Determination of the effective atomic numbers of Fe$_{x}$Cu$_{1-x} $binary ferroalloys using a nondestructive technique: Rayleigh-to-Compton scattering ratio


Abstract: The aim of the present study is to determine effective atomic numbers ($Z_{eff})$ of Fe$_{x}$Cu$_{1-x} $ binary ferroalloys using scattering of 59.54 keV gamma photons at 130$^{\circ}$ ($x=4.36{{\unicode{x212B}}}^{-1})$ scattering angle. For this purpose, the Rayleigh ($R)$ and Compton ($C)$ scattering intensities for the given alloys were measured using a monoenergetic beam of 59.54 keV gamma rays and the Rayleigh-to-Compton scattering ratio $R/C $was determined. Then the $Z_{eff}$ values of these alloys were determined by interpolating the $R/C$ of the material using the $R/C$ data of adjacent elements in between the $R/C$ of the alloys. For comparison, $Z_{eff}$s of alloys were also calculated using direct and interpolation methods in term of scattering $R/C$ and attenuation of gamma photons. Good agreement in relative differences between $Z_{eff}$s (experimental and theoretical) was found (maximum of $\le $3.3% for total att.-direct method) for the chosen alloys and the Rayleigh-to-Compton scattering ratio was shown to be a complementary approach to determine the effective atomic number of binary ferroalloys. In addition, a polynomial equation between the experimental $R/C$ values and the mass attenuation coefficients of alloys was developed to estimate the mass attenuation coefficient of different materials.

Keywords: Effective atomic number, Rayleigh-to-Compton scattering ratio, alloy

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