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論文

Microstructural evolution and mechanical instability of Mar-M509 superalloy fabricated by laser powder bed fusion under short-term thermal exposure

Cao, T.*; Wei, D.*; Gong, W.; 川崎 卓郎; Harjo, S.; 他10名*

Materials Science and Engineering A, 940, p.148534_1 - 148534_16, 2025/09

The thermal stability of microstructure and mechanical performance is crucial for the industrial application of laser powder bed fusion (LPBF) superalloy components in gas turbines and jet engines. This work investigated the microstructural evolution and strengthening mechanism of LPBF Mar-M509 cobalt-based superalloy before and after thermal exposure at 1200 $$^{circ}$$C using multi-scale microstructural characterization and in situ neutron diffraction tensile testing. The as-built Mar-M509 superalloy exhibited a heterogeneous microstructural features with coarse columnar and fine equiaxed grains, both containing dendritic and cellular substructures enriched with nanoscale carbides and high-density dislocations. The ultra high strength of the as-built sample was primarily attributed to dislocation-precipitation synergistic strengthening. After thermal exposure at 1200 $$^{circ}$$C for 4 h, the dendritic and cellular substructures disappeared and the dislocation density decreased significantly. This study reveals the microstructural evolution and instability of LPBF Mar-M509 superalloy under high-temperature exposure and the impacts on mechanical properties, which provides critical support for the development of cobalt-based superalloys in high-temperature application fields.

論文

Enhanced strength and ductility in an additively manufactured Al10SiMg alloy at cryogenic temperatures

Naeem, M.*; Rehman, A. U.*; Romero Resendiz, L.*; Salamci, E.*; Aydin, H.*; Ansari, P.*; Harjo, S.; Gong, W.; Wang, X.-L.*; 他3名*

Communications Materials (Internet), 6, p.65_1 - 65_13, 2025/04

The need for lightweight materials with mechanical integrity at ultralow temperatures drives the development of advanced alloys for cryogenic use. Additive manufacturing via laser powder bed fusion (LPBF) offers a scalable way to create alloys with tailored properties. Here, we show that LPBF-processed Al10SiMg exhibits a high ultimate tensile strength (395 MPa) and uniform elongation (25%) at 15 K. These enhancements stem from grain refinement, increased geometrically necessary dislocations, and stress partitioning between the Al matrix and the stiffer Si phase, aiding strain accommodation. ${it In-situ}$ neutron diffraction reveals that the Si phase, with its higher yield strength, bears most of the load, while the Al matrix undergoes continuous strain hardening, extending deformation capacity. These results highlight Al10SiMg's promise for cryogenic applications such as hydrogen storage, aerospace, and quantum computing hardware.

論文

Unusual low-temperature ductility increase mediated by dislocations alone

Naeem, M.*; Ma, Y.*; Tian, J.*; Kong, H.*; Romero-Resendiz, L.*; Fan, Z.*; Jiang, F.*; Gong, W.; Harjo, S.; Wu, Z.*; et al.

Materials Science & Engineering A, 924, p.147819_1 - 147819_10, 2025/02

 被引用回数:1 パーセンタイル:0.00(Nanoscience & Nanotechnology)

Face-centered cubic (fcc) medium-/high-entropy alloys (M/HEAs) typically enhance strength and ductility at cryogenic temperatures via stacking faults, twinning, or martensitic transformation. However, in-situ neutron diffraction on VCoNi MEA at 15 K reveals that strain hardening is driven solely by rapid dislocation accumulation, without these mechanisms. This results in increased yield strength, strain hardening, and fracture strain. The behavior, explained by the Orowan equation, challenges conventional views on cryogenic strengthening in fcc M/HEAs and highlights the role of dislocation-mediated plasticity at low temperatures.

論文

Enhanced cryogenic mechanical properties of heterostructured CrCoNi multicomponent alloy; Insights from ${it in situ}$ neutron diffraction

Naeem, M.*; Ma, Y.*; Knowles, A. J.*; Gong, W.; Harjo, S.; Wang, X.-L.*; Romero Resendiz, L.*; 他6名*

Materials Science & Engineering A, 916, p.147374_1 - 147374_8, 2024/11

 被引用回数:3 パーセンタイル:57.76(Nanoscience & Nanotechnology)

Heterostructured materials (HSMs) improve the strength-ductility trade-off of alloys, but their cryogenic performance under real-time deformation is unclear. We studied heterostructured CrCoNi medium-entropy alloy via ${it in situ}$ neutron diffraction at 77 K and 293 K. A significant mechanical mismatch between fine and coarse grains led to an exceptional yield strength of 918 MPa at 293 K, increasing to 1244 MPa at 77 K with a uniform elongation of 34%. This strength-ductility synergy at 77 K is attributed to high dislocation pile-up density, increased planar faults, and martensitic transformation. Compared to homogeneous alloys, HSMs show promise for enhancing cryogenic mechanical performance in medium-/high-entropy alloys.

論文

Dual nanoprecipitation and nanoscale chemical heterogeneity in a secondary hardening steel for ultrahigh strength and large uniform elongation

Wang, S.*; Wang, J.*; Zhang, S.*; Wei, D.*; Chen, Y.*; Rong, X.*; Gong, W.; Harjo, S.; Liu, X.*; Jiao, Z.*; et al.

Journal of Materials Science & Technology, 185, p.245 - 258, 2024/06

 被引用回数:17 パーセンタイル:98.00(Materials Science, Multidisciplinary)

Nanoprecipitates and nanoscale retained austenite (RA) with suitable stability play crucial roles in determining the yield strength (YS) and ductility of ultrahigh strength steels (UHSSs). However, owing to the kinetics incompatibility between nanoprecipitation and austenite reversion, it is highly challenging to simultaneously introduce high-density nanoprecipitates and optimized RA in UHSSs. In this work, through the combination of austenite reversion treatment (ART) and subsequent flash austenitizing (FA), nanoscale chemical heterogeneity was successfully introduced into a low-cost UHSS prior to the aging process. This chemical heterogeneity involved the enrichment of Mn and Ni in the austenite phase. The resulting UHSS exhibited dual-nanoprecipitation of Ni(Al,Mn) and (Mo,Cr)$$_{2}$$ C and nanoscale austenite stabilized via Mn and Ni enrichment. The hard martensitic matrix strengthened by high-density dual-nanoprecipitates constrains the plastic deformation of soft RA with a relatively low fraction, and the presence of relatively stable nanoscale RA with adequate Mn and Ni enrichment leads to a marginal loss in YS but keeps a persistent transformation-induced plasticity (TRIP) effect. As a result, the newly-developed UHSS exhibits an ultrahigh YS of 1.7 GPa, an ultimate tensile strength (UTS) of 1.8 GPa, a large uniform elongation (UE) of 8.5 percent, and a total elongation (TE) of 13 percent. The strategy of presetting chemical heterogeneity to introduce proper metastable phases before aging can be extended to other UHSSs and precipitation-hardened alloys.

論文

Cryogenic deformation behavior of a dual-phase Mg-Li alloy investigated by in-situ neutron diffraction

Gong, W.; Gholizadeh, R.*; 川崎 卓郎; 相澤 一也; Harjo, S.

Magnesium Technology 2024, p.89 - 90, 2024/03

Mg and its alloys generally exist as a single hcp crystal structure at room temperature. It is widely recognized that the application of Mg alloys is hindered by their limited formability at room temperature, primarily attributable to the scarcity of readily activated deformation modes within the hcp phase. The addition of Li in Mg alloy can stable the bcc phase at room temperature, and these dual-phase (hcp+bcc) Mg-Li alloys exhibit excellent formability. The Li-enriched bcc phase has been frequently considered as the origin for improving formability. However, these Mg-Li alloys show poor work-hardening ability and the resultant low strength at room temperature. Considering that the dislocation recovery can be suppressed by decreasing the deformation temperature and the activity of deformation mode may be changed with temperature, we investigated the deformation behavior of a commercial LZ91 magnesium alloy at cryogenic temperatures using in-situ neutron diffraction.

論文

Probing deformation behavior of a refractory high-entropy alloy using ${it in situ}$ neutron diffraction

Zhou, Y.*; Song, W.*; Zhang, F.*; Wu, Y.*; Lei, Z.*; Jiao, M.*; Zhang, X.*; Dong, J.*; Zhang, Y.*; Yang, M.*; et al.

Journal of Alloys and Compounds, 971, p.172635_1 - 172635_7, 2024/01

 被引用回数:3 パーセンタイル:23.52(Chemistry, Physical)

The grain orientation-dependent lattice strain evolution of a (TiZrHfNb)$$_{98}$$$$N_2$$ refractory high-entropy alloy (HEA) during tensile loading has been investigated using ${it in situ}$ neutron diffraction. The equivalent strain-hardening rate of each of the primary $$<hkl>$$-oriented grain families was found to be relatively low, manifesting the macroscopically weak work-hardening ability of such a body-centered cubic (BCC)-structured HEA. This finding is indicative of a dislocation planar slip mode that is confined in a few single-slip planes and leads to in-plane softening by high pile-up stresses.

論文

${it In situ}$ neutron diffraction study on the deformation behavior of the plastic inorganic semiconductor Ag$$_{2}$$S

Wang, Y.*; Gong, W.; 川崎 卓郎; Harjo, S.; Zhang, K.*; Zhang, Z. D.*; Li, B.*

Applied Physics Letters, 123(1), p.011903_1 - 011903_6, 2023/07

 被引用回数:4 パーセンタイル:47.87(Physics, Applied)

Bulk Ag$$_{2}$$S is a plastic inorganic semiconductor at room temperature. It exhibits a compressive strain greater than 50%, which is highly different from brittle conventional counterparts, such as silicon. Here, we present the experimental investigation of the deformation behavior in a plastic inorganic semiconductor Ag$$_{2}$$S using ${it in situ}$ neutron diffraction during compressive deformation at room and elevated temperatures. At room temperature, the lattice strain partitioning among $$hkl$$-orientated grain families could be responsible for the significant work-hardening behavior in the bulk Ag$$_{2}$$S with a monoclinic structure. The rapid accumulation of lattice defects and remarkable development of the deformation texture suggest that dislocation slip promotes plasticity. At 453 K, a monoclinic phase transforms into a body-centered cubic phase. A stress plateau appears at $$sim$$-4.8 MPa, followed by a rehardening state. The deformation mode of bulk Ag$$_{2}$$S at the initial stage is likely attributable to the migration of silver ions, and as strain increases, it is closer to that of room temperature, leading to rehardening.

論文

Si-addition contributes to overcoming the strength-ductility trade-off in high-entropy alloys

Wei, D.*; Gong, W.; 都留 智仁; Lobzenko, I.; Li, X.*; Harjo, S.; 川崎 卓郎; Do, H.-S.*; Bae, J. W.*; Wagner, C.*; et al.

International Journal of Plasticity, 159, p.103443_1 - 103443_18, 2022/12

 被引用回数:107 パーセンタイル:99.79(Engineering, Mechanical)

Face-centered cubic single-phase high-entropy alloys (HEAs) containing multi-principal transition metals have attracted significant attention, exhibiting an unprecedented combination of strength and ductility owing to their low stacking fault energy (SFE) and large misfit parameter that creates severe local lattice distortion. Increasing both strength and ductility further is challenging. In the present study, we demonstrate via meticulous experiments that the CoCrFeNi HEA with the addition of the substitutional metalloid Si can retain a single-phase FCC structure while its yield strength (up to 65%), ultimate strength (up to 34%), and ductility (up to 15%) are simultaneously increased, owing to a synthetical effect of the enhanced solid solution strengthening and a reduced SFE. The dislocation behaviors and plastic deformation mechanisms were tuned by the addition of Si, which improves the strain hardening and tensile ductility. The present study provides new strategies for enhancing HEA performance by targeted metalloid additions.

論文

Strengthening of high-entropy alloys via modulation of cryo-pre-straining-induced defects

Wei, D.*; Gong, W.; Wang, L.*; Tang, B.*; 川崎 卓郎; Harjo, S.; 加藤 秀実*

Journal of Materials Science & Technology, 129, p.251 - 260, 2022/12

 被引用回数:37 パーセンタイル:95.41(Materials Science, Multidisciplinary)

Owing to their attractive structure and mechanical properties, high-entropy alloys (HEAs) and medium-entropy alloys (MEAs) have attracted considerable research interest. The strength of HEAs/MEAs with a single face-centered cubic (FCC) phase, on the other hand, requires improvement. Therefore, in this study, we demonstrate a strategy for increasing the room-temperature strength of FCC-phase HEAs/MEAs by tuning cryo-pre-straining-induced crystal defects via the temperature-dependent stacking fault energy-regulated plasticity mechanism. Through neutron diffraction line profile analysis and electron microscope observation, the effect of the tuned defects on the tensile strength was clarified. This study discussed the possibility of developing single-phase high-performance HEAs by tuning pre-straining-induced crystal defects.

論文

Mechanical behaviors of equiatomic and near-equiatomic face-centered-cubic phase high-entropy alloys probed using ${it in situ}$ neutron diffraction

Wei, D.*; Gong, W.; 都留 智仁; 川崎 卓郎; Harjo, S.; Cai, B.*; Liaw, P. K.*; 加藤 秀実*

International Journal of Plasticity, 158, p.103417_1 - 103417_17, 2022/11

 被引用回数:54 パーセンタイル:98.44(Engineering, Mechanical)

In this study, we investigated the yielding and hardening behaviors of the Cantor alloy and FCC-phase Co-rich HEAs with different SFEs by in situ neutron diffraction combined with the first-principles method and electron-microscopy characterizations. The Co-rich HEAs exhibited a higher intrinsic yield strength than the Cantor alloy, mainly because of the larger shear modulus or modulus misfit, and grain refinement being more effective in improving the yield strength of low-SFE HEAs. Furthermore, higher flow stresses and better ductility of the Co-rich HEAs are attributed to the greater dislocation density and a larger number of stacking faults, which enhanced the strain-hardening rate during tensile deformation. The low SFE promoted mechanical twinning, and martensitic transformation contributed to higher strain-hardening rates.

論文

Rediscovery of Hall-Petch strengthening in bulk ultrafine grained pure Mg at cryogenic temperature; A Combined ${it in situ}$ neutron diffraction and electron microscopy study

Zheng, R.*; Gong, W.; Du, J.-P.*; Gao, S.*; Liu, M.*; Li, G.*; 川崎 卓郎; Harjo, S.; Ma, C.*; 尾方 成信*; et al.

Acta Materialia, 238, p.118243_1 - 118243_15, 2022/10

 被引用回数:44 パーセンタイル:97.03(Materials Science, Multidisciplinary)

Grain refinement can lead to the strengthening of metallic materials according to the Hall-Petch relationship. However, our recent results suggested that grain boundary sliding is the dominant deformation mode in bulk ultrafine grained (UFG) pure Mg at room temperature, leading to softening. Here, for the first time, we report that the Hall-Petch strengthening can be regained in bulk UFG pure Mg at cryogenic temperature. At 77K, the UFG pure Mg with a mean grain size of 0.6 $$mu$$m exhibited ultrahigh tensile yield strength and ultimate tensile strength of 309 MPa and 380 MPa, respectively. Combined ${it in situ}$ neutron diffraction and electron microscopy investigation indicated that residual dislocation structures and deformation twins hardly formed in the UFG specimen during tensile test at 298K. In contrast, fast accumulation of lattice defects and remarkable reorientation were evident at 77K, suggesting that the grain-boundary-mediated process was suppressed and the plastic deformation was dominated by dislocation slip and deformation twinning. In addition, all the pure Mg specimens exhibited pronounced strain hardening at 77 K, which was mainly attributed to the suppressed grain boundary sliding and dynamic recovery. The mean dislocation density and relative fractions of dislocations with various Burgers vectors of the UFG specimen deformed at 77K were determined quantitatively from neutron diffraction data.

論文

Two-step Mott transition in Ni(S,Se)$$_2$$; $$mu$$SR studies and charge-spin percolation model

Sheng, Q.*; 金子 竜也*; Yamakawa, Kohtaro*; Guguchia, Z.*; Gong, Z.*; Zhao, G.*; Dai, G.*; Jin, C.*; Guo, S.*; Fu, L.*; et al.

Physical Review Research (Internet), 4(3), p.033172_1 - 033172_14, 2022/09

A pyrite system NiS$$_{2-x}$$Se$$_x$$ exhibits a bandwidth controlled Mott transition via (S,Se) substitutions in a two-step process: the antiferromagnetic insulator (AFI) to antiferromagnetic metal (AFM) transition at $$xsim$$0.45 followed by the AFM to paramagnetic metal (PMM) transition at $$xsim$$1.0. Among a few other Mott systems which exhibit similar two-step transitions, Ni(S,Se)$$_2$$ is of particular interest because a large intermediate AFM region in the phase diagram would provide unique opportunities to study the interplay between the spin and charge order. By comparing and combining our muon spin relaxation studies and previous neutron scattering studies, here we propose a picture where the spin order is maintained by the percolation of "nonmetallic" localized and dangling Ni moments surrounded by S, while the charge transition from AFI to AFM is caused by the percolation of the conducting paths generated by the Ni-Se-Ni bonds.

論文

Regulation of strength and ductility of single-phase twinning-induced plasticity high-entropy alloys

Wei, D.*; Gong, W.; 川崎 卓郎; Harjo, S.; 加藤 秀実*

Scripta Materialia, 216, p.114738_1 - 114738_6, 2022/07

 被引用回数:52 パーセンタイル:97.96(Nanoscience & Nanotechnology)

Near-equiatomic single-phase twining-induced plasticity (TWIP) high-entropy alloys (HEAs) exhibit a good combination of strength and ductility, but their modest yield strength requires further improvement. Here, we propose a strategy for markedly enhancing their strength while retaining satisfactory ductility, taking advantage of the temperature dependence of the stacking fault energy. The room-temperature strength of a representative TWIP HEA was improved by the cryogenic pre-deformation-induced dislocations, martensite, nanotwins, and stacking faults. The tensile properties were further tuned by subsequent annealing to obtain partially recovered or recrystallized microstructures. The influence of regulated microstructures on the yield strength was clarified by neutron diffraction line profile analysis. This study presents possibilities for fabricating advanced HEAs by tuning the substructures.

論文

Strain hardening behavior of additively manufactured and annealed AlSi3.5Mg2.5 alloy

Zhang, X. X.*; Lutz, A.*; Andr$"a$, H.*; Lahres, M.*; Gong, W.; Harjo, S.; Emmelmann, C.*

Journal of Alloys and Compounds, 898, p.162890_1 - 162890_8, 2022/03

 被引用回数:10 パーセンタイル:62.14(Chemistry, Physical)

The ductility of the Al alloys produced by additive manufacturing (AM) has become a critical property, as the AM Al alloys are increasingly used in the automotive industry. However, the ductility of as-built AM Al alloys is relatively low, even with optimized AM conditions. The post-annealing treatment provides an efficient way to improve ductility. Previous investigation has shown that the annealed AM AlSi3.5Mg2.5 alloy possesses superior ductility. However, the plastic deformation micro-mechanisms of the annealed AM AlSi3.5Mg2.5 alloy remain unclear. In this study, in-situ neutron diffraction was employed to explore the annealed AM AlSi3.5Mg2.5 alloy. The evolutions of phase stresses, dislocation density, and crystallite size in the annealed AM AlSi3.5Mg2.5 alloy during tensile deformation were analyzed. The experimental investigation reveals that the dislocation density in the Al matrix of the annealed AM AlSi3.5Mg2.5 alloy increases slowly in the early plastic deformation stage, and it reaches a saturated level upon the following uniform deformation. The crystallite size decreases quickly in the early deformation stage, and then it decreases slowly. The Kocks-Mecking model and the Voce model can capture the strain hardening behavior well. The determined physical constitutive equations can be applied in continuum mechanical computer simulations.

論文

Metalloid substitution elevates simultaneously the strength and ductility of face-centered-cubic high-entropy alloys

Wei, D.*; Wang, L.*; Zhang, Y.*; Gong, W.; 都留 智仁; Lobzenko, I.; Jiang, J.*; Harjo, S.; 川崎 卓郎; Bae, J. W.*; et al.

Acta Materialia, 225, p.117571_1 - 117571_16, 2022/02

 被引用回数:97 パーセンタイル:99.64(Materials Science, Multidisciplinary)

Recently-developed high-entropy alloys (HEAs) containing multiple principal metallic elements have ex-tended the compositional space of solid solutions and the range of their mechanical properties. Here we show that the realm of possibilities can be further expanded through substituting the constituent metals with metalloids, which are desirable for tailoring strength/ductility because they have chemical interactions and atomic sizes distinctly different from the host metallic elements. Specifically, the metalloid substitution increases local lattice distortion and short-range chemical inhomogeneities to elevate strength, and in the meantime reduces the stacking fault energy to discourage dynamic recovery and encourage defect accumulation via partial-dislocation-mediated activities. These impart potent dislocation storage to improve the strain hardening capability, which is essential for sustaining large tensile elongation. As such, metalloid substitution into HEAs evades the normally expected strength-ductility trade-off, enabling an unusual synergy of high tensile strength and extraordinary ductility for these single-phase solid solutions.

論文

Quantifying internal strains, stresses, and dislocation density in additively manufactured AlSi10Mg during loading-unloading-reloading deformation

Zhang, X. X.*; Andr$"a$, H.*; Harjo, S.; Gong, W.*; 川崎 卓郎; Lutz, A.*; Lahres, M.*

Materials & Design, 198, p.109339_1 - 109339_9, 2021/01

 被引用回数:58 パーセンタイル:93.33(Materials Science, Multidisciplinary)

Here, in-situ neutron diffraction is employed to explore the residual strains, stresses, and dislocation density in the LPBF AlSi10Mg during loading-unloading-reloading deformation. It is found that the maximum residual stresses of the Al and Si phases in the loading direction reach up to about -115 (compressive) and 832 (tensile) MPa, respectively. A notable dislocation annihilation phenomenon is observed in the Al matrix: the dislocation density decreases significantly during unloading stages, and the amplitude of this reduction increases after experiencing a larger plastic deformation. At the macroscale, this dislocation annihilation phenomenon is associated with the reverse strain after unloading. At the microscale, the annihilation phenomenon is driven by the compressive residual stress in the Al matrix. Meanwhile, the annihilation of screw dislocations during unloading stages contributes to the reduction in total dislocation density.

論文

${it In situ}$ investigation of the microstructure evolution in Long-Period-Stacking-Ordered (LPSO) magnesium alloys as a function of the temperature

M$'a$this, K.*; Drozdenko, D.*; N$'e$meth, G.*; Harjo, S.; Gong, W.*; 相澤 一也; 山崎 倫昭*; 河村 能人*

Frontiers in Materials (Internet), 6, p.270_1 - 270_9, 2019/11

 被引用回数:8 パーセンタイル:28.82(Materials Science, Multidisciplinary)

Deformation behavior of two Mg-Zn-Y magnesium alloys, having a different fraction of the long-period-stacking-ordered (LPSO) phase, has been investigated at room temperature and 200$$^{circ}$$C by a combination of ${it in situ}$ neutron diffraction (ND) and acoustic emission (AE) measurements. The results indicate that the twinning in the magnesium matrix and the kinking in the LPSO phase strongly depend on the composition of the material and the testing temperature. Further, active deformation mechanisms and particularly the load transfer from the magnesium matrix to the LPSO phase define the mechanical properties of the investigated alloys.

論文

Investigation of the evolution of the microstructure in the directionally solidified Long-Period Stacking-Ordered (LPSO) magnesium alloy as a function of the temperature

Drozdenko, D.*; M$'a$this, K.*; Harjo, S.; Gong, W.; 相澤 一也; 山崎 倫昭*

Magnesium Technology 2019, p.33 - 36, 2019/02

 被引用回数:0 パーセンタイル:0.00(Engineering, Chemical)

The influence of the LPSO-phase orientation and the temperature on the deformation mechanisms of directionally solidified Mg-Zn-Y magnesium alloy has been investigated by neutron diffraction and acoustic emission (AE) technique. The results indicate that the kinking mechanism and activation of non-basal slip are significantly temperature and orientation dependent with respect to the loading axis.

論文

Odd and even modes of neutron spin resonance in the bilayer iron-based superconductor CaKFe$$_{4}$$As$$_{4}$$

Xie, T.*; Wei, Y.*; Gong, D.*; Fennell, T.*; Stuhr, U.*; 梶本 亮一; 池内 和彦*; Li, S.*; Hu, J.*; Luo, H.*

Physical Review Letters, 120(26), p.267003_1 - 267003_7, 2018/06

 被引用回数:40 パーセンタイル:86.24(Physics, Multidisciplinary)

We report an inelastic neutron scattering study on the spin resonance in the bilayer iron-based superconductor CaKFe$$_4$$As$$_4$$. In contrast to its quasi-two-dimensional electron structure, three strongly $$L$$-dependent modes of spin resonance are found below $$T_c$$ = 35 K. The mode energies are below and linearly scale with the total superconducting gaps summed on the nesting hole and electron pockets, essentially in agreement with the results in cuprate and heavy fermion superconductors. This observation supports the sign-reversed Cooper-pairing mechanism under multiple pairing channels and resolves the long-standing puzzles concerning the broadening and dispersive spin resonance peak in iron pnictides. More importantly, the triple resonant modes can be classified into odd and even symmetries with respect to the distance of Fe-Fe planes within the Fe-As bilayer unit. Thus, our results closely resemble those in the bilayer cuprates with nondegenerate spin excitations, suggesting that these two high-$$T_c$$ superconducting families share a common nature.

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