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Determination of the effective atomic number using elastic and inelastic scattering of γ-rays
Int. J. Appl. Radiat. lsot. Vol. 35, No. 10, pp. 965--968. 1984 Printed in Great Britain
0020-708X/84 53.00+0.00 Pergamon Press Ltd
Determination of the Effective Atomic Number Using Elastic and Inelastic Scattering of -Rays S. M A N N I N E N
and S. K O I K K A L A I N E N
University of Helsinki, Department of Physics, Siltavuorenpenger 20 D, SF-00170 Helsinki 17, Finland
(Received 5 January 1984; /n revisedform 7 March 1984) A simple method to determine the effective atomic number, Zd, of an unknown sample is presented. It is based on the measurement of the intensity ratio of elastic to inelastic photon scattering. The method has been applied to various compounds in the range ofZ~ ~ 20, using 24tAmas a radiation source. Good agreement with a theoretical prediction was obtained at scattering angles larger than 120°.
Introduction Numerous attempts have recently been made to use the ratio of elastic to inelastic photon scattering for various applied purposes such as, for example, biological applications and non-destructive testing and imagingY 4) In an earlier work ~6~an extensive theoretical and experimental study was performed to relate the experimental intensity-ratio to the effective atomic number of a sample. It was found that this is possible only if several experimental corrections were properly made to the measured data. Some of these corrections are, however, quite tedious and prevent the practical use of this method. The purpose of this work is to study whether it would be possible to avoid most of the problems in data processing and still obtain a reliable relationship between the ratio of elastic to inelastic scattering and Z ~ of an unknown sample. This study addresses two major questions: (1) What is the optimum scattering angle and (2) what are the possible limitations concerning the range of the atomic number Z? The photon source used in this study was 2'~Am, which emits 59.54-keV ~-rays and which is the most commoniy-used source for these kinds of applications. The answers to these questions have been looked for by first of all making measurements on a few pure elements as a function of the scattering angle and including all necessary steps in data processing. On the basis of these results another series of measurements has been performed on some compounds within a limited range of scattering angles. In the latter case, the possibility of avoiding the complicated corrections to the measured data is especially carefully examined. Method In special circumstances it is possible to relate-the ratio of elastic to inelastic scattering of photons
directly to the effective atomic number, Zd, of a sample. These circumstances include a balance between Z~, scattering angle 0 and wavelength ,~ of the primary radiation. (6) A rough estimate is that sin 0/~. should be larger than 20 n m - ' and the atomic number Z ~<20, if an 24'Am source is used. In that case a simple relationship (do/df~), I (do/d.q)~,,
~Z 2 /co0\2' _(
3 ~'" h 2 4nsin_02
u--~3-=~2] 2me 2 ~,
(l)
holds, coo and co, are the angular frequencies corresponding to the inelastic peak center and the primary energy, respectively. In this approximation the intensity of the elastic scattering is proportional to Z ~, whereas in the case of inelastic scattering it is proportional to Z. One can therefore define an effective atomic number for a compound i
(nl is the number of atoms Zi in one structure unit)
/~, n,Z~ '~
It should be stressed that this definition is meaningful only in connection with the elastic to inelastic scattering ratio. A measurement on the ratio of elastic to inelastic scattering would therefore yield the value of Z~r of an unknown sample via equation (l). A simple way to do that is to draw a parabola as a function of Z using equation (1), and after the experimental intensity ratio has been determined, the value for Z,~ can be immediately obtained from the curve.
965
966
S.M.~',,'~,qr~-~r and S. KOIKKALAL'qL~ Experimental
The details of the experimental arrangement have been given previously. (6) A well-collimated beam of 59.54-keV y-rays from a 45-mCi ~41Am source was used as a primary radiation. At the first stage of the experiment thin metal foils of AI, Fe and Nb were measured at five scattering angles (60 °, 90 °, 120° , 145° and 165°). The energy shifts from the elastic line to the center of the inelastic line were 3.28, 6.22, 8.91, 10.39 and 11.07 keV, respectively. Samples were located in an evacuated chamber, and the scattering geometry was symmetric in all cases, i.e. the incident beam and the scattered beam defined equal angles with the sample surface. A separate background measurement with the sample holder only was also performed at each scattering angle. After the background subtraction the following corrections were applied to the measured data [for details, see R ef. (6)]: (i) The low-energy tail of the detector-resolution function was subtracted both from elastic and inelastic lines. This should be done because of the overlap between the inelastic line and the tail of the elastic line. (ii) The absorption correction for primary and scattered 7-rays- (iii) Correction for the multiple photon-scattering effects. The intensity ratio of the elastic and inelastic scattering was finally calculated as the area ratio of the corresponding lines. In the second part of the experiment various compounds in the atomic-number region 10~< Z~ ~ 25 were measured. In order to check the reliability of the method, samples were of different thicknesses. Some of them were much thinner than the absorption half thickness, and some were almost totally absorbant. The usefulness of equation (2) to determine the effective atomic number was also checked by choosing compounds consisting of elements with very different atomic numbers. One of these compounds was calcium-hydroxy-apatite (Ca)0(OH)z(PO4)6), which has been used as a reference material in bone mineral-density measurements, c7)
Results and Discussion Because the aim of this work was to investigate the possibility that the measured elastic to inelastic scattering ratio could be used to directly determine the effective atomic number of an unknown sample, the following procedure was introduced: On the basis of earlier work (s) one finds that: (i) at least in the case of light elements (Z ~<25) and compounds all corrections to the measured data are quite small, (ii) the corrections for the multiple elastic and inelastic scattering will cancel out in the first order and (iii) the corrections for the sample absorption and for the tail of the resolution function also have an opposite effect to the measured intensity ratio. The only correction still left is the subtraction of the background which is straightforward to do. _ The first step along these lines was the optimization of the scattering angle. This was done using the
~. 9 0 *
4300-
//
_
°2°
0°
J
'j l
j
l
-
-
i
i
~
Al~Fe I0
20
Nb 30
40
Z
Fig. 1. The experimental elastic to inelastic intensity ratios for AI, Fe and Nb at the scattering angles ofg0 °, 120° and 145°. The parabolic Z'-dependence is also given in each ca$¢.
measurements of AI, Fe and Nb foils. It became clear that the angle of 60° was ruled out because the necessary approximations for the parabolic Z-dependence are true only for the first few elements. Also the angle of 165° turned out to be impractical. This was due to the fact that the absorption correction becomes more important at high scattering angles (the energy shift in the inelastic scattering is larger) and therefore this correction will have a dominant role and should not be omitted. A similar thing was seen for heavier elements at the scattering angle of 145L In Fig. 1 the experimental elastic to inelastic scattering ratios are given for the scattering angles of 90 °, 120° and 145°. A theoretical curve corresponding to the Z2-depcndence is also given in all cases. One can see that at the angle of 90° the agreement is obtained in the case of AI, but at the other two scattering angles the agreement is good even for Nb. It should be mentioned, however, that in the case of Nb this is not due to the goodness of the parabolic model but the cancellation of the errors in the approximations. The inelastic scattering factor for Nb corresponding to the scattering angle of 145° gives S = 38.5 instead of Z --41 .(8~This means the Z L approximation used in the elastic scattering fails by an equal amount because the experimental result supports the parabolic model. When Z ~<20, the error in the Zapproximation becomes smaller than I% for 24'Am radiation and the use of equation (1) is therefore justified. In most applications of the present method the interesting range of the atomic number has been Z ~ ,%<20. The second step therefore was to measure five compounds, SiO2, CaCO3, Cal0(OH)~(PO4)6, VSi2
Elastic
andinelastic scattering of7-raYS
967
TFe @
(a)8=~°
/
/
I0
;eAt
| -% 5
~ CoCO3
•
SiO z
I
I
15
I
20
25
Z
(¢) 8,145"
(0) 8=120'
Fe
/
-
)l
~/
10
FeAt
="
"5
5
At
//t
/ ~ Si~Oz ~ = COCO3 "! SiO2 %,
I
I
I
I
I
I
15
20
25
15
20
25
z
z
Fig. 2. The experimental elastic to inelastic intensity ratios for various compounds after the background subtraction at the scattering angles of (a) 90°, (b) 120° and (c) 145°. The effective atomic numbers have been calculated according to equation (2) and the statistical limits of uncertainty are shown. Also included arc the intensity ratios for A1 and F¢ after the background subtraction only. The parabolic Z:-dependence is also given at each scattering angle.
and FeAI. The values of their Z ~ calculated according to equation (2) are 11.2, 14.0, 15.1, 18.3 and 22.5, respectively. The only correction applied to the measured data was the substraction of the background
which was simply done by using the automatic facility included in the muldchannel analyscr. The results can be seen in Fig. 2. Also included are the experimental results for the Al and Fe measurements after the
968
S. M,~,,'NINENand S. KOIKKALAINEN
background subtraction, and for the theoretical parabolae calculated according to equation (I). It is easily seen that the scattering angle of 90 ° is too low to obtain a reasonable agreement with the Z2-dependence. In the other two cases the agreement is good. The small deviations from the smooth hne are mainly due to the role of the absorption correction because depending on the sample thickness and the atomic number, the cancellation with the tail correction varies. In any case, for all compounds the difference between the Z2-dependence and the experimental intensity-ratio is within 0.5% and the uncertainty in the absolute value of Z~r is less than 0.5%. Especially good agreement in the case of calciumhydroxy-apatite points out that the definition of the effective atomic number is correct. The results would be even better if only thin samples were used. As a summary one can conclude that using an 24~Am source the effective atomic number of an unknown sample can be determined with good accuracy providing that the scattering angle is between
120° and 145 °, and Zo~ < 20. The only necessary correction to the measured data is the subtraction of the background. This is particularly useful because the absorption correction for an unknown composition cannot be made. Compared with the earlier works ¢~'2'4~no calibration measurements are required. References 1. puumalainen P., Olkkonen H. and Sikanen P. Int. J, AppL Radiat. [sot. 28, 785 (1977). 2. Sch~.tzlerH. P. Int. J. AppL Radiat. lsot. 30, 115 (1977). 3. Cooper M. J., Rollason A. J. and Tuxworth R. W. 3.. Phys. E 15, 568 (1982). 4. Cesareo R. Nucl. Instrum. Methods 179, 545 (1981). 5. Holt R. S., Cooper M. J. and Jackson D. F. To be published. 6. Manninen S., Pitk/i.nen T., Koikkalainen S. and Paakkari T. Int. J. Appl. Radiat. Isot. 35, 93 (1984). 7. Puumalainen P., Uimarihuhta A., Alhava E. and Olkkonen H. Radiology 120, 723 (1976). 8. Hubbell J. H., Veigele W. J., Briggs E. A., Brown R. T., Cromer D. T. and Howerton R. J. J. Phys. Chem. Ref. Data 4, 471 (1975).
0020-708X/84 53.00+0.00 Pergamon Press Ltd
Determination of the Effective Atomic Number Using Elastic and Inelastic Scattering of -Rays S. M A N N I N E N
and S. K O I K K A L A I N E N
University of Helsinki, Department of Physics, Siltavuorenpenger 20 D, SF-00170 Helsinki 17, Finland
(Received 5 January 1984; /n revisedform 7 March 1984) A simple method to determine the effective atomic number, Zd, of an unknown sample is presented. It is based on the measurement of the intensity ratio of elastic to inelastic photon scattering. The method has been applied to various compounds in the range ofZ~ ~ 20, using 24tAmas a radiation source. Good agreement with a theoretical prediction was obtained at scattering angles larger than 120°.
Introduction Numerous attempts have recently been made to use the ratio of elastic to inelastic photon scattering for various applied purposes such as, for example, biological applications and non-destructive testing and imagingY 4) In an earlier work ~6~an extensive theoretical and experimental study was performed to relate the experimental intensity-ratio to the effective atomic number of a sample. It was found that this is possible only if several experimental corrections were properly made to the measured data. Some of these corrections are, however, quite tedious and prevent the practical use of this method. The purpose of this work is to study whether it would be possible to avoid most of the problems in data processing and still obtain a reliable relationship between the ratio of elastic to inelastic scattering and Z ~ of an unknown sample. This study addresses two major questions: (1) What is the optimum scattering angle and (2) what are the possible limitations concerning the range of the atomic number Z? The photon source used in this study was 2'~Am, which emits 59.54-keV ~-rays and which is the most commoniy-used source for these kinds of applications. The answers to these questions have been looked for by first of all making measurements on a few pure elements as a function of the scattering angle and including all necessary steps in data processing. On the basis of these results another series of measurements has been performed on some compounds within a limited range of scattering angles. In the latter case, the possibility of avoiding the complicated corrections to the measured data is especially carefully examined. Method In special circumstances it is possible to relate-the ratio of elastic to inelastic scattering of photons
directly to the effective atomic number, Zd, of a sample. These circumstances include a balance between Z~, scattering angle 0 and wavelength ,~ of the primary radiation. (6) A rough estimate is that sin 0/~. should be larger than 20 n m - ' and the atomic number Z ~<20, if an 24'Am source is used. In that case a simple relationship (do/df~), I (do/d.q)~,,
~Z 2 /co0\2' _(
3 ~'" h 2 4nsin_02
u--~3-=~2] 2me 2 ~,
(l)
holds, coo and co, are the angular frequencies corresponding to the inelastic peak center and the primary energy, respectively. In this approximation the intensity of the elastic scattering is proportional to Z ~, whereas in the case of inelastic scattering it is proportional to Z. One can therefore define an effective atomic number for a compound i
(nl is the number of atoms Zi in one structure unit)
/~, n,Z~ '~
It should be stressed that this definition is meaningful only in connection with the elastic to inelastic scattering ratio. A measurement on the ratio of elastic to inelastic scattering would therefore yield the value of Z~r of an unknown sample via equation (l). A simple way to do that is to draw a parabola as a function of Z using equation (1), and after the experimental intensity ratio has been determined, the value for Z,~ can be immediately obtained from the curve.
965
966
S.M.~',,'~,qr~-~r and S. KOIKKALAL'qL~ Experimental
The details of the experimental arrangement have been given previously. (6) A well-collimated beam of 59.54-keV y-rays from a 45-mCi ~41Am source was used as a primary radiation. At the first stage of the experiment thin metal foils of AI, Fe and Nb were measured at five scattering angles (60 °, 90 °, 120° , 145° and 165°). The energy shifts from the elastic line to the center of the inelastic line were 3.28, 6.22, 8.91, 10.39 and 11.07 keV, respectively. Samples were located in an evacuated chamber, and the scattering geometry was symmetric in all cases, i.e. the incident beam and the scattered beam defined equal angles with the sample surface. A separate background measurement with the sample holder only was also performed at each scattering angle. After the background subtraction the following corrections were applied to the measured data [for details, see R ef. (6)]: (i) The low-energy tail of the detector-resolution function was subtracted both from elastic and inelastic lines. This should be done because of the overlap between the inelastic line and the tail of the elastic line. (ii) The absorption correction for primary and scattered 7-rays- (iii) Correction for the multiple photon-scattering effects. The intensity ratio of the elastic and inelastic scattering was finally calculated as the area ratio of the corresponding lines. In the second part of the experiment various compounds in the atomic-number region 10~< Z~ ~ 25 were measured. In order to check the reliability of the method, samples were of different thicknesses. Some of them were much thinner than the absorption half thickness, and some were almost totally absorbant. The usefulness of equation (2) to determine the effective atomic number was also checked by choosing compounds consisting of elements with very different atomic numbers. One of these compounds was calcium-hydroxy-apatite (Ca)0(OH)z(PO4)6), which has been used as a reference material in bone mineral-density measurements, c7)
Results and Discussion Because the aim of this work was to investigate the possibility that the measured elastic to inelastic scattering ratio could be used to directly determine the effective atomic number of an unknown sample, the following procedure was introduced: On the basis of earlier work (s) one finds that: (i) at least in the case of light elements (Z ~<25) and compounds all corrections to the measured data are quite small, (ii) the corrections for the multiple elastic and inelastic scattering will cancel out in the first order and (iii) the corrections for the sample absorption and for the tail of the resolution function also have an opposite effect to the measured intensity ratio. The only correction still left is the subtraction of the background which is straightforward to do. _ The first step along these lines was the optimization of the scattering angle. This was done using the
~. 9 0 *
4300-
//
_
°2°
0°
J
'j l
j
l
-
-
i
i
~
Al~Fe I0
20
Nb 30
40
Z
Fig. 1. The experimental elastic to inelastic intensity ratios for AI, Fe and Nb at the scattering angles ofg0 °, 120° and 145°. The parabolic Z'-dependence is also given in each ca$¢.
measurements of AI, Fe and Nb foils. It became clear that the angle of 60° was ruled out because the necessary approximations for the parabolic Z-dependence are true only for the first few elements. Also the angle of 165° turned out to be impractical. This was due to the fact that the absorption correction becomes more important at high scattering angles (the energy shift in the inelastic scattering is larger) and therefore this correction will have a dominant role and should not be omitted. A similar thing was seen for heavier elements at the scattering angle of 145L In Fig. 1 the experimental elastic to inelastic scattering ratios are given for the scattering angles of 90 °, 120° and 145°. A theoretical curve corresponding to the Z2-depcndence is also given in all cases. One can see that at the angle of 90° the agreement is obtained in the case of AI, but at the other two scattering angles the agreement is good even for Nb. It should be mentioned, however, that in the case of Nb this is not due to the goodness of the parabolic model but the cancellation of the errors in the approximations. The inelastic scattering factor for Nb corresponding to the scattering angle of 145° gives S = 38.5 instead of Z --41 .(8~This means the Z L approximation used in the elastic scattering fails by an equal amount because the experimental result supports the parabolic model. When Z ~<20, the error in the Zapproximation becomes smaller than I% for 24'Am radiation and the use of equation (1) is therefore justified. In most applications of the present method the interesting range of the atomic number has been Z ~ ,%<20. The second step therefore was to measure five compounds, SiO2, CaCO3, Cal0(OH)~(PO4)6, VSi2
Elastic
andinelastic scattering of7-raYS
967
TFe @
(a)8=~°
/
/
I0
;eAt
| -% 5
~ CoCO3
•
SiO z
I
I
15
I
20
25
Z
(¢) 8,145"
(0) 8=120'
Fe
/
-
)l
~/
10
FeAt
="
"5
5
At
//t
/ ~ Si~Oz ~ = COCO3 "! SiO2 %,
I
I
I
I
I
I
15
20
25
15
20
25
z
z
Fig. 2. The experimental elastic to inelastic intensity ratios for various compounds after the background subtraction at the scattering angles of (a) 90°, (b) 120° and (c) 145°. The effective atomic numbers have been calculated according to equation (2) and the statistical limits of uncertainty are shown. Also included arc the intensity ratios for A1 and F¢ after the background subtraction only. The parabolic Z:-dependence is also given at each scattering angle.
and FeAI. The values of their Z ~ calculated according to equation (2) are 11.2, 14.0, 15.1, 18.3 and 22.5, respectively. The only correction applied to the measured data was the substraction of the background
which was simply done by using the automatic facility included in the muldchannel analyscr. The results can be seen in Fig. 2. Also included are the experimental results for the Al and Fe measurements after the
968
S. M,~,,'NINENand S. KOIKKALAINEN
background subtraction, and for the theoretical parabolae calculated according to equation (I). It is easily seen that the scattering angle of 90 ° is too low to obtain a reasonable agreement with the Z2-dependence. In the other two cases the agreement is good. The small deviations from the smooth hne are mainly due to the role of the absorption correction because depending on the sample thickness and the atomic number, the cancellation with the tail correction varies. In any case, for all compounds the difference between the Z2-dependence and the experimental intensity-ratio is within 0.5% and the uncertainty in the absolute value of Z~r is less than 0.5%. Especially good agreement in the case of calciumhydroxy-apatite points out that the definition of the effective atomic number is correct. The results would be even better if only thin samples were used. As a summary one can conclude that using an 24~Am source the effective atomic number of an unknown sample can be determined with good accuracy providing that the scattering angle is between
120° and 145 °, and Zo~ < 20. The only necessary correction to the measured data is the subtraction of the background. This is particularly useful because the absorption correction for an unknown composition cannot be made. Compared with the earlier works ¢~'2'4~no calibration measurements are required. References 1. puumalainen P., Olkkonen H. and Sikanen P. Int. J, AppL Radiat. [sot. 28, 785 (1977). 2. Sch~.tzlerH. P. Int. J. AppL Radiat. lsot. 30, 115 (1977). 3. Cooper M. J., Rollason A. J. and Tuxworth R. W. 3.. Phys. E 15, 568 (1982). 4. Cesareo R. Nucl. Instrum. Methods 179, 545 (1981). 5. Holt R. S., Cooper M. J. and Jackson D. F. To be published. 6. Manninen S., Pitk/i.nen T., Koikkalainen S. and Paakkari T. Int. J. Appl. Radiat. Isot. 35, 93 (1984). 7. Puumalainen P., Uimarihuhta A., Alhava E. and Olkkonen H. Radiology 120, 723 (1976). 8. Hubbell J. H., Veigele W. J., Briggs E. A., Brown R. T., Cromer D. T. and Howerton R. J. J. Phys. Chem. Ref. Data 4, 471 (1975).