Photon interaction study of organic nonlinear optical materials in the energy range 122–1330 keV

Author’s Accepted Manuscript Photon interaction study of organic nonlinear optical materials in the energy range 122keV to 1330keV Vishal V. Awasarmol, Dhammajyot K. Gaikwad, Siddheshwar D. Raut, Pravina P. Pawar www.elsevier.com/locate/radphyschem

PII: DOI: Reference:

S0969-806X(16)30343-7 http://dx.doi.org/10.1016/j.radphyschem.2016.09.012 RPC7269

To appear in: Radiation Physics and Chemistry Received date: 25 June 2016 Revised date: 21 August 2016 Accepted date: 6 September 2016 Cite this article as: Vishal V. Awasarmol, Dhammajyot K. Gaikwad, Siddheshwar D. Raut and Pravina P. Pawar, Photon interaction study of organic nonlinear optical materials in the energy range 122keV to 1330keV, Radiation Physics and Chemistry, http://dx.doi.org/10.1016/j.radphyschem.2016.09.012 This is a PDF file of an unedited manuscript that has been accepted for publication. As a service to our customers we are providing this early version of the manuscript. The manuscript will undergo copyediting, typesetting, and review of the resulting galley proof before it is published in its final citable form. Please note that during the production process errors may be discovered which could affect the content, and all legal disclaimers that apply to the journal pertain.

Photon interaction study of organic nonlinear optical materials in the energy range 122 keV to 1330 keV Vishal V. Awasarmol1, Dhammajyot K. Gaikwad 2, Siddheshwar D. Raut 3, Pravina P. Pawar4* 1-4

Department of Physics, Dr. Babasaheb Ambedkar Marathwada University, Aurangabad:

431004, India.E-mail:- [email protected] and [email protected] Fax: - +91 0240 2403113, 2403335 Abstract: In the present study, the mass attenuation coefficient (µm) of six organic nonlinear optical materials has been calculated in the energy range 122 keV to 1330 keV and compared with the obtained values from the WinXCOM program. It is found that there is a good agreement between theoretical and experimental values (< 3%). The linear attenuation coefficients (µ) total atomic cross section (st, a), and total electronic cross section (st, el) have also been calculated from the obtained µm values and their variations with photon energy have been plotted. From the present work, it is observed that the variation of obtained values of µm, µ, st, a, and st, el strongly depends on the photon energy and decreases or increases due to chemical composition and density of the sample. All the samples have been studied extensively using transmission method with a view to utilize the material for radiation dosimetry. Investigated samples are good material for radiation dosimetry due their low effective atomic number. The mass attenuation coefficient (µm), linear attenuation coefficients (µ), total atomic cross section (st, a), total electronic cross section (st, el), effective atomic numbers (Zeff), molar extinction coefficient (e),

mass energy absorption

coefficient (µen/ρ) and effective atomic energy absorption cross section (σa,

en)

of all sample

materials have been carried out and transmission curves have been plotted. The transmission curve shows that the variation of all sample materials decreases with increasing photon energy. Keywords: Mass attenuation coefficient (µm), linear attenuation coefficients (µ), total atomic cross section (st, a), total electronic cross section (st, el), effective atomic numbers (Zeff).

1. Introduction: The study of photon interactions with matter is important and the data on the transmission and absorption of X-rays and/or gamma rays in biological shielding and dosimetric materials assumed great significance by virtue of the diverse application in the field of medical physics and medical biology (Kaewkhao et.al 2008). The knowledge of absorption and scattering of gamma rays in material (i.e. alloy, plastic, soil, and biological materials) has become an interesting and exciting field of research (Manohara and Hanagodimath, 2007). The mass attenuation coefficient (mm) is a measure of the probability of interaction that occurs between incident photons and samples mass per unit area. This is the primary parameter needed to understand the diffusion and transmission of X-ray and gamma ray in the material (Manohara et al., 2008). The accurate value of photon mass attenuation coefficients are required to provide essential data in diverse fields such as radiation protection, computerized tomography, radiation dosimetry, gamma ray fluorescence studies, radiation biophysics etc. There have been number of research papers are available in the various energy ranges on the theoretical and experimental investigations to determine (μm) values in various elements and compounds/mixtures. Hubbell (1982) reported tables of (μm) values for 40 elements and 45 mixtures and compounds in the energy range from 1 keV to 20 MeV. These tables were replaced by Hubbell and Seltzer (1995) in the form of tabulation for all elements (Z=1-92) and 48 additional substances of dosimetric interest. Berger and Hubbell (1987) developed new tables for calculating (μm) values of total photon interaction processes such as the photoelectric effect, Compton effect and pair production and these processes are totally available in the form of XCOM software package by substituting the chemical composition/weight fraction of elements, compounds and mixtures for photon energies from 1 keV to 100 GeV. In (2001, 2004) Gerward et al., converted this program to Windows platform and this Windows version is being called WinXCOM. The value of the mass attenuation coefficients (mm) are widely used in research for solving different problems in radiation physics and radiation chemistry (Kaewkhao, et al., 2008). It is well known that mass attenuation coefficients strongly depend on the photon energy, the nature of the material and the density (Baltas et al., 2007). The other related parameters i.e. effective atomic numbers (Zeff), effective electron density (Neff), molar extinction coefficient (e), mass energy absorption coefficient (µen/ρ), and effective atomic energy absorption cross section

(σa,en) of compound materials can be derived by using mass attenuation coefficient data (Kiran Kumar and Venkata Reddy, 1997; El-Kateb and Rizk, 2000; Murthy, 2004; Gowda et al., 2005; Han et al., 2009; Han and Demir, 2009; Pawar and Bichile, 2013; Gaikwad et al., 2015; Ladhaf and Pawar, 2015; Kore et al., 2016). In case of compound materials, a single number cannot represent the atomic number uniquely across the entire energy range. The number represent atomic number in composites is called the effective atomic number and varies with the energy (Jackson and Hawkes, 1981). Hine (1952) suggested that the effective atomic numbers (Zeff) play a major role in photon interactions for compound materials. Accurate values of Zeff are widely used in the different fields like medical physics, radiation shielding, pharmaceutical and radiation dosimetry. The effective atomic number is closely related to the effective electron density. Therefore, the study of effective atomic numbers of compound material is very useful for various technological applications and also useful in radiation therapy and medical imaging. Thus, the theoretical and experimental studies on the interaction of X-ray and gamma rays attract the researcher. Numerous efforts have been taken on interaction of radiations with matter and reported that the energy region 5 keV to 1500 keV has tremendous application in medical and biological fields (Hubbell, 1999; Kurudirek et al., 2015; Demir et al., 2012; Manohara and Hanagodimath, 2007; Salehi et al., 2015). Nonlinear optical materials are considered as technological important materials because of their high usage for electronic and optoelectronics applications i.e.optical telecommunication, laser, optics, photonics, optical switching, data storage, dosimetry and radiation sensing. In the literature survey, there are almost no reports on the study of (m), (mm), (st, a),(st, el), (Zeff), (e), (µen/ρ), and (σa,en) of organic nonlinear optical materials. This prompted us to carry out the present work. In the present investigation, the mass attenuation coefficients and other related parameters for the organic nonlinear optical materials at photon energies 122 keV to 1330 keV have been experimentally measured and theoretically calculated. Also, the variation of investigated parameters versus photon energy is graphically presented. The experimental mm values have been checked using the results of WinXCOM calculations.

2. Theoretical calculations: 2.1 Linear attenuation coefficient and mass attenuation coefficient: A parallel beam of mono energetic X-ray or gamma ray photons passing through matter is attenuated due to absorption and scattering. This attenuation of beam is described by following equation (Pawar and Bichile, 2013; Kore and Pawar, 2014; Gaikwad et al., 2015; Ladhaf and Pawar, 2015):

I = I 0 exp(-m m t )

(1)

where I0 and I are the un-attenuated and attenuated photon intensities, µm (cm2gm-1) is mass attenuation coefficient of the materials and t (g/cm2) is the sample thickness. The photon mass attenuation coefficient for compound or mixture of element is given by mixture rule:

mm = åi Wi (mm )i

(2)

where Wi and (mm)i are the weight fraction and mass attenuation coefficient of the ith constituent element, respectively. For a chemical compound the fraction by weight (Wi) is given by: Wi =

ni Ai å j ni A j

(3)

Where Ai is the atomic weight of ith element and ni is the number of formula units. 2.2 Total atomic cross section and total electronic cross section: The values of mass attenuation coefficients were then used to determine the total molecular scattering cross section (st, m) determined using mass attenuation coefficient (mm) is given by,

s t ,m = mm (M N A )

(4)

where M= ∑i ni Ai is the atomic weight of the compound, NA is the Avogadro’s number (6.02486 ´ 1023 mol-1), ni is the total number of atoms in the molecule and Ai is the atomic weight of ith element in a molecule.

The total atomic cross section (st, a) has been determined from the following equation:

(s t , a )

=

1 å if i Ai (mm )i NA

(5)

Similarly, the total electronic cross-sections (st, el) have been determined from the following equation:

(s t ,el )

=

1 NA

åi

fi Ai (mm )i = s t Zi Z eff

(6)

Where fi = ni/∑jnj and Zi are the fractional abundance and atomic number of constituent element I, respectively, ni is the total number of atoms of the constituent element i and ∑j nj is the total number of atoms present in the molecular formula. 2.3 Effective atomic number: Rearranged the equation (6) yield the effective atomic numbers can be given as:

Z eff =

s t ,a s t ,el

(7)

2.4 Molar extinction coefficient: The value of e were determined using the following equation:

e = 0.4343´ N A ´ s t

(8)

2.5 Mass energy absorption coefficient and effective atomic energy absorption cross section: The value of mass energy absorption coefficient (µen/r) were determined using the following equation: N ö men æ = ç s m,en ´ A ÷ M ø r è

(9)

Similarly, the effective atomic energy-absorption cross section (sa, en) can be calculated using the following equation:

s a,en =

s m,en åi ni

(10)

The symbols ni and ∑i denote the number of atoms of the ith constituent element and the total number of atoms in the molecular formula, respectively.

Experimental Details: In the present investigation, the measurement of incident and transmitted photon energies were done with the help of narrow beam good geometry set up. The schematic arrangement of the experimental set up is shown in Fig.1. The six radioactive sources 54

Mn, and

60

57

Co,

133

Ba,

22

Na,

137

Cs,

Co were used in the present study. All these radioactive sources used in this study

were obtained from Bhabha Atomic Research Centre, Mumbai, India. Gamma rays of energy 122, 356, 511, 662, 840, 1170, 1275 and 1330 keV emitted by these radioactive sources were collimated and detected by a NaI (Tl) scintillation detector. The organic nonlinear optical materials such as 2-Aminofluorene (C13H11N), 9H-Carbazole-9-ethanol (C14H13NO), N-(2,4Dinitrophenyl)-L-alanine methyl ester (C10H11N3O6), 4-[4-(Dimethyl amino) styryl] pyridine (C15H16N2), and

4- [Bis[2-(acetyloxy) ethyl] amino] benzaldehyde (C15H19NO5) under

investigation were pellets shaped. The diameters of the samples were determined with the help of a travelling microscope. Attenuate (I) and un-attenuated (I0) intensitieswere amplified and analyzed by gamma ray spectrometry includes (2″×2″) NaI (Tl) crystal with an energy resolution of 8.2% at 662 keV and 8K multichannel analyzer. Stability and reproducibility of the arrangement were tested before and after each set of runs in the usual manner. To minimize the effects of small-angle scattering and multiple scattering events on the measured intensity, the transmitted intensity was measured by setting the channels at the full-width half-maximum position of the photo peak. Each sample pellet was weighed in a sensitive digital balance having a good accuracy 0.001 mg. The weighing was repeated several times to obtain consistent value of the mass. The mean of this set of values was taken to be the mass of the sample. Uncertainty in the measured mass per unit area is < 0.05 %. An optimum thickness (2
Hence, no small angle scattering corrections were applied to the measured data. All the organic nonlinear optical material samples used in the present study were of high purity (95.6 %) and hence uncertainty due impurity is < 0.075%. In the present study, the error due to the sample impurities can be high only when large percentage of high Z impurities is present in the sample. The non-uniformity of the sample material introduces a fraction of error of about half the root mean square deviation in mass per unit area. The photon built-up effect was reduced to minimum value by choosing optimum count rate and the counting time. The photon built-up effect, which is consequence of the multiple scattering inside the sample, depends on the atomic number and the sample thickness, and also on the incident photon energy. In the multichannel analyzer used in the present study, there was a built-in provision for dead time correction and always < 3 %. The errors in intensities I0, I, mass density (ρ) and thickness (t) were utilized to calculate maximum errors in mass attenuation coefficients through the following error formula:

æmö 1 Dçç ÷÷ = è r ø rt

2

2 æ DI0 ö DI ö æ I ö ÷÷ + æç çç ÷ + ç ln 0 ÷ è I ø è I ø è I0 ø

2

éæ D r ö 2 æ Dt ö 2 ù êçç ÷÷ + ç ÷ ú êëè r ø è t ø úû

(11)

where ΔI0, ΔI, Δρ and Δt are the errors in the intensities (I and I0), mass density (ρ) and thickness (t) of the biological samples, respectively. The estimated overall error in the measured data is found to be less than 4%. 4. Results and Discussion In this work the experimental and theoretical values of the linear attenuation coefficients (µ), mass attenuation coefficients (µm), total atomic cross section (st, a), total electronic cross section (st, el), effective atomic numbers (Zeff), molar extinction coefficient (e), mass energy absorption coefficient (µen/ρ) and effective atomic energy absorption cross section (σa, en) were measured at 122, 356, 511, 662, 840, 1170, 1275 and 1330 keV photon energies for six organic nonlinear optical materials. These all radiological parameters were determined using incident and transmitted intensity of gamma rays in a well collimated narrow beam good geometry setup displayed in Tables 1, 2, 3, 4, 5, 6, 7, and 8 respectively. Experimentally measured results of µ and µm for all samples at given photon energies are presented in Tables 1 and 2, respectively. The Figs. 2 and 3 also include the variation of

theoretically determined µ and µmvalues versus photon energy (E). It is observed from figures and tables that the µ and µm depends on photon energy (E) and decreases with increasing photon energy. The experimental values of µ and µm agree with theoretical values calculated using the WinXCOM program based on the mixture rule. Measured total atomic cross section (st, a) and total electronic cross section (st, el) for the studied organic nonlinear optical materials are tabulated in Tables 3 and 4 respectively. The typical plots of st, a and st, el versus photon energy (E) are displayed in Figs. 4 and 5 respectively. The behavior of st, a and st, el with photon energy (E) is almost similar to that of µ and µm. Results of Zeff for organic nonlinear optical materials were calculated from Eq. 7 using the values of µm and the same are given in Table 5. The Zeff= 0.533* Aeff relation is valid for the present case. A typical plot of Zeff versus photon energy (E) is plotted for all samples in Fig. 6. It is clearly seen from Table 5 and Fig. 6 that Zeff values for present samples vary and tend to be almost constant for higher gamma ray photon energy. The molar extinction coefficients of organic nonlinear optical materials are calculated using Eq. 8 and tabulated in Table 6. The typical variation of e versus photon energy (E) for all samples is shown in Fig. 7. It can be observed from Table 6 and Fig. 7 that the e initially decreases and tends to be almost similar in the high photon energy range. In the compound materials, like the organic nonlinear optical materials studied in the present case, mass energy absorption coefficient (men/r) and effective atomic energy absorption cross section (sa, en) for present samples were determined using Eqs. 9 and 10 and the same are given in Tables 7 and 8 and displayed in Figs. 8 and 9 respectively. Typical plot of men/r and sa, en versus photon energy (E) is displayed graphically for all samples in Figs. 8 and 9 respectively. It is clear from Figs. 8 and 9 that the variation of the all samples initially decreases with increasing photon energy. The variations of the all parameters were systematically studied in the given photon energy region.

5. Conclusion: In the present study, the mass attenuation coefficient of six organic nonlinear optical materials has been calculated at 122, 356, 511, 662, 840, 1170, 1275 and 1330 keV photon energies, respectively. This study concludes that any dosimetric material depends on its density, chemical composition and concentration of the elements that it contains. The all samples have

been studied extensively using transmission method with a view to utilize the material for radiation dosimetry. In this work, all these samples are attractive as a material for radiation dosimetry due their low effective atomic number. In this research mm were investigated to get sufficient information about linear attenuation coefficients (µ), mass attenuation coefficients (µm), total atomic cross section (st, a), total electronic cross section (st, el), effective atomic numbers (Zeff), molar extinction coefficient (e), mass energy absorption coefficient (µen/ρ) and effective atomic energy absorption cross section (σa, en) for organic nonlinear optical materials and it has been observed that the present data on mm values and other parameters are very useful in radiation therapy, diagnostic imaging, and other technological applications. In this paper first time we reported that the experimental data on (m), (mm), (st, a), (st, el), (Zeff), (e), (µen/ρ), and (σa, en) of organic nonlinear optical materials at different photon energy range.

Acknowledgments: The author (VVA) & (DKG) would like to thank University Grant Commission, New Delhi for providing RGNF.

References: Baltas H., Celik S., Cevik U., E-Yamaz, (2007), Measurements of mass attenuation coefficient and effective atomic number for MgB2 using X-ray energies, Radiation Measurements, Vol. 42, 55-60. Berger M.J., Hubbell J.H., (1987), (XCOM) Photon cross section on a personal computer. NBSIR. 87-3597. Creagh D.C. (1987), The Resoluation of Discrepancies in Tables of Photon Attenuation Coefficient, Nuclear Instruments and Methods A, Vol. 255, 1–16. Demir D., Tursucu A., Oznuluer T. (2012), Studies on mass attenuation coefficient, effective atomic number and electron density of some vitamins, Radiation Environment Biophysics, Vol. 51, 469-475. El-Kateb A.H., RizkR.A.M., Abdul-Kadar A.M., (2000), Determination of atomic cross-section and effective atomic numbers for some alloy, Annals of Nuclear Energy, Vol. 27, no.14, pp. 1333-1343. Gaikwad D.K, Pawar P.P., Selvam T.P., (2016), Attenuation cross sections measurements of some fatty acids in the energy range 122-1330 keV. Pramana- J. Phys. 87 (12), 1-7.DOI 10.1007/s12043-016-1213-y. Gerward L., Guilbert N., Jensen K.B., Levring H., (2001), X-ray absorption in matter. Reengineering XCOM. Radiation Physics and Chemistry, Vol. 60, 23-24. Gerward L., Guilbert N., Jensen K.B., Levring H., (2004), WinXCOM-A Program for calculating X-ray attenuation coefficients, Radiation Physics and Chemistry, Vol. 71, 653654. Gowda S., Krishnaveni S., Gowda R., (2005), Studies on effective atomic number and electron densities in amino acids and sugar in the energy range 30-1333keV, Nuclear Instruments and Methods in Physics Research B: Beam Interaction with materials and atoms, Vol. 239, no. 4, pp. 361-369. Han I., Demir L., (2009), Studies on mass attenuation coefficient, effective atomic and electron number of Ti and Ni alloy, Radiation Measurements, Vol. 44, 289-294. Han I., Demir L., Sahin M., (2009), Determination of mass attenuation coefficient, effective atomic number and electron number for some natural minerals, Radiation Physics and Chemistry, Vol. 78, no. 9, pp. 760-764.

Hine G.J., (1952), The effective atomic numbers of materials for various gamma interactions, Physics Review, Vol. 85, 725-737. Hubbell J.H., (1982), Photon mass attenuation and energy absorption, International Journal of Applied Radiation and Isotopes, Vol, 1269-1290. Hubbell, J.H.,(1999), Review of photon interaction cross section data in the medical and biological context, Phys.Med.Biol.44:R1-R22. Hubbell J.H., Seltzer S.M., (1995), Tables of X-ray mass attenuation coefficients and mass energy absorption coefficients 1 keV to 20 MeV for elements Z=1 to 92 and 48 additional substances of dosimetric interest, National Institute of Standards and Physics Laboratory. NISTIR 5632. Jackson, D.F., Hawkes, D.J., (1981),X-ray attenuation coefficients of elements and mixtures,Phys. Rep., Vol. 70, 169-233. Kaewkhao J., Laopaiboon J., Chewpraditkul W., (2008), Determination of effective atomic numbers and effective electron densities for Cu/Zn alloy, Journal of Quantitaive Spectroscopy & Radioactive Transfer, Vol. 109, 1260-1265. Kiran Kumar T., Venkata Reddy K., (1997), Effective atomic number for materials of dosimetric interest, Radiation Physics and Chemistry, Vol. 50, no.6, pp. 545-553. Kore P.S., Pawar P.P., (2014), Measurement of mass attenuation coefficient, effective atomic number and electron density of some amino acids, Radiation Physics and Chemistry, Vol. 98, 86-91. Kore P.S., Pawar P.P., Selvam T.P., (2016), Evaluation of radiological data of some saturated fatty acids using gamma ray spectrometry, Radiation Physics and Chemistry, Vol. 119, P. No. 74-79. Kurudirek, Murat, Onaran, Tayfur, (2015), Calculation of effective atomic number and electron density of essential biomolecules for electron, proton, alpha particle and multi-energetic photon interactions, Radiation Physics and Chemistry, Vol. 112, 125-138. Ladhaf B.M., Pawar P.P., (2015), Studies on mass energy absorption coefficient and effective atomic energy absorption cross-section for carbohydrates, Radiation Physics and Chemistry, Vol. 109, 89-94.

Manohara S.R., Hanagodimath S.M., (2007), Studies on effective atomic numbers and electron densities of essential amino acids in the energy range 1keV-100GeV, Nuclear Instruments and Methods in Physics Research B, Vol. 258, 321-328. Manohara S.R., Hanagodimath S.M., Gerward L., (2008), Studies on effective atomic number, electron density and kerma for some fatty acids and carbohydrates, Physics in Medicine and Biology, Vol. 53, no. 20, N377-N386. Murthy V.R. K., (2004), Effective atomic number for W/Cu alloy for total photon attenuation, Radiation Physics and Chemistry, Vol. 71, 667-669. Pawar P.P., Bichile G.K., (2013), Studies on mass attenuation coefficient, effective atomic number and electron density of some amino acids in the energy range 0.122-1.330 MeV, Radiation Physics and Chemistry, Vol. 92, 22-27. Suresh S., Ramanand A., Jayaraman D., Mani P., (2012), Review on Theoretical Aspect of Nonlinear Optics, Rev. Adv. Mater. Sci., Vol. 30, 175-183. Salehi D., Sardari D., Jozani M.S., (2015), Investigation of some radiation shielding parameters in soft tissue, Journal of Radiation Research and Applied Sciences, Vol. 8, 439-445.

Fig.1.The schematic view of the experimental set up.

C13H11N C14H13NO C10H11N3O6 C15H16N2 C15H19NO5

0.22 0.20 0.18 0.16

-1

m(cm )

0.14 0.12 0.10 0.08 0.06 0.04 0

200

400

600

800

1000

1200

1400

Energy (keV)

Fig. 2 The typical plots of m versus E for organic nonlinear optical materials.

C13H11N C14H13NO C10H11N3O6 C15H16N2 C15H19NO5

0.16

0.14

2

mm (cm /g)

0.12

0.10

0.08

0.06

0.04 0

200

400

600

800

1000

1200

1400

Energy (keV)

Fig. 3 The typical plots of mm versus E for organic nonlinear optical materials.

80

C13H11N C14H13NO C10H11N3O6 C15H16N2 C15H19NO5

75 70 65

st, a(barn/atom)

60 55 50 45 40 35 30 25 20 15 10 0

200

400

600

800

1000

1200

1400

Energy (keV)

Fig. 4 The typical plots of st, a versus E for organic nonlinear optical materials.

st, el(barn/atom)

21 20 19 18 17 16 15 14 13 12 11 10 9 8 7 6 5 4 3

C13H11N C14H13NO C10H11N3O6 C15H16N2 C15H19NO5

0

200

400

600

800

1000

1200

1400

Energy (keV)

Fig. 5 The typical plots of st, el versus E for organic nonlinear optical materials.

C13H11N C14H13NO C10H11N3O6 C15H16N2 C15H19NO5

4.8

4.6

Zeff

4.4

4.2

4.0

3.8

3.6 0

200

400

600

800

1000

1200

1400

Energy (keV)

Fig. 6 The typical plots of Zeff versus E for organic nonlinear optical materials.

2

e(cm /mole)

C13H11N C14H13NO C10H11N3O6 C15H16N2 C15H19NO5

21 20 19 18 17 16 15 14 13 12 11 10 9 8 7 6 5 4 3 0

200

400

600

800

1000

1200

1400

Energy (keV)

Fig. 7 The typical plots of Ɛ versus E for organic nonlinear optical materials.

C13H11N C14H13NO C10H11N3O6 C15H16N2 C15H19NO5

0.45 0.40 0.35

men/r

0.30 0.25 0.20 0.15 0.10 0

200

400

600

800

1000

1200

1400

Energy (keV)

Fig. 8 The typical plots of men/r versus E for inorganic nonlinear optical materials.

C13H11N C14H13NO C10H11N3O6 C15H16N2 C15H19NO5

0.50 0.45 0.40

sa,en

0.35 0.30 0.25 0.20 0.15 0.10 0

200

400

600

800

1000

1200

1400

Energy (keV)

Fig. 9 The typical plots of sa,en versus E for inorganic nonlinear optical materials.

C13H11N Exp Theo. 0.176 0.183 0.119 0.125 0.098 0.106 0.089 0.094 0.083 0.091 0.065 0.072 0.061 0.069 0.058 0.066

C13H14NO Exp Theo. 0.172 0.179 0.118 0.123 0.096 0.103 0.084 0.092 0.082 0.089 0.062 0.073 0.057 0.067 0.054 0.064

C10H11N3O6 Exp Theo. 0.209 0.218 0.138 0.149 0.119 0.126 0.105 0.111 0.101 0.109 0.082 0.087 0.075 0.081 0.072 0.078

C15H16N2 Exp Theo. 0.175 0.169 0.111 0.117 0.091 0.098 0.082 0.088 0.078 0.085 0.061 0.067 0.058 0.064 0.056 0.062

C15H19NO5 Exp Theo. 0.189 0.184 0.119 0.127 0.097 0.106 0.088 0.094 0.083 0.091 0.065 0.073 0.059 0.068 0.057 0.066

Energy keV 122 356 511 662 840 1170 1275 1330

C13H11N Exp Theo. 0.146 0.152 0.099 0.104 0.081 0.088 0.074 0.078 0.069 0.076 0.054 0.060 0.051 0.057 0.048 0.055

C13H14NO Exp Theo. 0.147 0.153 0.101 0.105 0.082 0.088 0.072 0.079 0.070 0.076 0.053 0.062 0.049 0.057 0.046 0.055

C10H11N3O6 Exp keV 0.144 0.151 0.095 0.103 0.082 0.087 0.073 0.077 0.070 0.075 0.057 0.060 0.052 0.056 0.050 0.054

C15H16N2 Exp Theo. 0.159 0.154 0.101 0.106 0.083 0.089 0.075 0.080 0.071 0.077 0.055 0.061 0.053 0.058 0.051 0.056

C15H19NO5 Exp Theo. 0.158 0.154 0.099 0.106 0.081 0.089 0.074 0.079 0.069 0.076 0.054 0.061 0.049 0.057 0.048 0.055

Table 2 Mass attenuation coefficient (mm) of organic nonlinear optical materials from 122 keV to 1330 keV

Energy keV 122 356 511 662 840 1170 1275 1330

Table 1 Linear attenuation coefficient (m) of organic nonlinear optical materials from 122 keV to 1330 keV

C13H11N Exp Theo. 44.0095 45.7239 29.7564 31.2848 24.5053 26.4717 22.2548 23.4636 20.7545 22.8619 16.2535 18.0489 15.2533 17.1465 14.5031 16.5448

C13H14NO Exp Theo. 51.5488 53.6497 35.3649 36.8184 28.7714 30.8573 25.1750 27.7015 24.5756 26.6495 18.5815 21.7404 17.0830 19.9871 16.1839 19.2858

C10H11N3O6 Exp keV 64.5394 67.4721 42.6145 46.0240 36.7473 38.8747 32.4241 34.4063 31.1889 33.5126 25.3217 26.8101 23.1601 25.0228 22.2337 24.1291

C15H16N2 Exp Theo. 59.2295 57.3342 37.5684 39.4638 30.7993 33.1347 27.7533 29.7840 26.3994 28.6671 20.6457 22.7103 19.6304 21.5934 18.9534 20.8488

C15H19NO5 Exp Theo. 76.9345 74.9741 48.4402 51.6055 39.4849 43.3292 35.8213 38.4607 33.7860 37.0002 26.4589 29.6975 24.0166 27.7501 23.2025 26.7765

Energy keV 122 356 511 662 840 1170 1275 1330

C13H11N Exp Theo. 11.6363 11.8128 7.8840 8.0937 6.5004 6.8517 5.9160 6.0752 5.5225 5.9212 4.3307 4.6767 4.0720 4.4433 3.8790 4.2877

C13H14NO Exp Theo. 13.5104 13.7862 9.2865 9.4766 7.5692 7.9467 6.6255 7.1368 6.4732 6.8683 4.8977 5.6059 4.5073 5.1545 4.2732 4.9740

C10H11N3O6 Exp keV 13.3686 13.7769 8.8943 9.5124 7.6895 8.0678 6.8056 7.1615 6.5577 6.9943 5.3419 5.6166 4.8939 5.2472 4.7039 5.0623

C15H16N2 Exp Theo. 16.3626 15.9031 10.3731 10.9260 8.4989 9.1680 7.6552 8.2372 7.2784 7.9250 5.6892 6.2746 5.4083 5.9652 5.2198 5.7591

C15H19NO5 Exp Theo. 19.8515 19.1268 12.5159 13.1912 10.2102 11.0830 9.2669 9.8424 8.7447 9.4728 6.8520 7.6078 6.2216 7.1100 6.0124 6.8611

Table 4 Total electronic cross section (st,el) of organic nonlinear optical materials from 122 keV to 1330 keV

Energy keV 122 356 511 662 840 1170 1275 1330

Table 3 Total atomic cross section (st, a) of organic nonlinear optical materials from 122 keV to 1330 keV

C13H11N Exp Theo. 3.7821 3.8707 3.7743 3.8653 3.7698 3.8635 3.7618 3.8622 3.7582 3.8610 3.7531 3.8593 3.7459 3.8589 3.7389 3.8587

C13H14NO Exp Theo. 3.8155 3.8916 3.8082 3.8852 3.8011 3.8830 3.7997 3.8815 3.7965 3.8801 3.7939 3.8781 3.7901 3.8776 3.7873 3.8774

C10H11N3O6 Exp keV 4.8277 4.8975 4.7912 4.8383 4.7789 4.8185 4.7643 4.8044 4.7561 4.7914 4.7402 4.7734 4.7324 4.7688 4.7266 4.7665

C15H16N2 Exp Theo. 3.6198 3.6052 3.6217 3.6119 3.6239 3.6142 3.6254 3.6158 3.6271 3.6173 3.6289 3.6194 3.6297 3.6199 3.6311 3.6202

C15H19NO5 Exp Theo. 3.8755 3.9198 3.8703 3.9121 3.8672 3.9095 3.8655 3.9077 3.8636 3.9060 3.8615 3.9036 3.8602 3.9030 3.8591 3.9026

Energy keV 122 356 511 662 840 1170 1275 1330

C13H11N Exp Theo. 11.5155 11.9641 7.7861 8.1860 6.4121 6.9266 5.8232 6.1395 5.4306 5.9821 4.2529 4.7227 3.9912 4.4865 3.7949 4.3291

C13H14NO Exp Theo. 13.4882 14.0380 9.2536 9.6339 7.5283 8.0741 6.5873 7.2484 6.4304 6.9731 4.8620 5.6886 4.4699 5.2298 4.2347 5.0463

C10H11N3O6 Exp keV 16.8874 17.6547 11.1505 12.0426 9.6153 10.1719 8.4841 9.0027 8.1609 8.7689 6.6257 7.0151 6.0601 6.5474 5.8177 6.3136

C15H16N2 Exp Theo. 15.4980 15.0020 9.8301 10.3261 8.0589 8.6700 7.2619 7.7933 6.9077 7.5010 5.4022 5.9424 5.1365 5.6501 4.9594 5.4553

C15H19NO5 Exp Theo. 20.1307 19.6177 12.6749 13.5031 10.3316 11.3375 9.3730 10.0636 8.8404 9.6815 6.9232 7.7706 6.2842 7.2611 6.0711 7.0063

Table 6 Molar extinction coefficients (e) of organic nonlinear optical materials from 122 keV to 1330 keV

Energy keV 122 356 511 662 840 1170 1275 1330

Table 5 Effective atomic numbers (Zeff) of organic nonlinear optical materials from 122 keV to 1330 keV

C13H11N Exp Theo. 0.3868 0.3927 0.2621 0.2691 0.2161 0.2278 0.1967 0.2020 0.1836 0.1968 0.1440 0.1555 0.1354 0.1477 0.1289 0.1425

C13H14NO Exp Theo. 0.3853 0.3932 0.2649 0.2703 0.2159 0.2266 0.1890 0.2035 0.1846 0.1959 0.1397 0.1599 0.1285 0.1470 0.1219 0.1419

C10H11N3O6 Exp keV 0.2992 0.3083 0.1991 0.2129 0.1721 0.1806 0.1523 0.1603 0.1468 0.1565 0.1196 0.1257 0.1095 0.1174 0.1053 0.1133

C15H16N2 Exp Theo. 0.4395 0.4272 0.2786 0.2935 0.2283 0.2463 0.2056 0.2213 0.1955 0.2129 0.1528 0.1685 0.1453 0.1602 0.1402 0.1547

C15H19NO5 Exp Theo. 0.4078 0.3929 0.2571 0.2710 0.2097 0.2277 0.1904 0.2022 0.1796 0.1946 0.1407 0.1563 0.1278 0.1460 0.1235 0.1409

Energy keV 122 356 511 662 840 1170 1275 1330

C13H11N Exp Theo. 0.4655 0.4725 0.3154 0.3237 0.2600 0.2741 0.2366 0.2430 0.2209 0.2368 0.1732 0.1871 0.1629 0.1777 0.1552 0.1715

C13H14NO Exp Theo. 0.4659 0.4754 0.3202 0.3268 0.2610 0.2740 0.2285 0.2461 0.2232 0.2368 0.1689 0.1933 0.1554 0.1777 0.1474 0.1715

C10H11N3O6 Exp keV 0.4456 0.4592 0.2965 0.3171 0.2563 0.2689 0.2269 0.2387 0.2186 0.2331 0.1781 0.1872 0.1631 0.1749 0.1568 0.1687

C15H16N2 Exp Theo. 0.4958 0.4819 0.3143 0.3311 0.2575 0.2778 0.2320 0.2496 0.2206 0.2402 0.1724 0.1901 0.1639 0.1808 0.1582 0.1745

C15H19NO5 Exp Theo. 0.4963 0.4782 0.3129 0.3298 0.2553 0.2771 0.2317 0.2461 0.2186 0.2368 0.1713 0.1902 0.1555 0.1778 0.1503 0.1715

Table 8 Effective atomic energy absorption cross sections (sa,en) of organic nonlinear optical materials from 122 keV to 1330 keV

Energy keV 122 356 511 662 840 1170 1275 1330

Table 7 Mass energy absorption coefficient (men/r) of organic nonlinear optical materials from 122 keV to 1330 keV

Highlights:-

The values of (μm) i.e. mass attenuation coefficients are calculated.

We report the values of total atomic cross-sections (st, a).

Measurement of electronic cross-sections (st.el) of nonlinear optical materials.

Comparison of all (μm),(st,a),(st,el) values with XCOM program.