A formula is given which allows to calculate the contribution of the nuclear capture, thermal diffuse and Bragg scattering cross-section to the neutron transmission through solid crystalline Beryllium. The formula takes into account the beryllium crystalline structure and its physical parameters. A computer program CRYSBE was developed to provide the required calculation. The calculated values of the total cross-section of polycrystalline beryllium at different temperatures were compared with the previously measured ones in the neutron energy range from 0.2 meV to 10 eV . The obtained agreement shows that the formula fits the experimental data . An agreement was also obtained for values of beryllium single crystal at both room and liquid nitrogen temperatures. The feasibility study on using a polycrystalline beryllium as a cold neutron filter is given. The optimum beryllium single crystal thickness, mosaic spread, temperature and cutting plane for efficiently transmitting the thermal reactor neutrons, while rejecting both fast neutrons and gamma ray accompanying the thermal ones are also given .
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