稀有金属(英文版) 2020,39(01),13-21

Neutron diffraction studies of permanent magnetic materials

Wen-Yun Yang Dong Liang Xiang-Dong Kong Jin-Bo Yang

State Key Laboratory for Mesoscopic Physics,School of Physics,Peking University

Collaborative Innovation Center of Quantum Matter

Beijing Key Laboratory for Magnetoeletric Materials and Devices

Department of Micro-nano Fabrication Technology,Institute of Electrical Engineering,Chinese Academy of Sciences

作者简介：*Xiang-Dong Kong e-mail:slkongxd@mail.iee.ac.cn;*Jin-Bo Yang e-mail:jbyang@pku.edu.cn;

收稿日期：7 January 2019

基金：financially supported by the National Key Research and Development Program of China (Nos. 2017YFA0403701,2016YFB0700901,2017YFA0206303 and 2017YFA0401502);the National Natural Science Foundation of China(Nos.51731001,11675006,11805006,51371009 and 11504348);

Neutron diffraction studies of permanent magnetic materials

Wen-Yun Yang Dong Liang Xiang-Dong Kong Jin-Bo Yang

State Key Laboratory for Mesoscopic Physics,School of Physics,Peking University

Collaborative Innovation Center of Quantum Matter

Beijing Key Laboratory for Magnetoeletric Materials and Devices

Department of Micro-nano Fabrication Technology,Institute of Electrical Engineering,Chinese Academy of Sciences

Abstract：

Neutron diffraction technology as an advanced material research technique has special advantages in studying magnetic materials compared to the conventional techniques such as X-ray diffraction(XRD),scanning electron microscopy(SEM),transmission electron microscopy(TEM),and X-ray photoelectron spectroscopy(XPS).In this review,the applications of neutron diffraction technology on permanent magnetic materials were briefly reviewed:(1) the determination of the crystal structure and magnetic structure of the typical permanent magnet material,(2) in situ neutron diffraction study of the crystal structure evolution of the permanent magnets,and(3) phase transition in permanent magnetic materials.

Keyword：

Neutron diffraction; Permanent magnetic materials; Crystal structure; Magnetic structure; Structure evolution; Phase transition;

Received： 7 January 2019

1 Introduction

Neutrons,the fundamental building bl_ocks of atomic nuclei,are released by a varⁱety of nuclear proc_esses,ancan be strongly diffracted b^y samples with ordered crystal/magnetic structur_e.The so-calle_d neutron diffraction provides a wealth of information on the structure of the diffracting sample in an analogous w^ay to the X-ray diffraction (XRD).Although the two techniques are in many ^ways analogous,neutron and XRD patterns obtained from the same samples differ s^ubstantially ^due to the fundamental differences in the scattering proc_ess.In m^any ways,these differences make the two techniques complementary;however,^the neutron diffraction shows special advantages in the studying of the magnetic materials an_d has the following advantages compared to the convention_al XRD,_scanning electron microscopy (SEM),t_ransmission electron microscopy ⁽TEM),an_d X-ra_y photoelectron spectroscopy (XPS),making the neutron diffraction an essential too_l fo^r condensed matter research.(1) Neutron shows high _compositional resolution and measurement accuracy and is especiall^y suitable for studying elements with low atomic number su^ch as H,Li,B,C,N,O,_and distinguishing between isotopes.₍2)Neutron has deep penetrating ability,and neutron diffraction technology is suitable _for studies of the material struct_ure and kinetics under conditions such as high and low temperatures,hig_h pressure,high magnetic field and electric fie_ld,and different atmospheres.(3) The characteristics of neutron witmagnetic moments make th^e neutron diffraction technology become one of the most powerful t_ools for ^studying magnetic structure_s.As early as 19₃6,the antiferromagnetic hypothesis was proposed,but this hypothesis coul_d not be verified experimentally until 1₉49.S_hull _et _al.[1,measured the magnetic structure of MnO by neutron diffraction,which proved the existence of antiferromagnetic structur_e.Nowadays,^the neutron diffraction technology has been widely ^used in the research of various magnetic materials and it plays an important role in the development of modern magnetic theory and the development of magnetic materials [ 3] .

Magnetism is one of t^he basic properties of m^atter.Magnetic functional materials have been ^widely ^used in various field_s,such as energy conversion,information storage,communications,_aerospace,_t^ransportation,and biomedical industries.Permanent magnetic materials,showing high coercivit^y and high remanence,can maintain a constant magnetic flux afte^r magnetization.Permanent magnetic functional devices have become indispensable in clean energy and low-carbon economic development.They are widely used in aircra_ft,missi_les,new ene^rgy vehic_lewind power,household appliances,communication devices,and computers.^Therefore,_research and development of high-performance magnetic materials have become the research frontier of the^se advanced functional materials.Since the properties of materials are closely related to structure (crystal and magnetic structures₎,in order to furthe^r improve the properties of materials and develop new ^materials,it is necessary to conduct in-depth and extensive b_asic research on t_he s_truct_ures of the mate^rials(structural and compositional properties).

In this paper,we will give a brief review about the application of the neutron diffraction technology in the permanent magnetic materials.For further informati_on,the readers are advised _t^o consult references,e_specially devoted to magnetic neutron scattering such as Refs.[

2 Neutron diffraction studies of permanent magnetic materials

2.1 Determination of crystal structure and magnetic structure of typical permanent magnet materials

At the annual meeting of the American Physical _Society held in Pittsburgh,US_A,in November 1983,Sagawa et al. [ 6] and Croat et al. [ 7] reported that the chemical csition of a ne^w type of magnet was Nd1₅Fe7₇B8,marking the birth of the third_-generation rare earth permanent magnet material Nd-Fe-B.T_hen,He_rbst et al. [ 8] use^d neutron diffractio_n techniques to determine the crystal structure and magnetic structure of this new ternary phaof Nd₂Fe₁₄B permanent magnets in 19₈4.St_udies have shown that the exact composition of ^the new tetragonal phase is R₂Fe₁₄B instead of the original esti_mated R₃Fe₂₀B.The analysis of the diffraction patterns shows Nd₂Fe₁₄B is a tetragonal structure (space group is P⁴₂/mnm),as shown in _Fig.1 [ 8] .Although the number of Batoms is small,it is indispensable for stabilizing the tetragonal structure.The room-temperature magnetic structure determined by the neutron diffraction data i_ndicates that Nd and Fe atoms are ferromagnetically couple_d along the c-axis of the tetragonal unit ce_ll.The average magnetic moment of the Fe atom is close to it_s saturati_on value at 300 K,while the magnetic moment of the Nd atom is less than 1.7_μв.

s,the In order to develop a _new g^eneration of permanent magnet materials,Coey and Sun_[9]and ^Yang et al. [ 10] started the introduction of interstitial ni_trogen,carb_on,and other elements int_o 2:17 and 1:12 m_aterials.It was fo_und that the interstitial atoms have significant^ly effects _on enhancing Curie temperature,increasing saturation magnetizatio_n,and changing fundamentally the magnetocrystalline anisotropy of the 2:17,₁:12,^or 1:7^[11]intermetallic compounds.The XRD atomic scattering factors are atomic number dependent,and for the N,Fe,a_nd Nd atoms,the XRD a_tomic _scattering factors ar_e 0.53×10^-14,3.3×10^-14,and 9.0×10^-14cm,respectivel_y.As _the XRD atomic scattering factor (N) is much smaller than that of Fe and Nd,^the X-ray scattering contribution from Natom can be negligible and so it is difficult to determi_neits crystalline positi_on and occupancy by XRD technology.However,_for ^the neutron _diffraction,the coherent neutron scattering lengths are not atomic number dependent and are0.94×10^-12,0.95×10^-12,and 0.75×10^-12_cm for the N,F^e,and Nd atoms,_respectivel_y.So,_the N a^tom can contribute to considerable scattering intensit_y,and its crystalline position and occupanc^y can be determined by the neutron diffraction technology.Yang et al. [ 12, 13] have used neutron diffraction technique t^o determine the position of the N element in the crystal and found _the interstitial atomic site o^f N in the crystal struc_tures.Figure 2 plot_s the typical crystallographic structures of interstitial 2:17 and 1:12 compounds.The neutron diffractio_n studies demonstrated that all these compounds crystallize in the same structure a^s theⁱr parent alloys,and N atoms enter the interstitial s_ites,leading to an expansion of the unit cel_l.It is revealed that non-magnetic atoms such as nitrogen,carbo_n,or hydrogen,added as interstitial atoms to the magnetic allo_y,have a sensitive regulation effect on the electronic structure_s,exchange interactions,and cryst_al fields of rare earth ions,thereby providing a new w^ay to prepare magnetic materials with vari^ous properties [ 14, 15] .

Fig.1 Crystal structure of Nd2Fe14B [8]

Pure manganese metal is antiferromagnetic,while quite a number of Mn-based systems exhibit ferromagnztism,including Mn-B,Mn-Al,Mn-Bi,Mn-Ga,Mn-Ge,Mn-Sb and Mn-As,etc.,among whichτ-Mn-Al,low-temperature phase Mn-Bi,and Mn-Ga alloys have good prospects for permanent magnet applications.Bruan and Goedkoop [ 16] and Yang et al. [ 17] have studied the crystal and magnetic structures ofτ-MnAl and MnAlC by neutron diffraction method (Fig.3).Mn1.11 Al0.89 alloy [ 16] has a body-centered tetragonal structure with 3 wt%Al and 97 wt%Mn at the(0,0,0)site and 86 wt%Al and 14 wt%Mn at the(1/2,12/,1/2) site.The magnetic moment of Mn atoms is oriented along the c-axis,and the direction of the magnetic moments of Mn atoms is opposite in different crystal positions.

Yang et al. [ 17] conducted a neutron diffraction study onτ-MnAlC alloys and analyzed its crystal and magnetic structures.It was found that the addition of a small amount of C would prevent Mn atoms from occupying (1/2,1/2,1/2) position,which forms antiferromagnetic coupling with Mn at (0,0,0) site,and improve the magnetic properties of MnAlC [ 18] .Further,the C atom is not at the position of the interstitial sites,but occupies the crystal position of Mn and Al atoms,so that the internal stress is released and the mechanical property is improved [ 18] .

Neutron diffraction experiments on Mn54Al46 and Mn51Al46C3 samples were done at 10 and 300 K,using a neutron wavelength of 0.17982 nm [ 19] .Since neutrons are also sensitive to light elements,the occupancy of C atoms in Mn51Al46C3 is then determined by neutron diffraction analysis.Two different C-occupation modes have been tested:(1) assuming that the C atom enters the substitution position,i.e.,(0,0,0) and (1/2,1/2,1/2) sites,and (2)assuming that the C atom enters the interstitial position,that is,the C atoms locate at the 2e position (0,1/2,1/2).As the C content increases,the lattice parameter a decreases slightly,while the lattice parameter c and the unit cell volume V increase significantly [ 19] .The increase in unit cell volume indicates that C atom may be in the interstitial position in the magnetic phase structure of Mn54-xAl46Cx,instead of the substitution point of Mn or Al atom.However,as C atom is much smaller than Mn atom and Al atom,it is more likely to enter the 2e position of (0,1/2,1/2).

The neutron diffraction spectra of Mn51Al46C3 are fitted by two different occupancy models [ 19] .For the substitution model,similar to previous studies,most of the Mn and Al atoms occupy (0,0,0) and (1/2,1/2,1/2) atomic positions,respectively,and few Mn and Al atoms occupy the(1/2,1/2,1/2) and (0,0,0) atomic positions,respectively.The C atom preferentially occupies the (1/2,1/2,1/2)atomic position,so the Mn atom at the (1/2,1/2,1/2)atomic position is reduced.At the same time,the magnetmoment of the Mn atom at the (0,0,0) position is slighincreased from 2.04μB to 2.14μB,whereas the magnetic moment of Mn atoms at the (1/2,1/2,1/2) site antiparalleto those at (0,0,0) site increases significantly,caustotal magnetic moment of the unit cell to be almost constant,which is consistent with magnetic measurements.The magnetic moment of the Mn atom at the (0,0,0)position is 2.30μв,and the total unit magnetic moment 1.9μB,which is 10%higher than the total magnetic moment of the unit cell without C.This fitting result dnot match the experimental data from magnetic measurements although for the interstitial model,a slightly smChi-square (χ2) value was obtained.So,the Coccupy the substitution position (1/2,1/2,1/2).

Fig.2 a Crystallographic structure of Th2Zn17-type R2Fe17N3 and b crystallographic structure of ThMn12-type R(Fe,M)12N (M=Cr,Ti,V,Mn,Mo...)

Fig.3 Structures ofτ-MnAl(C):a ideal structure ofτ-MnAl phase,b structure with C locating at substitution sites,and c structure with Clocating at interstitial sites [16-17]

The crystal and magnetic structures of MnxGa were investigated by powder neutron diffraction [ 20, 21] .With the decrease in Mn content,the structure of the MnxGa changes from DO22 structure (Mn3.0Ga) to L10 structure(Figs.4 and 5).The MnxGa structure can be described the DO22 structural model in which 2a-Ga and 2b-Mn are simultaneously replaced.This structural model is used tothe neutron diffraction patterns of MnxGa (x=1.2-3.0),explaining the transformation process of the two structures.For MnxGa,when x is reduced from 3.0 to 2.0,the 2a site is still substantially occupied by Ga atoms,and the Mn atom at 2b is partly replaced by Ga atoms.When x=1.8,a part of Mn atoms enter the 2a site,originally occupied by Ga atoms.At the same time,more Mn is replaced by Ga in the2b site.When x=1.2-1.6,the ratio of Mn and Ga atoms in the 2a and 2b is substantially same,and the structure transforms into the L10 structure.The magnetic moment of the Mn atom at the 2a/2b site in MnxGa is antiparallel to the magnetic moment of the 4d Mn atom,and the total magnetic moment of the unit cell is parallel to the magnetimoment of 4d.The neutron diffraction fitting results are shown in Fig.6.The magnetic moment of 4d Mn atom,about 2.1μв,is basically unchanged with the change of Mcomposition,while the magnetic moment of Mn atom at2a/2b site increases with Mn content in MnxGa increasing.The ferromagnetic materials YCo5,Y2Fe14B,Nd2Fe14B,and ThCo5 [ 22, 23, 24] have been studied by polarized neutron diffraction.The polarized neutron diffraction can be used to quantify the orbit and spin contributions to the magnetimoments at each Co position and to determine the wave function in different orbits.The neutron diffraction was used to determine the texture in Nd2Fe14B and AlNiCo magnets [ 25, 26] .Different degrees of texture can be obtained by treating Nd2Fe14B samples with external pulsed magnetic fields.The degree of texture was measured by neutron diffraction,and it was found that the degree of texture increased with the number of pulses.

Fig.4 Neutron diffraction patterns of MnxGa (1.2≤x≤3.0) at300 K [20]

2.2 In situ neutron diffraction study of crystal structure evolution

Owing to the huge increase in neutron flux and the use of large-angle detectors,in situ neutron diffraction studies can now be performed not only on time scales of hours to milliseconds,but also be used to study time-resolved physical or chemical processes.For example,it was used to study the microstructure formation process of high-performance Nd-Fe-B permanent magnets at the nanometer level.One of the effective ways to make anisotropic magnetic powder is the hydrogenation-decomposition-desorption-recombination (HDDR) process [ 27, 28] .Scientists have used in situ neutron diffraction to dynamically study the process and mechanism involved in the HDDR process [ 29, 30] .Since the acquisition of the diffraction pattern is time-resolved,the dynamics of the decomposition process can be studied.Figure 7 gives a comparison of the different decomposition dynamics for different operating conditions.It shows that by adjusting the temperature,the dynamics of iron formation in the hydrogenation-decomposition (HD) process can be slowed down,and the appearance of soft particles like Fe can be avoided so that the performance of the hard-magnetic material can be improved.

Fig.5 Obtained occupation numbers of a Mn atoms and b Ga atoms at different sites,and c refined lattice parameters a and c'of MnxGa (c'is twice c of the L10 cell) [20]

Fig.6 a Refined magnetic moments of Mn atom (μMn) at 2a/2b-site and 4d-site and b refined magnetic moments (Mf) of one unit cell versus x [20]

Fe-Pt alloy is another potential rare earth-free permanent magnet material.Self-assembled and chemically ordered Fe-Pt nanoparticle arrays show high magnetic anisotropy and are considered candidates for data storagemedia above 1550 T·m-2.The ordering process of nanocrystalline Fe-Pt alloys obtained by mechanical alloying was investigated in situ by powder neutron diffraction [ 31, 32] .Figure 8 shows the evolution of the neutron diffraction pattern of Fe50Pt50 powder obtained by mechanical alloying after milling for 4 h with the increase in temperature.A typical acquisition time for this diffraction pattern is approximately 3-5 min.In situ studies hshown the coexistence of several stages in the heat treatment process.The tetragonal ordered L10 FePt phase shows excellent magnetic properties,which results from the ordering of Fe and Pt atoms from the disordered facecentered cubic Al phase,and its non-stoichiometric phases such as Fe3Pt and FePt3 also depend on the processing conditions.From a technical point of view,for bulk materials,neutron diffraction has a deeper detection depthwhich is superior to XRD.Small-angle neutron scattering(SANS) is also an advantageous tool for detecting magnetic microstructures at mesoscopic scales (1-1000 nm),and it can be used to study permanent magnet materials.For example,scientists used SANS to study the size and magnetic field dependence of inhomogeneous magnetization regions and finally revealed the mesoscopic understanding of field-dependent magnetization reversal in NdFe-B nanocomposites [ 33, 34] .SANS along with XRD and magnetometry studies were carried out on 4-nm Fe-Pt nanoparticles [ 35] .Studies have shown that before annealing,the FePt nanoparticles consist of a metal core surrounded by a weakly magnetic or non-magnetic shell.Under the nitrogen atmosphere and the condition of hightemperature annealing above 600℃,the desired L10ordered structure can be produced so that the FePt nanoparticles have higher coercive force (4 T).At the satime,high-temperature annealing can also lead to sinteriand agglomeration of the fine particles.Understanding the structure and magnetic properties of such nanoparticlecomponents can point the way to the development of new data storage media.

Fig.7 a Diffraction pattern during Nd2Fe14B(D)x decomposition (stabilized at 720℃for 1 h);b evolution of Nd2Fe14B phase in HDDRprocess with decomposition performed at specified temperatures of 720,680,and 600℃ [4,29]

Fig.8 a Crystal structures of Fe-Pt alloys with Al and L1o phases and b evolution of powder neutron diffraction patterns measured at a heating rate of 0.8 K·min-1 for Fe50Pt50 powder milled at liquid nitrogen temperature for 4 h [4,31] ;the diffraction pephase is given in a

2.3 Phase transition of the magnetic structures

e The neutron diffraction is a direct method of determining the corresponding arrangement of magnetic moments and measuring the relationship between magnetism and temperature.

me ng It is well known that Nd2Fe14B compound exhibits a spin reorientation around 140 K,and its easy magnetization direction shifts from the c-axis to the oblique directLow-temperature neutron diffraction measurements were taken for R2Fe14B (R=Nd,Ho,Er,and Y) compounds [ 36] .It was found that there is a continuous spin reoritation in the Nd and Ho compounds from the c-axis to the intermediate direction in (110) plane with the decrease intemperature (Fig.9).The Er-compound exhibits a first order magnetic transition at 350 K,and its magnetization direction is rotated from the c-axis to the base direction at a low temperature.The Y compound maintains a c-axis orientation throughout the whole temperature range.

The relationship between the magnetic structure and magnetic phase transition of MnBi materials can be accurately determined by neutron diffraction technique and Rietveld analysis [ 37, 38, 39] .The neutron diffraction patterns of the MnBi from 10 to 700 K are shown in Fig.10.The relationship between the phase structure and composition of the sample with temperature is obtained by the Rietveld fitting.

Using the Rietveld fitting method,it is understood that the low-temperature phase MnBi has a NiAs-type hexagonal structure,the Mn atom occupies the 2a site,and the Bi atom occupies the 2c site.At room temperature,its lattice constants a=b=0.42854 (1) nm and c=0.61229 (1) nm,where the number in the bracket is error.The coupling between the Mn atoms is ferromagnetic.The lattice constants a and c have a transition near 100 K (Fig.11),indicating that the magnetic moment of the Mn atom undergoes spin reorientation around this temperature,from ab in-plane orientation to orientation along the c-axis.The jump change of the lattice constant coincides with the magnetocrystalline anisotropy from the ab plane to the caxis.When the value of cla is less than 1.425,the lowtemperature phase MnBi is in-plane anisotropy;when the c/a ratio is greater than 1.425,MnBi is uniaxial anisotropy,and the anisotropy field increases with the increase in c/a.When the value of c/a reaches 1.433,its magnetic structure changes from ferromagnetic to paramagnetic.Near the magnetic structure transition temperature of633 K,the c/a value of the nanocrystalline MnBi still does not change much,but in the bulk MnBi material,the ratio is reduced to 1.37.It is interested to point out that in the nanocrystalline MnBi,the lattice constants a and c do notappear discontinuous near 625 K,but there is a significant discontinuity near the temperature in the bulk material.The magnetic moment of Mn atoms changes slowly with the increase in temperature as shown in Fig.11b,and no discontinuity occurs near the spin reorientation temperature of100 K.Owing to the magnetic phase transition,the magnetic moment of Mn atoms decreases sharply around540-550 K,and the magnetic moment of each Mn atom is1.4μвat 600 K.

Fig.9 Low-temperature magnetic structure of Nd2Fe14B [36] ,where MFe is the magnetic moment of Fe atoms

Fig.10 Neutron diffraction patterns of LTP MnBi at different temperatures [38]

Fig.11 a Lattice parameters and b magnetic moments of MnBi at different temperatures obtained from ND data [39]

Considering that the contribution of the magnetic diffraction peak is mainly at small angles,the magnetic diffraction peaks of (002) and(200) are selected for observation,as shown in Fig.12.The contribution of magnetic properties to magnetic diffraction peaks can be seen from Fig.12.At 100 K or less,the magnetic scattering peak (002) contributes the most,and the contribution to (200) is almost zero.At 100 K or more,the magnetic phase contributes the most to the (200) plane diffraction peak.This indicates that the magnetic moment does have a spin reorientation around 100 K.By analysis,for the (002)plane,the neutron wave vector is perpendicular to the ab plane,and the magnetic moment in the ab plane contributes the strongest to the diffraction peak.For the (200) plane,the neutron wave vector is vertical to ab plane,and the magnetic moment along the c-axis at this time contributes the strongest to the diffraction peak.From the above results,it can be analyzed that the magnetic moment of manganese atoms in MnBi tends to be arranged along ab plane when it is below 100 K;when the temperature rises above 100 K,the magnetic moment of manganese atoms tends to follow c-axis alignment.From the analysis of the neutron diffraction spectrum,at around 100 K,it can be seen that the magnetic moment of Mn atoms in MnBi undergoes a process of rotation from ab plane to c-axis,which actually shows variation of magnetocrystalline anisotropy field of MnBi before and after 100 K.This is consistent with the spin reorientation observed on the thermomagnetic curve.

Fig.12 Intensities of (200) and (002) magnetic peaks for MnBi at different temperatures [38]

3 Summary

After decades of development,research and development of new permanent magnet materials have made great progress,but no material has been found with the maximum magnetic energy product which at rom temperature can exceed that of Nd-Fe-B.The new generation of permanent magnet materials must have higher saturation magnetization,strong magnetic anisotropy,and strong magnetic exchange than Nd-Fe-B materials,and these three physical quantities directly determine the external macroscopic magnetic properties of the materials such as magnetization,coercivity,and Curie temperature.Therefore,the research of new materials in the future must find new methods or new principles to comprehensively improve the above three physical quantities.In the process of exploration,it is necessary to use neutron diffraction technology,which can conduct more in-depth study on the crystal structure,magnetic structure,and intrinsic and microstructure-related properties of related materials,and explore the key mechanisms affecting material properties.It can provide the necessary theoretical guidance for the development of new materials and ultimately achieve new principles and methods for developing the next generation of new permanent magnet materials.From the example of the permanent magnet material discussed above,it can be seen that the neutron scattering study plays a great role in understanding the microstructure and determining the crystallographic position of the atom.The above structural characteristics determine the magnetic properties of the permanent magnet,such as magnetic moment,Curie temperature,magnetocrystalline anisotropy,and magnetization distribution.This understanding is essential to improve the magnetic properties of potential permanent magnet materials.In particular,neutron diffraction studies have helped determine the exact crystal position of light and small atoms (such as B,N,C) in permanent magnets,and the important role of non-magnetic atoms (such as N) in improving the magnetic properties of permanent magnets has also been proposed.On the other hand,the high penetration power of the neutrons is utilized to determine the degree of texture in the permanent magnets to improve the desired magnetic properties.These all indicate that neutron diffraction technology plays an important role in the field of permanent magnet materials.

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