This contribution is aimed at designing the optimal thickness of leadiron doublelayer container to store a radioactive waste releasing the photon energy at 1.3325 MeV and initial radiation intensity at 100 mSv/hr using the optimization design by MATLAB software. This design consisted of three parts of calculations to achieve 1000 times the radiation attenuation of container. The first was the logarithmic interpolation for the mass attenuation coefficient. The second was the bilogarithmic interpolation for the exposure buildup factor. The third was the contourplotting analytical technique for the optimal thickness of radiation container. The values of mass attenuation coefficient and exposure buildup factor were exactly validated as compared with the standard reference database. Furthermore, we have found that the optimal thickness was 3.2 cm for lead (1st layer) and 17.0 cm for iron (2nd layer). Container weight was 994.30 kg, whilst container cost was 167.30 USD. The benefit of our design can quickly and precisely apply for the radiation safety assessment of the occupational radiation workers who always work in the nuclear reactor area.
Although nuclear technology is very useful for researches and industries, maintenance of nuclear reactor is necessary for the safety reason. International Commission on Radiological Protection (ICRP) has suggested that the limitation of radiation exposure dose for occupational radiation worker is 20 mSv/year [
Here we have performed the calculations for shielding materials of lead and iron layers for a 1.3325 MeV and 100 mSv/hr gammaray by MATLAB software. This design is comprised of three parts. The first and second parts are the logarithmic interpolation for mass attenuation coefficient and the bilogarithmic interpolation for exposure buildup factor, respectively. These parts are compared with the standard reference database from National Institute of Standards and Technology (NIST) [
Objective function was defined as the gamma attenuation of doublelayer materials in a narrow (Figure
Geometry for gammaray attenuation for (a) a narrow beam geometry and (b) a board beam geometry.
To achieve 1000 times the radiation attenuation of container as informed by TINT and to follow the radiation dose limitation as informed by ICRP, our objective function was limited at 0.1 mSv/hr or
Method of interpolations: (a) logarithmic interpolation and (b) bilogarithmic interpolation.
For economical reason, constrained function of the doublelayer thickness of cylindrical container was limited at 30 cm or
For economical reason, constrained function of the container’s cost was limited at 800 USD or
Photon energy (
Overview flowchart of plotting a contour graph.
In detail, the mass attenuation coefficient
Flowchart of mass attenuation coefficient
Flowchart of exposure buildup factor
To investigate a validation of MATLAB, we firstly check
In our study, if we have
Calculated mass attenuation coefficient
Layer 







1 = lead  11.35 gm/cm^{3}  0.0566 cm^{2}/g  0.6424 cm^{−1}  21.0 cm  13.4904  4.7316 
2 = iron  7.874 gm/cm^{3}  0.0518 cm^{2}/g  0.4083 cm^{−1}  2.0 cm  0.8166  1.6681 
Summary of MATLAB calculation for (a) mass attenuation coefficient
To understand the effects of container thickness on the container weight and cost, the space or void inside the container
Variation of the space or void
However, when we assume
Container’s weight and cost from the optimal solution by MATLAB.



Weight (kg)  Cost (USD) 

7  7.0  11.0  808.40  404.60 
7  6.4  12.0  838.80  356.50 
7  5.7  13.0  860.00  305.00 
7  5.1  14.0  893.80  266.10 
7  4.5  15.0  929.40  231.30 
7  3.7  16.0  943.90  188.50 
7  3.2  17.0  994.30  167.30 
Contourplotting graph for determination of the optimal doublelayer thickness.
Finally, the optimal doublelayer thickness selected from the identified line is
To sum up, this optimization model concerns two merits. One is that the users are able to modify whatever the parameters (i.e., photon energy, initial intensity, material types and thicknesses, and material weight and cost) are to obtain the optimal thickness of materials of interests. Another one is that the simulation time is very fast just 10 sec.
From optimization model of the doublelayer shielding design and selection of lead and iron cylindrical container by MATLAB software to store the radioactive waste at 1.3325 MeV and 100 mSv/hr, we have found that the mass attenuation coefficient and exposure buildup factor were 0.056601 cm^{2}/g for lead, 0.051862 cm^{2}/g for iron and 4.7316 for lead, 1.6681 for iron, respectively. These numbers were the same as the standard reference database. The doublelayer thickness selected from the analysis on contourplotting graph was 3.2 cm for lead and 17.0 cm for iron to achieve 1000 times the radiation attenuation of container (0.1 mSv/hr). The total container weight and cost from these designed materials were 994.30 kg and 167.30 USD, respectively.
The authors declare no conflicts of interest.
This work was supported by King Mongkut’s Institute of Technology Ladkrabang, Bangkok 10520, Thailand. The authors also thank Kittiphot Songkaitiwong for helpful discussions.