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Effective atomic number studies in clay minerals for total photon interaction in the energy region 10 keV–10 MeV
Radiat. Phys. Chem. Vol. 48, No. 6, pp. 707-710. 1996 Copyright © 1996ElsevierScienceLtd Printed in Great Britain. All rights reserved PII: S0969-806X(96)00070-9 0969-806X/96 $15.00-1-0.00
Pergamon
EFFECTIVE MINERALS
ATOMIC
FOR
NUMBER
TOTAL
ENERGY
PHOTON REGION
STUDIES
IN
CLAY
INTERACTION 10 k e V - 1 0
IN
THE
MeV
T. K I R A N K U M A R , S. V E N K A T A R A T N A M and K. V E N K A T A R E D D Y t Jnanananda Laboratories for Nuclear Research, Andhra University, Visakhapamam 530 003, India (Received 28 February 1996; Revised 2 May 1996)
Abstract--Effective atomic numbers (Z,r) of different clay minerals are calculated for total photon interaction in the energy region 10 keV-10 MeV. The variation of Zo~ with energy is discussed by comparing with the similar studies made for alloys and compounds from our laboratory. Copyright © 1996 Elsevier Science Ltd
INTRODUCTION Several approaches (Stroosnijder and DeSwart, 1974; Saksena et al., 1974; Mudahar and Sahota, 1985; Mudahar and Sahota, 1986) have suggested the gamma ray transmission method as a convenient and accurate method for measurement of moisture content and density of soils. These measurements can be carried out in laboratories as well as fields. In field experiments soil could be used for shielding purposes because of its easy availability. Studies on the conditions affecting the attenuation of radiation through soil such as particle size and compaction achieved by pressure have been made (Gameel et al., 1978; EI-Kameel et al., 1983) The effective atomic numbers for some soil materials have been reported by Mudahar and Sahota (1988). As a further progress in this direction, we report the effective atomic numbers for fourteen clay minerals. It was pointed out by Hine (1952) that the effective atomic number for gamma ray interactions for materials composed of various elements can not be expressed by a single number and for each of the partial processes the number has to be weighted differently. Different studies reported from our laboratory (Parthasaradhi, 1968a; Parthasaradhi, 1968b; Siddappa et al., 1971; Rama Rao et al., 1963) found that Hine's predictions were correct. Most of the attempts made to determine the effective atomic numbers were restricted to alloys and compounds (Parthasaradhi, 1968b; Siddappa et al., 1971; Rama Rao et al., 1963; Chandra Lingam et al., 1984) and such attempts for clay materials appear to be very limited (Mudahar and Sahota, 1988). Keeping these points in view, the effective atomic numbers for total photon interactions for fourteen clay minerals in the energy range 10 keV-10 MeV have been estimated. The results are compared with similar studies in tTo whom all correspondence should be addressed.
alloys reported from our laboratories (Parthasaradhi, 1968b; Rama Rao et al., 1963). CALCULATIONOF EFFECTIVEATOMIC NUMBERS Calculation of effective atomic number of a mixture/alloy involves estimation of the partial/total cross sections and finding out the equivalent element that has the same cross section at that energy. The clay minerals for which effective atomic numbers are calculated and their most probable chemical compositions are given in Table 1 (Van Olphen and Fripiat, 1979). The theoretical values of attenuation coefficients for SiO2, A1203, TiO2, Fe203, MnO, MgO, CaO, Na:O, SO3, K20, P205, Li20 have been generated at energies 0.01, 0.015, 0.02, 0.03, 0.04, 0.05, 0.06, 0.08, 0.1, 0.15, 0.2, 0.3, 0.4, 0.5, 0.6, 0.8, 1, 1.5, 2, 3, 4, 5, 6, 8 and 10 MeV on a personal computer using XCOM (Berger and Hubbell, 1987). Then the attenuation coefficient of each clay mineral is calculated utilising the expression (/,t/P)clay =
n Z i=1
Wi~/P)i
(1)
where n is the number of constituents in the clay mineral, (ll/p)i is the respective attenuation coefficient and w~ is the fractional weightage of the ith element so that ~ w i = 1.
i=1
The attenuation coefficients are then converted into atomic cross sections, aday, using the expression ~/P)d~y n ~clay = N ~ ( w / A 3
(2)
where N is the Avogadro number, A~ and w~ are respectively atomic and fractional weights of the constituent elements of which the clay mineral is 707
T. Kiran K u m a r et al.
708
Table 1. Most probable composition of samples Comp. (%)
01
SiO2 A1203 TiO2 Fe203 MnO MgO CaO Na20 K20 P2Os SO3 LizO
63.84 22.24 0.50 3.45 0.01 4.87 2.88 1.73 0.40 0.08 0.35
02
03
53.53 66.03 43.95 0.30 0.03 0.02 0.58 0.06 0.01 0.01 0.17 29.03 0.20 0.34 0.08 3.19 1.37 0.04 0.10 0.02
13
04
05
06
07
5.43 0.98 0.06 1.44 0.05 42.50 2.61 0.13 0.09
47.73 0.95 0.04 2.07 0.05 48.86 0.24 0.08 0.03 0.09
0.04 99.30
75.15 9.72 0.74 3.08 0.10 8.35 2.03 0.14 0.74 0.02
0.05 0.02 0.56 0.05
I
1 II III
12
Montmorollonite Kalonite Laponite
N° 11
10 0.98
Comp. (%) SiO2 A1203 TiO2 Fe203 MnO MgO CaO Na20 K20 P2Os SO3 Li20
08 48.90 33.20 1.61 1.34
09 43.70 38.80 1.90 0.45
10 0.26 0.08 0.00 0.11
0.42 0.31 0.08 1.04 0.11
0.15 0.11 0.04 0.50 0.36
0.52 98.98 0.07 0.04
0.07
0.11
11 49.03 0.30 0.03 41.29 0.15 2.25 1.14 5.64 0.09 0.04
0.14
12 1.67 0.27 0.02 0.10 0.65 42.15 0.15 0.07
13 14 54.58 60.36 21.93 0.70 0.90 0.07 7.41 0.95 0.03 0.03 3.76 3 1 . 4 1 1.25 0.47 0.39 0.04 8.88 0.03 0.48 0.15
~01
f o r m e d . T h e d e n o m i n a t o r in e q u a t i o n (2) is t h e n u m b e r o f a t o m s p e r g r a m o f t h e clay m i n e r a l . Plots are drawn between the total photon cross s e c t i o n s in i n d i v i d u a l e l e m e n t s a n d t h e a t o m i c number of the elements for each energy. From these p l o t s t h e effective a t o m i c n u m b e r s o f e a c h m i n e r a l is o b t a i n e d b y i n t e r p o l a t i o n . T h e effective a t o m i c n u m b e r s (Zoo) so o b t a i n e d a r e g i v e n in T a b l e 2 f o r t h e s t a n d a r d e n e r g y grid. T h e v a r i a t i o n o f Zo~ w i t h e n e r g y f o r d i f f e r e n t c l a y m i n e r a l s is s h o w n in F i g s 1 - 5.
Table 2, Effective atomic numbers of clay minerals E (MeV)
01
02
03
04
05
06
07
0.01 0.10 0.20 0.30 0,50 1.00 5.00 10.00 E (MeV) 0.01 0.I0 0.20 0.30 0.50 1.00 5.00 10.00
11.85 10.85 10.31 10.31 10.26 10.24 10.35 10.44 08 11.54 10.63 10.21 10.21 10.16 10.12 10.24 10.33
tl.25 10.45 10.13 10.13 10.10 10.06 10.17 10.24 09 11.33 10.49 10.13 10.14 10.10 10.07 10.15 10.26
10.97 10.20 9.95 9.96 9.93 9.90 10.00 10.06 l0 16.64 15.80 14.54 14.16 14.03 13.95 14.34 14.64
11.55 11.74 10.33 10.31 10.27 10.25 10.35 10.41 11 15.64 14.38 12.34 11.96 11.75 11.69 12.04 12.35
11.24 10.47 10.13 10.13 10.10 10.07 10.18 10.23 12 14.07 12.79 11.73 11.52 11.42 11.39 11.65 11.86
10.88 10.25 10.06 10.06 10.02 9.99 10.08 10.13 13 12.86 11.66 10.84 10.77 10.67 10.66 10.82 10.97
11.81 10.81 10.30 10.29 10.23 10.20 10.33 10.43 14 11.18 10.41 10.09 10.11 10.07 10.05 10.13 10.19
Notation: 01--montmorillonite, 02--kaolinite, 03--1aponite, 04--magnesite, 05--~hrysotile, 06--gibbsite, 07--attapulgite, 0g---plastic clay, 09--flint clay, 10---calcite, ll--crocidolite, 12--gypsum, 13--illite, 14---talc.
I
103
104
E n e r g y (keV) Fig. 1. Variation of effective atomic n u m b e r with energy for montmorillonite, kaolinite and laponite.
DISCUSSION
54.24
Notation: 01--montmorillonite, 02--kaolinite, 03--1aponite, 04--magnesite. 05---chrysotile, 06---gibbsite, 07--attapulgite, 08--plastic clay, 09---flint clay, 10--calcite. ll---crocidolite, 12--gypsum, 13---illite. 14--talc.
[
102
It c a n be s e e n f r o m t h e t a b l e s a s w e l l a s figures t h a t f o r all clay m i n e r a l s t h e v a r i a t i o n o f Z ~ w i t h e n e r g y is m o r e o r less similar. T h e s l i g h t i r r e g u l a r i t i e s m a y be d u e to t h e e r r o r s in t h e i n t e r p o l a t i o n . T h e Zo~ v a l u e s t e a d i l y i n c r e a s e s in t h e r e g i o n 1 0 - 3 0 k e V a n d a f t e r 30 keV, it s t e a d i l y d e c r e a s e s u p t o 500 k e V . A f t e r w a r d s Z0~ a l m o s t r e m a i n s c o n s t a n t u p t o 1500 keV. A b o v e 1500 k e V Ze~ i n c r e a s e s w i t h i n c r e a s e in e n e r g y u p to 10 M e V . I n this e n e r g y r e g i o n , t h e i n c r e a s e in Z~s is s m a l l b u t continuous.
Variation o f Zea with energy in the region 10-1500 ke V T h e v a r i a t i o n o f Z~r w i t h e n e r g y ( 1 0 - 1 5 0 0 k e V ) m a y b e a t t r i b u t e d to t h e relative d o m i n a t i o n o f t h e p a r t i a l p r o c e s s e s , viz., p h o t o e l e c t r i c effect, c o h e r e n t scattering, incoherent scattering and pair production. It w a s r e p o r t e d b y P a r t h a s a r a d h i , (1968b) t h a t Zo~ f o r p h o t o e l e c t r i c p r o c e s s is a l w a y s g r e a t e r t h a n o r e q u a l to t h a t o f s c a t t e r i n g p r o c e s s , A t low e n e r g i e s
12--
llI
11
Gibbisite
N
t0 I
101
102
103
104
Energy (keY) Fig, 2. Variation of effective atomic number with energy for magnesite, chrysotile and gibbsite.
Effective atomic number studies
709
12 13 ~r ~ f ~,~ ~.,~ - x ~ \
[ II
Attapulgite Plastic clay I II
N
lllite Talc
12 1
II III
10
I
I
'
101
10 2
10 3
t'q
10 4
Energy (keV) Fig. 3. Variation of effective atomic number with energy for attapulgite, plastic clay and flint clay.
t0
101
the photoelectric effect is dominating and hence Z0~ for total interaction is mainly described by the Zo~ for this partial process. Similarly at higher energies the contribution due to scattering process will be more in comparison with photoelectric effect and this will have its effect on the Zo~ for total gamma ray interaction. Hence at low energies, where photoelectric effect dominates, Ze~ value is more and at higher energies, where scattering process dominates, Z~r value is less. Therefore, the Ze~ for total gamma ray interaction varies from a higher value at lower energies to a lower value at higher energies depending on the relative domination of the partial gamma ray processes one over the other. From the figures it may be observed that Z0n values for all minerals decrease from 30 keV to 500 keV. The present results confirm the observations made by Parthasaradhi (1968b) and Mudahar and Sahota (1988).
Variation of Zeg with energy from 1.5-10 MeV Rama Rao et al. (1963) reported that Zo~ of rhodium-platinum alloy for pair production cross section remains constant in the energy region 1.119 to 2 MeV. Mudahar and Sahota (1988) reported that 17
I II III
Calcite Crocidolite Gypsum
15
14I~ t~
13 - 12--
III
11 L l0
l01
10 2
10 3
10 4
Energy (keV)
Fig. 4. Variation of effective atomic number with energy for calcite, crocidolite and gypsum.
10 2
I
[
10 3
10 4
Energy (keV)
Fig. 5. Variation of effective atomic number with energy for illite and talc.
Z0, of some soils for total photon interactions slowly increase with increase in energy from 1.5 to 5 MeV. In the present studies it may be observed from the figures that there is slight but continuous increase in Zo, with energy in the energy region 1.5 to 10 MeV. In this region, the dominant processes are incoherent scattering and pair production. Hence as mentioned by Mudahar and Sahota (1988) this behaviour may be attributed to the mixed contribution of scattering and pair production interaction processes.
Variation of Z,1r with atomic numbers of the constituents Parthasaradhi (1968b) observed that variation in Z,~ for total gamma ray interaction also depends on the spread in the atomic numbers of the elements of which the material is composed. He noticed no significant variation in Z0~ of monel metal (Ni, 60; Cu, 33; Fe, 6.5; and Mn, 0.5%) in which the spread in atomic numbers is small and maximum variation in tungsten steel (W, 23; C, 0.77; Cr, 4.25; V, 1.6; Co, 11; and Fe 59.38%) in which the spread is high. In the case of tungsten steel Zo~ value dropped from 40 to 100 keV to 32 at 662 keV. In the present work, a total number of 13 elements are present in the samples and their atomic number range from 3 (Li) to 26 (Fe). Large variation in Zo~ is observed in crocidolite in which Z0~ has a maximum value at 30 keV (16.15) and minimum value at 1500 keV (11.65). Least variation in Zo~ is observed in gibbsite in which Zo~ has a maximum value at 20 keV (10.91) and minimum value at 1 MeV (9.99). From Table 1, it may be observed that in crocidolite, Fe203 is one of the major constituents which has Fe, a relatively high Z element among the constituents. Similarly, in gibbsite, A1203 is the major constituent which has A1, a relatively low atomic number element. Hence it
T. Kiran Kumar et al.
710
appears t h a t the v a r i a t i o n in Zo~ also depends o n the a t o m i c n u m b e r s of t h e m a j o r Constituents with which the material is composed. T h e results o b t a i n e d in the present study s u p p o r t the observations m a d e b y P a r t h a s a r a d h i (1968b).
REFERENCES
Berger M. J. and Hubbell J. H.(1987) XCOM: Photon Cross Sections on a Personal Computer. Nuclear Analysis Software, IAEA, Austria. Chandra Lingam S., Suresh Babu K. and Krishna Reddy D. V. (1984) Total gamma ray cross sections and effective atomic numbers in compounds in the energy region 32--662 keV. Ind. J. Phys. 58A, 285. EI-Kameel A. H., Saied M. H. and El-Attar A. L. (1983) Attenuation and Scattering coefficients of gamma rays through compressed powdered clay. Ind. J. Pure Appl. Phys. 21, 457. Gameel Y. S., Belal A. and El-kamel A. H. (1978) A new shield for screening soft X-ray radiation. Ind. J. Pure Appl. Phys. 16, 62. Hine G. J. (1952) The effective atomic numbers of materials for various gamma ray interactions. Phys. Rev. 85, 725. Mudahar G. S. and Sahota H. S. (1985) Optical thickness of Soil between source and detector for different gamma ray energies. J. Hydrol. 80, 265.
Mudahar G. S. and Sahota H. S. (1986) A new method for simultaneous measurement of soil bulk density and water content. Int. J. AppL Radiat. lsot. 37, 563. Mudahar G. S. and Sahota H. S. (1988) Effective atomic number studies in different soils for total photon interaction in the energy region 10-5000 keV. Int. J. App!. Radiat. Isot. 39, 1251. Parthasaradhi K. (1968a) Effective atomic numbers in compounds. Ind. J. Pure Appl. Phys. 6, 574. Parthasaradhi K. (1968b) Studies of the effective atomic numbers in alloys for gamma ray interactions in the energy region 100-662 keV. Ind. J. Pure Appl. Phys. 6, 609. Rama Rao J., Lakshminarayana V. and Jnanananda S. (1963) Effective atomic numbers of alloys for pair creation. Ind. J. Pure Appl. Phys. 1, 375. Saksena R. S., Chandra S. and Singh B. P. (1974) A gamma transmission method for the determination of moisture content in soils. J. Hydrol. 23, 341. Siddappa K., Khayyoom A., Parthasaradhi K. and Rama Rao J. (1971) Effective atomic numbers for photoelectric and incoherent scattering processes of gamma rays. Nucl. Sci. Engng 45, 94. Stroosnijder L. and DeSwart J. G. (1974) Column scanning with simultaneous use of 24~Am and t37Cs. Soil. Sci. 118, 61. Van Olphen H. and Fripiat (Eds) (1979) Data Handbook for Clay Materials and other Non-Metallic Minerals. Pergamon Press, Oxford.
Pergamon
EFFECTIVE MINERALS
ATOMIC
FOR
NUMBER
TOTAL
ENERGY
PHOTON REGION
STUDIES
IN
CLAY
INTERACTION 10 k e V - 1 0
IN
THE
MeV
T. K I R A N K U M A R , S. V E N K A T A R A T N A M and K. V E N K A T A R E D D Y t Jnanananda Laboratories for Nuclear Research, Andhra University, Visakhapamam 530 003, India (Received 28 February 1996; Revised 2 May 1996)
Abstract--Effective atomic numbers (Z,r) of different clay minerals are calculated for total photon interaction in the energy region 10 keV-10 MeV. The variation of Zo~ with energy is discussed by comparing with the similar studies made for alloys and compounds from our laboratory. Copyright © 1996 Elsevier Science Ltd
INTRODUCTION Several approaches (Stroosnijder and DeSwart, 1974; Saksena et al., 1974; Mudahar and Sahota, 1985; Mudahar and Sahota, 1986) have suggested the gamma ray transmission method as a convenient and accurate method for measurement of moisture content and density of soils. These measurements can be carried out in laboratories as well as fields. In field experiments soil could be used for shielding purposes because of its easy availability. Studies on the conditions affecting the attenuation of radiation through soil such as particle size and compaction achieved by pressure have been made (Gameel et al., 1978; EI-Kameel et al., 1983) The effective atomic numbers for some soil materials have been reported by Mudahar and Sahota (1988). As a further progress in this direction, we report the effective atomic numbers for fourteen clay minerals. It was pointed out by Hine (1952) that the effective atomic number for gamma ray interactions for materials composed of various elements can not be expressed by a single number and for each of the partial processes the number has to be weighted differently. Different studies reported from our laboratory (Parthasaradhi, 1968a; Parthasaradhi, 1968b; Siddappa et al., 1971; Rama Rao et al., 1963) found that Hine's predictions were correct. Most of the attempts made to determine the effective atomic numbers were restricted to alloys and compounds (Parthasaradhi, 1968b; Siddappa et al., 1971; Rama Rao et al., 1963; Chandra Lingam et al., 1984) and such attempts for clay materials appear to be very limited (Mudahar and Sahota, 1988). Keeping these points in view, the effective atomic numbers for total photon interactions for fourteen clay minerals in the energy range 10 keV-10 MeV have been estimated. The results are compared with similar studies in tTo whom all correspondence should be addressed.
alloys reported from our laboratories (Parthasaradhi, 1968b; Rama Rao et al., 1963). CALCULATIONOF EFFECTIVEATOMIC NUMBERS Calculation of effective atomic number of a mixture/alloy involves estimation of the partial/total cross sections and finding out the equivalent element that has the same cross section at that energy. The clay minerals for which effective atomic numbers are calculated and their most probable chemical compositions are given in Table 1 (Van Olphen and Fripiat, 1979). The theoretical values of attenuation coefficients for SiO2, A1203, TiO2, Fe203, MnO, MgO, CaO, Na:O, SO3, K20, P205, Li20 have been generated at energies 0.01, 0.015, 0.02, 0.03, 0.04, 0.05, 0.06, 0.08, 0.1, 0.15, 0.2, 0.3, 0.4, 0.5, 0.6, 0.8, 1, 1.5, 2, 3, 4, 5, 6, 8 and 10 MeV on a personal computer using XCOM (Berger and Hubbell, 1987). Then the attenuation coefficient of each clay mineral is calculated utilising the expression (/,t/P)clay =
n Z i=1
Wi~/P)i
(1)
where n is the number of constituents in the clay mineral, (ll/p)i is the respective attenuation coefficient and w~ is the fractional weightage of the ith element so that ~ w i = 1.
i=1
The attenuation coefficients are then converted into atomic cross sections, aday, using the expression ~/P)d~y n ~clay = N ~ ( w / A 3
(2)
where N is the Avogadro number, A~ and w~ are respectively atomic and fractional weights of the constituent elements of which the clay mineral is 707
T. Kiran K u m a r et al.
708
Table 1. Most probable composition of samples Comp. (%)
01
SiO2 A1203 TiO2 Fe203 MnO MgO CaO Na20 K20 P2Os SO3 LizO
63.84 22.24 0.50 3.45 0.01 4.87 2.88 1.73 0.40 0.08 0.35
02
03
53.53 66.03 43.95 0.30 0.03 0.02 0.58 0.06 0.01 0.01 0.17 29.03 0.20 0.34 0.08 3.19 1.37 0.04 0.10 0.02
13
04
05
06
07
5.43 0.98 0.06 1.44 0.05 42.50 2.61 0.13 0.09
47.73 0.95 0.04 2.07 0.05 48.86 0.24 0.08 0.03 0.09
0.04 99.30
75.15 9.72 0.74 3.08 0.10 8.35 2.03 0.14 0.74 0.02
0.05 0.02 0.56 0.05
I
1 II III
12
Montmorollonite Kalonite Laponite
N° 11
10 0.98
Comp. (%) SiO2 A1203 TiO2 Fe203 MnO MgO CaO Na20 K20 P2Os SO3 Li20
08 48.90 33.20 1.61 1.34
09 43.70 38.80 1.90 0.45
10 0.26 0.08 0.00 0.11
0.42 0.31 0.08 1.04 0.11
0.15 0.11 0.04 0.50 0.36
0.52 98.98 0.07 0.04
0.07
0.11
11 49.03 0.30 0.03 41.29 0.15 2.25 1.14 5.64 0.09 0.04
0.14
12 1.67 0.27 0.02 0.10 0.65 42.15 0.15 0.07
13 14 54.58 60.36 21.93 0.70 0.90 0.07 7.41 0.95 0.03 0.03 3.76 3 1 . 4 1 1.25 0.47 0.39 0.04 8.88 0.03 0.48 0.15
~01
f o r m e d . T h e d e n o m i n a t o r in e q u a t i o n (2) is t h e n u m b e r o f a t o m s p e r g r a m o f t h e clay m i n e r a l . Plots are drawn between the total photon cross s e c t i o n s in i n d i v i d u a l e l e m e n t s a n d t h e a t o m i c number of the elements for each energy. From these p l o t s t h e effective a t o m i c n u m b e r s o f e a c h m i n e r a l is o b t a i n e d b y i n t e r p o l a t i o n . T h e effective a t o m i c n u m b e r s (Zoo) so o b t a i n e d a r e g i v e n in T a b l e 2 f o r t h e s t a n d a r d e n e r g y grid. T h e v a r i a t i o n o f Zo~ w i t h e n e r g y f o r d i f f e r e n t c l a y m i n e r a l s is s h o w n in F i g s 1 - 5.
Table 2, Effective atomic numbers of clay minerals E (MeV)
01
02
03
04
05
06
07
0.01 0.10 0.20 0.30 0,50 1.00 5.00 10.00 E (MeV) 0.01 0.I0 0.20 0.30 0.50 1.00 5.00 10.00
11.85 10.85 10.31 10.31 10.26 10.24 10.35 10.44 08 11.54 10.63 10.21 10.21 10.16 10.12 10.24 10.33
tl.25 10.45 10.13 10.13 10.10 10.06 10.17 10.24 09 11.33 10.49 10.13 10.14 10.10 10.07 10.15 10.26
10.97 10.20 9.95 9.96 9.93 9.90 10.00 10.06 l0 16.64 15.80 14.54 14.16 14.03 13.95 14.34 14.64
11.55 11.74 10.33 10.31 10.27 10.25 10.35 10.41 11 15.64 14.38 12.34 11.96 11.75 11.69 12.04 12.35
11.24 10.47 10.13 10.13 10.10 10.07 10.18 10.23 12 14.07 12.79 11.73 11.52 11.42 11.39 11.65 11.86
10.88 10.25 10.06 10.06 10.02 9.99 10.08 10.13 13 12.86 11.66 10.84 10.77 10.67 10.66 10.82 10.97
11.81 10.81 10.30 10.29 10.23 10.20 10.33 10.43 14 11.18 10.41 10.09 10.11 10.07 10.05 10.13 10.19
Notation: 01--montmorillonite, 02--kaolinite, 03--1aponite, 04--magnesite, 05--~hrysotile, 06--gibbsite, 07--attapulgite, 0g---plastic clay, 09--flint clay, 10---calcite, ll--crocidolite, 12--gypsum, 13--illite, 14---talc.
I
103
104
E n e r g y (keV) Fig. 1. Variation of effective atomic n u m b e r with energy for montmorillonite, kaolinite and laponite.
DISCUSSION
54.24
Notation: 01--montmorillonite, 02--kaolinite, 03--1aponite, 04--magnesite. 05---chrysotile, 06---gibbsite, 07--attapulgite, 08--plastic clay, 09---flint clay, 10--calcite. ll---crocidolite, 12--gypsum, 13---illite. 14--talc.
[
102
It c a n be s e e n f r o m t h e t a b l e s a s w e l l a s figures t h a t f o r all clay m i n e r a l s t h e v a r i a t i o n o f Z ~ w i t h e n e r g y is m o r e o r less similar. T h e s l i g h t i r r e g u l a r i t i e s m a y be d u e to t h e e r r o r s in t h e i n t e r p o l a t i o n . T h e Zo~ v a l u e s t e a d i l y i n c r e a s e s in t h e r e g i o n 1 0 - 3 0 k e V a n d a f t e r 30 keV, it s t e a d i l y d e c r e a s e s u p t o 500 k e V . A f t e r w a r d s Z0~ a l m o s t r e m a i n s c o n s t a n t u p t o 1500 keV. A b o v e 1500 k e V Ze~ i n c r e a s e s w i t h i n c r e a s e in e n e r g y u p to 10 M e V . I n this e n e r g y r e g i o n , t h e i n c r e a s e in Z~s is s m a l l b u t continuous.
Variation o f Zea with energy in the region 10-1500 ke V T h e v a r i a t i o n o f Z~r w i t h e n e r g y ( 1 0 - 1 5 0 0 k e V ) m a y b e a t t r i b u t e d to t h e relative d o m i n a t i o n o f t h e p a r t i a l p r o c e s s e s , viz., p h o t o e l e c t r i c effect, c o h e r e n t scattering, incoherent scattering and pair production. It w a s r e p o r t e d b y P a r t h a s a r a d h i , (1968b) t h a t Zo~ f o r p h o t o e l e c t r i c p r o c e s s is a l w a y s g r e a t e r t h a n o r e q u a l to t h a t o f s c a t t e r i n g p r o c e s s , A t low e n e r g i e s
12--
llI
11
Gibbisite
N
t0 I
101
102
103
104
Energy (keY) Fig, 2. Variation of effective atomic number with energy for magnesite, chrysotile and gibbsite.
Effective atomic number studies
709
12 13 ~r ~ f ~,~ ~.,~ - x ~ \
[ II
Attapulgite Plastic clay I II
N
lllite Talc
12 1
II III
10
I
I
'
101
10 2
10 3
t'q
10 4
Energy (keV) Fig. 3. Variation of effective atomic number with energy for attapulgite, plastic clay and flint clay.
t0
101
the photoelectric effect is dominating and hence Z0~ for total interaction is mainly described by the Zo~ for this partial process. Similarly at higher energies the contribution due to scattering process will be more in comparison with photoelectric effect and this will have its effect on the Zo~ for total gamma ray interaction. Hence at low energies, where photoelectric effect dominates, Ze~ value is more and at higher energies, where scattering process dominates, Z~r value is less. Therefore, the Ze~ for total gamma ray interaction varies from a higher value at lower energies to a lower value at higher energies depending on the relative domination of the partial gamma ray processes one over the other. From the figures it may be observed that Z0n values for all minerals decrease from 30 keV to 500 keV. The present results confirm the observations made by Parthasaradhi (1968b) and Mudahar and Sahota (1988).
Variation of Zeg with energy from 1.5-10 MeV Rama Rao et al. (1963) reported that Zo~ of rhodium-platinum alloy for pair production cross section remains constant in the energy region 1.119 to 2 MeV. Mudahar and Sahota (1988) reported that 17
I II III
Calcite Crocidolite Gypsum
15
14I~ t~
13 - 12--
III
11 L l0
l01
10 2
10 3
10 4
Energy (keV)
Fig. 4. Variation of effective atomic number with energy for calcite, crocidolite and gypsum.
10 2
I
[
10 3
10 4
Energy (keV)
Fig. 5. Variation of effective atomic number with energy for illite and talc.
Z0, of some soils for total photon interactions slowly increase with increase in energy from 1.5 to 5 MeV. In the present studies it may be observed from the figures that there is slight but continuous increase in Zo, with energy in the energy region 1.5 to 10 MeV. In this region, the dominant processes are incoherent scattering and pair production. Hence as mentioned by Mudahar and Sahota (1988) this behaviour may be attributed to the mixed contribution of scattering and pair production interaction processes.
Variation of Z,1r with atomic numbers of the constituents Parthasaradhi (1968b) observed that variation in Z,~ for total gamma ray interaction also depends on the spread in the atomic numbers of the elements of which the material is composed. He noticed no significant variation in Z0~ of monel metal (Ni, 60; Cu, 33; Fe, 6.5; and Mn, 0.5%) in which the spread in atomic numbers is small and maximum variation in tungsten steel (W, 23; C, 0.77; Cr, 4.25; V, 1.6; Co, 11; and Fe 59.38%) in which the spread is high. In the case of tungsten steel Zo~ value dropped from 40 to 100 keV to 32 at 662 keV. In the present work, a total number of 13 elements are present in the samples and their atomic number range from 3 (Li) to 26 (Fe). Large variation in Zo~ is observed in crocidolite in which Z0~ has a maximum value at 30 keV (16.15) and minimum value at 1500 keV (11.65). Least variation in Zo~ is observed in gibbsite in which Zo~ has a maximum value at 20 keV (10.91) and minimum value at 1 MeV (9.99). From Table 1, it may be observed that in crocidolite, Fe203 is one of the major constituents which has Fe, a relatively high Z element among the constituents. Similarly, in gibbsite, A1203 is the major constituent which has A1, a relatively low atomic number element. Hence it
T. Kiran Kumar et al.
710
appears t h a t the v a r i a t i o n in Zo~ also depends o n the a t o m i c n u m b e r s of t h e m a j o r Constituents with which the material is composed. T h e results o b t a i n e d in the present study s u p p o r t the observations m a d e b y P a r t h a s a r a d h i (1968b).
REFERENCES
Berger M. J. and Hubbell J. H.(1987) XCOM: Photon Cross Sections on a Personal Computer. Nuclear Analysis Software, IAEA, Austria. Chandra Lingam S., Suresh Babu K. and Krishna Reddy D. V. (1984) Total gamma ray cross sections and effective atomic numbers in compounds in the energy region 32--662 keV. Ind. J. Phys. 58A, 285. EI-Kameel A. H., Saied M. H. and El-Attar A. L. (1983) Attenuation and Scattering coefficients of gamma rays through compressed powdered clay. Ind. J. Pure Appl. Phys. 21, 457. Gameel Y. S., Belal A. and El-kamel A. H. (1978) A new shield for screening soft X-ray radiation. Ind. J. Pure Appl. Phys. 16, 62. Hine G. J. (1952) The effective atomic numbers of materials for various gamma ray interactions. Phys. Rev. 85, 725. Mudahar G. S. and Sahota H. S. (1985) Optical thickness of Soil between source and detector for different gamma ray energies. J. Hydrol. 80, 265.
Mudahar G. S. and Sahota H. S. (1986) A new method for simultaneous measurement of soil bulk density and water content. Int. J. AppL Radiat. lsot. 37, 563. Mudahar G. S. and Sahota H. S. (1988) Effective atomic number studies in different soils for total photon interaction in the energy region 10-5000 keV. Int. J. App!. Radiat. Isot. 39, 1251. Parthasaradhi K. (1968a) Effective atomic numbers in compounds. Ind. J. Pure Appl. Phys. 6, 574. Parthasaradhi K. (1968b) Studies of the effective atomic numbers in alloys for gamma ray interactions in the energy region 100-662 keV. Ind. J. Pure Appl. Phys. 6, 609. Rama Rao J., Lakshminarayana V. and Jnanananda S. (1963) Effective atomic numbers of alloys for pair creation. Ind. J. Pure Appl. Phys. 1, 375. Saksena R. S., Chandra S. and Singh B. P. (1974) A gamma transmission method for the determination of moisture content in soils. J. Hydrol. 23, 341. Siddappa K., Khayyoom A., Parthasaradhi K. and Rama Rao J. (1971) Effective atomic numbers for photoelectric and incoherent scattering processes of gamma rays. Nucl. Sci. Engng 45, 94. Stroosnijder L. and DeSwart J. G. (1974) Column scanning with simultaneous use of 24~Am and t37Cs. Soil. Sci. 118, 61. Van Olphen H. and Fripiat (Eds) (1979) Data Handbook for Clay Materials and other Non-Metallic Minerals. Pergamon Press, Oxford.