces X-ray emission. The X-rays are detected by a Si(Li) detector and the PIXE spectrum is recorded. The proton beam proceeds on its way with an energy E, A E and is partially diffused on a thin carbon secondary target. A charged particle Si detector positioned at 90” gives a spectrum of elastically diffused protons allowing the calculation of the energy loss AE. As T= e-pm,
(5)
where m is the superficial shown that (Y= -In
T/AE’
mass of the sample,
it can be
(6)
with
Transmission determination teristic X-rays LYvalues. The described and
measurements allow the experimental of the T coefficients for a set of characand the calculation of the corresponding target preparation procedure has been tested elsewhere [4,6,8].
As the experimental parameters E,, the incident energy, p, the angle between the proton beam and the detector, and 0,, the emergence angles, are well known, relation (121 gives r as a function of (Y. The best experimental conditions have been established [lo] by evaluating the influence of the errors affecting the different parameters on the (Y determination but also by taking into account practical aspects such as sample surface roughness and X-ray background (bremsstrahlung). These conditions are: /3 = 45”, 0, = 120”, 0, = 40”; and E, = 2.35 MeV.
4. Comparison
between the two procedures
Table 1 allows one to compare the (Y values experimentally determined using the two types of targets (thick and intermediate) with the corresponding “theoretical values” calculated with the databases and the known composition of the samples. A few remarks can be formulated. When the intermediate thickness targets are used, the weak absorption CT= 1) of the energetic X-rays emitted by the heavy elements may explain the larger error associated with the corresponding (Y parameters. The fact that for very large values of a the intermediate thickness target method gives values smaller than the theoretical ones could be explained by granulometric effects, which increase the transmission of a granulous target in comparison with a homogeneous one, particularly when the absorption coefficient is large 121.The associated errors allow one to estimate the ultimate precision of the two methods. For thick targets, ten couples of measurements in the same pellet were performed and averaged. For intermediate targets from three to five different samples were used. In these conditions, the quality of the II. X-RAY
DETECTORS
1
2.06 f 0.07
2.40 fO.07
Exp. int. target
1.95*o.of,
Exp. int. target
0.76f0.02
1.39f0.04
8.52 f a.25
Exp. int. target
11.95
11.75*0.72
10.21* 0.30
Tbeor.
Exp. th. target
Exp. int. target
(geol)
10.10*0.5
Exp. th. target
IRSID
10.46 f 0.6
Theor.
761
~tO.23
10.75 i 0.38
9.93 f 0.6
7.49
f0.2
5.41f0.16
6.6 4.74f0.14
4.92fO.l
4.75 f0.3
3.06*0.09
3.57*O.LO
6.09iO.36
3.09 +0.06
3.25fO.19
3.06~0.09
2.92 * 0.05
3.06*0.18
3.75 f 0.06
3.88 f 0.24
3.59*0.11
(geol)
Exp. int. target
GXR-4
3.58 * 0.04
Exp. th. target
Them.
GSN (g&I 3.66 * 0.22
2.23*0.065
2.92io.09
E&p. int. target
7.07
2.58 f 0.065
10.11
2.65kO.16
Theor. 3.37iO.l
0.66
0.77 * 0.02
0.66 * 0.015
0.7 * 0.004
3.43f0.2
6.6
0.81 f 0.05 0.78f0.015
1.37*0.03
1.03f0.03
1.77 *o.os
1.55 fO.10
0.72 *0.02
0.05
o.s1*
Ca
and from thick or intermediate
1.44 f 0.06
K
considerations
1..59*0.1
Cl
from theoretical
Exp. th. target
9.44
2.08 + 0.04
Exp. th. target
BR (seal)
2.07*0.12
Tbeor.
NBS 1577 (biol)
2.27 f 0.14
Exp. th. target
obtained
Theor.
S
of the (I parameters
NBS1571 (biol)
Comparison
Table
3.24
1.76f0.05
1.78f0.035
1.93 f0.12
1.86f0.06
1.82iO.02
1.86iO.11
1.89 f 0.06
1.39 * 0.04
1.78fO.OS
2.09f0.12
1.17
1.14
1.4
0.22
0.3
Cr
sample experiments
2.03 * 0.06
2.18f0.13
0.37
0.5
Ti
thickness
10.05
1.67f0.02
1.66fO.l
0.92
0.96 f 0.095
0.9
1.1 ltO.08
1.1 f0.065
0.17
0.23
Mll
fO.O1
0.7
f0.035
1.3 f0.015
1.33 * 0.08
0.65 * 0.03
0.72io.Gz
0.74 f 0.045
0.65 f0.03
0.7
0.72 f 0.04
0.69 f 0.035
0.84f0.03
0.88 f 0.055
0.13
0.18
Fe
fO.l 1.52iO.09
1.6
0.46f0.03
0.47 f 0.03
0.45
0.72
0.07
0.1
CU
1.12*0.11
1.35 * 0.02
1.32 f 0.08
0.38
0.36
0.6
0.06
0.08
zn
s
G. Weber et al. / (Y parameters matrix effects correction method
results is at first sight equivalent. However, the calculation of the (Y values is not the final aim of the method; indeed, the (Y values are useful for calculating correction factors. Table 2 shows the precision associated with the correction factors when, for evident reasons, one performs only one single measurement on each sample. The precision seems to be generally better for thick targets. This better precision has a direct repercussion on the calculation of relative elemental concentrations in the sample. If we want however to obtain absolute concentrations, we must take other factors, liable to influence strongly the accuracy of the method, into account. There is essentially the determination of the stopping power for the thick targets and of the superficial mass for intermediate targets. Let us recall the role of the CF correction factor calculated from (Y values in both thick and intermediate target methods. It allows one to convert experimental PIXE X-ray peak area on an X-ray peak area
Table 2 Comparison
of the precision
of the correction
s NBS1571 (biol) th. target
int. target NBS 1577 (biol) th. target int. target
BR (geol) th. target int. target
GSN (geol) th. target int. target
GXR-4 (geol) th. target int. target
IRSID (geol) th. target int. target
factor
corresponding to the irradiation of the same quantity m of sample material if no matrix effects are present (no change of proton energy and no X-ray absorption). Using a thin target calibration curve, one can then obtain the mass of each PIXE detectable element present in the sample and therefore the relative concentrations. To obtain absolute concentrations it is necessary to know the mass m of the material irradiated by the proton beam. For intermediate thickness samples, this information is obtained by weighing the sample and calculating the superficial mass. For thick targets, one must be able to calculate the range of the proton beam in the target. This can be done if one knows the stopping power S(E). This normalization problem is common to all PIXE matrix correction procedures including the (Y parameter’s method. Here we shall not discuss these correction methods, but let us recall that all of them, the (Y parameter
for thick and intermediate
Cl
K
Ca
5.75 0.8 1.38 2.2
CF dCF/CF(%) CF dCF/CF(%)
5.99 2.9 1.82 5.2
5.74 2.5 1.63 4.1
5.63 0.8 1.43 2.7
CF dCF/CF(%) CF dCF/CF(%)
6.1 1.5 1.81 5.2
5.68 1.45 1.6 3.9
5.65 0.8 1.4 2.6
151
thickness
samples
Cr
Mn
Fe
Ti
(one single measurement).
CF dCF/CF(%) CF dCF/CF(%)
7.8 3.6 1.75 4.7
7.32 2.3 1.61 4
7.24 2 1.44 2.7
6.93 2.7 1.31 1.9
6.86 1 1.28 2
CF dCF/CF(%) CF dCF/CF(%)
7.99 1.4 1.82 5.2
7.63 1.6 1.63 4.1
7.06 0.8 1.4 2.6
6.82 3.3 1.25 2
6.75 0.4 1.22 2
8.15 2.1 2.24 6.9
7.77 2.2 1.95 5.7
7.02 1.3 1.61 4
10.86 5.8 2.04 6.1
9.45 3.2 1.82 5.2
CF dCF/CF(%) CF dCF/CF(%)
13.7 12.5 4.19 10.2
CF dCF/CF(%) CF dCF/CF(%)
15.47 14.9 3.31 9.2
14.66 8.8 2.77 8.3
7.5 1.6 1.34 2
7.41 0.9 1.3 2
Cu
Zn
6.76 0.7 1.36 2.1
6.91 1 1.28 2
7.24 0.85 1.26 2
7.8 3.6 1.36 2
II. X-RAY
7.77 0.08 1.32 2
DETECTORS
152
G. Weber et al. / (Y parameters matrix effects correction method
correction method excepted, require the use of hypotheses about the sample composition. In the case of thick targets, it has been shown elsewhere [lo] that, due to the definition of (Y= p/S(E), it is possible to evaluate S(E) when a set of (Y parameters has been determined for different elements present in the sample. Generally S(E) can be estimated with a precision of about 8%. Evidently S(E) or m are not necessary in favorable cases where the concentration of one major element of the sample can be obtained by an independent reliable method. The calculation of the absolute concentrations from the relative ones becomes then much more precise. For intermediate thickness samples a study concerning a large range of reference materials has been performed. It has been shown [8] that the experimentally determined precision of the method is within the range of lo-14% for elements whose concentrations lie between 15 ppm and 25%. These precision values are experimental data which are influenced by all the parameters involved in the PIXE measurement and the correction method: homogeneity of the raw material, target preparation (specially the weighing), calculation databases, calibration curves, etc. Precision is of course very important, but there are many other points to consider. 1) The intermediate thickness option is of course compulsory in the case where the quantity of material to be studied is too small to make a pellet. The same choice holds also for samples presenting themselves immediately under the adequate form, such as filters. An important advantage is the fact that the use of a secondary target to measure transmission of X-rays makes the (Y directly available even for trace elements. There are however many drawbacks associated with the intermediate thickness option. The target preparation and the experimental protocol are rather slow and require meticulosity, namely during weighing. Some very small grains (below 0.4 urn> may cross the Nuclepore backing. Native sulfur contained in volcanic samples may be lost by this way. As the proton beam is not stopped in the sample, contamination of the backing may be a problem for trace analysis and bromine-free Nuclepore backings are preferable to standard ones. The total amount of studied material is smaller than for thick targets and the question of its representativity must be considered. Finally, as seen before, granulometric effects may play a large role here because of the small thickness of the sample. 2) The option of infinite thickness targets presents many advantages. The preparation technique is very simple and with few possibilities of contamination or element loss occurrence. The possibility of direct bombardment of the sample is a very important advantage
when the nondestructive feature is required (archeology, works of art, etc.). The measurements are easy and the correction calculation fast. When the experimental parameters are settled, general purpose tables can give the matrix correction factors immediately [lo]. The representativity of the samples is generally better than for intermediate targets. Among the drawbacks of this option, we point out the necessity to interpolate between (Y’S obtained for elements giving statistically good PIXE peaks to obtain the (Y’S corresponding to trace elements. Absorption discontinuities associated with the presence of some major elements in the sample may increase the difficulties. Due to the necessity of defining accurately the geometrical conditions, it is difficult to realize a setup allowing the measurement of several samples without breaking the PIXE chamber vacuum. Finally, as two successive measurements on the same sample are necessary, one must take care of having no variation of the sample residual humidity during the experiment.
Acknowledgement We are indebted to the Institut Interuniversitaire des Sciences Nucleaires (Belgium) for financial support.
References (11 S.A.E. Johansson and J.L. Campbell, PIXE: A Novel Technique for Elemental Analysis (Wiley, New York, 1988). [2] P. Aloupogiannis, Ph.D. Thesis, Paris (1988). [3] P. Aloupogiannis, G. Robaye, I. Roelandts, G. Weber, J.M. Delbrouck-Habaru and J.P. Quisefit, Nucl. Instr. and Meth. B14 (1986) 297. [4] P. Aloupogiannis, G. Robaye, I. Roelandts and G. Weber, Nucl. Instr. and Meth. B22 (1987) 72. [5] F. Folkmann, Ion Beam Surface Analysis, vol. 2 (Plenum, New York, London, 1976) p. 747. [6] P. Aloupogiannis, Analusis 15 (7) (1987) 347. [7] P. Aloupogiannis, G. Weber, J.P. Quisefit, J.M. Delbrouck-Habaru, I. Roelandts, M.C. Rouelle and G. Robaye, Nucl. Instr. and Meth. B42 (1989) 359. [8] P. Aloupogiannis, G. Robaye, G. Weber, J.M. Delbrouck-Habaru and I. Roelandts, X-Ray Spectrom. 19 (1990) 133. [9] M. Collet, Thesis, University of Liege (19901. [lo] J.M. Delbrouck-Habaru, G. Weber, P. Aloupogiannis, G. Robaye and I. Roelandts, Nucl. Instr. and Meth. B73 (1993) 71. [ll] P. Aloupogiannis, Int. J. PIXE, to be published.