Partial and total mass attenuation coefficients , effective atomic number and effective electron number of different Maraging steel compositions

The total and partial mass attenuation coefficients for different Maraging steel compositions have been determined by using the WinXCom and MCNP5 programs. The effective atomic number, Zeff, and effective electron number, Neff, for the studied steels have been determined via the total mass attenuation coefficients μ/ρ, the total atomic and electronic cross sections (σa and σe) of the investigated steels. The shielding parameters μ/ρ, Zeff, and Neff have been calculated at the incident photon energy range of 1 keV–100 MeV. The calculated results of total and partial mass attenuation coefficients, the effective atomic number and the effective electron number by using MCNP5 program were found to be in good agreement with the theoretical results of the WinXCom program. The calculated data clarify that the different steel compositions under investigation have so far the same ability of gamma attenuation. Also, it was found that the total mass attenuation coefficients of the different investigated steels (cobalt free-Maraging steels) are comparable to the C250 standard steel (cobalt Maraging steel).


INTRODUCTION
Steels are used in the reactor core, fuel transport and storage, plant structures and a lot of other nuclear uses.The ultra-high strength of the most expensive Maraging steels is due to the precipitation of inter-metallic compounds (cobalt, nickel and molybdenum) during the aging process.Due to the sharp increase in the cobalt price, the development of a family of cobalt free Maraging steel is promoted.Titanium can be used as the primary strengthening element, replacing cobalt in steels (Vasudevan et al., 1990;Sha et al., 1993).On the other hand, chromium was added to increase the corrosion resistance of the proposed steels.The previous are the causes of porn new Maraging steel with different mechanical and technological properties.As a result of use on a large scale in the nuclear field (nuclear power plants such as fusion reactor, accelerator driven systems or the fission generation reactors) Maraging steels should be investigate as a shielding material.In order to achieve this purpose the radiation absorption mechanism in materials should be known.This can be represented by some physical parameters such as mass attenuation coefficients μ/ρ, effective atomic number Z eff and effective electron number N eff .Several investigators (Han andDemir, 2009a, 2009b;Baltas et al., 2007;Baltas and Cevik, 2008;Celik et al., 2008;Manjunathaguru and Umesh, 2007;Manohara et al., 2008aManohara et al., , 2008bManohara et al., , 2009aManohara et al., , 2009bManohara et al., , 2010;;Manohara andHanagodimath, 2007a, 2007b;Singh et al., 2008;Taylor et al., 2008;Gounhalli et al., 2012a;Sidhu et al., 2012;Gounhalli et al., 2012b;Kurudirek, 2014;Un andSahin, 2011, 2012;Akkurt, 2009;Limkitjaroenporn et al., 2013;Medhat and Wang, 2015;Elmahroug et al., 2015;Un and Caner, 2014) have made extensive studies for these shielding parameters in a variety of composite materials such as biologically important materials, semiconductor, alloys, dosimetric compounds, glasses, drugs, and explosives.The mass attenuation coefficient μ/ρ (cm 2 /g) is a measure of the probability of interactions of photon with matter (Hubbell, 1982(Hubbell, , 1999;;Hubbell and Seltzer, 1995).This coefficient is not constant but depends on the energy of the incident photon, and the density and atomic number of elements.For compound and mixtures, it depends on the effective atomic number Z eff and effective electron number N eff .However, as originally stated by Hine (Hine, 1952) the effective atomic number Z eff of a multi-element material is not a constant, it varies with the energy of the incident photon.
The advent of powerful processors and computer architectures since the early 1990's made possible the increasingly important utilization of Monte Carlo simulation programs to model complex systems, both from the point of view of the physics (type of particles and interactions, energy ranges, etc.) and from the point of view of a detailed geometrical description (Vaz, 2009).Wherefore, Monte Carlo simulations has rapidly increased in the scientific field, with applications such as radiation shielding optimization, component effects, support of scientific studies, and analysis of biological effects.The well-known WinXCom program is usually employed for calculating X-ray and gamma-ray attenuation coefficient and interaction cross sections of different materials (El-Khayatt et. al., 2014).The aim of this study is to provide available information concerning using this kind of steel as a gamma shielding in nuclear applications.So, WinXCom and MCNP5 programs were used to calculate the partial and total mass attenuation coefficients for different compositions of Maraging steels at photon energies (1 keV-100 MeV).The attenuation coefficient data were then used to obtain the effective atomic numbers Z eff and the effective electron number Reda and Halfa 25 N eff of the investigated materials.

THEORETICAL FORMULATIONS
A parallel beam of monoenergetic gamma-ray photons is attenuated in the matter, according to the Lambert-Beer exponential equation (1) where and are the transmitted and the incident beam intensity of photons, respectively, t and ρ are the material thickness and density, respectively, and μ/ρ is the mass attenuation coefficient.
For compound or mixture, the mass attenuation coefficient can be obtained from the coefficients of the constituent elements which are assumed to be additive to the weighted average where and ( ) are the fractional weight and the mass attenuation coefficient of the ith constituent element, respectively.This mixture rule is valid with the assumption that the effects of molecular binding and the chemical and crystalline environment are negligible.
Using the total mass attenuation coefficients of a material, the total atomic cross-section, σa, can be evaluated by the following relation (Manohara et al., 2008a(Manohara et al., , 2008b;;Akkurt, 2009;Elmahroug et al., 2015;Akkurt and El-Khayatt, 2013b;Gowda et al., 2004Gowda et al., , 2005;;Içelli et. al., 2011;Prasad et al., 1998) where NA is the Avogadro's number, Ai is the atomic weight of the ith constituent element of the material.Also, the total electronic cross-section, σe, can be obtained by the following formula (Manohara et al., 2008a(Manohara et al., , 2008b;;Akkurt, 2009;Elmahroug et al., 2015;Akkurt and El-Khayatt, 2013b;Gowda et. al., 2004Gowda et. al., , 2005;;Içelli et. al., 2011) Where fi is the fractional abundance (the number of atoms of element i relative to the total number of atoms of all elements in the mixture), Zi is the atomic number of the ith element in a mixture.

PROCEDURE OF THE INVESTIGATED STEEL Production
Five kilograms of each of tested Maraging alloys were melted from pure elements in vacuum arc melting furnace with non-consumable tungsten electrode and water cooled copper crucibles.Before melting, to minimize interstitial gases including oxygen and nitrogen from the furnace atmosphere, titanium getters were melted, and high purity argon was used as an inert gas.On the other hand, in this approach used materials were heated to 600°C to ensure water and crystalline water removing.New and developed batch of Maraging was loaded into the vacuum arc melting furnace with nonconsumable tungsten electrode crucible under vacuum with pressure 1 × 10 −3 mbar.The furnace was energized noting the power (based on voltage, current, and time in each setting) required for melting.To ensure homogeneity of the produced steel ingots, the produced steel ingots were melted twice, inverting the ingot after each melting.The chemical composition of produced steels was determined using spectrographic (SPGA).Metal forming and heat treatment of tested steels were reported elsewhere (Hossam et al., 2010;Halfa and Reda, 2015).Well prepared and polished steel ingots were optically examined using Axiovert 40 MAT, Carl Zeiss, Switzerland microscopy after chemical etching in the solution of 1 g CuCl2/30 ml HCl/50 ml HNO3/100 ml H2O (Hossam et al., 2010;Halfa and Reda, 2015).Non-destructive test shows that produced steel rod after metal forming and full heat treatment were free from porosity, holes, pipes and other surface defects.Table 1 shows the designed chemical composition of testing steel.

Microstructure
The microstructure of the investigated steels can be discussed from the micrograph photos shown in Figure 1.Based on Figure 1, the microstructure of the investigated steels in the optimum condition of heat treatment essentially consisted of packets of martensite, within prior-austenite grains.The austenite grains, which had transformed into packets of martensite, could still be recognized due to the preferential etching along their boundaries and also due to the fact that the martensite packets within an austenite grain did not extend beyond the respective prior-austenite grain boundary.The martensite substructure could not be observed because of the narrowness of the martensite laths.The substructure of lathe martensite consists predominantly of a high density of tangles dislocations within laths (Schmidt, 1988).

Mechanical properties
The tension ductility properties of testing steels were illustrated in Table 2.The tabulated data represent the effect of molybdenum (Mo), chromium (Cr) and titanium (Ti) on the mechanical properties of investigating steels.The contribution of different alloying elements in ultimate tensile strength indicates that the positive effect of Cr, Mo and Ti may be attributed to inter-metallic precipitation and solid solution strengthening mechanisms of each element as reported elsewhere (Halfa, 2007).

RESULTS AND DISCUSSION
Based on the chemical composition presented in Table 1, MCNP5 and WinXCom programs were used to calculate the total and partial mass attenuation coefficients μ/ρ for the Maraging steels, at the photon energy range of 1 keV-100 MeV.In this study, calculations of MCNP5 (MCNP5, 2003) were performed using the gamma source as a fixed point isotropic source with continuous nuclear cross-section data based on the ENDF/B-VI.The simulation runs with 4 x 10 7 particle histories, resulting in a total computational time of about 2.14 h.Tally type 4 was used in our calculations to estimate gamma registered in the detector per MeV.cm 2 .s -1 . The statistical uncertainty of the calculated data did not exceed 10% in all energy bins.A schematic diagram of geometry simulated by MCNP5 is shown in Figure 2, with source and detector opening 0.5 cm in radius.Figure 3(a) to (e) shows the variation of total and partial mass attenuation coefficients with the incident photon energy of gamma rays for the steels under investigation.It can be seen from this figure that the total mass attenuation coefficients for the investigated steels decrease with the increase in the incident photon energy.We can notice from Figure 3 that the values of total and partial mass attenuation coefficients calculated by MCNP5 program for all steels under investigation are in good agreement with their theoretical values calculated using WinXCom program.This good agreement can be also seen from the variation of the total mass attenuation coefficient via the incident photon energy presented in Figure 4 for the sake of comparison.It is observed from Figure 4 that the values of μ/ρ decrease very rapidly with an increase in    keV, the μ/ρ values start decrease very rapidly up to 9 MeV.Beyond 9 MeV, the values of μ/ρ start increase slowly as the incident photon energy approaches 100 MeV.The dependence of μ/ρ on incident photon energy can be explained by the dominance of partial processes of interaction of photons with materials (coherent scattering, incoherent scattering, photoelectric absorption and pair production).In the low energy region, as shown in Figure 3, the rapid decrease in the μ/ρ values may be due to the photoelectric absorption, which is the dominant process in the low energy region, where the cross section is inversely proportional to the incident photon energy as E 3 and it is also proportional to the atomic number as Z 4-

5
.The decrease in the μ/ρ values in the intermediate energy region (the incident photon energy beyond 8 keV up to 9 MeV) can be explained due to the Compton scattering process (incoherent), whose cross section is inversely proportional to the incident photon energy as E -1 and depends linearly on the atomic number Z.The values of μ/ρ increase slowly beyond 9 MeV due to the pair production process, whose cross section varies approximately as the square of the atomic number Z and is proportional to the incident photon energy as .The values of total mass attenuation coefficients μ/ρ have no obvious difference among all the investigated steels which can be attribute to the Z numbers of the major components in the steel alloys, they are all close to each other (Ni:28,Co:27,Cr:24,Fe:26,Ti:22).The exception is Mo:42, but it only makes up to 4% of the steel.On the other hand, the values of μ/ρ were calculated by using MCNP and WinXCom based on the mixture role which makes the effects of molecular binding and the chemical and crystalline environment are negligible (Sögüt et al., 2001(Sögüt et al., , 2002;;).It is worth mentioning that the behaviors of μ/ρ for our investigated steels with the incident photon energy are to some extent comparable with that of shielding materials introduced by (Medhat and Wang, 2015).Also, the values of μ/ρ for the steel under investigation in the present work can be compared with the values measured experimentally, calculated theoretically and simulated for some kinds of alloys (Akkurt, 2009;El-kameesy et al., 2011;Singh et al., 2015).
The effective atomic number Z eff values were determined for the steels under investigation by using the MCNP5 and WinXCom values of μ/ρ.The variation of Z eff values versus the incident photon energy was shown graphically in Figure 5, for MCNP5 and WinXCom programs.It is seen from Figure 5 that Z eff values for the investigated steels vary in the low incident photon energy due to the dominance of the photoelectric absorption process in this energy region.It is also seen from Figure 5  that in the low energy region, there is a discrepancy in Z eff values of MCNP5 program.This discrepancy may be due to the sensitivity of MCNP5 experiment setup for low incident photon energy and its value does not exceed 16%.The variation of the effective electron number N eff values against the incident photon energy for steels under study is shown graphically in Figure 6.It is clearly shown by Figure 6 that the energy dependence of N eff is similar to the effective atomic number Z eff , because of the linear relation between them as given by Equation 7.

Conclusions
In the present study the partial and total mass attenuation coefficients, effective atomic number and effective electron number have been calculated for different Maraging steel compositions by using the two programs (MCNP5 and WinXCom) over a wide range of incident photon energies from 1 keV to 100 MeV.It was found that the results of μ/ρ, Z eff and N eff are dependent on the incident photon energy, affected by the different photon interaction processes (coherent scattering, incoherent scattering, photoelectric absorption and pair production).The calculated results of μ/ρ, Z eff and N eff by using MCNP5 program were comparable with the theoretical results of WinXCom program.The results also show that there is no difference between the different compositions of the investigated steels as gamma attenuator.The present study also showed that the values of shielding parameters μ/ρ, Zeff and Neff of cobalt free steels (m3-m6) are in agreement with the values of shielding parameters as the standard steel C250.The presented data in this work nominate the investigated steels to be used in nuclear fields as a gamma ray shielding materials especially when moderate to high strength steel was needed.

Figure 4 .Figure 5 .
Figure 4.The variation of total mass attenuation coefficients of the investigated steels versus incident photon energy.

Figure 6 .
Figure 6.Variation of the effective electron number against the incident photon energy for the investigated steels.

Table 1 .
Chemical composition of the investigated steels, the density of steels (m3-m6) is approximately 7.86 g/cc while the density of steel C250 is 8.02 g/cc.

Table 2 .
Mechanical properties of the investigated steels.