- Email: [email protected]
Use of rutherford scattering on a secondary carbon target for correcting intermediate thickness sample PIXE measurements
Nuclear Instruments and Methods in Physics Research B14 (1986) 297-303 North-Holland, Amsterdam
297
USE OF RUTHERFORD SCATIXRING ON A SECONDARY CARBON TARGET FOR CORRECTING INTERMEDIATE THICKNESS SAMPLE PIXE MEASUREMENTS P. ALOUPOGIANNIS I.*), G. ROBAYE I), I. ROELANDTS J.M. DELBROUCK-HABARU I) and J.P. QUISEFIT 2,
3), G. WEBER”*,
‘I Experimental Nuclear Physics, University of Liege, B15 Sart-Tilman, B-4000 Lwge, Belgium ‘) Luboratoire de Chimie des milieux naturels ** , No. 717, Universire de Paris 7, 2 PI. Jussleu, 75251, Paris, Cedex 05, France ” Geologv, Pefrology and Geochemistry, University of Liege, B20, Sart-Tilman, B-4000 Liege, Belgium Received 9 September, 1985
A method is presented for correcting PIXE measurements on intermediate thickness targets. The correction deals with the X-ray attenuation and the incident proton energy loss. It is based on the simultaneous acquisition of the PIXE spectrum along with the energy distribution of protons elastically scattered by a thin secondary carbon foil located behind the PIXE target. These measurements allowed a linear correlation between the proton energy loss AE and the correcting demonstrated. The validity of these simplifying linear approximations is discussed. The method is applicable like aerosol impactor stages.
1. Introduction When PIXE is used for measuring elemental concentrations on intermediate thickness samples, (neither infinitely thick nor very thin), correction of concentration measurement is a rather difficult task. The decrease of ionization cross section due to the slowing-down of incident protons and the absorption of X-rays generated inside the sample have to be taken into account. If the sample thickness varies from one point to another, the problem becomes more complicated. Conically shaped deposits on single orifice impactors stages are wellknown examples of difficult samples. As cascade impactors have been found to be essential in atmospheric aerosols studies [l], many authors have published attempts to solve these problems. Iteration methods based on PIXE measurements itself imply the use of hypotheses about the deposit composition, because light elements are not directly detectable by this method. Maenhaut [2], for instance, dealing with marine aerosol impactor samples estimates a relative uncertainty in the X-ray attenuation correction, running as’high as 30 to 50%, due to both the hypothesis about composition and the type of sample. * Research associate of the National Fund of Scientific Research. ** Unite asso&& au C.N.R.S. Laboratoire de physicochimie de l’atmosphere.
0168-583X/86/$03.50 0 Elsevier Science Publishers (North-Holland Physics Publishing Division)
B.V.
factor for X-ray absorption to inhomogeneous
thickness
XF to be samples
Nelson et al. [3], have shown that backscattering measurements could be used for assessing low Z elements, but it requires a second measurement with a higher energy beam (16 MeV protons). This is obviously not practical for most PIXE laboratories working with small Van de Graaff accelerators. Carlsson et al. [l], have proposed a method based on the measurement of the X-ray attenuation coefficient by using an X-ray beam produced by irradiating a silver or a potassium target with a 2.55 MeV proton beam. Using a narrow collimator and a micrometer screw to shift the sample, they were able to obtain thickness profiles of the deposits. We propose here a new approach based on the simultaneous acquisition of the PIXE spectrum and of the energy spectrum of protons after their passage through the sample and their Rutherford scattering on a secondary carbon target. From this spectrum, we obtain, -after corrections, the equivalent thickness profile of the sample in a single measurement. Using the information contained in the diffused proton spectrum and, in some cases, from additional X-ray transmission measurements, we are able to define a procedure for correcting PIXE measurement. The main goal of this work was to discover a relationship between the proton energy loss distribution through the sample and the correction factor for the corresponding PIXE spectrum. We have therefore treated the problem both experimentally and theoretically.
P. Aloupogiunnis et al. / PIXE ana+is
298
of intermedialethickness samples
2. Theor?,
For a thin sample with the same superficial becomes
The two main physical phenomena to deal with are the variation of the X-ray excitation cross section as a function of proton energy and the attenuation of the resulting X-rays on their path out of the sample to the Si(Li) detector. Keeping in mind the fact that corrections for low energy elements (like S) are rather large and generally difficult to estimate for thick samples, a simple and fast procedure even with an admissible loss of accuracy has been developed. The X-ray yield of element i in a target of uniform intermediate thickness is given by the well-known relation:
BN. I r.thm =yN,m,u,(EO)
I
and finally =
IIT
u,
EC,
u,(Ea) ~ _ 0,
= SF (cross section factor)
= matrix density (g/cm3); = factor including detector geometry, fluorescence yield and detection efficiency; Np = incident proton number; E, = incident proton energy; E, = final proton energy: coefficient for characteristic X-ray p, = attenuation emitted by the element i; S(E) = stopping power at energy E; Nw = Avogadro number: = X-ray detector angle; 8 A, = atomic mass of the element i; u,(E) = excitation cross section; of the element i. c, = concentration This relation corresponds to the experimental situation where the beam spot is smaller than the sample surface and where the beam incidence is perpendicular to the sample. Eq. (1) shows that the calculation of the yield I, depends on the excitation cross-section data base. However in the case of intermediate samples, since the energy dependence of this cross section u,(E) is a rather slowly varying function. it can be approximated by P
(5)
and
I r.,,un
where
1 -exp(-K)
writing
K
1
K
o,(4) It.thin
1 -exp(-K)
Ei I,=BN~~c,+ J
mass, eq. (3)
=
= XF (X factor)
4 . SF. XF
(6) (7)
In order to evaluate these two correction factors, the following experimental procedures have been carried out.
B
u,(E,) +u,(Et)
a =
,
? L
in order to separate tors. We then have
]‘=A
the excitation
B&v Npc _ 1 - exp( -pph/sin ,(J,
I
p/sin
and absorption 0)
’
0
fac-
(2)
since C, = m,/m and ph = m, where m, = superficial mass of the mass of the element i; m = superficial sample; h = sample thickness. If we call K = pm/sin 0 I,=A
BN avNmol-ex~(-K)
I
pir
K
’
(3)
3. Experimental Fig. 1 shows the experimental setup used for simultaneous PIXE and proton energy loss measurements. The Si(Li) X-ray detector is positioned at 135” (lab). A 15.5 pg/cm* carbon foil, supported by a Teflon frame with a 20 mm diameter hole is positioned at 45” (lab) on a retractable holder behind the sample. A solid state detector at 8 (lab) = 90” allows the detection of protons elastically diffused by the carbon foil. A collimating system gives total protection to the particle detector from receiving particles scattered by the Teflon frame or by the sample. Teflon was selected because it produces only a very low X-ray background if it is struck by protons scattered by the sample. A computer driven holder allows precise positioning of the sample. A sighting telescope at t?(lab) = 0” helps for the initial settings. The light brown impact trace of the collimated proton beam on a Nucleopore target backing is also useful for that purpose. Care must be taken during vacuum pumping and atmospheric opening of the setup in order not to break the thin carbon foil. In our case, vacuum pumping is done simultaneously at the two sides of the beam collimator to avoid any air flow in the foil direction. The same carbon foil was used for three weeks with more than 50 pumping cycles. Despite of its fragility, the carbon foil presents many advantages. Campbell et al. [4] have recently used backscattering for measuring uniform thin target thicknesses. They used as a backscattering target a gold layer deposited by evaporation on glass. Such a target is, of course, easy to handle; but is not transparent to the beam, produces X-ray background and, if the sample studied is too thick, the
P. Aloupogiannis et al. / PIXE analysis
of intermediatethickness samples
-.-._.
299
w---I
1
---------n
2 x
r
-
Fig 2. Experimental setup for X-ray transmission measurements. (1) X-ray tube, (2) collimator, (3) movable fluorescent pellet holder, (4) aerosol sample, (5) mobile micrometer table, (6) collimator, (7) Si(Li) detector, (8) sighting lens.
by the PIXE method. The use of a 2 mm diameter spot has shown that the homogeneity is of the same order of magnitude (5%) as for actual atmospheric filters.
Fig. 1. Expe~mental setup for simultaneous PIXE and RBS measurements. (1) Si(Li) detector, (2) collimators, (3) TV camera, (4) carbon foil, (5) Si charged particle detector, (6) movable holder, (7) Faraday cup, (8) sighting lens, (9) aerosol sample, (10) aerosol sample holder, (11) incident proton beam, (12) vacuum chamber,
4. Results These experimental setups have been first used to study an impactor stage sampled in Athens. Fig. 3
T 1.0 -
due to RBS on the glass interferes with the protons scattered on gold. Moreover, the high level of backscattering on .the thick glass necessitates use of a low intensity beam to avoid pile-up. Fig. 2 shows the setup used for X-ray trans~ssion measurements. It is quite similar to that of Carlsson et al. [l] except for the X-ray source. An excitating X-ray beam from a standard X-ray tube strikes a fluorescent pellet fixed on a removable holder. A modified microscope plate allows accurate positioning of the samples in front of the small collimator of the Si(Li) detector. Initial settings are performed using of a sighting telescope. Samples of known composition were prepared following the method described by Pella et al. [S]. Standard IRSID 876-l powder was set in suspension in distilled water and filtered through a Nucleopore membrane. The homogeneity of these standards was checked continuum
0.6 -
0.6 -
0.4 -
0.2 -
-1
I
i
.0.5
0
/
0.5 Beam
Fig. 3. Transmission coefficient for Athens a function of X-ray beam position.
impactor
,
t
1
1.5
position
(mm1
sample as
P. Aloupogiunnis
300
et al. / PIXE
onu~vsis of rntermediate
thickness samples
: .. . . . .
I
. .:.
:.
. ..z .. . .. _/ :' i~....._..~._5.~CC.,_~.. .._ _ .-_.. -5.,_.-_s_..r.r..a~~__.*--
'... ;...... ..._.._ _ m
: ..‘.“. .: ‘. _._:.. ,“” -‘* ‘. ..>.A. _._,_~ -...-.._,._....-.._..--....%..._. r .. ...-..-.-._-r._.,.,.. .-
..
....’
L
r
.-. .
. . ... _..j ....: .__-..._‘.C”-. ....._.:. v.-..
.... ..... .. ...- .-, .._. - .___- ... ,_..-
.. ;_:._. /.., .-” ...._.,.m.--..-.-‘s. ..L... .._. 7.r..,...-.,___.._._
.*.._
.:.
...L... .,
1
.
2
..
x.. “W.__._ .., ......... _
:.
4 “.... %........
.:.*_.. ;..,..-..a.._. .::.;-. .-.*+.? ......L,.._. __‘. . :-....__.. .,..*~. ..._ ..-. .;.-__.:....._ -:.._-.. n_.._...2_,_ ....-.._.“. ,... - ...e :. .*-.. -..-..._. .’ :.. . . . . -, ,~_..‘.“--.-_.. ,,_/._.-..V.--....-._ _ -. .‘,‘_.. -.....,.... ,.: ., .-... _.. . ‘.‘._ 1 .*._.. ‘_-.y_--..r.--.-_...._ ..,-..._-....*...,..-:-:-.*... . i ,_..-._+;:.--~r-..__2.
-.
._-,.-... ._.....-L.-.-‘..+_.-._...- .....__........___...h._......
3
__
5
6
7
8
‘._.“f.... _. ‘... ‘%.
1.. __.._ ...__ .._._.__\._____.__i...__ g ......-.~.-....~..-~-.‘~.. :..._.?..._._. 2.I:{ .._._ ..,. __.._.._... r. ._ . ...._.......... ....
,.,.... _.*.---_;_.;i;..:
r
“....,
_
...\... _....:p
. . . . . -.._---.-..-
.
loz.
. ..-..l_..-.._.__
.-' _...:: .../..--.-.' .' _ ..._._-.__.... _.. C.... _._-..._.._._.__-. 1.8 1.6 1.4 1.2
11 '.. .-C.... ...... 2.0
2.2
Ep (MeV)
Fig. 4. Example of scattered steps, on Athens sample.
proton
energy distribution
for 0.5 mm diameter
2.5 MeV, 5 nA proton
beam with 0.25 mm displacement
P. Aloupogiannis et al. / PIXE analysis of intermediate thickness samples (XF-1)
t
301
(XF -1)
I
2-
01
0.2
0.3
0.4
0.5
0.6 AE,,(MeV)
Fig. 5. Correlation between XF and AE for Athens impaetor
stage.
Fig. 6. Correlation between XF and AE for IRSID 876-I samples.
shows the transmission coefficients, T = I/& obtained using a 0.5 mm diameter collimator with 0.25 mm displacement steps. Fig. 4 gives the corresponding proton energy distribution obtained when irradiating the same target spots with a 2.5 MeV, 0.5 mm diameter, 5 nA proton beam. From these results the correcting coefficient XF and the corresponding mean energy loss AE, corrected for the variations of the Rutherford scattering cross section as a function of proton energy, have been evaluated. Evidence for a rather good linear correlation between XF and AE is shown in fig. 5. This relationship becomes XF = AA E + 1; given that for an infinitely thin layer, A E = 0 thus XF = 1. This leads us to set the Y-axis unit to XF - 1. The linear regression coefficients were 0.969 for S, 0.984 for Ca and 0.936 for Fe. Given the difficulties of studying exactly the same spots with the two different setups, we decided to perform the same type of experiments using the homogeneous IRSID deposits previously described. Fig. 6 shows the XF, AE corresponding correlations. The linear regression coefficients were 0.996 for S, 0.991 for Ca and 0.995 for Fe. In order to evaluate possible enhancement effects during transmission experiments, we mea-
coefficients for the homogesured the S transmission neous samples using three different excitation pellets: S, S + 10% KBr and a composite pellet containing S, K, Ca, Fe, Zn, Br and MO. Table 1 shows that these enhancement effects are negligible here.
5. Discussion In order to check the possibility of generalizing the previous findings and thereby use a linear correlation between XF and A E, we have calculated, for sulfur in ten different matrices, sets of XF and AE pairs corresponding to several superficial masses. For a given superficial mass m (fig. 7), the XF coefficient is calculated using eq. (6) and the data base given by R. Theisen and D. Vollath [6]. A E is evaluated using a step by step procedure. The sample is considered as a stack of elementary thicknesses dm. For each dm we call the incident energy E, and calculate dE using the stopping power approximation given by Folkmann 171.
(8)
Table 1 Sulfur transmission coefficients for IRSID samples of different thicknesses. 7’= exp( - pm) = I/I,. Target
TA: S+KBr T,: pure S T,: multielement
Mass (mg/cm’) 0.25
0.445
1.07
1.31
2.15
3.57
3.93
5.29
0.777 0.781 0.787
0.596 0.563 0.586
0.338 0.331 0.367
0.277 0.279 0.275
0.151
0.038 0.029 0.032
0.029 0.024 0.027
0.017 0.008 0.010
0.144 0.128
P. Aloupogiannis et al. / PIXE analysis ofintermediate thickness samples
302
Thus
Eo
I
dE=S(E,)dm.
The energy after the slice d m is called E, = E, - d E. For the next step, we set E, = E, and, applying (8), we continue until Cdm = mo. Eventually AE = 1dE. These calculations have been performed for 0
El dm
E”
iEz:
(9)
E,-d E
I t Ef Fig. 7. Schematic discussion.
drawing
setting
the variables
used
in the
Al 203 90% Al,O,
+ 10% SiO,
CaCO,
20% Al,O,
+ 80% SiO,
20% Al,O,
+ 80% Fe,O,
MgO AgBr
co2
C
(XF-1+
Fe&),
In every case, a good linear correlation was found. The linear regression coefficient varied within 0.991 for AgBr and 0.9996 for C. Fig. 8 shows examples corresponding to AgBr, C and two geological matrices. For all of these ten matrices, the average deviation from a pure linear approximation is of the order of 10%. For the set of IRSID samples of known superficial masses m, we have calculated the global correction coefficient eq. (7) by using the linear correlation coefficient XF and the relationship (5) for evaluating SF. The cross-section has been calculated following the fitting procedure proposed by Reuter et al. [9]. We used them to obtain the corrected yield corresponding to PIXE measurements. Fig. 9 shows the uncorrected and corrected yields where the linear correlation seems obvious. Fig. 8. Examples of slopes for (XF - 1) as a function of A E. (1) AgBr matrix, (2) 20% Al & + 80% SiO,, (3) 20% Al ,O, + 80% Fe,O,, (4) carbon;
4u)
I 2
-
Ca
S 2
1
i
I
I
I
t
I
,i, 123456
123466 mg/cm’
Fig. 9. Fe, S and Ca yields I from PIXE measurements Uncorrected, (2) corresponding corrected yields.
mg/cm2
mg/cm* on IRSID
876-l
samples
as a function
of known
superficial
masses.
(1)
P. Aloupogiannis
et al. / PIXE analysis of intermediate
6. Conclusions We use the following method for calculating corrections to apply to PIXE measurements, using the proton A E to calculate both the cross-section factor SF and the X-ray absorption factor XF. For homogeneous thickness samples, such as total filters, because the scattered proton energy distribution is rather narrow and Gaussian shaped, we simply use the mean energy loss AE for determining SF. If the sampling conditions are such that an overall constancy of the matrix composition can be assumed for a series of samples, a few transmission measurements allow the recognition of the dependence of XF and A E for the whole series. For impactors, the local thickness of the samples is highly variable, it is thus necessary to divide the proton energy dist~bution into an histogram and to calculate the corrections as if the sample were composed of a series of several thickness fractions. Although the linear approximation used may introduce errors up to 10-l%, when the whole process is achieved (transmission, RBS and PIXE measurements), there is no need for using any hypothesis about the whole matrix composition, which is a real improvement compared to the methods evoked in the introduction.
thickness samples
We are indebted Sciences Nucleaires
303
to the Institut Interuniversitaire des (Belgium) for its financial support.
References [I] L.E. Carlsson, K.G. Malmquist, G.I. Johansson and K.R.
Akselsson, Nucl. Instr. and Meth. 181 (1981) 179. [2] W. Maenhaut, A. Selen, P. Van &pen, R. Van Grieken and J.W. Winchester, Nucl. Instr. and Meth. 181 (1981) 399. [3] J.W. Nelson, S. Bauman and H.C. Kaufmann, Nucl. Instr. and Meth. 181 (1981) 89. [4] J.L. Campbell, W.J. Teesdale and R.G. Leigh, Nucl. Instr. and Meth. B6 (1985) 551. [5] P.A. Pella, E.C. Kuehner and W.A. Cassat, Adv. in X-ray Anal. 19 (1976) 463. [6] R. Theisen and D. Vollath, Tables of X-ray mass attenuation coefficients (Verlag Stahleisen M.B.H., Dusseldorf, 1967). ]7] F. Folkmann, Ion beam surface analysis, vol. 2 (Plenum Press, New York and London, 1976) p. 747. [8] J.F. Janni, Atomic data and nuclear tables 27 (2/3) (1982) 147. (91 W. Reuter, A. Lurio, F. Cardone, J.F. Ziegler, J. Appl. Physics 46 (7) (1975) 3194.
297
USE OF RUTHERFORD SCATIXRING ON A SECONDARY CARBON TARGET FOR CORRECTING INTERMEDIATE THICKNESS SAMPLE PIXE MEASUREMENTS P. ALOUPOGIANNIS I.*), G. ROBAYE I), I. ROELANDTS J.M. DELBROUCK-HABARU I) and J.P. QUISEFIT 2,
3), G. WEBER”*,
‘I Experimental Nuclear Physics, University of Liege, B15 Sart-Tilman, B-4000 Lwge, Belgium ‘) Luboratoire de Chimie des milieux naturels ** , No. 717, Universire de Paris 7, 2 PI. Jussleu, 75251, Paris, Cedex 05, France ” Geologv, Pefrology and Geochemistry, University of Liege, B20, Sart-Tilman, B-4000 Liege, Belgium Received 9 September, 1985
A method is presented for correcting PIXE measurements on intermediate thickness targets. The correction deals with the X-ray attenuation and the incident proton energy loss. It is based on the simultaneous acquisition of the PIXE spectrum along with the energy distribution of protons elastically scattered by a thin secondary carbon foil located behind the PIXE target. These measurements allowed a linear correlation between the proton energy loss AE and the correcting demonstrated. The validity of these simplifying linear approximations is discussed. The method is applicable like aerosol impactor stages.
1. Introduction When PIXE is used for measuring elemental concentrations on intermediate thickness samples, (neither infinitely thick nor very thin), correction of concentration measurement is a rather difficult task. The decrease of ionization cross section due to the slowing-down of incident protons and the absorption of X-rays generated inside the sample have to be taken into account. If the sample thickness varies from one point to another, the problem becomes more complicated. Conically shaped deposits on single orifice impactors stages are wellknown examples of difficult samples. As cascade impactors have been found to be essential in atmospheric aerosols studies [l], many authors have published attempts to solve these problems. Iteration methods based on PIXE measurements itself imply the use of hypotheses about the deposit composition, because light elements are not directly detectable by this method. Maenhaut [2], for instance, dealing with marine aerosol impactor samples estimates a relative uncertainty in the X-ray attenuation correction, running as’high as 30 to 50%, due to both the hypothesis about composition and the type of sample. * Research associate of the National Fund of Scientific Research. ** Unite asso&& au C.N.R.S. Laboratoire de physicochimie de l’atmosphere.
0168-583X/86/$03.50 0 Elsevier Science Publishers (North-Holland Physics Publishing Division)
B.V.
factor for X-ray absorption to inhomogeneous
thickness
XF to be samples
Nelson et al. [3], have shown that backscattering measurements could be used for assessing low Z elements, but it requires a second measurement with a higher energy beam (16 MeV protons). This is obviously not practical for most PIXE laboratories working with small Van de Graaff accelerators. Carlsson et al. [l], have proposed a method based on the measurement of the X-ray attenuation coefficient by using an X-ray beam produced by irradiating a silver or a potassium target with a 2.55 MeV proton beam. Using a narrow collimator and a micrometer screw to shift the sample, they were able to obtain thickness profiles of the deposits. We propose here a new approach based on the simultaneous acquisition of the PIXE spectrum and of the energy spectrum of protons after their passage through the sample and their Rutherford scattering on a secondary carbon target. From this spectrum, we obtain, -after corrections, the equivalent thickness profile of the sample in a single measurement. Using the information contained in the diffused proton spectrum and, in some cases, from additional X-ray transmission measurements, we are able to define a procedure for correcting PIXE measurement. The main goal of this work was to discover a relationship between the proton energy loss distribution through the sample and the correction factor for the corresponding PIXE spectrum. We have therefore treated the problem both experimentally and theoretically.
P. Aloupogiunnis et al. / PIXE ana+is
298
of intermedialethickness samples
2. Theor?,
For a thin sample with the same superficial becomes
The two main physical phenomena to deal with are the variation of the X-ray excitation cross section as a function of proton energy and the attenuation of the resulting X-rays on their path out of the sample to the Si(Li) detector. Keeping in mind the fact that corrections for low energy elements (like S) are rather large and generally difficult to estimate for thick samples, a simple and fast procedure even with an admissible loss of accuracy has been developed. The X-ray yield of element i in a target of uniform intermediate thickness is given by the well-known relation:
BN. I r.thm =yN,m,u,(EO)
I
and finally =
IIT
u,
EC,
u,(Ea) ~ _ 0,
= SF (cross section factor)
= matrix density (g/cm3); = factor including detector geometry, fluorescence yield and detection efficiency; Np = incident proton number; E, = incident proton energy; E, = final proton energy: coefficient for characteristic X-ray p, = attenuation emitted by the element i; S(E) = stopping power at energy E; Nw = Avogadro number: = X-ray detector angle; 8 A, = atomic mass of the element i; u,(E) = excitation cross section; of the element i. c, = concentration This relation corresponds to the experimental situation where the beam spot is smaller than the sample surface and where the beam incidence is perpendicular to the sample. Eq. (1) shows that the calculation of the yield I, depends on the excitation cross-section data base. However in the case of intermediate samples, since the energy dependence of this cross section u,(E) is a rather slowly varying function. it can be approximated by P
(5)
and
I r.,,un
where
1 -exp(-K)
writing
K
1
K
o,(4) It.thin
1 -exp(-K)
Ei I,=BN~~c,+ J
mass, eq. (3)
=
= XF (X factor)
4 . SF. XF
(6) (7)
In order to evaluate these two correction factors, the following experimental procedures have been carried out.
B
u,(E,) +u,(Et)
a =
,
? L
in order to separate tors. We then have
]‘=A
the excitation
B&v Npc _ 1 - exp( -pph/sin ,(J,
I
p/sin
and absorption 0)
’
0
fac-
(2)
since C, = m,/m and ph = m, where m, = superficial mass of the mass of the element i; m = superficial sample; h = sample thickness. If we call K = pm/sin 0 I,=A
BN avNmol-ex~(-K)
I
pir
K
’
(3)
3. Experimental Fig. 1 shows the experimental setup used for simultaneous PIXE and proton energy loss measurements. The Si(Li) X-ray detector is positioned at 135” (lab). A 15.5 pg/cm* carbon foil, supported by a Teflon frame with a 20 mm diameter hole is positioned at 45” (lab) on a retractable holder behind the sample. A solid state detector at 8 (lab) = 90” allows the detection of protons elastically diffused by the carbon foil. A collimating system gives total protection to the particle detector from receiving particles scattered by the Teflon frame or by the sample. Teflon was selected because it produces only a very low X-ray background if it is struck by protons scattered by the sample. A computer driven holder allows precise positioning of the sample. A sighting telescope at t?(lab) = 0” helps for the initial settings. The light brown impact trace of the collimated proton beam on a Nucleopore target backing is also useful for that purpose. Care must be taken during vacuum pumping and atmospheric opening of the setup in order not to break the thin carbon foil. In our case, vacuum pumping is done simultaneously at the two sides of the beam collimator to avoid any air flow in the foil direction. The same carbon foil was used for three weeks with more than 50 pumping cycles. Despite of its fragility, the carbon foil presents many advantages. Campbell et al. [4] have recently used backscattering for measuring uniform thin target thicknesses. They used as a backscattering target a gold layer deposited by evaporation on glass. Such a target is, of course, easy to handle; but is not transparent to the beam, produces X-ray background and, if the sample studied is too thick, the
P. Aloupogiannis et al. / PIXE analysis
of intermediatethickness samples
-.-._.
299
w---I
1
---------n
2 x
r
-
Fig 2. Experimental setup for X-ray transmission measurements. (1) X-ray tube, (2) collimator, (3) movable fluorescent pellet holder, (4) aerosol sample, (5) mobile micrometer table, (6) collimator, (7) Si(Li) detector, (8) sighting lens.
by the PIXE method. The use of a 2 mm diameter spot has shown that the homogeneity is of the same order of magnitude (5%) as for actual atmospheric filters.
Fig. 1. Expe~mental setup for simultaneous PIXE and RBS measurements. (1) Si(Li) detector, (2) collimators, (3) TV camera, (4) carbon foil, (5) Si charged particle detector, (6) movable holder, (7) Faraday cup, (8) sighting lens, (9) aerosol sample, (10) aerosol sample holder, (11) incident proton beam, (12) vacuum chamber,
4. Results These experimental setups have been first used to study an impactor stage sampled in Athens. Fig. 3
T 1.0 -
due to RBS on the glass interferes with the protons scattered on gold. Moreover, the high level of backscattering on .the thick glass necessitates use of a low intensity beam to avoid pile-up. Fig. 2 shows the setup used for X-ray trans~ssion measurements. It is quite similar to that of Carlsson et al. [l] except for the X-ray source. An excitating X-ray beam from a standard X-ray tube strikes a fluorescent pellet fixed on a removable holder. A modified microscope plate allows accurate positioning of the samples in front of the small collimator of the Si(Li) detector. Initial settings are performed using of a sighting telescope. Samples of known composition were prepared following the method described by Pella et al. [S]. Standard IRSID 876-l powder was set in suspension in distilled water and filtered through a Nucleopore membrane. The homogeneity of these standards was checked continuum
0.6 -
0.6 -
0.4 -
0.2 -
-1
I
i
.0.5
0
/
0.5 Beam
Fig. 3. Transmission coefficient for Athens a function of X-ray beam position.
impactor
,
t
1
1.5
position
(mm1
sample as
P. Aloupogiunnis
300
et al. / PIXE
onu~vsis of rntermediate
thickness samples
: .. . . . .
I
. .:.
:.
. ..z .. . .. _/ :' i~....._..~._5.~CC.,_~.. .._ _ .-_.. -5.,_.-_s_..r.r..a~~__.*--
'... ;...... ..._.._ _ m
: ..‘.“. .: ‘. _._:.. ,“” -‘* ‘. ..>.A. _._,_~ -...-.._,._....-.._..--....%..._. r .. ...-..-.-._-r._.,.,.. .-
..
....’
L
r
.-. .
. . ... _..j ....: .__-..._‘.C”-. ....._.:. v.-..
.... ..... .. ...- .-, .._. - .___- ... ,_..-
.. ;_:._. /.., .-” ...._.,.m.--..-.-‘s. ..L... .._. 7.r..,...-.,___.._._
.*.._
.:.
...L... .,
1
.
2
..
x.. “W.__._ .., ......... _
:.
4 “.... %........
.:.*_.. ;..,..-..a.._. .::.;-. .-.*+.? ......L,.._. __‘. . :-....__.. .,..*~. ..._ ..-. .;.-__.:....._ -:.._-.. n_.._...2_,_ ....-.._.“. ,... - ...e :. .*-.. -..-..._. .’ :.. . . . . -, ,~_..‘.“--.-_.. ,,_/._.-..V.--....-._ _ -. .‘,‘_.. -.....,.... ,.: ., .-... _.. . ‘.‘._ 1 .*._.. ‘_-.y_--..r.--.-_...._ ..,-..._-....*...,..-:-:-.*... . i ,_..-._+;:.--~r-..__2.
-.
._-,.-... ._.....-L.-.-‘..+_.-._...- .....__........___...h._......
3
__
5
6
7
8
‘._.“f.... _. ‘... ‘%.
1.. __.._ ...__ .._._.__\._____.__i...__ g ......-.~.-....~..-~-.‘~.. :..._.?..._._. 2.I:{ .._._ ..,. __.._.._... r. ._ . ...._.......... ....
,.,.... _.*.---_;_.;i;..:
r
“....,
_
...\... _....:p
. . . . . -.._---.-..-
.
loz.
. ..-..l_..-.._.__
.-' _...:: .../..--.-.' .' _ ..._._-.__.... _.. C.... _._-..._.._._.__-. 1.8 1.6 1.4 1.2
11 '.. .-C.... ...... 2.0
2.2
Ep (MeV)
Fig. 4. Example of scattered steps, on Athens sample.
proton
energy distribution
for 0.5 mm diameter
2.5 MeV, 5 nA proton
beam with 0.25 mm displacement
P. Aloupogiannis et al. / PIXE analysis of intermediate thickness samples (XF-1)
t
301
(XF -1)
I
2-
01
0.2
0.3
0.4
0.5
0.6 AE,,(MeV)
Fig. 5. Correlation between XF and AE for Athens impaetor
stage.
Fig. 6. Correlation between XF and AE for IRSID 876-I samples.
shows the transmission coefficients, T = I/& obtained using a 0.5 mm diameter collimator with 0.25 mm displacement steps. Fig. 4 gives the corresponding proton energy distribution obtained when irradiating the same target spots with a 2.5 MeV, 0.5 mm diameter, 5 nA proton beam. From these results the correcting coefficient XF and the corresponding mean energy loss AE, corrected for the variations of the Rutherford scattering cross section as a function of proton energy, have been evaluated. Evidence for a rather good linear correlation between XF and AE is shown in fig. 5. This relationship becomes XF = AA E + 1; given that for an infinitely thin layer, A E = 0 thus XF = 1. This leads us to set the Y-axis unit to XF - 1. The linear regression coefficients were 0.969 for S, 0.984 for Ca and 0.936 for Fe. Given the difficulties of studying exactly the same spots with the two different setups, we decided to perform the same type of experiments using the homogeneous IRSID deposits previously described. Fig. 6 shows the XF, AE corresponding correlations. The linear regression coefficients were 0.996 for S, 0.991 for Ca and 0.995 for Fe. In order to evaluate possible enhancement effects during transmission experiments, we mea-
coefficients for the homogesured the S transmission neous samples using three different excitation pellets: S, S + 10% KBr and a composite pellet containing S, K, Ca, Fe, Zn, Br and MO. Table 1 shows that these enhancement effects are negligible here.
5. Discussion In order to check the possibility of generalizing the previous findings and thereby use a linear correlation between XF and A E, we have calculated, for sulfur in ten different matrices, sets of XF and AE pairs corresponding to several superficial masses. For a given superficial mass m (fig. 7), the XF coefficient is calculated using eq. (6) and the data base given by R. Theisen and D. Vollath [6]. A E is evaluated using a step by step procedure. The sample is considered as a stack of elementary thicknesses dm. For each dm we call the incident energy E, and calculate dE using the stopping power approximation given by Folkmann 171.
(8)
Table 1 Sulfur transmission coefficients for IRSID samples of different thicknesses. 7’= exp( - pm) = I/I,. Target
TA: S+KBr T,: pure S T,: multielement
Mass (mg/cm’) 0.25
0.445
1.07
1.31
2.15
3.57
3.93
5.29
0.777 0.781 0.787
0.596 0.563 0.586
0.338 0.331 0.367
0.277 0.279 0.275
0.151
0.038 0.029 0.032
0.029 0.024 0.027
0.017 0.008 0.010
0.144 0.128
P. Aloupogiannis et al. / PIXE analysis ofintermediate thickness samples
302
Thus
Eo
I
dE=S(E,)dm.
The energy after the slice d m is called E, = E, - d E. For the next step, we set E, = E, and, applying (8), we continue until Cdm = mo. Eventually AE = 1dE. These calculations have been performed for 0
El dm
E”
iEz:
(9)
E,-d E
I t Ef Fig. 7. Schematic discussion.
drawing
setting
the variables
used
in the
Al 203 90% Al,O,
+ 10% SiO,
CaCO,
20% Al,O,
+ 80% SiO,
20% Al,O,
+ 80% Fe,O,
MgO AgBr
co2
C
(XF-1+
Fe&),
In every case, a good linear correlation was found. The linear regression coefficient varied within 0.991 for AgBr and 0.9996 for C. Fig. 8 shows examples corresponding to AgBr, C and two geological matrices. For all of these ten matrices, the average deviation from a pure linear approximation is of the order of 10%. For the set of IRSID samples of known superficial masses m, we have calculated the global correction coefficient eq. (7) by using the linear correlation coefficient XF and the relationship (5) for evaluating SF. The cross-section has been calculated following the fitting procedure proposed by Reuter et al. [9]. We used them to obtain the corrected yield corresponding to PIXE measurements. Fig. 9 shows the uncorrected and corrected yields where the linear correlation seems obvious. Fig. 8. Examples of slopes for (XF - 1) as a function of A E. (1) AgBr matrix, (2) 20% Al & + 80% SiO,, (3) 20% Al ,O, + 80% Fe,O,, (4) carbon;
4u)
I 2
-
Ca
S 2
1
i
I
I
I
t
I
,i, 123456
123466 mg/cm’
Fig. 9. Fe, S and Ca yields I from PIXE measurements Uncorrected, (2) corresponding corrected yields.
mg/cm2
mg/cm* on IRSID
876-l
samples
as a function
of known
superficial
masses.
(1)
P. Aloupogiannis
et al. / PIXE analysis of intermediate
6. Conclusions We use the following method for calculating corrections to apply to PIXE measurements, using the proton A E to calculate both the cross-section factor SF and the X-ray absorption factor XF. For homogeneous thickness samples, such as total filters, because the scattered proton energy distribution is rather narrow and Gaussian shaped, we simply use the mean energy loss AE for determining SF. If the sampling conditions are such that an overall constancy of the matrix composition can be assumed for a series of samples, a few transmission measurements allow the recognition of the dependence of XF and A E for the whole series. For impactors, the local thickness of the samples is highly variable, it is thus necessary to divide the proton energy dist~bution into an histogram and to calculate the corrections as if the sample were composed of a series of several thickness fractions. Although the linear approximation used may introduce errors up to 10-l%, when the whole process is achieved (transmission, RBS and PIXE measurements), there is no need for using any hypothesis about the whole matrix composition, which is a real improvement compared to the methods evoked in the introduction.
thickness samples
We are indebted Sciences Nucleaires
303
to the Institut Interuniversitaire des (Belgium) for its financial support.
References [I] L.E. Carlsson, K.G. Malmquist, G.I. Johansson and K.R.
Akselsson, Nucl. Instr. and Meth. 181 (1981) 179. [2] W. Maenhaut, A. Selen, P. Van &pen, R. Van Grieken and J.W. Winchester, Nucl. Instr. and Meth. 181 (1981) 399. [3] J.W. Nelson, S. Bauman and H.C. Kaufmann, Nucl. Instr. and Meth. 181 (1981) 89. [4] J.L. Campbell, W.J. Teesdale and R.G. Leigh, Nucl. Instr. and Meth. B6 (1985) 551. [5] P.A. Pella, E.C. Kuehner and W.A. Cassat, Adv. in X-ray Anal. 19 (1976) 463. [6] R. Theisen and D. Vollath, Tables of X-ray mass attenuation coefficients (Verlag Stahleisen M.B.H., Dusseldorf, 1967). ]7] F. Folkmann, Ion beam surface analysis, vol. 2 (Plenum Press, New York and London, 1976) p. 747. [8] J.F. Janni, Atomic data and nuclear tables 27 (2/3) (1982) 147. (91 W. Reuter, A. Lurio, F. Cardone, J.F. Ziegler, J. Appl. Physics 46 (7) (1975) 3194.