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回收利用是稀土资源高效利用的可持续方案. 氢化破碎技术因其高效环保特性被广泛采用, 但氢破过程中产生的混合相会显著降低回收效率, 这对工艺的优化提出了新的挑战. 本文采用基于第一性原理计算结合机器学习方法, 通过德拜模型系统地探究了氢化破碎过程中关键稀土氢化物(如NdH2, NdH3, Nd2H5)的热力学行为. 研究结果表明, 在600 kPa压强下, 630 K左右的温度区间有望为氢化破碎工艺提供一个较为理想的操作条件. 在此条件下, NdH2能够实现自发氢化, 且能够有效抑制非稳定相的形成, 有助于提高稀土回收效率. 本研究还揭示了过高温度对NdH2热力学性质可能产生的不利影响, 进一步强调了在特定温度区间操作的重要性. 这些发现不仅为理解钕铁硼氢化过程的热力学机理提供了新的视角, 而且为工业应用中氢化破碎工艺参数的优化提供了理论参考.Recycling is a sustainable strategy for the efficient utilization of rare earth resources. Hydrogenation milling has been widely adopted because of its high efficiency and environmental benefits. However, the formation of unstable phases in the hydrogenation process significantly reduces recovery efficiency, which presents new challenges for process optimization. In this study, a combination of first-principles calculations and machine learning methods is employed to systematically investigate the thermodynamic behavior of key rare earth hydrides, such as NdH2, NdH3, and Nd2H5 in the hydrogenation milling process using the Debye model for lattice vibrations. The results show that a temperature centered at about 630 K at a pressure of 600 kPa may offer ideal operational conditions for the hydrogenation milling process. Under these conditions, NdH2 can undergo spontaneous hydrogenation, and the formation of unstable phases can be effectively suppressed, thereby improving rare earth recovery efficiency. This study also reveals the potential adverse effects of excessively high temperatures on the stability and reactivity of NdH2, further emphasizing the importance of operating within a specific temperature range. These findings provide new insights into the thermodynamic mechanisms of the hydrogenation process in Nd2Fe14B permanent magnet material. Furthermore, they offer theoretical guidance for the optimization of industrial hydrogenation milling parameters.
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Keywords:
- Nd2Fe14B /
- hydrogenation recycling process /
- thermodynamic properties /
- Debye model
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图 1 通过氢破工艺回收废弃钕铁硼磁体的机理流程图
Fig. 1. Schematic diagram of the mechanism for recycling discarded Nd2Fe14B magnets through the hydrogenation-breaking process.
图 3 比热容随温度的变化情况 (a) 3种钕氢化物的恒容比热容($ C_{\mathrm{v}} $)随温度的变化曲线; (b) 3种钕氢化物的恒压比热容($ C_{\mathrm{p}} $)随温度的变化曲线
Fig. 3. Variation of heat capacity with temperature. (a) Variation curves of constant volume heat capacity ($ C_{\mathrm{v}} $) with temperature for three types of Nd-hydrides; (b) variation curves of constant pressure heat capacity ($ C_{\mathrm{p}} $) with temperature for three types of Nd-hydrides.
图 4 热膨胀系数随温度的变化情况
Fig. 4. Variation of thermal expansion coefficient with temperature.
图 5 等温弹性模量随温度压强的变化情况 (a) 100, 300, 500, 700 kPa的压强下NdH2, NdH3, Nd2H5的等温弹性模量随温度的变化曲线; (b) 100, 300, 500, 700 kPa压强条件下3种钕氢化物的等温体积模量随温度变化率绝对值$ \left(\left| {\partial B}/{\partial T} \right| \right) $的线状图
Fig. 5. Variation of isothermal elastic modulus with temperature and pressure: (a) Variation curves of isothermal elastic modulus with temperature for NdH2, NdH3, and Nd2H5 under pressures of 100, 300, 500, and 700 kPa, respectively; (b) line graph of the absolute value $ \left(\left| {\partial B}/{\partial T} \right| \right) $ of the rate of change in isothermal bulk modulus with temperature for the three types of Nd-hydrides under pressures of 100, 300, 500, and 700 kPa.
图 6 热导率、热扩散系数随温度的变化情况 (a) 3种钕氢化物的热导率随温度的变化曲线; (b) 3种钕氢化物的热扩散系数随温度的变化曲线
Fig. 6. Variation of thermal conductivity and thermal diffusivity with temperature: (a) Variation curves of thermal conductivity with temperature for three types of Nd-hydrides; (b) variation curves of thermal diffusivity with temperature for three types of Nd-hydrides.
图 7 不同钕氢化物吉布斯自由能变化量$ {{\Delta }_{{\mathrm{r}}}}G $在100 kPa, 200 kPa, 300 kPa, 400 kPa, 500 kPa, 600 kPa以及700 kPa压强下随温度的变化情况 (a) NdH2; (b) NdH3; (c) Nd2H5
Fig. 7. Variation of gibbs free energy change $ {{\Delta }_{{\mathrm{r}}}}G $ of different Nd-hydrides with temperature under specific pressures of 100 kPa, 200 kPa, 300 kPa, 400 kPa, 500 kPa, 600 kPa, and 700 kPa: (a) NdH2; (b) NdH3; (c) Nd2H5.
图 8 凸包能($ E_{\rm{hull}} $)与凸包图 (a) 三种钕氢化物的凸包能随温度的变化曲线; (b) 三种钕氢化物在630 K温度下的稳定关系
Fig. 8. Convex hull energy ($ E_{\rm{hull}} $) and convex hull diagram: (a) Variation curves of convex hull energy with temperature for three types of Nd-hydrides; (b) stability relationships of three types of Nd-hydrides at 630 K.
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[1] Poenaru I, Patroi E A, Patroi D, Iorga A, Manta E 2023 J. Magn. Magn. Mater. 577 170777
[2] Liu X B, Kesler M S, Besser M F, Kramer M J, McGuire M A, Nlebedim I C 2021 IEEE Trans. Magn. 57 6
[3] Dirba I, Pattur P, Soldatov I, Adabifiroozjaei E, Molina-Luna L, Gutfleisch O 2023 J. Alloys Compd. 930 167411
Google Scholar
[4] Lixandru A, Poenaru I, Güth K, Gauß R, Gutfleisch O 2017 J. Alloys Compd. 724 51
Google Scholar
[5] Ojih J, Al-Fahdi M, Yao Y G, Hu J J, Hu M 2024 J. Mater. Chem. A 12 8502
Google Scholar
[6] Toher C, Plata J J, Levy O, De Jong M, Asta M, Nardelli M B, Curtarolo S 2014 Phys. Rev. B 90 174107
Google Scholar
[7] Xu C R, Shao L, Ding N, Jiang H H, Tang B Y 2024 Physica B 674 415589
Google Scholar
[8] Nenuwe N O, Yebovi A S 2024 Comput. Condens. Matte. 38 e00882
[9] Ning J L, Zhu Y L, Kidd J, Guan Y D, Wang Y, Mao Z Q, Sun J W 2020 npj Comput. Mater. 6 157
Google Scholar
[10] Vesti A, Music D, Olsson P A 2024 Nucl. Mater. Energy 39 101684
Google Scholar
[11] Sheridan R S, Harris I R, Walton A 2016 J. Magn. Magn. Mater. 401 455
Google Scholar
[12] Matin M A, Kwon H W, Lee J G, Yu J H 2014 J. Magn. 19 106
Google Scholar
[13] Michalski B, Szymanski M, Gola K, Zygmuntowicz J, Leonowicz M 2022 J. Magn. Magn. Mater. 548 168979
Google Scholar
[14] Kirklin S, Saal J E, Meredig B, Thompson A, Doak J W, Aykol M, Rühl S, Wolverton C 2015 npj Comput. Mater. 1 15
Google Scholar
[15] Saal J E, Kirklin S, Aykol M, Meredig B, Wolverton C 2013 Jom 65 1501
Google Scholar
[16] Li X T, Yue M, Zhou S X, Kuang C J, Zhang G Q, Dong B S, Zeng H 2019 J. Magn. Magn. Mater. 473 144
Google Scholar
[17] Habibzadeh A, Kucuker M A, Gökelma M 2023 ACS Omega 8 17431
Google Scholar
[18] Qin T, Zhang Q, Wentzcovitch R M, Umemoto K 2019 Comput. Phys. Commun. 237 199
Google Scholar
[19] Baroni S, Giannozzi P, Isaev E 2018 Rev. Mineral. Geochem 71 39
[20] Palumbo M, Dal Corso A 2017 J. Phys.- Condens. Mat. 29 395401
Google Scholar
[21] Otero-De-La-Roza A, Abbasi-Pérez D, Luaña V 2011 Comput. Phys. Commun. 182 2232
Google Scholar
[22] Togo A, Tanaka I 2015 Scr. Mater. 108 1
Google Scholar
[23] Bartel C J, Millican S L, Deml A M, Rumptz J R, Tumas W, Weimer A W, Lany S, Stevanović V, Musgrave C B, Holder A M 2018 Nat. Commun. 9 4168
Google Scholar
[24] Chen S Y, Zhang J L, Wang Y Z, Wang T F, Li Y, Liu Z J 2023 Metals 13 225
Google Scholar
[25] Deng B W, Zhong P C, Jun K, Riebesell J, Han K, Bartel C J, Ceder G 2023 Nat. Mach. Intell. 5 1031
Google Scholar
[26] Pan J 2023 Nat. Comput. Sci. 3 816
Google Scholar
[27] Blanco M A, Francisco E, Luaña V 2004 Comput. Phys. Commun. 158 57
Google Scholar
[28] Shamsuddin M 2024 Thermodynamic Measurement Techniques, Vol. Part F3193 of The Minerals, Metals Materials Series (Cham: Springer International Publishing) pp1–349
[29] Olivotos S, Economou-Eliopoulos M 2016 Geosciences 6 2
Google Scholar
[30] Rostami S, Gonze X 2024 Phys. Rev. B 110 014103
Google Scholar
[31] Bartel C J 2022 J. Mater. Sci. 57 10475
Google Scholar
[32] Drebushchak V A 2020 J. Therm. Anal. Calorim. 142 1097
Google Scholar
[33] Yamanaka S, Yoshioka K, Uno M, Katsura M, Anada H, Matsuda T, Kobayashi S 1999 J. Alloys Compd. 293-295 23
[34] Hu X, Wang H, Linton K, Le Coq A, Terrani K A 2021 Handbook on the material properties of yttrium hydride for high temperature moderator applications. Tech. rep., Oak Ridge National Laboratory (ORNL), Oak Ridge, TN (United States
[35] Vajda P, Daou J N 1996 Solid State Phenom. 49-50 71
Google Scholar
[36] Grinderslev J B, Møller K T, Bremholm M, Jensen T R 2019 Inorg. Chem. 58 5503
Google Scholar
[37] Pourarian F 2002 Physica B 321 18
Google Scholar
[38] Suwarno S, Lototskyy M V, Yartys V A 2020 J. Alloys Compd. 842 155530
Google Scholar
[39] Sheridan R S, Sillitoe R, Zakotnik M, Harris I R, Williams A J 2012 J. Magn. Magn. Mater. 324 63
Google Scholar
[40] Fultz B 2010 Prog. Mater. Sci. 55 247
Google Scholar
[41] Piotrowicz A, Pietrzyk S, Noga P, Myćka Ł 2020 J. Min. Metall. B 56 415
Google Scholar
[42] Xia M, Abrahamsen A B, Bahl C R, Veluri B, Søegaard A I, Bøjsøe P 2017 J. Magn. Magn. Mater. 441 55
Google Scholar
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