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Metal hydrides are promising moderator materials in advanced reactors, where their thermal neutron scattering cross sections significantly affect the accuracy of reactor design. This study uses special quasi random structure (SQS) and first-principles lattice dynamics methods to calculate parameters such as the phonon densities of states of sub-stoichiometric zirconium hydride (ZrHx) and yttrium hydride (YHx). Based on these parameters, thermal scattering law (TSL) data for sub-stoichiometric hydrides are generated using the nuclear data processing code NECP-Atlas. The influences of hydrogen content on the thermal scattering cross sections of hydrides and the effective multiplication factor (keff) values of critical assemblies are analyzed. The result shows that variations in hydrogen content within hydrides lead to differences in thermal scattering cross sections, consequently affecting the neutron transport calculations of nuclear reactor. For the ICT003 and ICT013 benchmarks loaded with ZrHx (with H/Zr ≈ 1.6), using the TSL data derived from ZrHx with other hydrogen content results in a maximum deviation of 104 pcm in keff. For the HCM003 benchmarks loaded with ZrH2, the use of TSL from ZrHx with other hydrogen content leads to a maximum deviation of 147 pcm in keff.
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Keywords:
- zirconium hydride /
- yttrium hydride /
- thermal neutron scattering law /
- thermal neutron scattering cross section
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图 1 δ相的ZrH1.41, ZrH1.59, ZrH1.69的超晶胞
Figure 1. Super cell of δ-ZrH1.41, δ-ZrH1.59 and δ-ZrH1.69.
图 2 δ相的YH1.31, YH1.59, YH1.81的超晶胞
Figure 2. Super cell of δ-YH1.31, δ-YH1.59 and δ-YH1.81.
图 3 不同氢含量下氢化物的归一化声子态密度 (a) ZrHx; (b) YHx
Figure 3. Normalized phonon density of state of hydrides with different hydrogen contents: (a) ZrHx; (b) YHx.
图 4 不同氢含量下ZrHx的热散射截面 (a) 氢的非弹性散射截面; (b) 氢的非相干弹性散射截面; (c) 锆的非弹性散射截面; (d) 锆的相干弹性散射截面
Figure 4. Thermal scattering cross sections of ZrHx with different hydrogen contents: (a) Inelastic scattering cross section of H; (b) incoherent elastic scattering cross section of H; (c) inelastic scattering cross section of Zr; (d) coherent elastic scattering cross section of Zr.
图 5 不同氢含量下YHx的热散射截面 (a) 氢的非弹性散射截面; (b) 氢的非相干弹性散射截面; (c) 钇的非弹性散射截面; (d) 钇的相干弹性散射截面
Figure 5. Thermal scattering cross sections of YHx with different hydrogen contents: (a) Inelastic scattering cross section of H; (b) incoherent elastic scattering cross section of H; (c) inelastic scattering cross section of Y; (d) coherent elastic scattering cross section of Y.
图 6 不同氢含量ZrHx中H的双微分散射截面 (a) 293.6 K; (b) 1200 K
Figure 6. Double differential scattering cross sections of H in ZrHx with different hydrogen contents: (a) 293.6 K; (b) 1200 K.
图 7 不同氢含量YHx中H的双微分散射截面 (a) 293.6 K; (b) 1200 K
Figure 7. Double differential scattering cross sections of H in YHx with different hydrogen contents: (a) 293.6 K; (b) 1200 K.
表 1 ICT003和ICT013系列基准题有效增殖系数计算结果
Table 1. The calculated effective multiplication factor for the ICT003 and ICT013 benchmarks.
基准题序号 ZrH1.59 ZrH2 ZrH1.69 ZrH1.41 keff keff 偏差/pcm keff 偏差/pcm keff 偏差/pcm ICT003_1 1.00308 1.00205 –103 1.00375 67 1.00412 104 ICT003_2 1.00791 1.00697 –94 1.00866 75 1.00864 73 ICT013_1 1.01204 1.01194 –10 1.01263 59 1.01274 70 ICT013_2 1.01189 1.01167 –22 1.01256 67 1.01272 83 
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表 2 HCM003系列基准题有效增殖系数计算结果
Table 2. The calculated effective multiplication factor for the HCM003 benchmarks.
基准题序号 ZrH2 ZrH1.69 ZrH1.59 ZrH1.41 keff keff 偏差/pcm keff 偏差/pcm keff 偏差/pcm HCM003_1 0.9976 0.99673 –87 0.99764 4 0.99705 –55 HCM003_2 0.99798 0.99692 –106 0.99776 –22 0.99686 –112 HCM003_3 0.99778 0.99685 –93 0.99745 –33 0.99689 –89 HCM003_4 0.99818 0.99718 –100 0.99784 –34 0.99693 –125 HCM003_5 0.99838 0.99691 –147 0.99789 –49 0.99707 –131 HCM003_6 0.99795 0.99678 –117 0.99741 –54 0.99705 –90
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