Calculation and analysis of thermal scattering law data of sub-stoichiometric metal hydrides

MA Yutu; ZU Tiejun; WU Hongchun; CAO Liangzhi

doi:10.7498/aps.74.20250928

Abstract

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 (ZrH_x) and yttrium hydride (YH_x). 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 (k_eff) 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 ZrH_x (with H/Zr ≈ 1.6), using the TSL data derived from ZrH_xwith other hydrogen content results in a maximum deviation of 104 pcm in k_eff. For the HCM003 benchmarks loaded with ZrH₂, the use of TSL from ZrH_x with other hydrogen content leads to a maximum deviation of 147 pcm in k_eff.

Keywords:

zirconium hydride /
yttrium hydride /
thermal scattering law data /
thermal neutron scattering cross section

Authors and contacts

School of Nuclear Science and Technology, Xi’an Jiaotong University, Xi’an 710049, China

Corresponding author: ZU Tiejun, tiejun@mail.xjtu.edu.cn

Funds: Project supported by the National Natural Science Foundation of China (Grant No. 12135019) and the National Key Research and Development Program of China (Grant No. 2022YFB1902600).

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References

[1]	Handbook on the Material Properties of Yttrium Hydride for High Temperature Moderator Applications, Hu X X, Wang H, Linton K, Le Coq A, Terrani K A https://www.osti.gov/servlets/purl/1808171/ [2021-7-15]
[2]	Paramonov D V, El-Genk M S 1994 Nucl. Technol. 108 157 Google Scholar
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[4]	Snoj L, Zerovnik G, Trkov A 2012 Appl. Radiat. Isotopes 70 483 Google Scholar
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[7]	Wang X, Tang M, Jiang M X, Chen Y C, Liu Z X, Deng H Q 2024 Chin. Phys. B 33 076103 Google Scholar
[8]	Mehta V K, Vogel S C, Shivprasad A P, Luther E P, Andersson D A, Rao D V, Kotlyar D, Clausen B, Cooper M W D 2021 J. Nucl. Mater. 547 152837 Google Scholar
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[17]	Trainer A, Forget B, Holmes J, Wormald J, Zerkle M 2025 Ann. Nucl. Energy 212 111034 Google Scholar
[18]	Wormald J, Zerkle M, Holmes J 2021 J. Nucl. Eng. 2 105 Google Scholar
[19]	Zerkle M L, Holmes J C, Wormald J L 2021 EPJ Web Conf. 247 09015 Google Scholar
[20]	Ge Z G, Xu R R, Wu H C, Zhang Y, Chen G C, Jin Y L, Shu N C, Chen Y J, Tao X, Tian Y, Liu P, Qian J, Wang J M, Zhang H Y, Liu L L, Huang X L 2020 EPJ Web Conf. 239 09001 Google Scholar
[21]	Zu T J, Wu C Y, Feng H, Ma Y T, Cao L Z, Wu H C, Tang Y Q 2024 Prog. Nucl. Energy 177 105420 Google Scholar
[22]	Placzek G 1952 Phys. Rev. 86 377 Google Scholar
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[24]	Fleming N C 2021 Ph. D. Dissertation (North Carolina: North Carolina State University
[25]	Jain A, Ong S P, Hautier G, Chen W, Richards W D, Dacek S, Cholia S, Gunter D, Skinner D, Ceder G, Persson K A 2013 APL Mater. 1 011002 Google Scholar
[26]	Kresse G, Furthmüller J 1996 Comput. Mater. Sci. 6 15 Google Scholar
[27]	Gonze X, Lee C 1997 Phys. Rev. B 55 10355 Google Scholar
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[29]	He Q M, Zheng Q, Li J, Wu H C, Shen W, Cao L Z, Liu Z Y, Xu J L 2021 Ann. Nucl. Energy 151 107978 Google Scholar
[30]	Briggs J B, Scott L, Nouri A 2003 Nucl. Sci. Eng. 145 1 Google Scholar

Cited By

图 1 δ-ZrH_1.41, δ-ZrH_1.59, δ-ZrH_1.69的超晶胞

Figure 1. Super cell of δ-ZrH_1.41, δ-ZrH_1.59 and δ-ZrH_1.69.

DownLoad: Full-Size Img PowerPoint

图 2 δ-YH_1.31, δ-YH_1.59, δ-YH_1.81的超晶胞

Figure 2. Super cell of δ-YH_1.31, δ-YH_1.59 and δ-YH_1.81.

DownLoad: Full-Size Img PowerPoint

图 3 不同氢含量下氢化物的归一化声子态密度　(a) ZrH_x; (b) YH_x

Figure 3. Normalized phonon density of state of hydrides with different hydrogen contents: (a) ZrH_x; (b) YH_x.

DownLoad: Full-Size Img PowerPoint

图 4 不同氢含量下ZrH_x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 ZrH_x 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

DownLoad: Full-Size Img PowerPoint

图 5 不同氢含量下YH_x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 YH_x 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.

DownLoad: Full-Size Img PowerPoint

图 6 不同氢含量ZrH_x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 ZrH_x with different hydrogen contents: (a) 293.6 K; (b) 1200 K.

DownLoad: Full-Size Img PowerPoint

图 7 不同氢含量YH_x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 YH_x with different hydrogen contents: (a) 293.6 K; (b) 1200 K.

DownLoad: Full-Size Img PowerPoint

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	ZrH_1.59	ZrH₂		ZrH_1.69		ZrH_1.41
基准题序号	k_eff	k_eff	偏差/pcm	k_eff	偏差/pcm	k_eff	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

DownLoad: CSV

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	ZrH_1.69		ZrH_1.59		ZrH_1.41
基准题序号	k_eff	k_eff	偏差/pcm	k_eff	偏差/pcm	k_eff	偏差/pcm
HCM003_1	0.99760	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

DownLoad: CSV

[1]	Handbook on the Material Properties of Yttrium Hydride for High Temperature Moderator Applications, Hu X X, Wang H, Linton K, Le Coq A, Terrani K A https://www.osti.gov/servlets/purl/1808171/ [2021-7-15]
[2]	Paramonov D V, El-Genk M S 1994 Nucl. Technol. 108 157 Google Scholar
[3]	Evans J A, Sweet R T, Medvedev P G, Wagner A R, Parisi C, Lange T L, Perez E, Rice F, Jue J F, Woolstenhulme E, Arafat Y 2024 J. Nucl. Mater. 598 25 Google Scholar
[4]	Snoj L, Zerovnik G, Trkov A 2012 Appl. Radiat. Isotopes 70 483 Google Scholar
[5]	Betzler B R, Ade B J, Jain P K, Wysocki A, Chesser P C, Kirkland W M, Cetiner M S, Bergeron A, Heidet F, Terrani K 2022 Nucl. Sci. Eng. 196 1399 Google Scholar
[6]	Mehta V, Vogel S, Kotlyar D, Cooper M 2022 Metals 12 199 Google Scholar
[7]	Wang X, Tang M, Jiang M X, Chen Y C, Liu Z X, Deng H Q 2024 Chin. Phys. B 33 076103 Google Scholar
[8]	Mehta V K, Vogel S C, Shivprasad A P, Luther E P, Andersson D A, Rao D V, Kotlyar D, Clausen B, Cooper M W D 2021 J. Nucl. Mater. 547 152837 Google Scholar
[9]	ENDF-6 Formats Manual, Brown D A https://www.nndc.bnl.gov/endfdocs/ENDF-102-2023.pdf [2023-9-28]
[10]	Tang Y Q, Zu T J, Yi S Y, Cao L Z, Wu H C 2020 Annals of Nuclear Energy 153 108044 Google Scholar
[11]	Squires G L 1996 Introduction to the Theory of Thermal Neutron Scattering (Massachusetts: Courier Corporation) p30
[12]	Zu T J, Tang Y Q, Wang L P, Cao L Z, Wu H C 2021 Ann. Nucl. Energy 161 108489 Google Scholar
[13]	Wang L P, Wan C H, Cao L Z, Wu H C, Sjstrand H 2021 Ann. Nucl. Energy 151 107920 Google Scholar
[14]	Švajger I, Fleming N, Hawari A, Laramee B, Noguere G, Snoj L, Trkov A 2025 Nucl. Eng. Technol. 57 103834 Google Scholar
[15]	Mehta V K, Cooper M W D, Wilkerson R B, Kotlyar D, Rao D V, Vogel S C 2021 Nucl. Sci. Eng. 195 563 Google Scholar
[16]	Mehta V K, Rehn D A, Olsson P A T 2024 J. Nucl. Eng. 5 330 Google Scholar
[17]	Trainer A, Forget B, Holmes J, Wormald J, Zerkle M 2025 Ann. Nucl. Energy 212 111034 Google Scholar
[18]	Wormald J, Zerkle M, Holmes J 2021 J. Nucl. Eng. 2 105 Google Scholar
[19]	Zerkle M L, Holmes J C, Wormald J L 2021 EPJ Web Conf. 247 09015 Google Scholar
[20]	Ge Z G, Xu R R, Wu H C, Zhang Y, Chen G C, Jin Y L, Shu N C, Chen Y J, Tao X, Tian Y, Liu P, Qian J, Wang J M, Zhang H Y, Liu L L, Huang X L 2020 EPJ Web Conf. 239 09001 Google Scholar
[21]	Zu T J, Wu C Y, Feng H, Ma Y T, Cao L Z, Wu H C, Tang Y Q 2024 Prog. Nucl. Energy 177 105420 Google Scholar
[22]	Placzek G 1952 Phys. Rev. 86 377 Google Scholar
[23]	Coherent Scattering Law for Polycrystalline Beryllium, Borgonovi G M https://www.osti.gov/servlets/purl/4049796 [1969-5-16]
[24]	Fleming N C 2021 Ph. D. Dissertation (North Carolina: North Carolina State University
[25]	Jain A, Ong S P, Hautier G, Chen W, Richards W D, Dacek S, Cholia S, Gunter D, Skinner D, Ceder G, Persson K A 2013 APL Mater. 1 011002 Google Scholar
[26]	Kresse G, Furthmüller J 1996 Comput. Mater. Sci. 6 15 Google Scholar
[27]	Gonze X, Lee C 1997 Phys. Rev. B 55 10355 Google Scholar
[28]	Gajdos M, Hummer K, Kresse G, Furthmueller J, Bechstedt F 2006 Phys. Rev. B 73 045112 Google Scholar
[29]	He Q M, Zheng Q, Li J, Wu H C, Shen W, Cao L Z, Liu Z Y, Xu J L 2021 Ann. Nucl. Energy 151 107978 Google Scholar
[30]	Briggs J B, Scott L, Nouri A 2003 Nucl. Sci. Eng. 145 1 Google Scholar

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